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This is to certify that the

thesis entitled

DYNAMIC MODEL OPTIMIZATION
USING COMPUTATIONAL TECHNIQUES

presented by

Mark Lee Davis

has been accepted towards fulfillment
of the requirements for

JAMS— degree in _Me_chan1cal Engineering

\jvu’iz t /‘6’L—(
Major professor ”1/,

L/

Date 2/24/92

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

Michigan State

1 LEBRARY
3 University

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

DATE DUE DATE DUE DATE DUE |

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

|__
| II

MSU Is An Afflnnetlve Action/Equal Opportunity Institution
cMMmG-nt

 

 

 

 

 

 

 

 

 

DYNAMIC MODEL OPTIMIZATION
USING COMPUTATIONAL TECHNIQUES

By
Mark Lee Davis

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1992

ABSTRACT

DYNAMIC MODEL OPTIMIZATION
USING COMPUTATIONAL TECHNIQUES

BY

Mark Lee Davis

Simulation modeling software can create and solve a set of differential equations and
provide numerical results of the system state responses. Optimization software can
explore a design space, searching for a feasible solution which best satisfies a given cost
function. Our objective is to establish an interface between these two types of software
packages, so the strengths of each are joined in an effort to reduce design time while
ensuring accuracy. A specific interface between modeling and optimization software has
been established using ENPORT for simulation and OPTDESBYU for optimization. By
using this interface dynamic responses can be optimized with respect to system design
variables for any bond graph model. Design time can be reduced while maintaining
confidence in the results.

DEDICATION

To my devoted and loving wife Diana
and
My sons Mark, Brian and Eric

ACKNOWLEDGMENTS

I would like to begin by expressing my appreciation to the College of
Engineering, the Department of Mechanical Engineering and the CASE Center for
the support that made this opportunity of a lifetime possible. My thanks go to the
CASE Center staff consultants who, with great satisfaction, answered my many
questions. I would like to thank Dr. Clark Radcliffe for both his service as a
committee member and also his valuable input to the final thesis document. Finally I
wish to express my thanks to professors Ronald Rosenberg and Alejandro Dfaz my
co-advisors. With the wisdom and guidance displayed by these men this
accomplishment was possible.

TABLE OF CONTENTS

LIST OF TABLES .................................................................................................. viii
LIST OF FIGURES ................................................................................................ ix
NOMENCLATURE ............................................................................................... xi
1 INTRODUCTION 1
1.1 Motivation ................................................................................................... l
1.2 Basic Problem .............................................................................................. l
1.3 Organization of Thesis ................................................................................ 2
2 CURRENT STATUS 3
2.1 Simulation Using EN PORT ........................................................................ 3
2.2 Optimization Using OPTDES ..................................................................... 4
2.3 Interfacing ENPORT and OPTDES ............................................................ 5
2.3.1 Describing the Interface Connection .................................................. 6
3 AN APPLICATION EXAMPLE 8
3.1 Introduction ................................................................................................. 8
3.2 Design Problem Considerations .................................................................. 8
3.3 Bond Graph Design ..................................................................................... 13
3.4 Optimization Problem ................................................................................. 14
3.4.1 Objective Functions .......................................................................... 14
3.4.2 Model and Optimization Parameters ................................................ 15
3.5 Results ......................................................................................................... 17
3.5.1 Problem 1 Summary ......................................................................... 17
3.5.2 Problem 2 Summary ......................................................................... 21
3.5.3 Problem 3 Summary ......................................................................... 26
3.6 Discussion .................................................................................................. 3O

vi

4 CONCLUSIONS . 31
4.1 Summary ...................................................................................................... 31
4.2 Recommendations ....................................................................................... 31

APPENDICES

A DESIGN AND IMPLEMENTATION CONSIDERATIONS 33
A.l Introduction ................................................................................................ 33
A2 Design Variables ........................................................................................ 33
A3 Analysis Functions ..................................................................................... 34
AA General Model Design ............................................................................... 36

B MULTIPLE FORCING SYSTEM PROBLEM 38
B.1 Introduction ................................................................................................ 38
B.2 Posing the MFS Optimization Problem ..................................................... 38
B.3 AF-Vector Build for the MFS Problem ..................................................... 39
B.4 Setting Up the MFS Problem In OPTDES ................................................ 39
B.5 Determining the Objective Function Value ............................................... 40
B.6 Summarizing the MFS Optimization Problem .......................................... 40

C USER WRITTEN SUBROUTINES AND SAMPLES 42
Cl Introduction ................................................................................................ 42
C2 User Written Generator (U SRGEN.FOR) ................................................. 42
CS User Written Menu (U SRMEN.FOR) ....................................................... 45
CA User Written AF—Vector Build (U SRAFN.FOR) ...................................... 48

D HOW TO USE THE OPTIMIZATION INTERFACE 51
DJ Introduction ................................................................................................ 51
D2 Executing the DSMOPT Command File ................................................... 51
D3 Executine ANAPRE .................................................................................. 63

E MANAGING THE INTERFACE SYSTEM 69
El Interface Directory ..................................................................................... 69
E2 OPTDES Directory .................................................................................... 69

E3 Command File DSMOPT Maintenance ..................................................... 7O

vii

F INTERFACE COMPUTER PROGRAMS 71
El Introduction ................................................................................................ 71
F2 ANASUB.FOR .......................................................................................... 72
F3 DSMOPTCOM ......................................................................................... 102
R4 SYSPRMEDT ........................................................................................... 11 1
RS SYSDATEDT ........................................................................................... 113
R6 CDESZDPT ............................................................................................... 115

G APPLICATION EXAMPLE DATA 117
G] Introduction ................................................................................................ 117
G.2 Input Vector (U) Datafiles ......................................................................... 117
GB ENPORT Output Files ............................................................................... 121
G4 Optimization Datafiles ............................................................................... 131
6.5 ANAPRE Data Entry ................................................................................. 137
G6 Signal Generator Bond Graph ................................................................... 138

LIST OF REFERENCES ....................................................................................... 140

Table 3.4.1
Table 3.4.2.1
Table 3.4.2.2
Table 3.4.2.3
Table 3.5.1.1
Table 3.5.2.1
Table 3.5.3.1
Table 3.6.1
Table G.5.l

LIST OF TABLES

Problem Characterization

 

 

Analysis Variables
Performance Measurements

 

Analysis Functions

 

Problem 1 Results

 

Problem 2 Results

 

Problem 3 Results

 

Problem 2 Results Comparison

 

ANAPRE Data Entry List

 

viii

14
15
15
16
17
21
26
30
137

Figure 1.2.1
Figure 2.1.1
Figure 2.2.1
Figure 2.3.1
Figure 2.3.2
Figure 2.3.1.1
Figure 3.2.1
Figure 3.2.2
Figure 3.2.3
Figure 3.2.4
Figure 3.3.1
Figure 3.5.1.1

Figure 3.5.1.2

Figure 3.5.1.3
Figure 3.5.2.1

Figure 3.5.2.2
Figure 3.5.2.3

Figure 3.5.2.4
Figure 3.5.3.1

Figure 3.5.3.2

Figure 3.53.3

LIST OF FIGURES

Mechanical Positioner

 

ENPORT Data Flow -
OPTDES Data Flow

 

ENPORT - OPTDES Connection

 

Interface Function

 

ENPORT - OPTDES- INTERFACE Connection” .... ...... ......

5 D.O.F. Suspension System

 

 

Road Profile 1 - Severe Bump _ -
Road Profile 2 - Highway Condition No. 1

 

Road Profile 3- Highway Condition No. 2 -

 

5 DOF Bond Graph

 

Objective Function and Active Constraint Responses to

 

Initial Design Variables: Problem 1
Objective Function and Active Constraint Responses to
Optimal Design Variables: Problem 1

 

Objective Function Iteration History: Problem 1 .........
Objective Funtion Response to Initial Design
Variables: Problem 2 .....

 

Active Constraint Response to Initial Design
Variables: Problem 2

 

Objective Function and Active Constraint Responses to
Optimal Design Variables: Problem 2

 

Objective Function Iteration History: Problem 2 .............. ..

Objective Funtion Response to Optimal Design
Variables: Problem 3

 

Active Constraint Response to Optimal Design
Variables: Problem 3 - - .....

 

Objective Function Iteration History: Problem 3..

18

19
20

-22

23

24
25

-27

-28

Figure A.3.1
Figure A.4.1
Figure B.3.1
Figure D.3.1
Figure F.1.1
Figure G.6.1

X

 

 

 

 

Performance Evaluation Data Flow 35
User Entry of System Parameters 37
Example of MFS AF-Vector 39
Branching Tree for ANAPRE Execution 64
ENPORT, OPTDES and INTERFACE Data Flow ........... 71
Signal Generator Bond Graph 139

 

AF
AV

DV

MFS
NFF

aaaaga

OF
OP
PM
PM

NFFCN

NOMENCLATURE

ANALYSIS FUNCTION

ANALYSIS VARIABLE

DEGREES OF FREEDOM

DESIGN VARIABLE

EFFORT/FLOW

MULTIPLE FORCING SYSTEM

NUMBER OF FORCING FUNCTIONS
FORCING FUNCTION NUMBER

NAMED PARAMETER

NUMBER OF PERFORMANCE MEASUREMENTS
NUMBER OF INPUT VARIABLES

NUMBER OF STATE VARIABLES

NUMBER OF OUTPUT VARIABLES
OBJECTIVE CONSTRAINT

OBJECTIVE FUNCTION

OBJECTIVE PERFORMANCE
PERFORMANCE MEASUREMENT
PERFORMANCE MEASUREMENT METHOD
STATE VARIABLE INITIAL CONDITIONS
ENPORT MODEL OUTPUT RESPONSE

xi

1.1

1.2

CHAPTER 1
INTRODUCTION

Motivation

Simulation software can create and solve a set of differential equations and
provide numerical results of the system state responses. Optimization software can
explore the design space, searching for a feasible solution which best satisfies a
given cost function. In general simulation software does not have the capability to
systematically search a design space for an optimal solution. The user must do this
by hand, guessing design variable changes. Similarly, optimization software is not
capable of assembling and solving a set of differential equations; this task must be
done by the user. Each of these software package types has limitations in providing
a complete service to the design engineer. Our objective is to establish an interface
between these two types of software packages. By doing so the strengths of each
will be joined in an effort to reduce design time while ensuring accuracy.

Basic Problem

In dynamics design considerations often relate to controlling the transient or
steady state response for an excited system. The desired response will be a function
of the individual system components and their inter-relationships. Hence changing
component values will alter the system response. Consider a mechanical position
control system.

1.3

r’ xm

 

 

 

 

 

F(t) K1 \

_. Mass VVW§

+§

C1 \

«SESVEQ EV? W\
Figure 1.2.1

Mechanical Positioner

Typical design objectives include minimizing settling time or rise time, setting
displacements, and so on. Each objective requires a particular design. The design
variables of this system might be the spring, mass and damper parameters. These
parameters will typically be bounded by design limitations. The question then
becomes "Which combination of design variables best meets the objective?"
Optimization is a systematic process of searching for the feasible design which best
satisfies an objective function. In a 1-DOF problem like this analytical results may
be obtainable. However, in multi-DOF problems analytical solutions are not easily
found and the search space becomes very large. With our interface it is possible to
optimize a multi-DOF model relative to a specific objective with proven
computational techniques.

Organization of the Thesis

In chapter 2 an overview of modeling and optimization software is discussed.
The advancement made by the interface software is described. An example
illustrating use of the interface is presented in chapter 3. The problem is a 5 DOF
suspension system posed and solved 3 different ways. Chapter 4 will conclude the
report with a summary and recommendations. In the appendices the reader will find
discussion detailing the interface. In appendix A design considerations made in
ENPORT [1] and OPTDES [2] will be discussed. Appendix B will discuss a special
class of problem where the system is driven by multiple inputs. To expand the
interface capablilites the user can create their own program model which can be used
with the ENPORT model. These user written subroutines are discussed in appendix
C. Appendix D is the users guide.

CHAPTER 2
CURRENT STATUS

2.1 Simulation Using ENPORT

ENPORT is a modeling and simulation software package which aids in the
performance assessment of dynamic systems. ENPORT is based on bond graph
theory. It combines a set of standard block diagrams and bond graph elements to
build system models. With ENPORT the user can create output files of the state
equations describing the model behavior.

This software is typical of simulation packages in that it is capable of
determining the state response of an N-DOF system but does not explore the design
space in search of an optimal design solution. Given a specific set of design
variables, ENPORT generates a set of output responses.

. ENPORT
Y I I NP

 

 

 

 

MODEL DESIGN
RESPONSE VARIABLE
OUTPUT VALUES
Figure 2.1.1
ENPORT Data Flow

With ENPORT the user must enter a set of design variables by hand, then
examine the system response to determine design changes. To provide a convenient
way to search the design space ENPORT can describe the set of design variables
using named-parameters (NP). By changing the NP vector the user can study new

4

designs. By examining the output responses (Y) the user can determine if the new
design is better, feasible, and which changes can improve the model performance.
Optimizing with simulation software is obviously burdensome to the design
engineer.

2.2 Optimization Using OPTDES

OPTDES is a design optimization software package. Within OPTDES many
optimization algorithms for exploring the design space are offered. The user can
control the design search by changing the step size, convergence tolerance, and other
parameters. The design space can be scaled, which improves algorithm performance
and identifies active constraints more simply. OPTDES provides many post-
processing features. OPTDES is typical of most optimization software in that it
passes a set of independent design variable values (AV) to the model and receives a
set of analysis function values (AF) back from the model. To start the optimization
process the user provides an initial design point (AVG) and the final optimized
design is returned (AVf).

 

 

AF . , AV
----- -| MODEL —----.
(ANAFUN)
mi}... visa.
RESPONSE VALUES

 

OUTPUT
L—‘i OPTDES

Avfi QAV0
I USER I

 

 

Figure 2.2.1
OPTDES Data Flow

The analysis functions are used to evaluate the performance of the model to
determine the best feasible design. With OPTDES the user must develop and
program the set of equations describing the model. The equations program name
used with the OPTDES software is ANAFUN. In an N-DOF problem this process
will require much time and allows for errors to creep into in the model. When

5

designing, an engineer requires accuracy and speed in building a model, which
optimization software does not provide.

2.3 Interfacing ENPORT and OPTDES
The interface is intended to combine the equation solving capabilities of
ENPORT with the design space exploration power of OPTDES. By doing this
models built in ENPORT can be optimized.

I MODEL

 

 

 

 

 

 

 

MODEL DESIGN
RESPONSE VARIABLE
OUTPUT VALilES
AF | AV
OPTDES I
AVr i iAVo
LUSELJ
Figure 2.3.1
ENPORT - OPTDES Connection

FIGURE 2.3.1 illustrates the ideal interface between ENPORT and OPTDES.
This figure shows the relationships between the AV and NP vectors and the Y and
AF vectors. The ENPORT model receives a set of design variables (AV/NP) from
OPTDES and returns the analysis functions (Y IAF) for evaluating the system
performance. The purpose of the interface is to make the transition from the variable
forms AV to NP and Y to AF.

6

As seen from FIGURE 2.3.2 the NP and AV vectors are the same. This allows
the ENPORT model to receive design variables directly. Output from the

 

Y I MODEL
4 I (ENPORT)

 

 

 

 

 

OPTDES I

Aw i LAV.
mu

 

Figure 2.3.2
Interface Function

ENPORT model is a function of time. As a result the time response must be
evaluated to provide OPTDES with the analysis functions in the proper format, a
constant value (i.e. AB = max IX(t)I).

2.3.1 Describing the Interface Connection
Enport has the capability of generating a Fortran file defining a set of N
coupled first-order differential equations from the system graph model. This
ENPORT file can be used to calculate the state derivatives for a given set of
initial conditions. Within OPTDES (in subroutine ANAFUN) is an
integration routine (4th order Runge-Kutta) which can call the ENPORT
Fortran file and produce a time response of the system.

7

MODEL l

g Y i LNP
IINTERFACE
I (ANAFUN)

 

 

 

AF OPTDES } AV l

Afo HIVo
LUSERJ

Figure 2.3.1.1
ENPORT - OPTDES - INTERFACE Connection

 

 

OPTDES passes the design variables to the interface through the AV
vector. The interface calls the ENPORT Fortran file, passing the design
variables through the NP vector. ENPORT returns a time history to the
interface through the Y vector. The interface now evaluates the time history
and returns the analysis function values to OPTDES through the AF vector.
One consideration in designing this link was to establish a standardized call to
the ENPORT Fortran file, which makes this connection possible for any bond-
graph model. In addition this connection will work with any filcname given
to the ENPORT Fortran file. This allows for a library of models to be created
from which the user can select one for optimization.

3.1

3.2

CHAPTER 3
AN APPLICATION EXAMPLE

Introduction

To illustrate the capabilities of the interface the design of a 5-DOF suspension
system was used. The problem posed here is a re-creation of the one given by Haug
and Arora [3]. In their solution they employed analytical methods to determine the
state equations and the derivatives of the design functions with respect to the design
variables. Using computational methods this model was optimized. With this
interface the state equations will be generated by ENPORT. OPTDES will then
determine the necessary gradients to explore the design Space. With the interface the
design engineer is responsible for building the bond-graph in ENPORT and posing
the optimization problem in OPTDES. As we shall see the results obtained for the
objective function using the design interface were within 5% of those obtained by
Hang and Arora for each problem.

Design Problem Considerations
The following schematic illustrates the 5 DOF suspension system being

designed.

 

 

 

 

 

 

 

 

Figure 3.2.1
5 D.O.F. Suspension System

The system is excited by tire displacements due to interaction with the road
surface. Three surfaces were considered representing a severe bump and two
different highway conditions. For modeling purposes the tire displacement profiles
were differentiated one time. The result is a velocity profile of the tire input The
velocity can be modeled as a source of flow into the ENPORT model. The following
velocity profiles were used.

fife—o

6m
5.50

4.50

10

velocity _profile

 

 

 

 

 

{iii——

 

/ \

 

 

 

 

 

 

 

 

//

 

 

 

NX=>IA

I
I
I
I
~71...__./

 

 

 

 

 

 

 

 

 

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Figure 3.2.2
Profile 1 - Severe Bump

his-ft
6m.

11

velocity _profile

 

5.00

 

4.00

 

3.00

 

2.00

 

1.00

 

aco—

4.00

 

 

 

 

' -3.oo

 

4.00

 

em

 

 

 

 

 

 

 

Figure 3.2.3

Profile 2 - Highway Condition No. 1

VM

his-ft
1.20

LN

0.80

0.60

0.40

0.20

-0.40

«0.60

0.80

4.00

4.20

12

velocity _profile

 

 

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 \ 0.20' 0.40 0.60

Figure 3.2.4
Profile 3 - Highway Condition No. 2

0.80

1.00

13
3.3 Bond Graph Design
The bond-graph model of Figure 3.3.1 was built in ENPORT. This model
represents the suspension system. SFl represents velocity input to the front tire and
SF2 is velocity input to the rear tire.

12 Illéiaklmoct—JiicF—mai

  

 

211
522 ‘45-! t-z
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Figure 3.3.1

5 D.O.F. Bond Graph

3.4

14

3.4 Optimization Problem
Three different optimization problems will be posed. In each case the objective
is to minimize the maximum seat force ensuring driver comfort. Each problem is
characterized by road conditions.

Table 3.4.1
Problem Charachterization

 

 

 

 

Problem Road Vehicle
No. Profile(s) SW9“)
(In/sec)
1 1 450
2 2, 3 960/ 960
3 l, 2 450/ 960

 

 

 

 

 

Problems 2 and 3 will illustrate a problem where the system is optimized to
responses for more than one input.

3.4.1 Objective Functions
The objective function for each problem is posed in the following way:

Probleml Min‘P = MaxlE.1M1(t,b)|

Problem 2 Min‘I’ = Max | E.1Mi(t.b)l
i = 2,3

Problem 3 Min‘I’ = Max I E.1M2(t,b)l

Note: Subscripts represent velocity profiles.

E.1M is the effort (i.e., force) at the
seat.

