- , ~, “-3. p ‘ n. . _ swim‘mdfiyu \ » - . w‘ , , ‘7 .,,V.. ’1‘ \ Illilll‘l'illll‘uflllllll llilflifill " 3 1293 01024 0145 This is to certify that the thesis entitled IMPROVING VISUALIZATION TECHNIQUES USING BOND GRAPH METHODS presented by JENNIFER LYNN 0RDWAY has been accepted towards fulfillment of the requirements for MASTERS degree in MECHANICAL ENGINEERING zécflm m ya Major professor Date M Q?! /qg§’ 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LtBRARY M'cmgan State University V PLACE u RETURN BOX to roman w. checkout flan your ncord. ro AVOID FINES mum on or baton m duo. DATE DUE DATE DUE DATE DUE l | l MSU I. An Affirm“ Action/Equal Opportmtty lmtttwon mm: IMPROVING VISUALIZATION TECHNIQUES USING BOND GRAPH METHODS By Jennifer Lynn Ordway A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Mechanical Engineering Department of Mechanical Engineering 1995 ABSTRACT IMPROVING VISUALIZATION TECHNIQUES USING BOND GRAPH METHODS By Jennifer Lynn Ordway Interpretation of simulation results becomes more difficult as the complexity of a system increases. Current methods of viewing results usually involve plots of variables versus time. When investigating the behavior of a system as a whole, time plots can become confusing. In these cases, scientific visualization of the system behavior becomes a matter of great importance. This thesis presents a significantly improved visualization method that allows engineers to view results and connect them to a graphical model. The design is based on the bond graph as a modeling representation of physical systems and the PC-DOS version of ENPORT as a simulation tool. In order to aid in the comprehension of the system’s dynamic behavior, power variable results generated in ENPORT are displayed on the corresponding bond graph as the bond color or width. Two systems, a simple mechanical oscillator and a flatbed trailer suspension system were modeled and simulated to demonstrate the benefits of a dynamic display when attempting to understand physical behaviors. Dedication In remembrance of my Grandpa, Jack D. Ordway, whom I love with all my heart. iii ACKNOWLEDGMENTS I would like to express my sincere thanks and gratitude to my major professor, Dr. Ronald Rosenberg, for his support and guidance throughout the development of this work. In addition, I would like to thank the members of my thesis committee: Drs. Alejandro Diaz and Clark Radcliffe. Their encouragement and input were very valuable to me. My gratitude also extends to the members of the ENPORT development group who have been great sources of knowledge and a pleasure to work with. Special thanks go to all of my family and friends, especially my parents; Crystal and Gerald Walmsley, and James and Judith Ordway. Their love, support, and guidance are the most precious gifts they could give me. Above all, thanks to God, who helps me enjoy happy times and pulls me through rough ones. iv TABLE OF CONTENTS List of Tables ................................................ vii List of Figures ............................................... viii Nomenclature ................................................. x Chapter 1 - Introduction ......................................... 1 1.1 Problem Definition ...................................... 1 1.2 Research Objectives ..................................... 3 1.3 Description of Thesis Organization ........................... 4 Chapter 2 - Visualization Examples Using the Dynamic Display Module ....... 6 2.1 Mechanical Oscillator Modeling Example ..................... 6 2.2 Automobile Modeling Example ............................. 12 Chapter 3 - Implementation of the Dynamic Display Module ............... 23 3.1 File Importing ......................................... 23 3.2 Dynamic Display Module Features Implemented ................ 25 Chapter 4 - Conclusions ......................................... 36 4.1 Summary of Contributions ............................... 36 4.2 Areas for Further Research ............................... 37 Appendix A - User's Manual ...................................... 4O Appendix B - Program Documentation and Code ........................ 50 Appendix C - Example Model Files ................................. 156 References ................................................. 1 61 vi LIST OF TABLES Table 1. Mechanical Oscillator Model Equations ........................ 7 Table 2. Car Suspension Model Equations ........................... 15 vii LIST OF FIGURES Figure 1. Schematic of a Mechanical Oscillator ......................... 6 Figure 2. Bond Graph of Mechanical Oscillator ........................ 7 Figure 3. Efforts of Bonds for Mechanical Oscillator .................... 8 Figure 4. Flows of Bonds for Mechanical Oscillator ..................... 