15

3.4.2 Model and Optimiation Parameters
The analysis variables used are

 

 

 

 

 

 

 

 

Table 3.4.2.1
Analysis Variables
AV DESCRIPTION NODE wwggm‘ 13131.1,“
1 Seat Spring Cl 600 6000
2 Front Spring C2 2400 12000
3 Rear Spring (:3 2400 12000
4 Seat Damper R1 24 600
5 Front Damper R2 30 960
6 Rear Damper R3 30 960

 

 

 

 

 

 

 

The performance measurements are

Table 3.4.2.2
Performance Measurements

 

 

 

 

 

 

 

PM DESCRIPTION VBL Affg‘m‘éfl
1 Seat SpringDisp QJQ '167
2 Seat Force E.lM 0121- F0“-
3 Front Spring Disp Q.2Q .417
4 Rear Spring Disp Q.3Q .417
5 Front Tire Compr QAQ .167
6 Rear Tire Compr Q.SQ .167

 

 

 

 

 

 

The AF vectors will have the following formats in SETUP:

16

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3.4.2.3
Analysis Functions
Constraint Value
AF PM PROBLEM 1 PROBLEM 2 PROBLEM 3
l 1 < .167 < .167 < .167
2 2 r 0.0 1": 0.0 < 500
3 3 < .417 < .417 < .417
4 4 < .417 < .417 < .417
5 5 < .167 < .167 < .167
6 6 < .167 < .167 < .167
7 1 ---- < .167 < -167
8 2 ..-. u < 0.0 * 0.0
9 3 .... < .417 < .417
10 4 an < .417 < .417
11 5 .... < .167 < .167
12 6 ---- < .167 < .167
13 1 ---- * 0.0 ---

 

 

 

 

 

 

 

* Objective Function
** Objective Function Set Member

lSRe

Ihc

dcs
of

3.5

17
3.5 Results
The results of each problem are presented in a set of tables and compared to
those reported by Haug and Arora. Included with each problem is a graphical
representation of the seat force and active constraint for both initial and optimized
design variables. These graphs were produced using ENPORT. A graphical history
of the objective function values is also included.

3.5.1 Problem 1 Summary
In problem one the most significant difference was in the seat damper
values (see Table 3.5.1.1). The optimized value was 142% greater than the
Hang and Arora solution. The optimized values for the objective functions
were within 1% of each other. Figures 3.5.1.1 and 3.5.1.2 illustrate the seat
force and the front spring displacement for initial and optimized design
variables. These results were achieved in 7 iterations (see Figure 3.5.1.3).

 

 

 

 

 

 

 

 

Table 3.5.1.1
Problem 1 Results
AV “AUG 8‘ ARORA Sgti'fi‘ss DI’FEFIECREETVTCE
or 600.0 600.0 “-00
C2 2400.0 2400.0 0.00
C3 2902.8 2400.0 - 17.32
R1 154.7 3750 142.04
R2 930.2 926.3 - 0.42
R3 960.0 960.0 0.00
93g, 193.1 1915 -0.83

 

 

 

 

 

 

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Objective_Function

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.“)

 

 

 

 

 

 

LI!) 2.“) 3.1!) 4.1!) 5.00 6.“)

Figure 3.5.1.3
Objective Function Iteration History: Problem 1

 

7.“:

21

3.5.2 Problem 2 Summary

The results (see Table 3.5.2.1) in problem 2 are very similar with a
3.4% difference in seat force values. The front damper values had the largest
difference of 39.4%. These results were produced using the GRG algorithm
in 7 iterations (see Figure 3.5.2.5). Road profile 2 produced the highest seat
force at initial DV values. Figure 3.5.2.1 illustrates the initial seat force
response. The active seat force for optimized DV values is created by road
profile 3. Figure 3.5.2.3 shows the optimized seat force response. The active
constraint is the rear tire compression for road profile 3. Figures 3.5.2.2 and
3.5.2.3 shows the tire compression for initial and optimized DV values

 

 

 

 

 

 

 

 

respectively.
Table 3.5.2.1
Problem 2 Results
OPTDES PERCENT

AV "AUG 8‘ “ORA RESULTS DIFFERENCE
Cl 600.0 600.0 "-00
C2 2400.0 2400.0 0.00
C3 2400.0 2400.0 0.00
R1 107.2 105.0 - 2.1
R2 551.0 333.9 - 39.4
R3 453.7 439.6 - 3.1
OBJ

FCN 94.1 97.3 3.4

 

 

 

 

 

 

NVNWCNFO Q3\O \RC

22

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3.3 2:»:

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23

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24

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3.? 2&3 .

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210.00

200.00

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140.11)

130.00

120.00

1 10.00

100.“)

90.00

25

Objective_Funcdon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00

1.00 2.00 31!) 40) 5.00

Figure 3.5.2.4
Objective Function Iteration History: Problem 2

6.“)

7.1!)

26

3.5.3 Problem 3 Summary

The results for problem 3, see Table 3.5.3.1, show a difference in seat
force values of approximately 4%. The AV values were very close except for
the rear damper which had a 205% difference. In this problem the dependent
constraints bounding the feasible set were not active at the optimal design
point. The active constraints were the simple bounds for each DV at the
optimal design point. Each spring was at its lower bound and each damper
was at its upper bound. Figure 3.5.3.1 illustrates the seat force for initial DV
values. Figure 3.5.3.1 shows the seat force for optimized DV values. These
results were produced using the GRG algorithm after 8 iterations (see Figure
3.5.3.3). In this problem, as in problem 1, the front spring displacement
constraint is violated (see Figure 3.5.1.1) for the initial DV values. Figure
3.5.3.2 shows the front spring displacement for the optimized DV values.

 

 

 

 

 

 

 

 

Table 3.5.3.1
Problem 3 Results
Av HAUG & ARORA Sguiiiss nfigrfigim
Cl 600.0 6004) 0'00
(:2 2400.0 2400-0 0'00
C3 2400.0 2400.0 0.00
R1 559.0 600.0 6-84
R2 941.3 960.0 1.99
R3 3140 960.0 205.00
33% 77.6 74.4 - 4.11

 

 

 

 

 

 

27

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3:3” 2:3...
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mvHHNuHN Nm\m \No

28

n Ease...— ”moEatsw :wfiofi 352.5 3 mom—.88: 23.3.80 0.53.

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150.00
145.00
140.00
135.00
130.00
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120.00
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95.00
90.00
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L
I I
1 1
0.00 2.00 4.00 6.00 8.00
Figure 3.5.3.3

 

 

Objective Function iteration History: Problem 3

30

3.6 Discussion

In each problem the optimal DV values were found using the GRG algorithm.
The search parameters were not changed from their default settings. In a problem of
this nature there are many local minimums. Different optimization algorithms will
step through the design space differently. As a result different optimal solutions will
be found. This is one explanation for the differences in results between OPTDES
and the optimization method used by Haug and Arora. To illustrate this idea further
problem 2 was solved using a combination of SQP and GRG algorithms. The
problem was started using the SQP method. On the 15th design the GRG method
was used to complete the optimization problem. As seen from the results in TABLE
3.6.1 an entirely new solution was found.

Table 3.6.1
Problem 2 Results Comparison

 

 

 

 

 

 

 

 

 

 

 

 

 

AV rgsygrfig 1 R%§TUII).¥§ 2 D¥§F1E€§gllvq1éE
C1 600.0 2711.9 352.0
C2 2400.0 2400.0 0.00
C3 2400.0 2400.0 cm
R1 105.0 35.0 -66.7
R2 333.9 278.9 -16.5
R3 439.6 418.9 .4.7
38% 973 92.4 -5.0

 

The seat force was reduced by 5%. The most interesting differences were
found in the seat spring and damper. This example shows how important it is for the
designer to employ good optimization techniques to thoroughly research a problem
before making any determinations.

4.1

4.2

CHAPTER 4
CONCLUSIONS

Summary

An interface between modeling software and optimization software has been
established using ENPORT and OPTDESBYU. With this interface dynamic
responses can be optimized with respect to system components (e.g. springs, masses,
and dampers). The interface uses the equation solving capabilities of ENPORT with
the design space exploration facilities of OPTDES. The interface has been
generalized to optimize any bond graph model with minimal user input. Also the
designer can develop a library of designs to call upon. With this interface design
time can be reduced while maintaining confidence in the results.

Recommendations

The interface established here is just the first step in fully integrating simulation
and optimization software. Through use of this interface and advancements in the
areas of simulation and optimization ideas for improvement will result. In
developing this interface some of the following thoughts about improvements have
come to mind:

- Use initial design conditions from ENPORT to create the datafile in
CONVEN. This will help to reduce time and redundant effort.

- Create a standardized format in ANAPOST to write a file of optimized
design variables. This file could be used to pass these values back to
ENPORT.

- Expand the numerical integration capabilities of ANAFUN. This
could be done by formatting ANAFUN to call the ENPORT
integration library.

31

32

- Eliminate prompts for NX, NY, and NU if confidence is high for the
accurracy of the values now being passed.

- Develop new methods of performance evaluation for the system
response.

APPENDICES

APPENDIX A

DESIGN AND IMPLEMENTATION CONSIDERATIONS

A.l

A.2

APPENDIX A
DESIGN AND IMPLEMENTATION CONSIDERATIONS

Introduction
When creating the bond graph and posing the optimization problem the user
must
- Select elements for design variables
- Determine how system performance is measured
When selecting design variables in ENPORT those elements are identified
using the named-parameter option. These elements create the NP vector. The
system performance is determined by selecting model outputs. These outputs build
the Y vector (See Figure 2.3.1).

Design Variables

The named-parameter feature plays a key role in properly building the bond
graph for optimization. The named-parameter option describes an element used in a
node equation by a variable name. Usage of this option is discussed in chapter 6 of
the ENPORT Reference Manual on pages 6-4a and 6-4b. When the ENPORT
Fortran file is generated, elements described by a named-parameter will be coded
with the variable name. These elements will be passed values through the AV
vector when the interface software calls the ENPORT Fortran file (See Figure
2.3.1.1). The relationship between the AV and NP vector is one to one.

33

A.3

AV(l)
AV(2)

 

AWm

 

M

NP(l)
NP(2)

NP(n)

 

 

The user must know the size and read order of the NP vector created in the
ENPORT Fortran file. This information is needed when running CONVEN.

Analysis Functions

The interface is responsible for interpreting the time response (Y vector) of the
model. The following performance measurement methods (PMM) are used to

evaluate the model output

zxmw>g

Maximum Value

Average Value

RMS Value

Minimum Value

Absolute Maximum Value
Absolute Minimum Value

Any combination of these can be selected for a problem. The size and order of
the AF vector is a function of the output vector,Y, and the number of PMS
selected. The subroutine ANAFUN will call subroutine perform to evaluate the

model response (Y vector).

35
III-null“
PM.“ PMa PM.- PMs Pm. PM“

PERFORM
(PERFORMANCE EVALUATOR)

.4 1y
, Y -

ANAFUN MODEL
(INTERFACE) (ENPORT)
- NP * *
AVf AV0

Figure A.3.1
Performance Evaluation Data Flow

 

 

 

Perform will call any of the PM subroutines depending on which methods are
selected. Perform will also call the PMM subroutines in the order they were
selected. In each PMM subroutine the output response is analyzed and PM values
are returned. The PMs are on a one to one basis with the Y vector.

 

 

 

PM(1) Y0)
PM(2) Y(2)
PM(n)I Yin)

 

As the PMM subroutines are called the PM vectors are assembled to form the
AF vector

AA

36

PM

%

PM

 

 

Hence the size of the AF vector is
#AF members = # Y members " #PMMs selected
The AF vector is sorted first by PM then by PM. Therefore, if

 

PMM = 2
AF = 6
and AF will be sorted as
AF(l) = PM(l)
AF(2) = PM(2) ------ For PMM(l)
AF(3) = PM(3)
AF(4) = PM(l)
AF(S) = PM(2) I ----- For PMM(2)
AF(6) = PM(3)

 

The size and order of AF must be known for setting constraints in SETUP. As
a service to the user an option to view the AF vector is available when executing the
interface software.

General Model Design

Up to this point the discussion has centered around building a specific model
for a specific optimization problem. However, using the named-parameter option to
its fullest extent the user can build generalized models to solve many different
optimization problems. The named-parameter option can be used to define physical
parameters besides design variables. These physical parameters are passed values
using the system input vector U. These values are entered once before optimizing
and remain fixed. They are not design variables. Referring to figure 2.3.1.1 and

 

 

37

 

 

 

MODEL ANAPRE
(ENPORT) f (USER)
‘1 1“" “1
|' ANAFUN ‘ e

 

 

 

I (INTERFACE) 1
AF | Av

 

OPTDES I

AVfI iAVo
LIISELJ

 

 

Figure A.4.l
User Entry of System Parameters

expanding this diagram to the one seen in Figure A.4.1. In this figure it can be
seen that subroutine ANAFUN will call subroutine ANAPRE. This call is made
one time to collect information necessary to execute the optimization process. At
this point the user can enter information which profiles the bond graph model being
optimized.

Consider the mechanical position control system in Figure 1.1.1. Suppose F(t)
and m are fixed and K1 and C1 are the DVs. The ENPORT model could be built
accordingly and optimized. Now suppose the mass was changed to a new fixed
value. A new model would be generated using the new mass value. On the other
hand a general bond graph can be created identifying the mass using the named-
parameter option. The mass is identified as a member of the U vector (declared as
external in ENPORT). Now the user can simply re-enter a new mass value, thru
ANAPRE, to execut a new optimization problem in lieu of creating a new bond
graph. The U vector values can be entered using a datafile or interactively. See
appendix D.2 EXECUTING ANAPRE for details. Also see appendix E.2 for
creating an interactive menu. It is recommended that the user begin by entering
data using a datafile.

APPENDIX B

MULTIPLE FORCING SYSTEM PROBLEM

APPENDIX B
MULTIPLE FORCING SYSTEM PROBLEM (MFS)

8.1 Introduction
This is a special class of problem and requires the usage of a general model
design. Suppose the mechanical positioner is designed to minimize settling time.
In addition the postioner can cycle at two different frequencies; 60 and 30 hertz
(assume a constant amplitude). Now the system must be optimized to satisy two
different forcing functions. In this case the same force is applied at two different
natural frequencies such as
F1(t) = Fosin out
F 2(t) = Fosin (th
The best design possible is when the system has the same settling time at each

frequency.

B.2 Posing the MFS Optimization Problem

The problem would be posed as
Min ‘1‘
where
‘I’ = Max {t1, t2}
t1 = Settle time at 01
t2 = Settle time at (112

Subject to Constraints
“"jkmin < “"jk <°'J
and Simple Bounds

egmin‘ 98 < egmax

kmax

where
1,2, .. l; l = no. of forcing systems
1,2, m; m = no. of performance mess. methods

38

8.3

B.4

39

1,2, .. n; n = no. of performance measurements
ktll constraint response for the

jth performance measurement method for the

ith forcing system.

Gg = gth design variable.

k
@jk

AF-Vector Build for the MFS Problem

This type of problem adds another dimension to the AF vector. For each set of
driving conditions subroutine ANAFUN will be repeated, hence the AF vector will
grow in magnitude of order n. The user must be aware of this to pose the
optimization problem in CONVEN and SETUP. Consider the example in appendix
A.3. With two forcing systems the AF vector would now have 12 members

#AF = { 2(=I) x 2(=m) X 3(=n) }

 

 

 

 

 

AF(l) = PM(l)
AF(2) = PM(2) , ----- PMM(l)
. = M13) NFF(l)
AF(4) = PM(l)
AF(S) .-. PM(2) I ----- PMM(2)
* = M13)
AF(7) = PM(l)
AF(8) = PM(2) ..... PMM(l)
. = M13) NFF(2)
AF(10) = PM(l)
AF(ll) = PM(2) ~ ..... PMM(2)
" AEQZL_=JM13)

 

Figure B.3.l
Example of MFS AF Vector
Setting up the MFS Problem in OPTDES
Now suppose the third PM is used to measure the objective performance then
the objecitve function set, 9, is
Q = {AF(3), AF(6), AF(9), AF(12)}
‘I' = Max {0}
To solve this problem an additional AF member is required. This member is
‘1’. Hence, from Figure B.3.1 the additional AF member is
AF(13) = ‘I‘
Also an additional AV member is required. This value will be referred to as A.
A is used as the objective function. Now using the mechanical positioner where C1
and K1 are the AVs then the additional AV member is

40

AV(3) = A
A must have an arbitrary initial value (A0) that is at least greater than all
members of the objective function set. Then in this example
A0 > Max {0}
This initial value for A0 is entered the same as all AV values when CONVEN

is executed.
Now in SETUP A can have bounds of

0<A<Ao

The objective function set members are set less than zero in SETUP where

AF (3) < 0
AF (6) < 0
AF(9) < 0
AF (12) < 0

The additional AF member is declared the objective function in SETUP where
v AF(13)

B.5 Determining the Objective Function Value
Recall that in this example the third PM was used to measure the objective
performance which is why AF(3), AF(6), AF(9), and AF(12) are the objective

function set members (refer to Figure B.3.1).

AF(3) = «>in - A where i=1, j=3, k=l
AF (6) = ¢"k - A where 1:], i=3, k=2
AF(9) = oijk - A where i=2, j=3, k=l
AF(12) = ¢'jk - A where i=2, i=3, k=2
AF(l3) = ‘1’ = A2

A is an independent variable which must be lowered to minimized ‘I’. A will
have lower bounds set by the constraint set 9. These OCs, Q, will become active as
A is lowered. The OCs are functions of the AVs. Hence the optimization algorithm
will adjust the AVs to lower the OC values in order to lower A.

3.6 Summarizing the MFS Optimization Problem
These calculations are performed internally and are based on responses entered
by the user when executing the optimization software. Therefore the user is not
responsible for understanding or setting up this calculation process. The user must
be aware that they are posing an MFS problem. They must know which PM is

41

measuring the OP and how to determine the proper AV and AF sizes. To
summarize the user must do the following for

ANAPRE
- Enter the number of forcing systems (NFF)
- Enter the size of the Objecive Function Set (generally equals NFF)
- Enter index No. for PM member measuring the OP

CONVEN
- Calculate and enter the size of the AV vector
#AV = #NP + l
- Calculate and enter the size of the AF vector
#AF = #PMM it #PM x #NFF + l

SETUP
- Declare the additional AF member as the Objective Function
- Set the additional AV member with the proper bounds in SETUP

Internal calculations are based on entries to these prompts. See appendix 0.5
to see how this information was entered for the application example in chapter 3.
The multiple forcing system procedure described here was used in problem 2.

Note that in problem 3 of the application example the objective function set
size was 1. In this problem the first forcing system was used to determine
constraints only. The overall technique previously described to determine the
objective function is not necessry. Now AV and AF are determined as follows:

#AV = #NP
#AF = #PMM x #PM x #NFF.

APPENDIX C

USER WRITTEN SUBROUTINES AND SAMPLES

APPENDIX C
USER WRITTEN SUBROUTINES

C.l Introduction
These options are available to expand the capabilities of the interface as
requirements become more sophisticated. With this option the user can write E/F
models, create menus for an interactive session and build the AF vector to desired
specifications. The checkfile option should be used when debugging these
subroutines.

C.2 User Written Generator (USRGEN.FOR)

This subroutine is used to model Effort/flow systems. USRGENFOR must
be written to return the instantaneous Effort/flow value for each source. When
creating the ENPORT Fortran file each source of effort or flow is identified as a
single external source. Hence if there are 2 sources of flow (as in the application
example in chapter 3) driving the model USRGEN will generate and return a U(l)
and U(2) value. USRGEN can also be used in MFS problems. The subroutine
statement must be written as:

SUBROUTINE USRGEN (NFFCN,T,U)

Where
focn = forcing system No.
t = time
U = U - vector

focn and t are passed to USRGEN and U is returned. A sample program is
included. This sample will generate the road profiles used in the application
example in chapter 3.