9 Figure 5. Dynamic Display of Mechanical Oscillator at Initial Time ......... 10 Figure 6. Dynamic Display of Mechanical Oscillator Power ............... 11 Figure 7. Schematic of Flatbed Trailer Suspension System ................ 13 Figure 8. Bond Graph Representation of Flatbed Trailer Suspension ......... 14 Figure 9. Road and Corresponding Vertical Velocity Profile .............. 16 Figure 10. Forces on the Front and Rear Tires ........................ 17 Figure 11. Power Variable Response for Flatbed Trailer (Time=0.10 seconds) . 18 Figure 12. Power Variable Response for Flatbed Trailer (Time=0.18 seconds) . 18 Figure 13. Power Variable Response for Flatbed Trailer (Time=0.21 seconds) . 19 Figure 14. Power Variable Response for Flatbed Trailer (Time=0.25 seconds) . 19 Figure 15. Power Variable Response for Flatbed Trailer (Time=0.35 seconds) . 20 Figure 16. Power Variable Response for Flatbed Trailer (Time=0.45 seconds) . 20 Figure 17. Power Variable Response for Flatbed Trailer (Time=0.55 seconds) . 21 Figure 18. Width Legends Available in the Dynamic Display .............. 29 viii Figure 19. Color Legends Available in the Dynamic Display .............. 30 Figure 20. Time Legend for the Dynamic Display ...................... 30 Figure 21. Dynamic Display Module Graphical Display .................. 31 Figure 22. Examples of Bonds of Varying Widths ...................... 33 Figure 23. Examples of Bonds with Interior Points ..................... 33 Figure A-l. Main Menu for Dynamic Display ......................... 40 Figure A-2. Model File Options Menu .............................. 41 Figure A-3. Results File Options Menu ............................. 42 Figure A—4. Dynamic Display Configuration Window ................... 44 Figure A-S. Initial Screen of the Dynamic Display ..................... 47 ix NOMENCLATURE C -Capacitance E - Effort F - Flow F - Force I - Inductance P - Momentum Q - Displacement t - Time V - Velocity X - Horizontal Displacement Y - Vertical Displacement Chapter 1 Introduction 1.1 Problem Definition 1.1.1 Importance of Simulations and Visualization In the past, engineers have analyzed and optimized designs through iterative processes or trial and error. Often, engineers will overdesign in order to reduce the time it takes to test different designs. In some situations, these methods are practical and cost effective. However, in areas where tolerances are low and design specifications are stringent, simulations allow the engineer to test designs theoretically to determine effectiveness without spending money to build the actual design. Simulations are essential to engineering work in order to reduce costs and increase efficiency. In cases where there are opposing design criteria, such as reducing weight while maintaining strength, it would be costly and time consuming to build many models and test them for strength and weight. Simulations provide an engineer with a way to see what designs will most likely be best without the expense and time required to do trial and error testing. 1 2 The simulation results will only be valid if the model is valid. Therefore, modeling is the most important aspect of any simulation. Many computer programs have been designed that will perform simulations by numerical integration. These programs allow engineers to focus their energy into creating valid models instead of creating ways to simulate these systems. Once a simulation has been performed, the engineer has an abundance of information to analyze. In an attempt to understand the physical behavior of systems, various visualization techniques can be used to interpret the results. The most common visualization technique used is viewing of plots of variables versus time. These prove most useful when the behavior of a particular variable or subset of variables is under investigation. However, in large systems, the number of variables of interest may be too large to display with any meaning on a time plot. Some other method of visualization would be helpful. Due to the complexity of designs in such fields as automotive and aerospace, most engineering designs consist of components in several power domains. For example, automobile engines generally have mechanical, rotational, electrical, and hydraulic components. Bond graphs are very well suited to systems that include more than one power domain. Another advantage of using bond graphs for modeling is that the system equations can be obtained directly from the graphical model. Computer software is available to create solutions to bond graph 3 models given system parameters. One such program is ENPORT. This program allows the engineer to create a two-dimensional bond graph model, numerically solve the system equations, and view the results. One method of visualization using bond graph models is to view the magnitude of a variable, such as effort or flow, being displayed as the corresponding bond's width and/or color. This method was successfully implemented in ENPORT in the UNIX environment (Ermer 1994) for both two- dimensional and three-dimensional bond graphs. 1.2 Research Objectives The goal of this research was to implement a system that would enhance the ENPORT PC—DOS environment by providing an additional tool for visualizing the behavior of a physical system. Once the user has created a bond graph model and enters the system parameters, ENPORT generates the system equations, then solves them by numerical integration over a desired time interval. Currently, ENPORT allows the user to output data in a table format or with plots of variables versus time. The new Dynamic Display module will allow for a third kind of output that enables visualization of the dynamic behavior of the system by tying together the bond graph model and the results obtained from simulations. A major 4 goal of this research is to allow an engineer to visualize how the power, effort, or flow moves about the system during a given time. To meet this objective, the current ENPORT Model Builder module was altered to provide a power-related animation directly tied to the system bond graph structure. The Dynamic Display module imports a model file and the corresponding results file from the Model Builder and Solver modules of the PC- DOS version of ENPORT. The animation consists of varying the color and width of the bonds in a two dimensional bond graph model of a system based on the user defined power variable of effort, flow, or power. This research was preceded by line-width variation in ENPORT to display time-averaged power variables on the system graph (Rosenberg and Zhou 1988) and development of a dynamic display of time-varying quantities on the system graph in the UNIX version of ENPORT (Ermer 1994). 1.3 Description of Thesis Organization This thesis consists of an introduction to the problem, examples of the results achieved, presentation of the implemented design, and conclusions concerning this implementation. The current chapter presents the problem and the motivation for the research as well as the order of presentation of the other sections of this paper. Chapter 2 illustrates the concept of dynamic display and its 5 application to the solution and visualization of practical problems. Chapter 3 includes a complete discussion of the Dynamic Display module and the features implemented in response to the problem statement. Finally, Chapter 4 presents a summary of what was accomplished and areas of further research. Appendices are included which contain more detailed information about the examples and the computer program that was used to implement this research. Appendix A contains a user’s manual for operation of the Dynamic Display module in the PC-DOS version of ENPORT. Appendix B contains the code listings for the software used to create the Dynamic Display module. The ENPORT model files for the examples are available in Appendix C. A list of references used to carry out this research is also included in this document. Chapter 2 Visualization Examples Using the Dynamic Display Module 2.1 Mechanical Oscillator Modeling Example In engineering systems, a common component of models of physical systems is a simple mechanical oscillator. To get a basic understanding of how a dynamic display can be useful, the mechanical oscillator as shown in Figure 1 was studied. The system consists of a mass attached to ground with a spring and damper in parallel. This example, while simple, will provide easily visualized dynamic system behavior. \le l:|:J R C l Figure 1. Schematic of a Mechanical Oscillator 7 A bond graph of the system was constructed in the Enport Model Builder module as shown in Figure 2. The physical components and their corresponding nodes are listed in Table 1. The model file for this system, “Mechoscenp”, is located in Appendix C and includes the model description and parameters as well as the equations generated by the Model Builder module. SE (:1 4 1 2 1v Jun 5 :3 l a Figure 2. Bond Graph of Mechanical Oscillator Table 1. Mechanical Oscillator Model Equations Physical Component Node Name Node Type Node Equation Velocity of mass 1V 1 Junction e1+e2+e3+e5 = e4 Applied Force SE Source of Effort e4 = 19.62 Spring C1 Capacitive Element el = 5 . q] Dashpot R Resistive Element e5 = 3 . f5 Inertia of the Mass 1 Inertial Element f3 =p3/2 Backlash C2 Capacitive Element e2 = $1,412; backlash 8 The system equations were solved in the Solver module and results were obtained and stored in the results file, “Mechoscbdt”. The system was numerically integrated by the Runga-Kutta integrator from 0 to 10 seconds with an accuracy of 0.1 seconds. The initial conditions were set to zero and all the variables were saved. Time plots of the results can be seen in Figures 3 and 4, which show the efforts and flows of the bonds over the time record. From these figures, it can be seen that the system has damped oscillations. The two capacitive bonds have efforts that are in phase, but are out of phase with the effort of the inertial and resistive bonds. P — _ '1 Q, 1 .