C.2.l Sample Program: USRGEN

42

FORTRAN FILE
USRGEN.FOR

WRITTEN
BY

MARK DAVIS

43

C. ***************************************************************

c.----Subroutine USRGEN:
c.
c.---Purpose: This subroutine serves as an interface between the
c. subroutine Anasub.for and the user. This user may
c. code in values or equations to describe external
c. inputs to the system.
c.
c.---Variables used:
c. Passed variables
c. --------------------------------------
c. T - The instantaeous time
c. U - The external function vector
c.
c. Local variables
c. --------------------------------------
c. tlag - Time lag between front and rear wheels
c. trl a Initial response time for the rear wheel
C. tr2 = Second phase response time for the rear wheel
0. tf2 - Second phase response time for the front wheel
c. tt - Initial phase response time with time delay
c.
subroutine USRGEN(nffcn,t,u)
c.
C. Define passed variables
c.
double precision t,u(1)
c.
0. Define local variables
c.
double precision tlag, trl, tr2, tf2, tt, wl, w2,
+ MASS(20),TF(20)
c.
REAL sp, wb, 11, 12, ya
Integer iwave, nffcn
Common lextmen/ sp(10), wb(10), 11(10), 12(10), ya(10),
iwave(10)
c.
c. Determine velocity input for the front wheel. The time .488
c. represents the
c. phase shift necessary for the second cos function to begin
c. at 180 degrees.
c. This will match the asymptotes of the two functions. .48 is
c. of the second cos function.
c.
c. Natural frequencies
c.
pi - 3.14159265d0 .
wl - pi*sp(nffcn)/ll(nffcn)
w2 - pi*sp(nffcn)/12(nffcn)
c.
c. Periodic times
0.
t1 - 11(nffcn)/sp(nffcn)
t2 - (11(nffcn)+12(nffcn))/sp(nffcn)
c.
0. Front wheel initial velocity
0.

Ifin - Iwave(nffcn)

44

DO 10 ISW - 1,Ifin

10
c.
20

C.

00000

000

IPER - ISW
IF(t .le. isw*t2)goto 20

continue

t1 - iper*t1+(iper-l)*t2

t2 - iper*t2

if (t .lt. t1) then

u(l) - -Ya(nffcn)*w1*sin(wl*t)
elseif (t .le. t2) then

u(l) = Ya(nffcn)*w2*sin(w2*(t-tl))
else

u(l) - 0.
endif

. Determine velocity input for the rear wheel. The is a time
. lag between these inputs equal to:
time lag a (wheel basel/(Speed of car)

tlag - wb(nffcn)/sp(nffcn)
trl - t1 + tlag
tr2 - t2 + tlag

if (t .lt. tlag) then

u(2) - 0
elseif (t .lt. trl) then

tt - t - tlag

u(2) - -Ya(nffcn)*w1*sin(w1*tt)
elseif (t .le. tr2) then

u(2) - Ya(nffcn)*w2*sin(w2*(t-trl))
else

u(2) - 0.
endif

. SET REMAINING EXTERNAL INPUTS

MASS(1)-9.01
MASS(2)-139.75
MASS(3)-3416.7
MASS(4)'3.0
MASS(5)'3.0

TF(1)-.8333333
TF(2)-3.333333
TF(3)-6.666667

0(3) -MASS(1)
0(4) -MASS(2)
0(5) -MASS(3)
0(6) -MASS(4)
0(7) -MASS(S)
0(8) -TF(l)
0(9) -TF(2)
0(10)-TF(3)
return

end

45

Q3 User Written Menu (USRMEN.FOR)

This subroutine is used to read in values necessary to execute USRGEN. The
option is available to the user to enter data via the keyboard or by data files. A
common storage file must be used to pass data from USRMEN to USRGEN. The
name and formatting of the common file is left to the programmer. This file does
not receive or return any variables via the subroutine statement. This file must
also include the integration variable common statement INTVAR if data is
collected for multi-forcing system (NFF = # of forcing functions)

COMMON/INTVAR/Tl,T2,h,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF

A sample program written to operate in conjunction with USRGEN is
included. This sample is written to be used with the generator described in C2.

C.3.l Sample Program: USRMEN

FORTRAN FILE
USRMEN.FOR

WRITTEN
BY

MARK DAVIS

46

. ***************************************************************

.----Subroutine USRMEN

----Purpose: This subroutine allows the user to create a more
interactive model of the external inputs. This
program can be called from anapre allowing for
different conditions to be used without
re-programming subroutine ENPGEN.

.----Variables used:
Passed variables

sp = vehicle speed

wb - wheelbase of vehicle

11 - lst length of road undulation
12 - 2nd length of road undulation
Ya - amplitude of road undulation
isw - number operiods

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Subroutine USRMEN

c. .

c. Define passed variables

c.
Dimension sp(10),wb(10),ll(10),12(10),ya(10),iwave(10)
Character iagn*l
Real sp, wb, 11, 12, ya
Integer iwave

c.
Common lintvar/ T1,T2,h,xin(20),nx,ny,ns,nu,nff,iend,uaf
Common /extmen/ sp, wb, 11, 12, ya, iwave

c. '

do 20 i - 1,nff
10 Write (*,102) 1
Write (*,100)
Read (*,*) sp(i), wb(i), 11(i), 12(i), ya(i), iwave(i)
write (*,101) sp(i), wb(i), 11(i), 12(i), ya(i),
+ iwave(i)
Read (*,200) iagn
If (iagn .eq. 'y') goto 10

20 continue
c.
100 format (lx,'Enter the following simulation parameters',/,
+ 1x,'. ' 1 - Vehicle Speed',/.
+ 1x,’ 2 - Wheelbase’,/,
+ 1x,’ 3 - Half-wavelength # 1',/,
+ lx,’ 4 - Half-wavelength # 2',/,
+ lx,’ 5 - Amplitude’,/,
+ 1x,’ 6 - No. of periods',/.
+ 131' '.$)
101format(1x,'You entered the following simulation parameters’,/,
+ lx,’ Vehicle Speed =',f7.2,/,
+ 1x,’ Wheelbase =',f7.2,/,
+ 1x,’ Half-wavelength #1 =',f7.2,/,
+ lx,’ Half-wavelength #2 =',f7.2,/,
+ 1x,’ Amplitude -',4X,f3.1,/:
+ lx,’ No. of periods =',4x,i3,//,
+ 1x,’Do you wish to re-enter these values’,/,
+ 1x,’ y - yes n = no',/,
+ 1X,’ 'rs)

47

102 format (1x,’Your are entering loading conditions no.',i3)
C.
200 format (al)
C.
return

end

48

Q4 User Written AF - Vector Build (USRAFN.FOR)
This subroutine allows the user to build the AF-vector as desired. This
subroutine is used independently of the other user 'written subroutines. The
subroutine statement must read as:

SUBROUTINE USRAFN(NFFCN,NPM,AV,AF)

Where
NFFCN = Forcing system Number
NPM = Number of Performance Measurements
AV = Analysis Variable Vector
AF = Analysis function Vector

Variables NFFCN, NPM, and AV are passed to USRAFN and AF is returned.
A sample is included. This sample was written to use with an MFS problem. In
this sample the AF vector is the size of the PM vector. Each PM value is
compared for each forcing system and only the worst case value is returned. This
is just one idea for how this subroutine could be used.

C.4.l Sample Program: USRAFN

FORTRAN FILE
USRAFN.FOR

WRITTEN
BY

MARK DAVIS

49

C‘k'k'k‘k***********************************************************

C.----Subroutine USRAFN
C.
c.----Purpose: This subroutine determines the maximum value from
c. the objective function set. In addition all AF
C. components which are elements of the obj fcn set
C. will have their return values calculated.
C. In addition the objective function value used by
c. optdes will be calculated.
C.
C.----Variables used:
c. Passed variables
C. --------------------------------------
C. af - the analysis function array
c. ny - number of output variables
C. nff - number of forcing functions
C. npm - number of performance variables
C. nobj- size of objective function
C.
subroutine USRAFN(NFFCN,NPM,AV,AF)
c.
C. Define passed variables
C.
Dimension zf(lO),af(1),av(l),dumaf(10,10,100),obfcn(10)
Double Precision dumaf, af, av
Real zf, amax, acur
Integer rfact, ncont, npm, naf, iavn, obfcn
C.
Common /intvar/ T1,T2,h,xin(20),nx,ny,ns,nu,NFF,IEND,UAF
Common /objfcn/ nobj,obfcn,icstr,iavn
C. -

c. Determine repeating factor and number of calculated af
C. constraints
.rfact = npm*ny

C.
C. Set AF vector
c.
If (obfcn(1) .lt. 0) then
C.
C. Sort the af vector
C. .
C. i - num of forcing functions
C. j a num of performance criteria
C. k - num of output variables
C. -
do 20 i = l,nff
do 20 j - 1,npm
do 20 k = l,ny
iaf - (i-1)*ny*npm +(j-l)*ny + k
20 dumaf(i,j,k) = af(iaf)
c.
C. Re-Initialize af
C.
do 22 i=1,nff*npm*ny
22 af(i)=0
C.

C. Determine max values for each constraint

50

do 35 j - 1,npm
do 30 k = 1,ny
naf - (j-1)*npm + k
amax - dumaf(l,j,k)
do 25 i - 1,nff
acur = dumaf(i,j,k)
if(acur .gt. amax)then
af(naf) = acur**2

else
af(naf) = amax**2
endif
25 continue
30 continue
35 continue
C.
C. Set the AF vector obj fcn constraints
C.
C. Set obj fcn
C.
AF(rfaCt+1) = AV(iavn)**2
C.
ELSE
C.
C. Determine obj fcn subset
c.
Do 50 i=l,nobj
iaf - obfcn(i)
50 zf(i) - af(iaf)
C.
C. Determine Max value
C.
amax - zf(l)
Do 55 i-1,nobj
if(zf(i) .gt. amax)then
amax - zf(i)
else
amax = amax
endif
55 continue
C.

C. Set the AF vector obj fcn constraints

Do 60 i-1,nobj
iaf - obfcn(i)

60 AF(iaf) a AF(iaf) - AV(iavn)
c O n
C. Set the Obj Fcn value
C.
AF(rfact+1) - AV(iavn)**2
C.
ENDIF
C.
return

end

APPENDIX D

HOW TO USE THE OPTIMIZATION INTERFACE

D.l

D.2

APPENDIX D
HOW TO USE THE OPTIMIZATION INTERFACE

Introduction

The entire interface is menu driven. All aspects of the design problem can be
executed from the top level command file DSMOPT. When either CONVEN or
CDESIGN are invoked subroutine ANAPRE will be executed. The following
directions will explain how to execute and use the Design Simulation and Model
Optimization Interface in a DEC VAX/V MS environment.

Executing the DSMOPT Command File
At the command prompt enter

> @dsmopt (rot

and the following menu appears:
tit...tfitttttttitit.titttttttttttttttitttttttt
"' MAIN MENU "
tittttttttttttttttttt*tttt‘ttttttttttttttttttt
" Please make the following selection "‘
" Enter E = execute ENPORT "
" D = create/edit DATA FILES "'
* O = execute OPTDES *
" C = execute CHECKFILE ‘
" X = exit the session "

t0.$0.0.ttfitttttttttttfittttfitttltttttfitttfitttt

At this point the user will begin the menu selection process. To leave
DMSOPT enter X. The preceding options will be discussed separately.

51

52
11.2.1 Invoking ENPORT

.ltttittttfittttttfitCCOO.##t‘lfit.tttttfittttfiitt

* MAIN MENU ‘

Cttttitttltltttttttittttttttltfittfifitttttlttttt

‘ Please make the following selection "
‘ Enter E = execute ENPORT ‘ "
‘ D = create/edit DATA FILES "‘
“ O = execute OPTDES "
" C = execute CHECKFILE "
‘ X = exit the session "
fittttitttttttttttttit...tttttttttttttttttttltt

From the main menu select option E

Following is a transcript of the ENPORT session.

‘ 53

6.1.1.2 ENPORT State Equations File

****************************************
****************************************

** **
** ENPORT—7 **
** **
** BOND GRAPH/BLOCK DIAGRAM **
** PROCESSOR **
** for **
** NONLINEAR SYSTEMS **
** **
** Version 3.3 **
** **
** Developed by **
** Rosencode Associates **
** Lansing, Michigan **
** **

****************************************
****************************************

(C)1989. Rosencode Associates Inc.
All rights reserved.

Date: 01/20/92 Time: 14:30:09

*Comment. The trapping mode has been turned off/on at this point.

Utilities options

 

Menu, Command, Trap, Debug, Return? (full): R

ENPORT-7 options

Initialize for a new model or load an existing model
Title input or modification

Graph description or modification
Equation description for nodes

Solve for the time response of the system
Display the results

File the model for later reference

Return to the operating system from ENPORT
Manage the file directory

Utilities- mode_set, trap, debug, terminal
Optimize the design

Help

Enter option (R): F

”WUMMQHH

moo:

54

Filer options

E: write Enport model file

write System equations to file
matrix-x eXeC file

write matrix-x User_code_block file
write ACSL input file

write Adams DIFP function file
Return to main menu

Help

mwuyqu
2
H
p.
('9‘
0

Enter option (R): 0

*** Please select some output variables
or you will get no output from Matrix-x.

Output list (Y) options

A: Add variables to current list

D: Delete variables from current list
E: set current list to Empty

S: Show current list

H: Help

R: Return

Enter option (R): A

Ready to add output variables.
(Enter blank line to quit.)

Enter output variable: F.1M
Enter output variable: E.1M
Enter output variable: Q.ZQ
Enter output variable: 0.30
Enter output variable: 0.40
Enter output variable: Q.SQ
Enter output variable:

Output list

Add, Delete, Empty, Show, Help, Return? (full): S
There are 7 output variables (Y).

Y( 1): Q.1Q
Y( 2): F.1M
Y( 3): E.1M
Y( 4): Q.2Q
Y( 5): 0.30
Y( 6): Q.4Q
Y( 7): Q.SQ

Output

list

Add, Delete, Empty, Show, Help, Return? (full): R

55

Please define the INPUT variable types for the Matrix-x file.

Types

Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter

are

time
type
type

type
type
type
type
type
type
type
type
type
type

"E": external input (to the block),
“I": internal input (within block),
"R": RP vector input.

for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for
for

468
28
488
498
68
518
88
98
218
228
238
298
258
288
248
548
558
578
588
E.5W
E.2W
E.1W
B.4W

HHHHHHHHHHHHHHHHHHHHHHH

Please define the Named-Parameter types for the Matrix-x file.

Types

Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter

are

type
type
type
type
type
type
type
type
type
type
type
type
type
type
type

"E": external (to block),
internal (within block),

"I":

"R":

for
for
for
for
for
for
for
for
for
for
for
for
for
for
for

RP vector.

W1
W2
PHIl
PHIZ
PHI3
PHI4
T1
T2
T3
T4
T5
AMPl
AMPZ
AMP3
PHIS

NMMMMMMMMMMMMMM

 

u: rial-M vlufifiruEEEE-DLEEEEEEEEEE

U"
0)

Enter type for PHI6
Enter type for C1
Enter type for C2
Enter type for C3
Enter type for C4
Enter type for C5
Enter type for R1
Enter type for R2
Enter type for R3
Enter type for R4
Enter type for R5
Enter type for 11
Enter type for 12
Enter type for 13
Enter type for I4
Enter type for IS
Enter type for SE1
Enter type for SE2
Enter type for SE3
Enter type for SE4
Enter type for SE5
Enter type for TF1
Enter type for TF2
Enter type for TF3

NMMMMMMMMMMMMHHQEEHHEEEM

Please enter a model file name for Matrix-x (MODELO): EXMPLl

The title to be written to the file is:
5 Dof Suspension System W/Variable Flow Source - WO/Grav. Effects

Is that okay? (Y):
User_Code_Block file written: EXMPL1.USR
MATSETUP.DAT file written: EXMPL1.DAT

RP definition file written: EXMPL1.RPD

Filer options

adams_Diff, Return, Help? (full): R

1m

bltbifill‘IlIOIIIIllllll I!
MLTGESDDIR . Mano-Wu . n1.

57

ENPORT-7 options
I: Initialize for a new model or load an existing model
T: Title input or modification
: Graph description or modification
: Equation description for nodes
° Solve for the time response of the system
Display the results
° File the model for later reference
: Return to the operating system from ENPORT
: Manage the file directory‘
Utilities- mode_set, trap, debug, terminal
Optimize the design
Help

Enter option (R): R

”MOVING

EEOC!!!

Do you want to leave ENPORT? (N): Y

58
0.2.2 Creating/Editing Data Files

The main menu appears

titfit.tOtttttttfittttOttitttttttltfiltttt.ttfittfi

"' MAIN MENU '

Cttttifi#tttttttttttttttlCOOCCOOCCOOCCCOOOCCOOC

* Please make the following selection *
"' Enter E = execute ENPORT ’
* D = create/edit DATA FILES "
"' O = execute OPTDES "
"‘ C = execute CHECKFILE "'
" X = exit the session '

tfitttfittttittttttttltfitttfittttititttitttfiti...

From the main menu select 12.
The next menu appears

tttttttttttttlittttttttttttttttttttttttttftitl
How many Data files are you creating

conditions must be described

by a separate data file.
titttttttttit!titt*Citt*ttlttttttttttttttttttt

O O O O O

t
.
* Note: Each set of system driving
.
Q

Enter number

Now suppose the model is optimized analyzing its behavior for two different
flow models. This will require two data files. Each data file has a set of members
which describe one flow model. If beginning this problem then 2 would be an
appropriate response. To edit an existing file then 1 is the correct response.

The next menu appears

#****#**t.itCtttittiitfittttttfitittttttttttttit

Create/Edit datafile No: X

Please enter Datafile Name
Example: DRSYSl (limit 6 char)

O O O O O O
O O O O O O

Note: Do not enter filetype .dat
ittit.ittit!ti##ttttttttttt*Cttttttttttttttttt

Enter filename

59

If you are creating a new file then enter a unique name. If you wish to edit an

existing file then enter the name of that file.

Note: '1' Do not enter filetype (.dat will be assigned)
‘1' Limit names to six (6) characters

The following verification menu appears

......tttfitltttfiCCOOCCCOOOCOCOCOOOCOOOCOO

‘ You Entered: FFFFFF "
. um__ C
‘ Is this correct (Y or N) ‘

OOQOOOOitCitittOtCOOOCIOOOCOOCCOOOCOOOOOO

When Y is selected an active editing mode is invoked. Enter the data and
save the files. Use edit commands for the DEC/V AX operating system.

If creating U-Vector data files then enter data as a column vector with 1 entry

per line.

If you are creating an experimental data file enter the data as an array. The
first column must be time (T) and the following columns represent a time history
for each input variable. If an input is zero for a particular analysis then zero's
must be entered. This process will be repeated based on the entry for the number
of data files being created.

D.2.3 Executing OPTDES
The following menu appears

tilttttttfittttfitttiititttttfi..tttfitlttfitiilttt

" MAIN MENU '

OOCOQCOCOOOCOOCCCCCCfitttttttttttltttttfiitttttt

" Please make the following selection ‘
"' Enter E = execute ENPORT "
"' D = create/edit DATA FILES "
‘ O = execute OPTDES ‘
" C = execute CHECKFILE "
" X = exit the session "'

itOCOOOOOOOCOOOICOOOQOOOOCOOOOOCOOOQOOOC.0...‘

From the main menu select option Q.

The following menu appears

ttfittttiltttttttttttttttttttitttttitittttttfitt

" Please enter model name from ENPORT "
t t
‘ Example: MODELO "
t t
" Note: Do not include filetype "

.#.##*#*t.*tittttltt*tttttt#tlOtttttlttttttfifit

Enter the system state equations filename created in EN PORT.
Note: Do not enter filetype (handled internally)

The following verification menu appears

ttttttttttt##0##tit.ttttttttttttttttttttittttt
You entered:

.
i
"' FF FFFF
.
4:

Is this correct (y or n)
tittttttttttttttitttfitttttttttttttttttttCit...

Upon continuation the file management process occurs. The following menu
appears.

61
**##***##**t##t***#**¢**¥*#***¢¥t*$t##ttifittfit

" OPTIMIZATION MENU "

Otttfitfitttfitfittfitttttit.Cttttttfifififittfittfifitttfi

‘ Select one of the following options "
" C = compile all program "
‘ I = compile individual programs "
" L = link to optimization files "
* S = create setup executable "‘
" RC = run CONVEN.EXE "‘
" RS = run SETUP.EXE "
" RD = run CDESIGNEXE "
" M = return to main menu "
' X = exit the session “
Cttttttttttttttt*tttfittOtttttttttttttttttttttt

At this point any user written subroutines must be compiled. Two choices
are available to do this C and I. If C is entered all subroutines are compiled and
this menu will re-appear. If I is entered then the following menu appears:

Otttfittfittittittttfitttttfittttfifitttt.tttlttfitti

* The number of programs to be compiled "'
tttttttttttttttttttttttt##tttttttttltttttttttt

Then the following menu appears

Qt!*0tt.13*ttt03“.O.titOtttttttttttttttttfitfii

‘ Enter the program name "
tttttfitttttttttttttttttltttttttttltttttttttttt

This prompt will be repeated based on your previous response.

62

At this point all files are compiled and the optimization menu re-appears:

OtfittitttttltittttttiltfitittfittfiitlttttfitOi...

" OPTIMIZATION MENU "‘
OOOOOCOOOOOCOOOCOOCOtCt...tiltttttttttlfiltfilfit
" Select one of the following options "
"' C = compile all program ‘
"' I = compile individual program "
"' L = link to optimization files ‘
‘ S = create setup executable "'
* RC = run CONVEN.EXE "'
" R8 = run SETUP.EXE "'
" RD = run CDESIGN.EXE *
’ M = return to main menu "'
‘ X - exit the session ‘

t.tittCtitt0“t#00tttttfitttttttttttt¢tttl##1##

QntinnJe

At this point option L must be entered even if no programs were compiled.
This is necessary to link the model file to the optimization software. This is only
necessary once if the model file has not changed. Two messages will appear to
verify that the CONVEN and CDESIGN executable files have been created. The
menu will re-appear.

Qntims

This option is only necessary once to create the SETUP executable file.
QntienBS:

This option executes CONVEN. This will create the initial design point.
QntionBS

This option executes SETUP. This will define the design space.
OntionBD

This option executes CDESIGN. This will perform the optimization process.
QntinnM

Returns the user to the main menu.
Cation}!

Exits the user from DMSOPT.

D.2.4

D.3

63

CONVEN, SETUP and CDESIGN all execute OPTDES software. When
CONVEN and CDESIGN are selected the ANAPRE subroutine will be invoked.
This is a pre-processor used to set up the optimization problem (see Executing
ANAPRE). After each program has ran the optimization menu will re-appear.

Executing the Checkfile
From the main menu select option (I,

it...titttttfittttt¢ttit.tfiflifittfitttttttttttitt

" MAIN MENU "

tfitttittitfitiit!C##Ottit##ifitttttfifittttfittfitfil

‘ Please make the following selection ‘
" Enter E = execute ENPORT ‘
" D = create/edit DATA FILES "
* O = execute OPTDES "
"' C = execute CHECKFILE "‘
* X = exit the session "

*#¢¢*.**ttttittttit**##***#*tittttitfitttlttllt

Checkfile executes ANAMAIN which assists in constructing the user-written
subroutines. ANAMAIN is a menu driven program which will determines a set of
performance measurements for a given set of analysis variables. Once the
subroutines are returning the correct values for a given input then the optimization
software can be executed. ANAMAIN is much like executing CONVEN except
results are obtained quicker. The user will prompted for the no. of AV's and their
values. The subroutine ANAFU N will be executed and a set of AF values will be
returned. No changes in executing ANAPRE are required.

Executing ANAPRE

ANAPRE is a pre-processing subroutine used to collect information
necessary for executing the interface software. This program will be called when
CONVEN and CDESIGN are executed. An overview of how ANAPRE is
executed is as follows.

D.3.l

64

ANAPRE_
SYSTEM PARAMETERS

EXTERNAL FORCING
INTEGRATION PARAMETERS
INITIAL CONDITIONS

.LILAIEL. ENTER I.C.'s
PERFORMANCE MEASUREMENT METHODS

._IL_£MM5-L_UPPER BOUNDS

 

 

JLINEELI
L_OB.IECT IVE FUNCTIONS
.__If_QBJsNEL INDEX NUMBERS

.....ILOBJENEL INDEX NUMBERS

AF VECTOR BUILD
|_IL_Ans_=_L DISPLAY AF VECTOR

 

 

Figure 0.3.1
Branching Tree for ANAPRE Execution

The following instructions are for entering data using ANAPRE. These
prompts will be seen following OPTDES messages when either CONVEN or
CDESIGN have been executed.

System Parameters

The following menu will appear:

 

Number of State Variables (NX) X
Number of Output Variables (NY) Y
Number of External Inputs (NU) U
Number of Forcing Conditions (NFF) F

Default values for X, Y, and U will be obtained from the summary xxx.rpd
file. If this file is unavailable then the default values will be zero. F will have a
default value of 1. Values for X,Y and U can be obtained from the system state
equations file if they are unknown (See ENPORT user's manual appendix C).

D3.

65
D.3.2 External Forcing
If NU is greater than 0 then the model is being driven by a set of external
inputs. The following sub-menu will appear:

EntcLExtemaLEarametm

E = Enport Model Generator
0 = User Written Generator
D = Experimental Data

 

The following menus will appear for each response.

Enter E
Enter Datafile Information
Name of Datafile No (x)

Enter 11
Do you wish to use your own menu (Y or N)

If X then subroutine USRMEN is invoked
If N then

Enter Datafile Information
Name of Datafile No (x)

Enter [2

Enter Datafile Information
Name of Datafile No (x)
Number of Data Pts for File No: (x)

In each case the user is entering the name of the datafile which is housing the
U-Vector values. These prompts will be repeated based on the entry for NFF.
When using experimental data these files must be edited to accommodate when
(To .ne. 0). If option D was entered the program will continue. If options E or U

were entered the following menu will appear:

Please select one of the following

- Continue

View the data entered
Re-enter the data files

”<0
II 111

C will continue the program

V will display the data entered as it is stored in the 125, matrix. The above menu
will re-appear.

66

R will re-initialize 125, and all data files must be re-entered. The above menu will
re—appear.

D.3.3 Integration Parameters
The following prompt will appear:

 

Initial Time Value (To)

Ending Evaluation Time (ET)
Number of Integration Steps

To can be greater 0
FT must be greater than To

The number of integration steps must be less than 1024
After this information is entered the following message will appear:

The Integration Step Size (H) is: X

D.3.4 Initial Conditions
The following menu will appear:

Enterlnitialflanditinnsflnrm
N

The default is N and will appear. To continue press enter. To enter initial
conditions enter Y. When initial conditions are entered the following prompt will

appear.
Initial Conds for State Variable i:

Where i is a counter displaying index number for the corresponding state
variable. It is important to know how ENPORT has ordered the state variables to
enter the lC's correctly. The order can be viewed in ENPORT where IC's are set
or the state equation file can be edited to view how the X—Vector is ordered. This
prompt will be repeated until i=NX.

D.3.5

D.3.6

67

Performance Measurement Methods
The following menu will appear:

EmumummmmmmMmmmmummmuummm

Maximum Displacement
Ave DiSplacement

RMS Value

Minimum Displacement
Absolute Max Disp
Absolute Min Disp

 

zxmw>z
II II II II 11 11

Enter the appropriate letters (no spaces or delimiters required). Selections
will be verified.

For each PMM selected a value for each PM will be calculated. Hence,
more constraints could be created than will be used. Therefore, understanding
how the AF-Vector is built is important when selecting constraints in SETUP.

Objective Functions

If NFF is greater than 1 then menus gathering information about the objective
function will appear. If NFF is equal to one then proceed to the AF build
message.

The following prompt will appear if NFF > 1:

i
Objective Function Set Size i

The default value i is equal to NFF. If the set size entered is greater than 1
then additional prompts will appear. One of two cases will occur:

Case 1:
Ifsetsizei: l<i<NFF
AV Comparator Value
AF Objective Function Set Member
Case 2:

Ifsetsizeizl<i=NFF

AV Comparator Value

D.3.7

 

68
PM used to measure OP

In both cases the user is asked for which analysis variable (AV) is being used
as A.

In case 1 the user must determine which analysis functions will be used in the
objective function set. This prompt will be repeated based on the number entered
for the set size.

In case 2 the user must determine which performance measurement is being
used as the objective function. The index number entered corresponds to the Y-
Vector index number.

AF Vector Build
The following prompt will appear:

- N)
No of members X N

The size of the AF—vector is calculated and displayed in the prompt statement
(X). The default reply is N and is displayed. To continue press enter. To view
how the AF-vector will be built in PERFORM enter Y.

APPENDIX E

MANAGING THE INTERFACE SYSTEM

 

E.l

B.2

APPENDIX E
MANAGING THE INTERFACE SYSTEM

Interface Directory
This directory should be set up to contain the following files:

ANASUB.FOR - Used for OPTDES

ANAMAIN.FOR - Used for checking files

USRGEN.FOR - Dummy file

USRMEN.FOR - Dummy file

USRAFN.FOR - Dummy file

SYSPRM.EDT - Creates Screen display of System Parm
SYSDAT.EDT - Passes System Parms from ENPORT to OPTDES
CDES2/OPI‘IONS - Used to create CDESIGN.EXE

The three Dummy files are necessary for creating the executables if user
written subroutines are not used.

The EDT files are edit command files executed form DSMOPT. They are
used to manage the model library and to pass information from ENPORT to
OPTDES. These files reduce user input.

The options file contains the OPTDES subroutines used for creating the
executable file CDESIGN .

OPTDES Directory
This directory is used for storing the compiled optimization programs.
Managing these files is discussed in the OPTDES.BYU users manual.

At this time DSMOPT uses object files SCRHP and PENHP when creating
CDESIGN.EXE. These files declare the type of CRT and plotter being used.
Versions also exist for Textronix and SUN. DSMOPT should be modified to
incorporate the CRT and plotter flexibility available.

69

70

E3 Command File DSMOPT Maintenance

When the directories for the Interface and optimization files have been created
it is necessary to set two symbols used in DSMOPTCOM. The symbols are:

OPTFI - Path name to the optimization software
USEFI - Path name to the Interface software

DSMOPTCOM can be edited using the DEC/VAX EDIT command. These
symbols are at the beginning of the executable code.

APPENDIX F

INTERFACE COMPUTER PROGRAMS

APPENDIX F
INTERFACE COMPUTER PROGRAMS

F.l Introduction
The following figure illustrates the flow of data between ENPORT, OPTDES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
   

 

 

 

 

 

 

 

 

 

 

 

 

and the INTERFACE programs.
LUSRM ' :' “EN;
§ 0
’ DSNX. ‘ ‘
LANAPRE NY’NU ENPMEN I‘m “M I USR01.RPD I
as 2. \I USR01. DAT I
SC H, NF U 1
CONVEN _
OPTDES ENPORT
AFT Asfc . :Mifi!!l
I AVHSCDS X,,,,SCAVTU
I ANAFUN I.— ’1 SOLVRKI...F fl USR01.USR
T : AV Y SEW—*1 JU X”Y
I“ Y AF SC
_____ :_ 18C 1- ENPGEN I
:_y§RAFN_. PERFOR us A . U
sc__ _ J_ _ _ _
' ...QSBEEH- '
SC = SYSTEM CONSTANTS
{NX,NY,NU,NFF,T1,T2,H}
- - -. = OPTIONAL
— — — = DATA FILE TRANSFER
Figure F. 1. 1

Dynamic Modeling and Optimization Data Flow

71

72

F.2 ANASUB.FOR
This is the primary subroutine which is called by the main program in
OPTDES. ANASUB will call SOLVRK and PERFORM which in turn call
subsequent subroutines. ANASUB is responsible for receiving the AV vector from
OPTDES and returning the AF vector.

COMPUTER PROGRAM
ANASUB.FOR

WRITTEN
BY

MARK DAVIS

73

C****************************************************************

C.----SUBROUTINE ANAFUN WRITTEN BY: MARK DAVIS 9/22/91
C.

C.----PURPOSE: THIS SUBROUTINE WILL PRODUCE TIME HISTORY DATA
USING THE ENPORT CREATED MODEL. THIS INFORMATION
CAN BE USED TO OPTIMIZE SYSTEM RESPONSES OF A
MULTI-DEG OF FREEDOM DYNAMIC SYSTEM DESIGN.

...GIVEN ARGUMENTS

AV() = ANALYSIS VARIABLES
AF() = ANALYSIS FUNCTIONS
...RETURNED ARGUMENTS

O
****************************************************************

SUBROUTINE ANAFUN (AV,AF)
...ARGUMENTS

INTEGER DBUG, NYY, NYCNT, NFF, NPM
PARAMETER (NYY-20, NYCNT=4096)

DOUBLE PRECISION AV(l), AF(l), TV(NYCNT), yout(NYY,NYCNT)

0 0 0 00 0000 0000000

INTEGER NOBJ,OBFCN,ICSTR,IAVN

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV,YOUT

COMMON /TRACER/ IDBGR(20)

COMMON /OBJFCN/ NOBJ,OBFCN(10),ICSTR,IAVN

SET DEBUG TRACER l-YES, 2-NO

DBUG - 2

. NFFCN set the number of different forcing functions for
analysis ‘
DO 10 NFFCN-1,NFF

CALL SOLVRK(NFFCN,AV)

00 0 000 000

. Dbugging aid

IF(DBUG.EQ.2)GOTO 1
CALL YRESLT(NYY)
CONTINUE

CALL PERFORM(NFFCN,AV,AF,NPM)

CONTINUE

Set the AF vector values determined by the objective function
set.

OOOHO OH
O . .

IF (NOBJ .GT. 1) CALL ENPAFN(NPM,AV,AF)
IF (UAF .EQ. 'y' .or. UAF .EQ. 'Y’)
+ Call usrafn(nffcn,npm,av,af)
. Optional print operation

0(?

C: -

74

if(idbgr(1) .eq. 1) then
do 12 i-l,ny*npm*nff
write(*,*)'this is af out',af(i)

else
continue
endif
return
end

C * * ***********‘k‘k‘k‘k‘k***********************************************

0

0000

0
1

0000000

(7 017(3

SUBROUTINE SOLVRK(NFFCN,AV)
INTEGER ITIME, NU, INFO(4), IP(1), DBUG, NYY, NYCNT
PARAMETER (NYY-ZO, NYCNT=4096)

DOUBLE PRECISION AV(l)

DOUBLE PRECISION T,X(NYY,NYCNT),XDOT(NYY,NYCNT),U(40),

XT(NYY), VT(NYY),XI(NYY),XO(NYY),
XD(NYY),YRR(NYY),DR

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT),YOUT(NYY,NYCNT)
COMMON /TRACER/ IDBGR(20)

nxt - 0
dr - 0.00

do 5 icond=l,nx
xi(icond) = xin(icond)
continue

info(l)
info(2)
info(3)
info(4)
IST

0
0
l
1
(

Tl/H) + 1

THIS IS USED FOR DBUG PURPOSES

WRITE(*,*)'MASS-’,AV(1),' K4-’,AV(2),' DAMP3=',AV(3)
WRITE(*,*)'ENTER 1 TO DISPLAY '

READ (*,*) IDIS

IDIS - 2

IEXT - 2

. BEGIN RUNGE-KUTTA INTEGRATION

do 60 Intg-1,NS

000

18
19

75

IF(INTG .LT. IST)GOTO 7
ICNT - INTG - ((T1)/H)
TV(ICNT) - DR

T0 - DR

T - T0

do 10 j11-1,nx
x0(j11) - xi(j11)
xt(j11) * xi(j11)
continue

IF(IDIS.EQ.1)
+ write(*,*)'1st disp’,xt(1)

IF(NU .gt. 0)
+ CALL ENPGEN(nffcn,t,u)
CALL zzzzzz(INFO,T,U,NU,XT,VT,NX,YRR,NY,AV,IP)

. Save the specified output variables (Y-vector)

IF (INTG .LT. IST) GOTO 19
DO 18 IY-1,NY
YOUT(IY,ICNT) 3 YRR(IY)
if(idbgr(2) .eq. 1)
+ write(*,*)'this is yrr out',yrr(iy)
CONTINUE

T - TO + h*0.5

DO 20 JL2-1,Nx
xt(j12) - x0(j12) + vt(j12)*h*0.5
xd(le) - vt(j12)

continue

wwl - vt(l)*h*.5
IF(IDIS.EQ.1)

+ write(*,*)'2nd disp',xt(l)
IF(Iext.eq.l)
+ write(*,*)'u(l)-’,u(l),’T-',T,’yout-',yout(l,icnt)

IF(NU .gt. 0)
+ CALL ENPGEN(nffcn,t,u)
CALL zzzzzz(INFO,T,0,NU,XT,VT,NX,YRR,NY,AV,IP)

T - TO + H*0.5
do 30 j13-1,nx
xt(j13) = x0(j13) + vt(jl3)*h*0.5
xd(j13) - xd(j13) + 2.*vt(jl3)
continue

ww2 - vt(l)*h*.5
IF(IDIS.EQ.1)

+ write(*,*)'3rd disp',xt(l)
IF(Iext.eq.1) I
+ write(*.*)' U(1)='.U(1).' T=',T

IF(NU .gt. 0)
+ CALL ENPGEN(nffcn,t,u)
CALL zzzzzz(INFO,T,U,NU,XT,VT,NX,YRR,NY,AV,IP)

76

C.
T - TO + H
do 40 jl4-1,nx
xt(jl4) - x0(jl4) + vt(jl4)*h
. xd(jl4) - xd(jl4) + 2.*vt(jl4)
40 continue
C.
ww3 - vt(l)*h
IF(IDIS.EQ.1)
+ write(*,*)'4th disp',xt(1)
IF(Iext.eq.l)
+ write(*,*) ' U(l)=’,0(l),' T=',T
C.
IF(NU .gt. 0)
+ CALL ENPGEN(nffcn,t,u)
CALL zzzzzz(INFO,T,U,NU,XT,VT,NX,YRR,NY,AV,IP)
C.
IF(IDIS.EQ.1)
+ write(*,*)'init disp’,x0(l)
IF(Iext.eq.1)
+ write(*,*)' U(l)-',U(1),' T=',T
C.
do 50 j15=1,nx .
xi(j15) = x0(j15) + (vt(j15) + xd(j15))*h/6.
50 continue
c.
IF(IDIS.EQ.1)
+ write(*,*)'new init disp’,xi(1)
IF(Iext.eq.1)
+ write(*,*)' end 1 itteration '
c write(*,*)'******enter any num******'
c read(*,*) icont
C.
dr = dr + h
C.
60 CONTINUE
C
DBUG = 2
IF(DBUG.EQ.2)GOTO 1
CALL YRESLT
1 continue
C
return
end
C

C****************************************************************

SUBROUTINE ANAPRE

C.

C.

C conditions.

C

C

C

C ---- VARIABLES: T1 -
C T2 -
C H -
C XIN =

This Subroutine will be used for entering integration

---- PURPOSE: DEFINE VARIABLES USED
FOR INTEGRATION

INITIAL TIME

FINAL TIME

INTEGRATION STEP SIZE

STATE VARIABLE ITIAL CONDITION

000000000

000

000

C.