— ”1"" -5 l L I a I L l 4 a nut: Lumen ”ariablc: 1 El 2 22 3 1 21 5 ES flaxlml: 2.12361 2.423401 Z.‘lZl+Ol Z.1ZE+01 2.123481 flint”: -1 .mt-Dl -1 .7BE+D1 -1 .783481 -1 .msfll -1 JOB-81 Figure 3. Efforts of Bonds for Mechanical Oscillator ' l T r I F r . 1 -1 2 3 4 5 L a L 1 A l I 1 i I L in mm LUbfll variable: 1 r1 2 r2 3 r3 1 r4 5 rs llaximn: 3.213430 3.212439 3.21am 3.242439 3.24243 mm»: ammo 4.61m; 4.5412439 4.64249 4.51340 Figure 4. Flows of Bonds for Mechanical Oscillator A dynamic display was created from the model file and the results file. The dynamic display at the initial time is shown in Figure 5. The width and color legends show that the variable being displayed on the bonds is power. The maximum and minimum values of the power during the time record are also shown in these legends. The time legend shows the current time and the time step size between results data. Several times of the dynamic display at varying times are shown in Figure 6 . From these figures, visualization of the transfer of system power between components is possible. 10 COLOR KEY. 0 35402 SE C1 If ml 0. “+00 1 WIDTH MKEY: 100x - 0 35902 50% (A) OX — O .OCEHTD TIME LEGEND: TIME: QMHD ares». 0.10900 GRAPH: Harvard Back Utes Hadron Options List l'lle Return numerical Flztlclp l'Zznone Filmore Human Figure 5. Dynamic Display of Mechanical Oscillator at Initial Time Initially, the system power begins transferring from the applied force to the inertial element. The system power can be seen being dissipated by the damper after about 0.2 seconds. Power begins transferring to the conductive elements as it flows out of the inertial element indicating that the springs are being compressed after about 0.7 seconds. At approximately 1.1 seconds, the system appears to have no power. The conductive elements begin stretching back at about 1.3 seconds. Eventually, all the oscillations will be damped out. ll Time = 0.0 SlE/ ]<. Time = 0.7 Time= 1.5 Time = 0.1 SE C1 Time=1.1 SE C1 Time = 2.0 SE C1 Time = 2.5 Figure 6. Dynamic Display of Mechanical Oscillator Power From this example, the usefulness of the dynamic display becomes clear. The dynamics of the system can be easily viewed and visualized from this type of display. Time plots are somewhat abstract since the only thing that connects them to the 12 system is their labels. The dynamic display, by nature, clearly illustrated the transfer of power throughout the system. 2.2 Flatbed Trailer Suspension System Model In the automotive industry, design of adequate suspension systems that will damp road vibrations is essential. A simulation of a simple flatbed trailer suspension system encountering a hill was performed in order to demonstrate the use of the Dynamic Display module on systems larger than the mechanical oscillator. Figure 7 shows a sketch of a flatbed trailer suspension system model. The flatbed trailer body is modeled as a 4 meter long slender uniform body and the suspension systems are located 0.5 meters from each end. This two-dimensional model assumes that the motion of the flatbed trailer is limited to small angles of rotation and that the tires never lose contact with the ground. A bond graph of the model was constructed using the Model Builder module and can be seen in Figure 8. For this model, the mass was assumed to be evenly distributed across the trailer. The ENPORT model file, “Flatbedenp”, for this example is located in Appendix C along with the equilibrium initial conditions used. l3 front suspensi .3 n front tire oooooooooooo Figure 7. Schematic of Flatbed Trailer Suspension System 14 2M 1M 91 IM .—\-——1 VCT—SEW 1 R0T—————MR0T 13F CSR TF’F CSF w 12F / 9R 9F 11F 1SRq—OSR OSF-——‘-‘~18F 4 I \0: 10R FISFI 8R 8F RSF GR SP M/HRT——-1WHR 1WHF——->IWHF / / SF! SF 7F 7R SEWR 0m OTF SEWF I / fl 2R 1TH 1R 1F 1TF L=R Prflx 4R CTR RTR SFR SPF RTF CTF Figure 8. Bond Graph Representation of Flatbed Trailer Suspension The bond graph model was subjected to a road profile consisting of a small hill. The hill was modeled as a ramp function that was 4 meters wide and 0.2 meters high. The vertical velocity due to the ramp was modeled by a pulse source of flow connected to the front and rear tires. A diagram of the road profile and the corresponding source of flow can be seen in Figure 9. The velocity was input to the fiont tire at the time the ramp was encountered. The same velocity was input to the rear tire after a time delay which is dependent on the horizontal velocity of the flatbed trailer. The delay was calculated for a constant horizontal velocity of 100 km/hr, a typical highway speed. The specific values for the delay and the duration of the pulse are available in Table 2 as well as a summary of the equations used for this simulation. 