77

NX - NUMBER OF STATE VARIABLES
NY - NUMBER OF OUTPUT VARIABLES
NS 3 NUMBER OF INTEGRATION STEPS
NU - NUMBER OF EXTERNAL SOURCES
NFF - NUMBER OF FORCING FUNCTIONS
OBJ = OBJECTIVE FUNCTION NUMBER

CMAX = UPPER BOUND LIMITS ON THE Y-VECTOR
OUTPUT VARIABLES

INTEGER Nx, NY, NS, IEND, NYY, NFF, INF, NOBJ, ICSTR,
IAVN, OBFCN, IDBGR, NSTEP, DOBJ

INTEGER NNX,NNY,NNO,NMEM

PARAMETER(NYY=20,NOB=10)

DIMENSION XIN(nyY). CMAX(nyy)

REAL T1, T2, H, XIN

REAL CMAX

CHARACTER IMAX*1, IPAR*7, ACOND*l, ISW*1, UAF*1, AFBLD*1

COMMON /INTVAR/ Tl,T2,H,XIN,NX,NY,NS,N0,NFF,IEND,UAF

COMMON /TRACER/ IDBGR(20)

COMMON /MAXVAL/ CMAX

COMMON /PAROPT/ IPAR

COMMON /OBJFCN/ NOBJ,OBFCN(10),ICSTR,IAVN

Set default values

. Open

icmx 2
NX 8
NY -
NU -

NOBJ

Ic>om3fl

l
datafile with nu,ny and nx values

open(unit-12,fi1e-'zzzzzz.dat’,form-'formatted',
statusa’unknown')

read (12,*,end-10)NNU,NNY,NNX

Close(unit=12)

C. Prompt the user for the number of state variables

C

000

10

Write(*,118)
Write(*,100) NNX
Read (*,200) NX
if(NX .eq. 0)then
NX - NNX
else
NX - NX
endif

. Prompt the user for the number of output variables

Write(*,101) NNY
Read (*,201) NY
if(NY .eq. 0)then
NY - NNY
else
NY = NY
endif

78

C.
C. Prompt the user for the Number of external source parameters.
C. If NU>0 then call enpmen. Enpmen will prompt for the data
C. files describing each set of external forcing systems (nff).
C.
Write(*,109) NNU
Read (*,201) nu
if(NU .eq. 0)then
NU - NNU
else
N0 - N0
endif
C.
C. Prompt the user for the number of forcing functions
C.

inf - l
Write(*,112) INF
Read (*,201) NFF
if(nff .eq. 0)then
nff - inf
else
nff - nff
endif

Call ENPMEN if NU>0
If (nu .gt. 0) call enpmen

Prompt the user for the intial start time

0.3000 000

5 Write(*,119)
Write(*,lOZ)
Read (*,202) t1

. Prompt the user for the and evaluation time

000

Write(*,103)
Read (*,203) t2

. Prompt the user for the integration step size

000

Write(*,104)
Read (*,200) nstep

H - (t2 - tl)/nstep
Write(*,121) H

. Calculate the number of integration steps to use

000 0 0

ZS = T2/H
NS = ZS
IEND - (T2 - Tl)/H

. Prompt the user for initial conditions on the state variables

000

79

acond - 'N'
48 Write(*,114) acond

Read (*,207) acond

if(acond .eq. ' ')then
acond - 'n'
goto 60

elseif(acond .eq. 'y' .or. acond .eq. 'Y')then
goto 49

elseif(acond .eq. 'n' .or. acond .eq. 'N')then
goto 60

else
goto 48

endif

49 ivar - 0
do 50 icond-l,nx
ivar - icond
Write(*,105) ivar
Read (*,205) xin(icond)
50 continue

C.
C. Select Performance Measurement Methods
C.
60 write (*,110)
read (*,208) Ipar
C.
locl
loc2
loc3
loc4
locS
loc6
loc7

index(ipar,'m')
index(ipar,'a')
index(ipar,'r')
index(ipar,’v')
index(ipar,’s')
index(ipar,'x’)
index(ipar,'n’)

NPM - 0

IF (LOC1 .GT. NPM) NPM
IF (LOC2 .GT. NPM) NPM
IF (LOC3 .GT. NPM) NPM
IF (LOC4 .GT. NPM) NPM
IF (LOCS .GT. NPM) NPM
IF (LOC6 .GT. NPM) NPM
IF (LOC7 .GT. NPM) NPM

LOC1
LOCZ
LOC3
LOC4
LOCS
LOC6
LOC7

LOC8 - LOC1 + LOCZ + LOC3 + LOC4 + LOCS + Loc6 + Loo?

IF (LOC8 .EQ. 0) THEN
WRITE(*,111) ipar
GOTO 60

ELSE
Continue

ENDIF

If (LOC4 .gt. 0)then
Do 62 I-1,ny
62 Cmax(i) - 0

 

80

C. Enter the upper bounds necessary for using the maximum
C. violation calculation.
C.

65

000

0000

mOOOOOO

05000

. Call

. Call

. View

C.

C.

Write(*,107)
Do 65 Inx-1,ny
Write(*,lOB) Inx
Read (*,*) Cmax(inx)
Else
Continue
Endif

for objective function size only if multiple external

forcing systems or more than 1 perf meas method is being used.

If (nff .gt. 1) Goto 66
If (nff .le. 1) Goto 67

. Prompt the user for the objective function number
Note: This is only necessary if the objective function

is the max/min of a set of constraints. This is
typical for problems with multiple external driving
systems.
Write(*,120)
Write(*,ll3) nff*npm
Read (*,201) nobj
if(nobj .eq. 0)then
nobj - nff
else
nobj - nobj
endif

subroutine enpobj to determine the objective function set
If (nobj .gt. 1) Call Enpobj(npm)
the Analysis function build

afbld = 'N'
If (Nobj .gt. 1)then
nmem.- nff*npm*ny + l
Else
nmem - nff*npm*ny
Endif

Write(*,122) nmem, afbld

Read (*,207) afbld

if(afbld .eq. ' ')then
afbld = 'n'

elseif(afbld .eq. 'y' .or. afbld .eq. 'Y')then
call afbild(AV,AF,NMEM)

elseif(afbld .eq. 'n' .or. afbld .eq. 'N')then
continue

else

goto 67

endif

Prompt the user to see if they wish to re-edit the af vector

81

me

Uaf - 'N'
Write(*,106) uaf
Read (*,207) UAF
if(UAF .eq. ' ')then

UAF - 'n'
elseif(UAF

continue
elseif(UAF

continue
else

goto 68
endif
.********************Print Switches are Off********************
. Set print switches
.****************The Default Setting is Left on****************
do 70 i-1,20

idbgr(i) - 2

.eq. 'y' .or. UAF .eq. ’Y')then

.eq. 'n' .or. UAF .eq. 'N')then

00000000000000010

C)

law-'N'
Write(*,117)isw
Read (*,207)isw
If (isw .eq. '
isw - 'n'
goto 78
Elseif(isw .eq.
goto 78
ElseIf (isw .eq.
Write(*,115)
Read (*,207) ISW
Do 74 i-1,4
Write(*,116) i

Q
N)

')then

'n’ .or. isw .eq. 'N’)then

’y')then

000000000000000000000004

74 read(*,*) idbgr(i)
else
goto 72
endif

78 continue
.*******************End Print Switches*************************
118 format(' ',///////.

+ ' Enter System Driving Parameter Values',/,

+ I ................................................

+ _________________ I
100 format(llx,’Number of State Variables (NX) ’,12,' ',$)
101 format(llx,'Number of Output Variables (NY) ',12,’ ’.$)
112 format(llx,'Number of Forcing Conditions (NFF) ',I2,' ’.$)
109 format(llx,'Number of External Inputs (N0) ',12,' ',$)

C.***************************************************************

119 format(' ',/, '

+ ' Enter Integration Parameter Values',/,

+ I ................................................

+ ----------------- ')
102 format(llx,'Initial Time Value (T0) '.$>
103 format(llx,'Ending Evaluation Time (TF) '.$)
104 format(llx,'Number of Intergration Steps '.$)
121 format(",//,5x,'The Integration Step Size (H) is:',e12.6)

82

C.**************************************************************

106 format(' '1/(

+ ’ Are You Using Subroutine USRAFN (Y or N)',/,

+ I ..............................................
+ """""" 'r/r

+ ' '.a2.' us)

C.**************************************************************

110 format(’ ’,/,
+' Enter the Performance Measurement Methods to be used',/,

+1 .......................................................
+ TTTTTTTTTT 'i/I
+ 11x,’ M - Maximum Displacement ',/.
+ 11x,’ A - Ave Displacement ’,/.
+ llx,’ R - RMS Value ',
+ 11x,’ v - Max Violation Integral ',/.
+ 11x,’ S - Minimum Displacement ',/,
+ 11x,’ X - Absolute Max Disp ',/,
+ 11x,’ N - Absolute Min Disp ’./,
+ 118.’ ’.$)

111 format(llx,'You Entered ',a7,’ None of’,/,
+ 11x,'These are Valid Try Again’)

107 format(llx,'You must enter the upper bound limits to use',/,

+ 11x,’ the maximum violation performance option.',/,
+ 11X,' -------------------------------------------- ')
108 format(13x,'0pper Bound for Perf. Meas. #:',i3,': ',$)

C.***************************************************************

120 format(' ',/.
+' Enter Objective Function & Constraint Information',/,
+l .......................................................
+ __________ I) .
113 format(llx,'Objective Function Set Size ',i2,' '.$)
C.***************************************************************

114 format(’ ',/,

+ ' Enter Initial Conditions (Y or N) ’,/,

+ I ................................................

+ TTTTTTTTT 'r/r

... I - 232/ 1's)

105 format(llx,'Initial Conds for State Variable',i3,': ',$)
Co****************************************************************

115 format(llx,’ lst switch prints AF vector' ,/,

+ 11x,’ 2nd switch prints YRR history in solvrk' ,/,
+ 11x,’ 3rd switch prints perform call' ,/.
+ 11x,’ 4th switch prints yperf build of af’)
116 format(l3x,’ Enter setting for switch number',i3,/,
+ 13x,’ 1 - on 2 = off '35)
117 format(' ',/,
+ ' Set print switches on to view builds (Y or N) ',/,
+ ...............................................
+ --------- 'r/r
+ I ’,32,' '($)
122 format(' ',/,
+ ' Do You Wish to View the AF-Vector Format (Y or N) ',/,
+ ................................................
+ --------- 'I/I
+ ' No of members:',i3,' ',a2,' ',$)

000

000

0

00000000

000000000000

1200
1201
2202
2203
2204
2205
2207
£208

83

format (i4)
format (i4)
format (e6.0)
format (e6.0)
format (e4.2)
format (e8.2)
format (a1)
format (37)

return
end

- **************************************************************

SUBROUTINE ANAPOS

INTEGER NYY, NYCNT

PARAMETER (NYY=20, NYCNT-4096)

COMMON /RESOUT/ TV(NYCNT)pyout(NYY,NYCNT)

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF

RETURN
END

-'**************************************************************

SUBROUTINE ANAGRA
COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF

RETURN
END

**************************************************************
‘**************************************************************

OPTIMIZATION SUBROUTINES

‘**************************************************************
‘**************************************************************

-—-- SUBROUTINE PERFORM

---- PURPOSE: DEFINE THE DYNAMIC PERFORMANCE OF THE SYSTEM
---- OUTPUT

VARIABLE: YPERF(I,J) = DATA ARRAY OF EACH DESIGN VARIABLE

PERFORMANCE

I - PERFORMANCE VARIABLE
J = DESIGN VARIABLE

O O O O OOOOOOOOOOOOOOOOOOOOOO

---- SYSTEM

+-++-+

+

PERFORMANCE
VARIABLES YMAX(I

YMIN(I
YABS(I
YINT(I
TMAX(I
TMIN(I
TABS(I
YMEAN(
YRMS(I
YOVR(I
SUBROUTINE PERFO
CHARACTER Ipar*7

INTEGER DBUG, NY

84

) = SYSTEM RESPONSE MAXIMUM DEFLECTION
) ‘ SYSTEM RESPONSE MINIMUM DEFLECTION
) = ABSOLUTE MAXIMUM DEFLECTION

) - INTEGRAL FOR MAXIMUM DEFLECTION

) - TIME AT WHICH MAX VALUE OCCURS

) - TIME AT WHICH THE MIN VALUE OCCURS

) - TIME AT WHICH ABS MAX VALUE OCCURS

I) ' SYSTEM RESPONSE MEAN VALUES
) = SYSTEM RESPONSE ROOT MEAN SQUARE VALUES
) = PERCENT OVERSHOOT OF YMAX VS. YMEAN

RM(NFFCN,AV,AF,NPM)

PERF, NYY, NYCNT, NFFCN, NPM

PARAMETER (NYPERF-S, NYY-ZO, NYCNT=4096)

DOUBLE PRECISION

DOUBLE PRECISION

DOUBLE PRECISION

COMMON /INTVAR/
COMMON /RESOUT/
COMMON /OBJFCN/
COMMON /EXTOUT/
COMMON /TRACER/
COMMON /PAROPT/

PERF - IDBGR(3)
PRFO - IDBGR(4)

IF(PERF
CALL PMAX(YMAX,

YPERF(NYY,NYPERF), AV(l),
AF(l), ZOUT(2,NYY,NYCNT)

YMAX(NYY), TMAX(NYY), YMEAN(NYY),
YRMS(NYY), YSST(NYY), YOVR(NYY),
YLIN(NYY), YOFF(NYY), TOFF(NYY),
RTIM(NYY), YERR(NYY), YEXP(NYY),
YMIN(NYY), TMIN(NYY), TSMAX(NYY)

TSMIN(NYY), YPP(NYY,2), TPP(NYY,2),
YINT(NYY), YABS(NYY), TABS(NYY),
YNAB(NYY), TNAB(NYY)

T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
TV(NYCNT), YOUT(NYY,NYCNT)
NOBJ,OBFCN(10),ICSTR,IAVN

ZOUT

IDBGR(20)

IPAR

.EQ. 1)PRINT *,'CALLING PMAX'
TMAX,TSMAX,YPP,TPP,YABS,TABS,YINT)

85

IF(PERF .EQ. l)PRINT *,’CALLING PMEAN’
CALL PMEAN(YMEAN)

C
IF(PERF .EQ. l)PRINT *,’CALLING PRMS'
CALL PRMS(YRMS)
C
IF(PERF .EQ. l)PRINT *,'CALLING POVR'
CALL POVR(YMAX,YMEAN,YOVR)
C
IF(PERF .EQ. l)PRINT *,'CALLING PMIN’
CALL PMIN(TMAX,YMIN,TMIN,TSMIN,YNAB,TNAB)
C
locl - index(ipar,’m')
loc2 - index(ipar,'a')
loc3 - index(ipar,'r’)
loc4 - index(ipar,'v')
loc5 - index(ipar,’s')
loc6 - index(ipar,'x')
loc7 - index(ipar,'n')
C.
DO 25 IVAR - 1,NY
IF (locl .ne. 0) goto 10
17 IF (Loc2 .ne. 0) goto 11
18 IF (loc3 .ne. 0) goto 12
19 IF (loc4 .ne. 0) goto 13
20 IF (locS .ne. 0) goto 14
21 IF (loc6 .ne. 0) goto 15
22 IF (loo? .ne. 0) goto 16
goto 25
C.
10 YPERF(IVAR,LOC1) - Ymax(IVAR)
GOTO 17
11 YPERF(IVAR,LOC2) - YMEAN(IVAR)
GOTO 18
12 YPERF(IVAR,LOC3) - YRMS(IVAR)
GOTO 19
13 YPERF(IVAR,LOC4) - Yint(IVAR)
GOTO 20
14 YPERF(IVAR,LOC5) - YMIN(IVAR)
GOTO 21
15 YPERF(IVAR,LOC6) = Yabs(IVAR)
GOTO 22
16 YPERF(IVAR,LOC7) - Ynab(IVAR)
C
25 CONTINUE
C
C BUILD THE AF VECTOR
C
NPM - 0
IF (LOC1 .GT. NPM) NPM - LOC1
IF (LOC2 .GT. NPM) NPM - LOC2
IF (LOC3 .GT. NPM) NPM - LOC3
IF (LOC4 .GT. NPM) NPM - LOC4
IF (LOCS .GT. NPM) NPM - LOCS
IF (LOC6 .GT. NPM) NPM - LOC6
IF (LOC7 .GT. NPM) NPM - LOC7.

86

C
Ibeg - (nffcn-1)*npm + 1
Ifin = nffcn*npm
IPY - 0
C
DO 40 IY - Ibeg,Ifin
ipy - ipy + 1
DO 40, IP-1,ny
I - (IY - l)*ny + IP
C

C Dbugging aid
If(Prfo .eq. 1)
+ write(*,*)'this is yperf’,yperf(ip,ipy)
c
40 AF(I) - YPERF(Ip,Ipy)
C Dbugging aid
DBUG - 2
IF(DBUG.EQ.2)GOTO 1
CALL YPRFRM(YPERF,NYPERF,NYY)

1 CONTINUE
C.
C.
C.
RETURN
END
C.
C. NOTES

C. NEED TO DETERMINE confidence interval for THE CALCULATED

C. RESULTS BASED ON ENOUGH DATA POINTS TAKEN.

C. **********************‘k***************************************
C.----SUBROUTINE PMAX

c.
C.----PURPOSE

C. THIS SUBROUTINE WILL DETERMINE THE MAXIMUM VALUES
C. FOR THE SYSTEM RESPONSE VARIABLES
C.
SUBROUTINE PMAX(YMAX,TMAX,TSMAX,YPP,TPP,YABS,TABS,YINT)
C.
INTEGER dbugZ, NYY, NYCNT
PARAMETER(NYY=20, NYCNT-4096)
C.
DOUBLE PRECISION YMAX(1), TMAX(1), TSMAX(1), YPP(NYY,1),
+ TPP(NYY,1), YABS(1), TABS(1), YINT(1)
C. .
COMMON /INTVAR/ T1,T2,H,XIN(NYY),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT), YOUT(NYY,NYCNT)
COMMON /MAXVAL/ CMAX(NYY)
C.

dbugZ - 2

87

DO 10 IVAR=1,NY

20

10

30

40

ZMAX - -10000
ZTMX - 0
DO 20 IMAX-1,IEND
IF(ZMAX.LT.YOUT(IVAR,IMAX))THEN
ZTMX - TV(IMAX)
ZMAX - YOUT(IVAR,IMAX)
ELSE
ZTMX - ZTMX
ZMAX - ZMAX
ENDIF
CONTINUE
TMAX(IVAR) - ZTMX
YMAX(IVAR) - ZMAX
CONTINUE

DO 40 IVAR=1,NY
Zabs - -10000
ZTab - 0
DO 30 IMAX-1,IEND
IF(Zabs .LT. abs(YOUT(IVAR,IMAX)))THEN
ZTab = TV(IMAX)
Zabs - abs(YOUT(IVAR,IMAX))
ELSE
ZTab - ZTab
Zabs - Zabs
ENDIF
CONTINUE
Tabs (IVAR) - ZTab
Yabs(IVAR) - Zabs
CONTINUE

IMXV - 2
ITIM - (tZ/H) + 1

Do 45 Ivar-1,ny
sumodd - 0.
sumeve - 0.
Do 50 Isuma2,Itim-1,2
Cout - abs(Yout(ivar,Isum))
Sumodd - Sumodd +
Cout - Cmax(Ivar) + abs(Cout - Cmax(Ivar))
if(IMXV .eq. 1)
print *,'summodd-',sumodd,’cout-',cout,'cmax-',cmax(ivar)

continue

Do 60 Isum93,Itim-2,2
Cout - abs(Yout(Ivar,Isum))
Sumeve - Sumeve +
Cout - Cmax(ivar) + abs(Cout - Cmax(Ivar))
if(IMXV .eq. 1)
print *,'sumeve-’,sumeve,’cout-’,cout,'cmax=',cmax(ivar)
continue

C0 - abs(Yout(Ivar,1))
Ct - abs(Yout(Ivar,Itim))

0 00000000

20

10

88

F0 - C0 - Cmax(Ivar) + abs(CO - Cmax(Ivar))

FT - Ct - Cmax(Ivar) + abs(Ct - Cmax(Ivar))

if(IMXV .eq. 1)print *,’F0=',f0,’ FT=',ft
Yint(IVAR) - (F0 + FT + 4*Sumodd + 2*Sumeve) * (H/3)
return
end

. ********‘k‘k‘k*‘k‘k‘k*‘k*‘k'k'k*******************************~k**********

.----SUBROUTINE PMIN

.----PURPOSE

THIS SUBROUTINE WILL DETERMINE THE MINIMUM VALUES
FOR THE SYSTEM RESPONSE VARIABLES

SUBROUTINE PMIN(TMAX,YMIN,TMIN,TSMIN,YNAB,TNAB)

DOUBLE PRECISION YMIN(l), TMIN(l), TMAX(1), TSMIN(1),
YNAB(1) , TNAB(1)

INTEGER dbugZ, NYY, NYCNT
PARAMETER(NYY-20, NYCNT34096)

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT), YOUT(NYY,NYCNT)

dbugZ - 2

DO 10 IVAR-1,NY

ZMIN - 10000

ZTMN - 0

IST = (TMAX(IVAR)/H)+1

DO 20 IMIN-1,IEND
IF (ZMIN .GT. YOUT(IVAR,IMIN)) THEN

ZTMN - TV(IMIN)
ZMIN - YOUT(IVAR,IMIN)

ELSE
ZTMN - ZTMN
ZMIN - ZMIN
ENDIF
CONTINUE

TMIN(IVAR) - ZTMN
YMIN(IVAR) - ZMIN
CONTINUE

DO 40 IVAR-1,NY
Zabs - 10000
ZTab a 0

30

40

0

0 0 00000000

30

35

89

DO 30 IMIN-1,IEND
IF(Zabs .GT. abs(YOUT(IVAR,IMIN)))THEN
ZTab - TV(IMIN)
Zabs - abs(YOUT(IVAR,IMIN))
ELSE
ZTab - ZTab
Zabs - Zabs
ENDIF
CONTINUE
TNAB(IVAR) - ZTab
YNAB(IVAR) - Zabs
CONTINUE

return
end

. **************************************************************

.----SUBROUTINE PMEAN

.----PURPOSE

THIS SUBROUTINE WILL DETERMINE THE MEAN VALUE OF THE
OUTPUT VARIALBLES SPECIFIED IN THE YOUT VECTOR.