15 Table 2. Flatbed Trailer Body and Suspension Model Equations Node Name Node Type Node Equation Parameter IM Inertial Element F2 = P2M / MVEH MVEH = 600 kg SEW Source of Effort ElM = WVEH WVEH = -5886 N mor Inertial Element FRI = PRl/JVEH JVEH = 800 kg m2 TFR Transformer F 13R = DR * F14R DR = 1.5 E14R = DR * E13R TFF Transformer F12F = DF * F13F DF = 1.5 E13F = DF * E12F CSF Capacitive Element E1 IF = KSUS * Q1 1F KSUS = 10000 N/m RSF Resistive Element EIOF = DSUS * FlOF DSUS = 1700 Ns/m CSR Capacitive Element E1 1R = KSUS * Q1 1R KSUS = 10000 N/m RSR Resistive Element EIOR = DSUS * F 10R DSUS = 1700 Ns/m IWHR Inertial Element F6R = P6R / MWH MWH = 20 kg IWHF Inertial Element F6F = P6F / MWH MWH = 20 kg SEWR Source of Effort E7R = WWT WWT = -l96.2 N SEWF Source of Effort E7F = WWT WWT = -196.2 N CTR Capacitive Element E4R = KTIR * Q4R KTIR = 180000 N/m CTF Capacitive Element E4F = KTIR * Q4F KTIR = 180000 N/m RTR Resistive Element E3F = DTIR * F3F DTIR = 6000 Ns/m RTF Resistive Element E3R = DTIR * F3R DTIR = 6000 Ns/m SFR Source of Flow FIR = SLOPE; SLOPE = 0.05 FIR = 0; t{ 1 0.05.333/ Figure 9. Road and Corresponding Vertical Velocity Profile To create a dynamic display of power of the system, the model and the corresponding results file were loaded into the Dynamic Display module. Figure 11 shows the power of the system when the front tire initially comes in contact with the hill. The power can be seen moving through the suspension system and up into the body of the trailer in Figure 12. In Figures 13 and 14, the color was varied as well as the width. Both tires are in contact with the hill in Figure 13. The front tire has just reached the top of the hill in Figure 14 and a large power transfer from the spring of 17 the front tire corresponding to the release of some of the power stored in the spring. Figure 15 shows the system right after the rear tire has reached the top of the hill. The power in the rear of the trailer is concentrated in the tire while the power in the front of the trailer is concentrated in the suspension system. As the system begins to stabilize, as shown in Figure 16, the power is shown in the front and rear suspension systems as well as in the body of the vehicle. Figure 17 shows that as the system nears steady state, the rotational power diminishes. WET/1107101. Date: “03/20/95 Tine: Email 1 T u I v I v r f . P i ___.J L- -1 .J i 1 g I . L L l . 0 ma: 1.00 variable: 1 ma 2 an? auxin-u: 3.45.03 3.45am flint-ta: 2.00903 2.00043 Figure 10. Forces on the Front and Rear Tires 2M 1114 F11 IM ———L1vc‘———ssw 1nor ————II~1F101 A TFflF 13F 12R CSR ‘Q 139 Tit-.121: /CSF an 9F 11F __‘. 18H ‘— 039 08F 18F 10F 101:1 RSR 01:1 8F RSF BR 6F I'M-m w————— 11mm 1wr=———Lerr-' an as W 7Fl sewn 0m 0r1= 2F SEWF 1m //21: 13 1F 1TF 4F SFF RTF ‘ ch CTR RTR SFR Figure 11. Power Variable Response for Flatbed Trailer (Time = 0.10 seconds) 2M 1 F11 1111! ‘——1vc—_'Lsew mar ———h-Inor A real: 13F 121% can "a 139 TFF csr= \ 4 12F 1 an r-'—L9F 18F "F 39 ‘—— 033 os 10,, 1011 F139 an a: RSF en 6F MI-m f—— 1an 1WF———LMHF m 51" 7F 71:1 sewn 0m 07? 2F SEWF A \ 1m 1R 11F 1TF 4F A ’3” R crn RTR SFR SFF arr ch Figure 12. Power Variable Response for Flatbed Trailer (Time = 0.18 seconds) 2M 11 F11 IM ewe—Lees» 1Ror—————Llnor 1:31-— TFF CSF 412': 9F % 8F RSF RSF! 8F 8R 1WHF‘ // 1 7’1? 5R \ a." SEWF 1 DIR «SEWF .c ..-:"',:i=er “L. #F firm ""“ “'— 19 $31? 1TF wfij}: 1 3‘3 CTR RTR SFR SFF RTF Figure 13. Power Variable Response for Flatbed Trailer (Time = 0.21 seconds) 2M 1:, R1 IM‘———1vc—n§ssw 1Ror~..-—————mor 13F 1. CSR TFF CSF ‘ 11F! ’7' K 99 4 12F 9F PM": /1SR“m_OSR CSF—L1SF 10F 10R nsn 8F: :31: ‘RSF 6R MHR ‘——-—-—— 1WHR 1WHFq.————MHF / 41$ 15 sewn 0m OTF\ ,3”: £3! 2 :5- 1TR "" :32 1F: 1F 1TF _ ‘33 4F / -R .1 is A 49 ”i CTR RTF-l SFR SPF RTF CTF Figure 14. Power Variable Response for Flatbed Trailer (Time = 0.25 seconds) 20 2M 1 F11 1M ‘———1vcdssw 1am —————Llnor 14R TF5", 131: 129 0310 "a 131:1 TFF 21: CSF 1 S T— OSFI 03F— 15F 10.: A \ FISH 01:1 8F RSF 68 6F MHFI ————h- 1WHR 1WHFT————MHF 5a 6F 7': 7n sewn 0TH OTF 2F SEWF A 1110 11:1 1F 1TF 4': % V" M CTR RTR SFR SPF RTF ch Figure 15. Power Variable Response for Flatbed Trailer (Time = 0.35 seconds) 2M 1 H1 IM ————LIVCASEW IROT -‘—————-IROT 14H "11; 13‘ 12H ”\“1 ‘3" "fix /W a: 11F 138Aosn OSF‘———-1SF m, 11/01:: \ RSR 8R W RSF 6? MHH ‘— 1wH1=1 1WHF‘—————MHF 7H 58 G: SEW 0TH OTF Z: SEWF m \ 1TH 19 1F 1TF 4F 4/411’ '3“ ”N CTR RTR SFR SPF RTF CTF Figure 16. Power Variable Response for Flatbed Trailer (Time = 0.45 seconds) 21 2M 1 F11 IM —LIVCASEW 190T ‘—-———-——-IROT [’4 rear 13F 121:1 can \11: 138 TFF 2F cse 189 A 031:1 03hr:1 9': 1SF‘4 f— 10F 108 nsn an 8F nse I'W‘HR —————h- 1an 1wHF————LIer-' an 5F 7F 71:1 sewn 013 are 2F sewe 21:1 HT! 1 1n 1 1F 1re 4e 43 '33 I \ cm RTR sen see RTF ch Figure 17. Power Variable Response for Flatbed Trailer (Time = 0.55 seconds) From a dynamic display, changes in the sign of data are clearly evident from either the direction of the bond changing or a change in the sign of the label on the bond. In this example, it is very clear when an element is adding or removing power from the system. This can also be very useful for model verification. For example, from a dynamic display of the effort in the flatbed trailer model, one could show that the force in the tires was never negative. The dynamic display provides valuable qualitative information about the system behavior. Information and insight gained from viewing the dynamic display can be utilized best if used in conjunction with time plots. Once a problem area or an area of interesting behaviors is detemiined from the dynamic display, time plots and tables 22 of the data can be used for quantitative analysis of the system. The dynamic display can be used as a method of sorting through the abundance of data generated when numerical simulations of large systems are performed to determine parts of the system that should be analyzed in more detail. Chapter 3 Implementation of the Dynamic Display Module This chapter contains a description of the implemented design and discussion of the reasons for the design choices. Program code referenced in this chapter can be found in Appendix B. 3.1 File Importing The Dynamic Display module requires knowledge of the bond graph model structure and the response data obtained from the computer generated solution of the system equations to produce the dynamic display for visualization. This information is obtained from the Model Builder and Solver modules of Enport. Once the user has created a bond graph model in the Model Builder module and input the system parameters, the system equations are generated. This information is then used by the Solver module to numerically integrate the equations over a desired time interval and obtain the solution. 23 24 3. 1. 1 Importing Model Files Model files are created in the Model Builder module of Enport. The Model Builder module is used to create a bond graph and define the system equations. Once a model has been made in the graphical editor, the system equations obtained from the model can be viewed and edited. In order to solve the equations, they must be sorted by the Model Builder and saved with the bond graph to a model file with the suffix “.enp”. The file “ddfill .for” contains the code that handles model file loading and viewing. The Dynamic Display module needs the information to recreate the bond graph model only. Although the system equations are not loaded, they may be viewed from the Dynamic Display module. This option enables the user to view exactly what equations were solved. 3.1.2 Importing Results Files Results files are binary and have the suffix “.bdt”. They contain the results generated by the Solver module. In the Solver module, the user must specify solution control information such as initial conditions, the type of integrator desired, the time interval, and the time storage interval. Once output variables have been chosen, the Solver numerically integrates the sorted equations obtained from the model file and generates the results file. 25 To create a dynamic display, the user needs to save only effort and flow variables in the Solver module since the dynamic display is limited to effort, flow, or power. If power is desired for display, the user will need to save the effort and flow of every bond that they will want to display since the Dynamic Display module multiplies the effort and the flow to get the power. The program code in the file “ppinflfor” allows for user selection of the results file and the variables to be displayed. Variables desired for display are selected from a list of the variables saved in the results file. Bonds that do not have the correct type of result data available to them will appear gray and have a width of 1 pixel in the dynamic display. The data from the results file will be loaded as needed by the subroutine “getres” in the file “ddispl .for”. This subroutine accesses the results directly by record number based on the time of the results being displayed. 