SUBROUTINE PMEAN(YMEAN)

DOUBLE PRECISION YMEAN(1), YSUM
INTEGER NSO, NYY, NYCNT
PARAMETER(NYY=20, NYCNT=4096)
DOUBLE PRECISION YMEAN1(NYY)

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT), YOUT(NYY,NYCNT)

imn - 2

ITIME - (T2)/(H)

IBEG - (T1/H)+1.
ISTO - IBEG + 2

ISTE - ISTO + 1.
AVET - (T2 - T1)

DO 40 INY-1,NY

SUMODD - 0.0
SUMEVE = 0.0

DO 30 ISUM=ISTO,ITIME-1,2
SUMODD 8 SUMODD + (YOUT(INY,ISUM))

SUMEVE ' SUMEVE + (YOUT(INY,ISUM))

F0 - (YOUT(INY,IBEG))
FT - (YOUT(INY,ITIME))

40
C.

C.

90

IF(IMN .EQ.1)

+ PRINT *,’THIS IS THE FINAL TIME',TV(ITIME),TV(ITIME-1)
YMEAN(INY) - (l/AVET)*(F0 + FT + 4*SUMODD + 2*SUMEVE)*(H/3)

return
end

C. **'k**********************************************************

0 00000

.----SUBROUTINE PRMS

.----PURPOSE: TO DETERMINE THE ROOT MEAN SQUARE VALUE OF

THE OUTPUT DATA.
SUBROUTINE PRMS(YRMS)
INTEGER NYY, NYCNT
PARAMETER(NYY=20, NYCNT-4096)
DOUBLE PRECISION YRMSl(NYY)
DOUBLE PRECISION YSST(1), YRMS(1), YNUM

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT), YOUT(NYY,NYCNT)

IRMS - 3

ITIME = (TZ/H)
IBEG - (Tl/H)+1.
ISTO 3 IBEG + 2
ISTE B ISTO + 1
AVET 8 t2 - t1

DO 20 INY-1,NY

SUMODD - 0.0
SUMEVE = 0.0

DO 10 ISUM?ISTO,ITIME-1,2
IF(IRMS.EQ.1)WRITE(*,*)'SUMODD-',SUMODD
SUMODD - SUMODD + abs (YOUT(INY, ISUMH

DO 15 ISUM=ISTE,ITIME-2,2
IF(IRMS.EQ.1)WRITE(*,*)’SUMEVE=',SUMEVE
SUMEVE 3 SUMEVE + abs (YOUT(INY, ISUM))

F0 - abs(YOUT(INY,IBEG))
FT = abs(YOUT(INY,ITIME))

IF(IRMS.EQ.2)WRITE(*,*)’FO-',F0,' FT-',FT,' SUMODD-’,SUMODD,

' SUMEVE=',SUMEVE,' ITIME-',TV(ITIME)

YRMS(INY) =(1/AVET)*(F0 + FT + 4*SUMODD + 2*SUMEVE)*(H/3)

IF(IRMS.LE.2)WRITE(*,*)'YRMSl=',YRMSl(1),’ YRMSB',YRMS(1)

RETURN
END

91

C.**************************************************************

C.----SUBROUTINE POVR

C:----PURPOSE: TO DETERMINE THE PERCENT OVERSHOOT
C. SUBROUTINE POVR(YMAX,YMEAN,YOVR)

: DOUBLE PRECISION YMAX(1), YMEAN(1), YOVR(1)

INTEGER NYY, NYCNT
PARAMETER(NYY=20, NYCNT=4096)

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON /RESOUT/ TV(NYCNT), YOUT(NYY,NYCNT)

DO 10 IVAR = 1,NY
IF(YMEAN(IVAR).ne.0)THEN
YOVR(IVAR)-((YMAX(IVAR)-YMEAN(IVAR))/(YMEAN(IVAR)))*100.
ELSE
YOVR(IVAR) - 100.
ENDIF
10 CONTINUE

RETURN
END
C.

C.***************************************************************
C.***************************************************************

C.
C. DEBUGGING PROGRAMS
C.
C.***************************************************************
C.***************************************************************
c
SUBROUTINE YRESLT
c
INTEGER NYY, NYCNT
PARAMETER(NYY-20, NYCNT-4096)
c
COMMON/INTVAR/tl,t2,h,xin(20),NX,NY,NS,NU,NFF,IEND,UAF
COMMON/RESOUT/TV(NYCNT), YOUT(NYY,NYCNT)
C
write(*,*) ' TIME position THIS IS YRESLT '
write(*,*)NX,NY,NS,NU,IEND
c

do 120 idv-1,IEND
write(*,*)TV(IDV),' ',yout(1,idv),' ',YOUT(2,IDV)
120 continue

return
end

92

C ***************************************************************
C
subroutine yprfrm(YPERF,NYPERF,NYY)
C .
DOUBLE PRECISION YPERF(NYPERF,1)
C
COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,IEND,UAF
C
DO 40 IY - 1,NY
DO 40 IP - 1,NYPERF
40 write(*,*) YPERF(IP,IY)
C
return
end
C.
c

C****************************************************************
C

subroutine maxchk(ayout,ymax)
double precision ayout,ymax(1)

c

write (*,*)’ayout -’,ayout,’ ymax =',ymax(1)
c

return

end

C****************************************************************
c

subroutine MINCHK(XMIN,YMIN)

double precision XMIN,YMIN(1)

c
write (*,*)'XMIN =',XMIN,’ YMIN =',YMIN(1)
c
return
end
C****************************************************************
c.----Subroutine ENPGEN: GENERATOR = -U- vector
c.
c.----Purpose: This subroutine is the standard interface which
c. extracts the appropriate U-vector from DS when
c. multiple forcing systems are used.
Subroutine ENPGEN(nffcn,t,u)
c.
C. Define passed variables
c.
Double Precision t,U(1),dtim,ctim,tratio,uratio
Integer nffcn,icnt,inxt
Character Icls*l
c.
Common /intvar/ T1, T2, h, xin(20), nx,ny,ns, nu, NFF, IEND, UAF
Common /drvsys/ DS(1500, 10), ICLS
c.
c write(*,’(a)')'icls in enpgen',icls

If (Icls .eq. 'e' .or. Icls .eq. 'E') Goto 10
If (Icls .eq. 'u' .or. Icls .eq. 'U') Goto 30
If (Icls .eq. 'd' .or. Icls .eq. 'D') Goto 50

 

10
12

54

56

90

C91

93

Do 12 j-1,nu
U(j) - DS(j,nffcn)
Goto 90

Call Usrgen(nffcn,t,u)
Goto 90

Continue
Icnt - (nffcn-1)*(nu+1) + 1
nend - (nffcn-1)*(nu+1) + nu
Ctim - 0
Dtim - 0
i - 1
do while (t .gt. dtim)

dtim - DS(i,icnt)

i - i + 1
write(*,*)'t-’,t,' dtims',dtim,' i-',i
enddo

inxt - i + 1

ctim - DS(inxt,icnt)

tratio - (t - dtim)/(ctim - dtim)
write(*,*)’ctim-',ctim,' tratio-',tratio

if(t .gt. 0) then

uratio - ((dtim — t)/t)
else

uratio - 0
endif

If(uratio .lt. .02)then

m - 0
do 54 j-icnt,nend
k - j+1
m - m+l
u(m) - DS(i,k)
else
m - 0
do 56 j-icnt,nend
k - j+1
m - m+1
u3 - ds(inxt,k) - ds(i,k)
u(m) = tratio*u3 + ds(i,k)
endif
thtinue

do 91 j-l,nu
write(*,*)u(1),u(2)
return

end

94

c .***************************************************************

c.----Subroutine ENPMEN
c.
c.----Purpose: This subroutine is the standard interface used for
c. entering the parameters for multiple driving
c. systems. To use this subroutine the user mmst set
c. up a datafile for each driving system. Each
c. datafile is 1 U vector. These datafiles are then
c. read into an array (D8) which is nothing more than
c. a set of column U vectors. Each column is then
c. passed to ENPGEN as required for analysis.
c.
subroutine ENPMEN
c.
c. Define passed variables
c.
Dimension fname(lO), ndpt(10)
Character fname*30, isel*l
Real DS
Integer ndpt
c.
Common /intvar/ T1,T2,h,xin(20),nx,ny,ns,nu,NFF,IEND,UAF
Common /drvsys/ DS(1500,10), ICLS
c.
Write(*,108)
5 Write(*,104)
Read (*,201) Icls
If (Icls .eq. 'e' .or. Icls .eq. 'E’)Then
goto 10
Elseif(Icls .eq. 'u' .or. Icls .eq. 'U’)then
goto 30
Elseif(Icls .eq. 'd' .or. Icls .eq. 'D')then
goto 50
Else
goto 5
Endif
c.
10 do 12 i-1,10
do 12 j-1,1500
12 ds(j,i) - 0
c.
Write(*,109)
lend-1
If(ICLS .eq. ’d’ .or. ICLS .eq. ’D')Iend = 2
do 16 i=1,nff
Write(*,106) i
Read (*,200) fname(i)
Open (12,file=fname(i),status='unknown’)
do 15 j=1,nu
Icnt - i*Iend - (Iend - 1)
do 14 k-1,Iend
Read (12,204,end-16) DS(j,icnt)
Icnt - Icnt + 1
14 Continue
15 Continue

Close(12)
16 Continue

95

c.
18 Write (*,101)
Read (*,201) isel
If (isel .eq. ’c' .or. isel .eq. 'C') goto 90
If (isel .eq. 'v' .or. isel .eq. 'V') goto 20
If (isel .eq. 'r' .or. isel .eq. 'R') goto 10
goto 18
c.
cccccc20 Do 22 i-1,nff
20 Write (*,102) (fname(i), i=l,nff)
DO 24 j=1,nu
24 Write (*,103) j,(DS(j,k), k=1,nff)
cccccc Write (*,*) ' ’
cccccc22 continue
goto 18
C.
30 Write(*,105)
Read (*,201) isel
If(Isel .eq. ’y' .or. Isel .eq. 'Y')Then
goto 32
Elseif(Isel .eq. 'n’ .or. Isel .eq. ’N’)Then
goto 32
c.
Else
goto 10
Endif
c.
32 Call Usrmen
’ Goto 90
c.
50 do 52 i=1,10
do 52 j-1,1500
52 ds(j,i) - 0.
c.
Write(*,109)
do 53 i-l,nff
write(*,106)i
read (*,200)fname(i)
Write(*,107)i
53 read (*,205)ndpt(i)
c.
do 58 k=1,nff
open(unit-12,file=fname(k),forme'formatted’,status='unknown')
m - (k-1)*(nu+1) + 1
1 = m + nu
do 56 j - l,ndpt(k)
56 Read (12,*,end=57) (DS(j,i),i=m,l)
57 Close (unit-12)
58 Continue
c.
c do 60 j=1,ndpt(1)
c60 write(*,*)ds(j,1),ds(j,2),ds(j,3),ds(j,4),ds(j,5),ds(j,6)
c
90 continue

101

102

103
108

104

105

109
106
107
C.

200
201

204
205

OOOOOOOOOOOOOOOOOOOO

+-++-+ + +-+ + +-+ +-+ +-+

+ +

96

format (17x,'Please select one of the following',/,

l7x,’ C - Continue',/,

17x,’ V - View the data entered’,/,

17x,’ R - Re-enter the datafiles’,/,

17X,’ '13)
format (17x,' ’,//,20x,'DS Matrix Build’,/,

1x,’File Names: ’,a12,’ ',a12,' ’,a12,' ',a12,
' ',a12,' ',a12,//,

5x,’ ------------------------------------------- ')

format (3x,’U comp t',i3,'-',e11.5,' ',e11.5,' ',e11.5,
' ',e11.5,' ',e11.5,' ',e11.5)

format (llx,' ’,/,
13x,'Enter System Driver Parameters',/,
13x,’ ------------------------------------------ ')
format (17x,'How is The Forcing System Being Modeled':/;
17x,’ ---------------------------------------- , ,

l7x,’ E - Enport model generator',/,
l7x,’ U - User written generator',/,
l7x,’ D - Experimental data',/,
17x,’ ',$)

format (13x,'Do you wish to use your own menu',/,

13x,’ Y - Yes N = No ',/,
13xr' . 'rS)
format (17x,'Enter Datafile Information ')
format (17x,' Name of File NO:',12,' ',$)

format (17x,' Number of Data Pts for File NO:',i2,' ’,$)

format (a30)
format (a1)
format (d12.5)
format (14)

return
end

. **************************‘k‘k‘k****‘k**************‘k‘k‘k‘k'k‘k‘k‘k‘k‘k‘k‘k‘k‘k‘k
. ‘k*************************‘k‘k‘k‘k‘k********************************

.----Subroutine ENPAFN

.--—-Purpose: This subroutine determines the maximum value from

the objective function set. In addition all AF
components which are elements of the obj fcn set
will have their return values calculated.

In addition the objective function value used by
optdes will be calculated.

.----Variab1es used:

Passed variables
af - the analysis function array
ny - number of output variables
nff - number of forcing functions
npm - number of performance variables
nobj- size of objective function

Subroutine ENPAFN(NPM,AV,AF)

97

c.
c. Define passed variables
c.
Dimension zf(lO), af(l), av(l), dumaf(10,10,100)
Double Precision dumaf, af, av
Real zf, amax, acur
Integer rfact, ncont, npm, naf, nobj, obfcn, icstr, iavn
c.
Common lintvar/ T1,T2,h,xin(20),nx,ny,ns,nu,NFF,IEND,UAF
Common /objfcn/ nobj,obfcn(10),icstr,iavn
c.

c. Determine repeating factor and number of calculated af
c. constraints.

rfact - npm*ny

ncont - npm*ny*nff

c.
c. Set AF vector
C.
If (obfcn(1) .lt. 0) then
c.
c. Sort the af vector
c.
c. i - num of forcing functions
c. j - num of performance criteria
c. k - num of output variables
c.
do 20 i - 1,nff
do 20 j - 1,npm
do 20 k - 1,ny
iaf - (i-1)*ny*npm +(j-1)*ny + k
20 dumaf(i,j,k) - af(iaf)
c.
C. Determine max values for each constraint
c.
do 35 j - 1,npm
do 30 k - l,ny
naf - (j-1)*npm + k
amax - dumaf(1, j,k)
do 25 i - 1,nff
acur - dumaf(i,j,k)
if(acur .gt. amax)then
zf(naf) - acur
else .
zf(naf) - amax
endif
25 continue
30 continue
35 continue
c.
c. Set the AF vector obj fcn constraints
e.

do 40 i-icstr,ncont,rfact
40 AF(i) - AF(i) - AV(iavn)
c.

98

c. Set obj fcn
c.
‘ AF(ncont+1) - AV(iavn)**2
c.
ELSE
c.
c. Determine obj fcn subset
c.
Do 50 i-1,nobj
iaf - obfcn(i)
50 zf(i) - af(iaf)
c.
c. Determine Max value
c.
amax - zf(l)
Do 55 i-1,nobj
if(zf(i) .gt. amax)then
amax - zf(i)
else
amax - amax
endif
55 continue
c.
c. Set the AF vector obj fcn constraints
c.
Do 60 i-1,nobj
iaf - obfcn(i)
60 AF(iaf) - AF(iaf) - AV(iavn)
c.
c. Set the Obj Fcn value
c.
AF(ncont+1) - AV(iavn)**2
c.
ENDIF
c.
return
end
c .***************************************************************
c.----Subroutine enpobj
c.
c.----Purpose: This subroutine sets the objective function value
c. to be the maximum of the ith constraint for a set
c. of j' forcing functions. (where j' - 1,2...j
c. forcing functions). This subroutine should be
c. used when multiple forcing functions are used for
c. analysis.
c.
c.----Variables used:
c. Passed variables
c. --------------------------------------
c. NOBJ - determines the size of the
c. objective function set.
c. obfcn - the objective function set.
c. icstr - the ith performance measurement.
c. iavn - analysis variable number
c. used for the obj fcn.

99

C.
subroutine enpobj(npm)
c.
c. Define passed variables
c.
Integer npm, nobj, obfcn, icstr, iavn
c.
Common lintvar/ T1,T2,h,xin(20),nx,ny,ns,nu,NFF,IEND,UAF
Common lobjfcn/ nobj,obfcn(10),icstr,iavn
c.
do 5 i-l,10
5 obfcn(i)-0
c.
c.
If (nobj .eq. nff*npm) then
obfcn(l) - -1
Else
Write(*,104)
Write(*,102)
Read (*,200) iavn
Do 10 i-1,nobj
Write(*,101) i
10 Read (*,200) obfcn(i)
Endif
c.
c.
c.
If(obfcn(1) .lt. 0)then
Write(*,104)
Write(*,102)
Read (*,200) iavn
Write(*,103)
Read (*,200) icstr
Else
Continue
Endif
c.
104 format (' ',/,
+ 11x,'Enter Index Numbers for the Following',/,
+ 11x,’ ----------------------------------------- ')
101 format (11x,' ',/,
+ 11x,'AF Objective Function Set Member',i3,’ ',$)
102 format (11x,'AV Objective Function Comparator ’,$)
103 format (11x,'Perf Meas used as the Obj Fcn ',$)
c.
200 format (i3)
c.
return
end
C. **************************************************************
C.—---Subroutine Matwr
C.
Subroutine MATWR(string)
C
Character String*72
C.

Write (*,100) string

100

100

Format (a72)

return
end

C*************************************************************

C
C

O

000

01

.----Subroutine afbild
C.