3.2 Dynamic Display Module Features Implemented A configuration must be chosen for running the Dynamic Display module that sets the variables representing bond width and color, the way negative data will be handled, and time advancement. Other viewing options are available when the graph is displayed. Configurations may be set by loading a configuration file or by menu selections. The file “ddcfgwfor” contains the subroutines that implement the file 26 operations and the configuration menu window located under the “Options” menu in the main menu. 3.2.1 Variable Choices and Bond Coding At most, the user may choose to display one of the following types of variables for a given run: effort, flow, or power. This choice was made because when one type of variable is represented by width and another type by color, the display becomes confusing and it is hard to visualize how the system is behaving. This situation would be further complicated by the handling of negative values. Currently, the color and width only represent the absolute value of the variable. Negative data can be indicated by either switching the direction of the bond or by a negative sign appearing by the bond name. If different variables were represented by color and width, 0 choice would have to be made on how to handle negative values for width and color separately. While this can be done, it generates a display that can be more confusing than useful. The width and color of the bonds may be chosen to be constant instead of varying with time. Maintaining a constant width will be useful in cases where the system is very big and larger bond widths distort the graph or cover bond labels. Constant color was provided so that black and white hard copies of the display could be made without having some of the bonds appear gray from grayscaling of the 27 colors. The color can also show the power type. This may be desirable in cases where more than one power domain is present in a system. When the bond width or color is determined by the effort, flow, or power; the maximum and minimum of all the variables selected for display are calculated by the subroutine “getres” in the file “ddispl .for”. The maximum and minimum are found by comparing the absolute value of all the results that will be used in the display. The largest value will be the maximum and the smallest value will be the minimum. The minimum value will usually be zero. The resulting range of the variables is divided by the number of different widths or colors possible to determine the increments between widths or colors. Since different maximum widths may be desired for different size systems, the user can choose the desired maximum width to be between two and eight pixels when width is variable. The maximum width will represent the largest magnitude values of the variable while a width of one pixel will represent the values closest to zero. The subroutine ”findwd" in the file ”ddisp2.for" determines the bond width based on the ratio of the current results to the maximum value of the variable type during the time interval. When the width is constant, the width may be set between one and eight pixels. 28 The color range for variable color includes eight colors with the highest values represented by the lightest color and the smallest values represented by the darkest color. Bond color is determined in the subroutine “findcl” in the file “ddisp2.for” based on the ratio of the current results of the variable to the maximum value of the variable type in the system over the time interval. The colors used to represent the power type are consistent with those in the Model Builder module. When the color is chosen to be constant, the user may pick from a list of 12 colors with which to display the bonds. A legend containing information on the width may be shown on the computer screen during the display. Eight different width legends are shown in Figure 18. Due to the fact that the type of variable being shown is also displayed in the legend, there are 22 width legends possible. For variable width, the legends display what type of variable is being displayed, the scale, and the maximum and minimum of the variable type. When the width is constant, a message indicating this is displayed in the legend. The width legend is drawn by the subroutine “wdlgnd” in the file ”ddispl .for”. There are five possible color legends; three of which are displayed in Figure 19. When the color is determined by power type, the color legend displays the colors and the corresponding power types. A message is displayed if color is held constant. The color legend is drawn by the subroutine “crlgnd” in the file ”ddisp1.for". 29 inTH KEY: wTfiTH KEY: wTOTH KEY: EFFORT EFFORT EFFORT - _ 80% _ — 80x — — 50% 50% — — 40% _ — — 0x —— 0 .00E+00 0x — 0 .00E+00 0x — 0 .00E+00 WIDTH KEY: w_—‘IOTH KEY: M‘DTH KEY: EFFORT EFFORT EFFORT 100% _ 0 .20E+02 1 00% _ 0 .20E+02 1 00% — 0 .20E+02 75x — 67x .