Subroutine afbild(AV,AF,NMEM)

DOUBLE PRECISION AV(lO), AF(100)

. Call data dialogue subroutine

INTEGER NYY, NYCNT, NFF, NDX, INDX, obfcn, nobj, iavn,
NPM, NMEM, icstr

PARAMETER(NYY-20, NYCNT=4096)

DIMENSION FCN(nyy). CSTR(100)

CHARACTER FCN*32, IPAR*5, AGN*1, CSTR*2

Common /objfcn/ nobj,obfcn(10),icstr,iavn

COMMON /INTVAR/ T1,T2,H,XIN(20),NX,NY,NS,NU,NFF,OS,IEND
COMMON /PAROPT/ IPAR

locl - index(ipar,'m')
loc2 - index(ipar,'a')
loc3 - index(ipar,’r')
loc4 - index(ipar,'v')
loc5 - index(ipar,'s')
loc6 - index(ipar,'x’)
loc7 - index(ipar,’n')

if (locl .gt. 0) fcn(locl)
if (loc2 .gt. 0) fcn(loc2)
if (loc3 .gt. 0) fcn(loc3)
if (loc4 .gt. 0) fcn(loc4)
if (loc5 .gt. 0) fcn(loc5)
if (loc6 .gt. 0) fcn(loc6)
if (loc7 .gt. 0) fcn(loc7)

’maximum value'
'mean value'

’root mean square’
'max violation'
'minimum.va1ue '
'absolute max '
'absolute min '

NPM - 0

if(locl .gt. npm) npm - locl
if(loc2 .gt. npm) npm - loc2
if(loc3 .gt. npm) npm = loc3
if(loc4 .gt. npm) npm - loc4
if(locS .gt. npm) npm - loc5
if(loc6 .gt. npm) npm - 1006
if(loc7 .gt. npm) npm = loc7

Ifin - fo*Ny

DO 5 I-1,fo*Npm*Ny
Cstr(I) = ' '

101

If (Nobj .eq. 1) Then
Write(*,105)
Read (*,200) icstr
cstr(icstr) - ’*'
Elseif (obfcn(1) .lt. 0) Then
. Do 10 i-Icstr,fo*Npm*Ny,Ny
10 Cstr(I) - ’**’
Else
Do 15 I-1,10
Indx - Obfcn(I)
If(Indx .ne. 0)

+ Cstr(Indx)-’**’
15 Continue
Endif
c.
Ip - 1
Do 25 j-1,fo
Do 25 i-1,Npm,l
c IP - (j-1)*Ny*Npm + (I-l)*NY + 1
c IEP - (j-l)*Ny*Npm + i*ny
Write(*,104)fcn(i)
Do 20 K=1,NY
Write(*,106) Cstr(Ip), Ip, K
20 Ip - Ip + 1
25 Continue
c.
If (Nobj .eq. 1) Then
Write(*,108)
Else
Write(*,103)nmem
Write(*,107)
Endif
c.
103 format(le,’ *AF(’,i2,’) Objective Function’)
104 format(Sx,a32)
105 format(llx,’Enter AF Index # of the Objective Function’)
106 format(le,a2,’AF(’,iZ,’) Y-Output(’,i2,’)’)
107 format(’ ’,/,10x,’** - Objective Function Set Member’)
108 format(’ ',/,10x,’* - Objective Function’)
C.
200 format(i4)
C.
RETURN

END
C . *‘k‘k'k‘k‘k'k‘k‘k‘k'k‘k'k'k'k*********************************‘k‘k'k'k‘k'k'k‘k‘k'k‘k‘k‘k

102
F.3 DSMOPT.COM
This is the DEC command file that controls the interface environment. From
this file the user can execute any phase of the model building or optimization
process desired.

COMPUTER PROGRAM
DSMOPT.COM

WRITTEN
BY

I*
!
It
I
l
I
l*
I
I*
l
I*
I
3
It
I
I
I
I
I
I
I
I
l*
I
I
I

i

$.
$
$
$.
$
$
$*
S
S
$
$
$
$
$.
$.
$.
$
$.
$.
$.
$
$.
$.
$.
$.
$.
$!
$!
$!
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$

103

**************************************************************

----Filename: DSMOPT.COM
***************************************************************
----Purpose: Provide user with menu driven interface between
the ENPORT simulation/modeling software and
OPTDES.BYU optimization software.
**************************************************************

-—--Written BY: Mark Davis
***************************************************************

—---Date Commissioned: September 20, 1991
***************************************************************
----External Files: ENPMOD.EDT — SYSPRM.EDT - SYSDAT.EDT
CDE82.0PT - ENPLIN.USR
***************************************************************
----Setup: When installed this command file must have two
symbol-names changed:
OPTFI - Directory name where OPTDES Subroutines
reside.
USEFI - Directory name where INTERFACE
Subroutines reside.
ENPFI - Directory name where ENPORT model files
reside
***************************************************************

----Modification History:

Date Programmer Description of Changes

***************************************************************

set noverify
optfi - "PROJECT6:[optdes]"
usefi - "user3:[davism.ca1tech]"

dir _nam - f$directory()
enpfi - dir _nam

fi_exist - f$file_attributes("usrgen.for","uic")
the _message -- f$message($status)
good _gen - f$extract(10, 10, the _message)

f good_gen .eqs. "NOSUCHFILE" then goto usegen

genfi - enpfi
goto chkmen

usegen:
genfi - usefi

chkmen:

fi_exist - f$file_attributes("usrmen.for","uic")
the _message -- f$message($status)

good_ men - f$extract(10, 10, the _message)

if good4men .eqs. "NOSUCHFILE" then goto usemen
menfi - enpfi

goto chkafn

usemen:
menfi - usefi

(DUTUMMJD{OUMMMDiDUMMWfl£DUMMHD<DODUMMMD(DUMMMDiDUMMMDflDUMMMD(DODUHM{DUMMMD{DUMMM3(DUOUMMWD

chkafn:
fi_exist - f$file_attributes("usrafn.for","uic")
the_message -- f$message($status)

good_afn - f$extract(10,10,the_message)

104

if good_afn .eqs. "NOSUCHFILE" then goto useafn
afnfi - enpfi
goto continueon

useafn:
afnfi - usefi

continueon:

write
write
write
write
write
write

again:

write
write
write
write
write
write
write
write
write
write
write
write
write

sys$output
sys$output
sys$output
sys$output
sys$output
sys$output

sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output
sys$output

inquire choice

if
if
if
if
if

choice
choice
choice
choice
choice
write sys$output "enter c

.eqs.
.eqs.
.eqs.
.eqs.
.eqs.

goto again

enport:
assign/user_mode sys$command sys$input

enport

goto again

datafi:

cntdf - 1
write sys$output ""
write sys$output ""

"C"
"D"
"E"
"O"
"x"

This is the MSU Simulation/Optimization"
Design System

***************************************"

*

MAIN MENU

*"

***************************************N

* Please make
* - Enter E -
D —
O
C

* *If*

X

execute ENPORT
create/edit DATAFILES
- execute OPTDES

- execute CHECKFILE
- exit the session

the following selection *"

*fl
*8.
*8!
*II
1*"

***************************************"

then goto begin
then goto datafi
then goto enport
then goto begin
then goto endit
or o or

e OIX

only try again"

UMMMDUMW(DOMM&DMHWOWMMDUMMRDUMMRDUMMQDUHMihMHWUWMRDUMMiDUMMKD”PMWDUWM(DUMMKDUMM<DUMM£0MHW

105

write sys$output ""

write sys$output N ****************************************N
write sys$output " * How many Datafiles are you creating *"
write sys$output " * *"
write sys$output " * Note: Each set of system driving *"
write sys$output " * conditions must be described *"
write sys$output " * by a separate datafile. *"
write sys$output N ****************************************N
inquire numdf ""

entdf:

write sys$output ""

write sys$output N ****************************************N
write sys$output " * Create/Edit datafile No: "’cntdf’" *"
write sys$output " * --- *"
write sys$output " * Please enter Datafile Name *"
write sys$output " * Example: DRSYSl (limit 6 char) *"
write sys$output " * *
write sys$output " * Note: Do not enter filetype .dat *"
write sys$output N ****************************************N
inquire dfnam ""

dfnmck:

write sys$output "“

write sys$output N ****************************************N
write sys$output " * You Entered: "’dfnam’" *"
write sys$output ” * ------- *"
write sys$output " * Is this correct (Y or N) *"
write sys$output N ****************************************N
inquire dfcor ""

if dfcor .eqs. "Y" then goto dfedit

if dfcor .eqs. "N" then goto entdf

goto dfnmck

dfedit:

assign/user_mode sys$command sys$input
edit/edt 'dfnam’.dat

if cntdf .eq. numdf then goto again
cntdf - cntdf + 1

goto entdf

begin:

1nkchk - 1

write sys$output ""

write sys$output ""

write sys$output ""

write sys$output N ***************************************N
write sys$output " * Please enter model name from ENPORT *"
write sys$output " * *"
write sys$output " * .EXAMPLE: MODELO *"
write sys$output " * *"
write sys$output " * Note: Do not include filetype *"
write SYS$OUtPUt N ***************************************N

inquire staeqs ""

'm40VHMiDUWMWDUHM(hflflMihUMMRD”WMWDUhMRDUMM£hUHW€0UHM£DUMMKDUWMWDUMW{DUHM(DUMMiDUMM£DUMM£DMHDUWM

eqns:
write
write
write
write
write
write
write
write
write
write

106

sys$output
sys$output
sys$output
sys$output "
sys$output "

***************************************N
* You entered:

sys$output " * *u
sys$output " * "’staeqs’" *u
sys$output " * —————— *u

* Is this correct (y or n)
***************************************N

sys$output "
sys$output "

inquire filcor ""

if filcor
if filcor

.eqs.
.eqs.

"Y" then goto sysparm
"N" then goto begin

goto eqns

sysparm:
edp :== "edit/edt/command="’USEFI’"enpmod.edt"
edp ’staeqs’.usr

fortran zzzzzz.for

syp :-- "edit/edt/command-"’USEFI’"sysprm.edt"
syp ’staeqs’.dat

write
write
write
write
write

sys$output
sys$output
sys$output
sys$output "
sys$output ""

Please note the system parameter values"

type zzzzzz.dat

del zzzzzz.dat;*

syf :-- "edit/edt/command-"’USEFI’"sysdat.edt"
syf ’staeqs’.dat

if choice .eqs. "C" then goto chkfi

if choice .eqs. "0" then goto optdes

chkfi:

write sys$output ""

write sys$output ""

write sys$output ""

write sys$output N ***************************************N
write sys$output " * CHECKFILE MENU *"
write sys$output N ***************************************N
write sys$output " * Please make the following selection *"
write sys$output " * Enter C - compile all user progs*"
write sys$output " * I - compile indiv programs*"
write sys$output " * L - link programs *"
write sys$output " * R = run RUNPRO.EXE *"
write sys$output " * M = return to main menu *"
write sys$output " * x - end this session *"
write sys$output N ***************************************N
inquire compl ""

if compl .eqs. "C" then goto compall

if compl .eqs. "I" then goto compind

if compl .eqs. "R" then goto runpro

if compl .eqs. "M" then goto again

if compl .eqs. "L" then goto linkfi

if compl .eqs. "X" then goto enditt

write sys$output " enter A or I or L only try again"

{DMM‘U} mmmmmmmmmm mmmmmmm mmmmmmmmmmmmm

mmmmmmmmm

107
goto chkfi

runpro:

assign/user_mode sys$command sys$input
run runpro

goto chkfi

compall:

if lnkchk .eq. 2 then goto lnkmsg
fortran usrgen.for

fortran usrmen.for

fortran usrafn.for

goto linkfi

compind:
count - 1
write sys$output ""

write sys$output " ******************************************n

write sys$output " * The number of programs to be compiled*"
write sys$output " ******************************************n

inquire numcom ""

loopl:
write sys$output ""

write sys$output n ******************************************n

write sys$output " *

Enter the program name

*0.

write sys$output n ******************************************n

inquire prog ""
fortran/debug/nooptimize ’prog’.for
if count .eq. numcom then goto linkfi
count - count + 1

goto loopl

linkfi:
if lnkchk .eq. 2 then goto lnkmsg
del ’enpfi’runpro.exe;*

link/executable-runpro ’usefi’anamain.obj, ’usefi’anasub.obj,
'enpfi’zzzzzz.obj,. ’genfi’usrgen.obj,
’menfi’usrmen.obj, ’afnfi’usrafn.obj

write sys$output "

write sys$output " Executable file RUNPRO has been created

write sys$output "
del zzzzzz.fOr;*
del zzzzzz.obj:*
lnkchk - 2

goto chkfi

(D(DUMMMD(00?Uhm%h{hflbvhm4h(DUDUMMMb£DUMMWfl{DOGUNMMD(DUMMRDQDUWMMD{DODUMMWflihUMMMD(DOD“HM(DO¥MHM

108

optdes:
write sys$output ""
write sys$output "“
write sys$output ""
write sys$output N ******************************************N
write sys$output " * OPTIMIZATION MENU *"
write sys$output N ******************************************N
write sys$output " * Select one of the following options *"
write sys$output " * C - compile all user progs *"
write sys$output " * I - compile individual progrs *"
write sys$output " * L - link to optimization files*"
write sys$output " * S - create setup executable *"
write sys$output " * RC - run CONVEN.EXE *"
write sys$output " * RS 8 run SETUP.EXE *"
write sys$output " * RD - run CDESIGN.EXE *"
write sys$output " * M - return to main menu *"
write sys$output " * X - end session *"
N ******************************************N

write sys$output
inquire optdl ""
if optdl .eqs. "C" then goto comana
if optdl .eqs. "I" then goto indana
if optdl .eqs. "L" then goto linana
if optdl .eqs. "S" then goto creset
if optdl .eqs. "RC" then goto conven
if optdl .eqs. "RS" then goto setup
if optdl .eqs. "RD" then goto cdesign
if optdl .eqs. "M" then goto again

if optdl .eqs. "X" then goto enditt
goto optdes

conven:
assign/user_mode sys$command sys$input
run conven
goto optdes

setup:

assign/user_mode sys$command sys$input
run setup

goto optdes

cdesign:

assign/user_mode sys$command sys$input
run cdesign

goto optdes

comana:

if lnkchk .eq. 2 then goto lnkmsg
fortran anasub.for

fortran zzzzzz.for.

fortran usrgen.for

fortran usrmen.for

fortran usrafn.for

goto optdes

{AUTUMM> <0£DODUMMWD£0000PMt {DUDUMMJW{DUI

(DUGUMMJDIDUMMMD{D(OUDU>

indana:

count - 1

write sys$output
write sys$output
write sys$output
write sys$output
inquire numcom

loopl:
write
write

sys$output
sys$output
write sys$output
write sys$output
inquire prog

109

******************************************N

* The number of programs to be compiled*"
******************************************N

******************************************N

* Enter the program name *"
******************************************N

fortran/debug/nooptimize ’prog’.for
if count .eq. numcom then goto optdes

count - count + 1

goto loopl

linana:

if lnkchk .eq. 2 then goto lnkmsg
delete ’enpfi’conven.exe:*
link/executable-’enpfi’conven ’optfi’conven.obj, -

write sys$output
write sys$output
write sys$output

’optfi’consub.obj, -
’optfi’meneds.obj, -
’optfi’menutl.obj, -
’optfi’menpro.obj, -
’optfi’menout.obj, -
’optfi’sysvms.obj, -
’usefi’anasub.obj, -
'enpfi'zzzzzz.obj, -
'genfi’usrgen.obj, -
’menfi’usrmen.obj, -
’afnfi’usrafn.obj
II

has been created "
II

Executable file CONVEN

delete ’enpfi’cdesign.exe:*

! cdesZ/options

1ink/executab1e=’enpfi’cdesign —

write sys$output
write sys$output
write sys$output
del zzzzzz.for;*
del zzzzzz.obj:*
lnkchk - 2

goto optdes

lnkmsg:

write sys$output
write sys$output
write sys$output
write sys$output

’usefi’anasub.obj,
’genfi’usrgen.obj,
’afnfi’usrafn.obj,

’enpfi’zzzzzz.obj, -
’menfi’usrmen.obj, -
’usefi’cdesZ/options

II

Executable file CDESIGN has been created "

The files have been linked already. You "
must return to the main menu to create a "
new executable file. "

mmmmmm

MMMMMMMMM

110

if choice .eqs. "C" then goto chkfi
if choice .eqs. "0" then goto optdes

goto again

creset:

link/executable-’enpfi'setup 'optfi’setup.obj,

write sys$output "
write sys$output "
write sys$output "
goto optdes

enditt:

del zzzzzz.dat;*
endit:

exit

’optfi’dissub.obj,
’optfi’varsub.obj,
’optfi’funsub.obj,
’optfi’comsub.obj,

’optfi’sdbsub1.obj,
’optfi’sdbsub2.obj,

’optfi’menset.obj,
’optfi’meneds.obj,
’optfi'menutl.obj,
'optfi’menpro.obj,
’optfi’menout.obj,
’optfi’sysvms

Executable file SETUP has been created"

113
F5 SYSDAT.EDT
This is the DEC command edit file. This file will execute a series of edit
commands. These commands are used to edit the ENPORT .DAT output file to
read the number of state variables, outputs, and inputs when ANAPRE is executed.

COMPUTER PROGRAM
SYSPRM.EDT

WRITTEN
BY

MARK DAVIS

112

set nofnf

set nonum

set nosummary

set noverify

del 24 thru 400

del 1 thru 17

sub/outputs/OUTPUTS (Y-VECTOR)/1 thru lOO/notype
sub/INPUTS/INPUTS (U-VECTOR)/1 thru lOO/notype
SU/STATES/STATES (X-VECTOR)/1 THRU lOO/NOTYPE

ex zzzzzz.dat

set
set
set
set
del
del
del
del

114

nofnf
nonum
nosummary
noverify

24 thru 400
22

20

1 thru 18

ex zzzzzz.dat

1 15
E6 CDESZ.OPT
This is the DEC command options file. This file is used when an executable
line is to long for exection from within the command file. This file contains all the
names of the subroutines used for linking with ANASUBFOR to create the
executable file CDESIGN.EXE.

COMPUTER PROGRAM
CDESZ.OPT

WRITTEN
BY

MARK DAVIS

PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:

PROJECTS

[optdes]design.
[optdes]calsub.
[optdes]profun.
[optdes]params.
[optdes]setvar.obj,

[optdeslexplor.obj,

[optdes]grgalg2.obj,

obj, -
obj,
obj,
obj,

:[optdes]qpsolv.obj,
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:

[optdes]lpsolv.obj,
[optdes]approx2.obj,
[optdes]combin1.obj,
[optdes]plosub.obj,
[optdeslscrtek.obj,
[optdes]meneds.obj,
[optdes]menpro.obj,
[OPTDES]sysvms.obj

116

PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:
PROJECT6:

[optdes]displa.obj,
[optdes]propro.obj,
[optdes]runa1g.obj,
[optdes]histor.obj,
[optdes]grgalgl.obj,
[optdes]sqpalg.obj:
[optdes]slpalg.obj,
[optdes]approxl.obj,
[optdes]tolers.obj,
[optdes]combin2.obj,
[optdes]grasub.obj,
[optdes]penHP.obj, -
[optdes]menut1.obj,
[optdes]menout.obj,

APPENDIX G

APPLICATION EXAMPLE DATA

APPENDIX G
APPLICATION EXAMPLE DATA

G.l Introduction
The following information was used to execute the application example solved
in chapter 3. The input vector information describes the operating parameters of the
bond graph. Items such as mass, trf, frequencies and amplitudes are set from these
data files. The ENPORT output files are generated by ENPORT when the Fortran
file is generated. The optimization data files were generated from OPTDES. These
files contain information describing the setup of the optimization problem

G.2 Input Vector (U) Datafiles
These data files profile the bond graph model used in the application example.

117

DATA FILE
PROF LDAT

WRITTEN
BY

MARK DAVIS

HI—‘I—‘OOOOI—‘Dw

1.
4.

.67

118

.9270000
.81750000
.0000000000
.0

.5000000
.8666667

.8

.12

.067

387

638
094

-l.638

9.

500000
8666667
01

139.75
3416.7

mwooooooww
000000

.0

.83300000000
.33330000000000
.66667000000

DATA FILE
PROF2.DAT

WRITTEN
BY

MARK DAVIS

119

11
3 770
8 00 .
2000770
...... 0
6000001

DATA FILE
PROF3.DAT

WRITTEN
BY

MARK DAVIS

1%

a o 4 n7 ”an
54 9 .

6 fl 0 29 3 1 6 336

2 000000130.000910000000836

.000 e no so 0 e o .8 e 034 ooooooooo to.

0.. 101010080.10913330000003

121

0.3 ENPORT Output Files I
These files were produced by ENPORT. They describe the bond graph model.
The .USR file contains the state equations written in compilable fortran code. The
remaining data files contain information about the structure of the bond graph
model.

FORTRAN FILE
USRGLUSR

GENERATED
FROM

ENPORT

122

C****** MATRIXx User Code_Block file written by ENPORT ***********

C _
C File Name: USER01.USR
C
C 5 Dof Suspension System W/Variable Flow Source - WO/Grav.
C Effects
C SystemLBuild User_Code_Block USR01
C
C*****************************************************************
C
SUBROUTINE USR01(INFO,T,U,NU,X,XDOT,NX,Y,NY,RP,IP)
C
IMPLICIT DOUBLE PRECISION (A-Z)
CHARACTER STRNG*8
DOUBLE PRECISION T, U(*), X(*), XDOT(*), Y(*), RP(*)
INTEGER IP(*), INFO(4), NU, NX, NY, I
LOGICAL INIT, STATE, OUTPUT
EXTERNAL MATWR
C

C*****************************************************************
C
INIT - INFO(Z).NE.0
STATE - INFO(3).NE.0
OUTPUT - INFO(4).NE.O
C
C---- Check the problem size...
C 0
IF (INIT) THEN
STRNG-I****I
IF (NU.NE.29) STRNG-’inputs.’
IF (NX.NE.10) STRNG-’states.’
IF (NY.NE. 6) STRNG-’outputs.’
IF (STRNG.NE.'****’) THEN
INFO(1) - -2
CALL MATWR(’ ’)
CALL MATWR(’ *** Error calling USR01.’)
CALL MATWR(’ Incorrect number of ’//STRNG)
RETURN
ENDIF
ENDIF
C
C---- Get the time and the states X...
C
IF (STATE.OR.OUTPUT) THEN'
TIME- T

050
P5M
Q3Q
P2M
P3J
PlM
010
020
P4M
Q40

X( 1)
X( 2)
X( 3)
X( 4)
X( 5)
X( 6)
'X( 7)

123

W1 - U( 1)
W2 - U( 2)
PHIl - U( 3)
PHI2 - U( 4)
PHI3 - U( 5)
PHI4 - U( 6)
T1 - U( 7)
T2 - U( 8)
T3 - U( 9)
T4 - U(10)
T5 - U(11)
AMPl - U(12)
AMP2 - U(13)
AMP3 - U(14)
PHIS - U(15)
PHI6 - U(16)
Il - U(l7)
12 - U(18)
I3 - U(19)
I4 - U(20)
I5 - U(21)
SE1 - U(22)
SE2 - U(23)
SE3 - U(24)
SE4 - U(25)
SE5 - U(26)
TF1 - U(27)
TF2 - U(28)
TF3 - U(29)
C
C
C1 - RP( 1)
C2 - RP( 2)
C3 - RP( 3)
R1 - RP( 4)
R2 - RP( 5)
R3 - RP( 6)
C
C---- Evaluate the system equations...
C
C4 - 1.80000E+04
C5 - 1.80000E+04
R4 - 6.00000E+01
R5 - 6.00000E+01
S468 - AMP3 * SIN( W1 *TIME )
$28 - AMPl * SIN( W1 *TIME )
C ...... STEP
IF (TIME .GE. Tl ) THEN
S488 - 1.00000E+00
ELSE
S488 - 0.
ENDIF

S498 - AMP2 * SIN( W2 *TIME )

C ......

124

STEP

IF (TIME .GE. 0.00000E+00)
SSS - PHIZ

ELSE
SSS - 0.

ENDIF

$518 - AMP2 * COS(

STEP

IF (TIME .GE. 0.00000E+00)
SBS - PHIl

ELSE
S88 - 0.

ENDIF

STEP

IF (TIME .GE. T2 )
S9S - -1.00000E+00

ELSE
S9S - 0.

ENDIF

STEP

IF (TIME .GE. 0.00000E+00)
SZlS - PHI3

ELSE
$218 - 0.

ENDIF

822$ - AMPl * COS(

STEP

IF (TIME .GE. 0.00000E+00)
$238 - PHI4

ELSE
823$ - 0.

ENDIF

STEP

IF (TIME .GE. T4
$298 - -1.00000E+00

ELSE
329$ - 0.

ENDIF

STEP

IF (TIME .GE. 0.00000E+00)
$253 - PHI5

ELSE
825$ - 0.

ENDIF

STEP

IF (TIME .GE. 0.00000E+00)
828$ - PHIS

ELSE
$288 - 0.

ENDIF

STEP

IF (TIME .GE. T3 )
$248 - -1.00000E+00

ELSE
824$ - 0.

ENDIF

THEN

W2

THEN

THEN

THEN

W1

THEN

) THEN

THEN

THEN

THEN

*TIME

*TIME

)

i

C ......

125

STEP
IF (TIME .GE. T5 ) THEN
$548 - 1.00000E+00
ELSE
854$ - 0.
ENDIF
STEP
IF (TIME .GE. T3 ) THEN
855$ - 1.00000E+00
ELSE
$558 - 0.
ENDIF
857$ - 1.00000E+00
558$ - 1.00000E+00
E5W - SE5
E2W - SE2
E1W - SE1
E4W - SE4
MTFl - TF1
MTF2 - TF2
MTF3 - TF3
SlOS - 1.00000E+00 *SZS *S488
8118 - 1.00000E+00 *S49S *SSS
$123 - -1.00000E+00 *SSlS *SBS
S308 - 1.00000E+00 *S4SS *SZlS
S318 - 1.00000E+00 *SZZS *8238
$378 - 1.00000E+00 *SZSS *S498
S365 - -1.00000E+00 *5288 *SSIS
$158 - 1.00000E+00 * S463

+1.00000E+00
.00000E+00
+1.00000E+00

*
S455 *
*
S448 - 1.00000E+00 * S303
*
*
*

I
H

+1.00000E+00
.00000E+00
+1.00000E+00

$388

I
...:

S34S - 1.00000E+00 *SZ4S *S44S
S338 - 1.00000E+00 *S44S *3548
S398 - 1.00000E+00 *SSSS *8385
ESQ - C5 * QSQ
F5M - (1./ I5 ) * P5M
E3Q - C3 * Q3Q
F2M - (1./ 12 ) * P2M
F3J - (1./ I3 ) * P3J
FlM - (l./ Il ) * PlM
ElQ - C1 * QlQ
E2Q - C2 * Q2Q
F4M - (1./ I4 ) * P4M
E4Q - C4 * Q4Q
F1R1 - 1.00000E+00 *MTFl *F3J
F2R1 - 1.00000E+00 *MTF2 *F3J
F3R1 - 1.00000E+00 *MTF3 *F3J
SlSS - 1.00000E+00 *S483 *S4SS
817$ - 1.00000E+00 *S9S *S45S
S408 - 1.00000E+00 *829S *S38S
818$ - 1.00000E+00 * SlSS
+1.00000E+00 * Sl7S

8198
S358
S418
S428

F4VS
F5VS
F5V

ESF
F3V

E3F
F1V

E1F1
F2V

E2F
F4V

E4F
ESV

E3V
EIV
E2V
E4V

E1R2
E2R2
E3R2
S438
356$
853$
S328
$138
$148
$18

8208
838

S48

SSS

8508
S78

3528
ESVM
ESVS

1.00000E+00

.00000E+00

1.00000E+00

.000002+00

1.00000E+00

.OOOOOE+00

1.00000E+00

.OOOOOE+00
1.00000E+00
1.00000E+00
1.00000E+00

-l.00000E+00
R5

-1.00000E+00

+1.00000E+00

-1.00000E+00
R3
1.00000E+00

-1.00000E+00

+1.00000E+00
R1
1.00000E+OO

+1.00000E+00

-1.00000E+00
R2
1.00000E+00

-1.00000E+00
R4
1.00000E+00

+1.00000E+00
1.00000E+00

+1.00000E+00
1.00000E+00

+1.00000E+00
1.00000E+00

+1.00000E+00
1.00000E+00

+1.00000E+00
1.00000E+00
1.00000E+00
1.00000E+00

838$

8388

S443

S448

S458

S458

S468

S468

S488

S488

S498

S495

851$

851$

ESV

ESV

********
(I)
w
w
(0

*Sl9S
*S428

*ElV
*E2V
*E3V

*

FSQ
FSF
ESM

FSW
F3VS
FSVM
E3R1
E3T
E3VS
F30
F3F
E2M

F2W
F2T
F3T
F1T
F3R2
F2R2
E3J

F1R2
ElRl
E1VM
ElT
FIVM
ElM

F1W
FlQ
F1F1
E2R1
E2T
E2VS
F2Q
F2F
E4M

F4W
FZVS
F4VM
E4VM
E4VS
F4Q
F4F

ENDIF

F5V

F5V

-1.00000E+00

+1.00000E+00

-1.00000E+00

F5M

F5M

FSM

E3V

E3V

E3V

F3V

F3V

-1.00000E+00

-1.00000E+00

-1.00000E+00

-1.00000E+00

F2M

F2M

F2M

F2M

F3J

F3J
1.00000E+00

-1.00000E+00

-l.00000E+00

F3J

E1V

E1V

E1V

FlM
1.00000E+00

-1.00000E+00

FlM

F1V

F1V

E2V

E2V

E2V

F2V

F2V

-1.00000E+00

+1.00000E+00

-1.00000E+00

F4M

F4M

F4M

E4V

E4V

F4V

F4V

*fi**

127

ESW
E3V
ESV

E2W
E2V
E3V
E1V

E3R2
E2R2
E1R2

E1V
E1W

E4W
E2V
E4V

128

C
C---- Store the state derivatives XDOT...
C
IF (STATE) THEN
XDOT( 1) - F5V
XDOT( 2) - E5M
XDOT( 3) - F3V
XDOT( 4) = E2M
XDOT( 5) - E3J
XDOT( 6) - ElM
XDOT( 7) - F1V
XDOT( 8) - F2V
XDOT( 9) - E4M
XDOT(lO) - F4V
ENDIF
C
C--—- Store the output list Y...
C
IF (OUTPUT) THEN
Y( 1) - 010
Y( 2) - ElM
Y( 3) - 020
Y( 4) ' 030
Y( 5) - Q40
Y( 6) = QSQ
ENDIF
C
RETURN
END
C

C****************************************************************

DATA FILE
USR01.RPD

GENERATED
FROM

ENPORT

129

// MATRIXx RP-name exec file written by ENPORT
//

// File name: USER01.RPD

//

// Assignment of U and NP variables for RP use

Cl - 1.20000E+03
C2 - 3.60000E+03
C3 - 3.60000E+O3
R1 - 1.20000E+02
R2 - 3.00000E+02
R3 - 3.00000E+02
//

RP( 1) - C1

RP( 2) - C2

RP( 3) - C3

RP( 4) - R1

RP( 5) - R2

RP( 6) - R3

// End of the file.

DATA FILE
USR01.DAT

GENERATED
FROM

ENPORT

130

// Matrix-x MATSETUP file written by ENPORT.
//

// File name: USER01.DAT
//

//

// Create a superblock ENPSUP
BUILD
EDIT SUPER-BLOCK
ENPSUP

0

//

// Define user_code_block
DEFINE BLOCK

2
USER CODE BLOCK
BLOCK NAME
ENPUSR
NUMBER OF INPUTS

29
NUMBER OF OUTPUTS

6

NUMBER OF STATES

10
PARAMETER ENTRY

1
Y

6, 0

// RP Parameters
.2000E+03
.6000E+03
.6000E+03
.2000E+02
.0000E+02
.0000E+02

wwwaH

// Initial conditions
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00
.0000E+00

0000000000

//
// Define connections
CONNECT BLOCKS
EXTERNAL OUTPUT
6
2
Y
//
// Return to main menu
TOP
//
// End-of-file

131
6.4 Optimization Datafiles
These datafiles were produced by OPTDES. They describe the optimization
problem set up for each problem solved in the application example.

DATA FILE
FINAL LDAT

GENERATED
FROM

OPTDES

AV
1200.000000
AV
3600.000000
AV
3600.000000
AV
120.0000000
AV
300.0000000

NROWV

"U'U'U'U'U'U

<P
vP
<P
<P
(P
(P

AV
300.0000000
AF
0.1722275019
AF
249.4954987
AF
0.6293675303
AF
0.3334497809
AF
0.1466183811
AF
0.8452641964E-01
END
NDV - 6
DV# #MP
1 1
2 1
3 1
4 1
5 1
S 1
ROW AV}
1 1
2 2
3 3
4 4
5 5
6 6
DP? IMP
1 1
2 1
3 1
4 1
5 l
6 1
ROW AF!
1 l
2 2
3 3
4 4
5 5
6 S
NCM - 0

F‘HFJF‘HFJ

FJF‘HFJPJH

- 6

132

000000

4 conl
4 con2
4 con3
4 con4
4 con5

4 con6

MINIMUM

NDF -

600.0000000

2400.000000

2400.000000

24.00000000

60.00000000

60.00000000
COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

ALLOWABLE
.1670000000

.4170000000
.4170000000
.1670000000
.1670000000

000000

.0000000000E+00

COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

NROWC - 0

6

NROWF -
MAXIMUM
6000.000000
12000.00000
12000.00000
600.0000000
960.0000000
960.0000000

RANGE
0.1670000000
100.0000000
0.4170000000
0.4170000000
0.1670000000
0.1670000000

DATA FILE
FINALZDAT

GENERATED
FROM

OPT DES

AV
1200.000000
AV
3600.000000
AV
3600.000000
AV
120.0000000
AV
300.0000000
AV
300.0000000

V
<

500.0000000

IE

0.1075993851

3’:

-348.1452789

E}

0.3541334569

2’:

0.1583947688

E

0.7996477932E-01

3?

0.3714266419E-01

ii

0.4795477167E-01

3’:

-359.1307068

fl

0.2524786294

E

0.2371307760

fl

0.1370741427

E

0.1428910345

35

250000.0000
END

2
O
<
I
‘4

NROWV -

a.
P‘HPHFJPHHF4fi

'U'U'U'U'U'U'U

133

11 seat spring
12 front spring
11 rear spring
11 seat damper
12 front damper
11 rear damper
7 opj fcn
17 pl seat sprg disp
13 p1 seat force
16 p1 frt sprg disp
17 p1 rear sprg disp
17 pl frt tire compr
18 p1 rear tire compr
17 p2 seat sprg disp
13 p2 seat force
16 p2 frt sprg disp
17 p2 rear sprg disp
17 p2 frt tire compr
18 p2 rear tire compr
18 objective function
7 NDF - 13 NROWF -
MINIMUM MAXIMUM
600.0000000 6000.000000
2400.000000 12000.00000

2400.000000
24.00000000
60.00000000
60.00000000
0.0000000000E+00

12000.00000
600.0000000
960.0000000
960.0000000
500.0000000

13

w
0
2

mmdmehWNHfidmmbWNl-J

HFJFJH
tunJHco

w
0
2

AV#
1 1
2 1
3 1
4 1
5 1
6 1
7 1
IMP
l (P
1 <P
1 (P
1 <P
1 <P
l <P
1 (P
1 (P
1 <P
1 <P
l <P
l (P
1 vP
AF#
1 1
2 1
3 l
4 1
5 l
6 1
7 1
8 1
9 1
10 1
11 1
12 1
13 l
0 NROWC

COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

134

ALLOWABLE

0000000000000

COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

- 0

.1670000000
.0000000000E+00
.4170000000
.4170000000
.1670000000
.1670000000
.1670000000
.0000000000E+00
.4170000000
.4170000000
.1670000000
.1670000000
.0000000000E+00

RANGE

0.1670000000

1.000000000
0.4170000000
0.4170000000
0.1670000000
0.1670000000
0.1670000000

1.000000000
0.4170000000
0.4170000000
0.1670000000
0.1670000000

1.000000000

DATA FILE
FINAL3.DAT

GENERATED
FROM

OPTDES

AV
1200.000000
AV
3600.000000
AV
3600.000000
AV
120.0000000
AV
300.0000000
A

<

300.0000000

E

0.1722275019
249.4954987
.6293675303
.3334497809
.1466183811

.1075993851
151.8547211

E Eofiofiofiofiofi E

0.3541334569

E

0.1583947688

%

.8452641964E-01

0.7996477932E-01

E

0.3714266419E-01

END
NDV - 6
DVI

‘3!

I!

C)
O\thtnhah‘£<BCn¢>qur4
E
mmewwpwwpwwHH

"U'U'U'U'U'U

NROWV

HFJF‘HPJP‘

- 6

135

000000

4 conl
4 con2
4 con3
4 con4
4 con5
4 con6
4 con7
7 obj fcn
4 con8

4 con9

U'l

con10

U'l

conll

NDF -
MINIMUM
600.0000000
2400.000000
2400.000000
24.00000000
60.00000000
60.00000000

COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

12

NROWF -
MAXIMUM
6000.000000
12000.00000
12000.00000
600.0000000
960.0000000
960.0000000

12

o
"l
#1

OmdmmfiwNH

*
IDCD~JOKUHbLuhahnfib4PJF‘HWJFJP‘PHHIJPJP‘fi

DJF‘H
NJHw:

0

<P
(P
(P
(P
(P
(P
(P
vP
<P
<P
<P
<P

0F4F‘HFJPH4FJHFJF‘HPJ

NROW

136

ALLOWABLE
0.1670000000
500.0000000
.4170000000
.4170000000
.1670000000
.1670000000
.1670000000

.4170000000
.4170000000
.1670000000
.1670000000

0000000000

.0000000000E+00

COEFF

.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000
.000000000

- O

RANGE

0.1670000000

500.0000000
0.4170000000
0.4170000000
0.1670000000
0.1670000000
0.1670000000

100.0000000
0.4170000000
0.4170000000
0.1670000000
0.1670000000

137
6.5 ANAPRE Data Entry List
In order to execute the optimization problems the following information is

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

required.
Table 6.5.1
ANAPRE Data Entry List
VARIABLE PROBLEM 1 PROBLEM I PROBLEM 1
Nx 10 10 10
NY 6 6 6
NU 29 29 29
NFF 1 2 2
DATAFILE PROF1.DAT PROF2.DAT PROFl.DAT
pm
TO 0 0 0
TF 4.0 4.0 4.0
NO. INTG STEPS 1000 1000 1000
INITIAL CONDS. N N N
PMM ‘ x 5‘ x
08.) ECTIVE SET SIZILE 1 2 1
AV OBJECTIVE No} 7 --
PM NO. | 2 ' .-
OBJ. FUNCTION AF NO. 2 13 8
NO OF AV FCNS 6 7 6
NO. or AF FCNS. 6 13 12
AV(l) 1200 1200 1200
AV(Z) 3600 3600 3600
AV(3) 3600 3600 3600
MM) 120 120 120
AVG) 300 300 300
AV(6) 300 300 300
AV(7) "' 500

 

 

138

6.6
Signal Generator Bond Graph

The following bond graph was used to produce the velocity input to the wheels
of the suspension system.

...—«.5 ES: 3:22.99 35%

 

 

      

 

 

 

~66 Huang—r.—
_ mo Dam _ f mm Dam 4. "m .532
a N
a a on 0%
mm
E. Dmm mo FADE n h #90 ab 3—
3 2n
Um 01m
3 e @
an an Dam
a
”0 UK” u—V ON <5 HUM—m 4 o 3 - E
” 3% an no. .
l .
“NV <0 uxm a
u>n

He 95. .2 $85

 
 

 

.a I
<~ cum
.3 .5..- ...§ 3..
. v To I 23.
a. . IS. 5:: . x l
E an as . o

 

LIST OF REFERENCES

[1] Rosenberg, R., The ENPORT Reference Manual, 7th Edition, Rosencode
Associates, Lansing ML, 1990.

[2] Bailing, R., and Free, and J., Parkinson, A., OPT DESBYU User's Manual,
Release 4.0, Design Synthesis, INC, Provo, UT, 1989.

[3] Hang, 13.1., and Arora, J .S., Applied Optimal Design, Mechanical and Structural
Systems, John Wiley & Sons, 1979.

140

 

NSTRTUE

I|II| IIIIII III I||I IIIIIII III II III IIIII II III III