— 503 _ 50x — 25x _ 0x —0.00E+00 0x —0.00E+00 0x —0.00E+00 wTOTH KEY: wT‘OT' l-l KEY: EFFORT 100% — 0 .20E+02 0% —— 0 .00E+00 Width is constant. Figure 18. Width Legends Available in the Dynamic Display 30 EDI—'39- KEY’I COLOR KEY: CCILDR KEY: POWER TYPE EFFORT ._ General 1 00% m 0 .1 0E +01 Color is constant. Mechanical I _ Rotational ': Electric-a! 50% Hydraulic Thermal 0% 0 .00E +00 Figure 19. Color Legends Available in the Dynamic Display The time legend displays the time and the time step between results. An example of the time legend is shown in Figure 20. Every time the graph is redrawn, the legend is updated with the new time. The time legend is created in the subroutine “tmlgnd” in the file “ddispl .for”. TIME LEGEND: TIME: 0.?0E+00 STEP: 0.10E+00 Figure 20. Time Legend for the Dynamic Display The user may choose to not show the legends, also. In this case, the logical variable "LEGEND" in the "sysdrw" subroutine will be "FALSE"; and the time will be displayed below the graph instead of in the legend. The width and color legends are not shown at all. The graph will then be displayed on a larger screen which is the 31 same size as the editing screen in the model builder. This option is especially desirable if the user uses the program frequently and is familiar with the legends. 3.2.2 Frame Advancement Options When the dynamic display is begun, the bond graph model initially appears as it does in the Model Builder, scaled to fit the screen; with bond color determined by power type and a bond width of one pixel. Once the dynamic display has been started, the graph will change to show the chosen variables. An example of the Dyamic Display screen can be seen in Figure 21. This screen also allows the user to select viewing options for the display which may include displaying causality, removing the legends, and zooming in on a part of the graph. COLOR 1- [.1 What-l IIPE N 1M R1 IMV—“fllcv—SN 1R01’ -——-——-—AIROT ‘ \\ [II-1R .\ 1’an 13" 129 /\ \ CSR / \ TFF CSF N19 f, 11:: \ 4 1 7? 9H A \. ‘ 3F ,- 11F 188Y——-—-Osn CSF—418}: ‘ IUH ‘ ‘ RSR DR 1}” RSF uAD‘H E 8? Watt“: ormw MHH V———-—- IWHF IWHF———————‘-MHF /y 1 A \ “F { //’ ‘H “a 5; \ / ‘\_ SM _OTFI OTF ‘ ”F SM l/AH/ A \\_‘ _1TR 1R 1r 1TF_ 4r 4”; W '3‘ \\\ C R 11 SFR SFF RTF CTF Figure 21. Dynamic Display Module Graphical Display 32 When the user wants to be able to proceed through the time record at leisure, manual frame advancement may be chosen. This allows the user to move forward or backward through the time record of the results step by step. At each time step, the results are read in using the subroutine “getres” and the system is redrawn by the subroutine “sysdrw”, which calls many other subroutines. While moving through the time record, the user has many options available in menu form, such as zooming in or out or displaying the causality of the bonds. These options will be discussed further. To facilitate animation of the results, automatic frame advancement is available. If this is chosen, the user may then enter the desired time between frames. This time can be anywhere between 0.00 and 9.99 seconds. In this way the user could choose the time advancement to occur with spacing equivalent to the time step between results and thus see the results in real time. If the results cannot be displayed as fast as desired, the results will be displayed as fast as possible. The subroutines ”settim” and ”gettim” are used In the suboutine "ddcntr' to keep track of the time. When the final time is reached, the last result will be displayed along with a menu of options similar to that for manual frame advancement. 3.2.3 Drawing the System Since bond width may vary, depending on the user choices, a new bond was designed. To make bonds of varying widths, a polygon function is used. The resulting 33 bonds have a closed arrow head, as can be seen in Figure 22. The subroutine “drarow” in the file “ddisp2.for” determines the indices of the arrow based on the desired width and endpoints of the bond. For cases where there are no interior points, the polygons are also drawn by this subroutine. ” 111 Figure 22. Examples of Bonds of Varying Widths When there are interior points in a bond, that is, the bond is not straight, the line segments are sent to the “drarow” subroutine and the points on each segment are determined. These points are saved in an array for all the line segments and then sent to the subroutine “inter”, which determines the intersections of the line segments and draws the resulting polygon. Examples of the resulting bonds are shown in Figure 23. Figure 23. Examples of Bonds with Interior Points 34 3.2.4 Options Available During Display For large systems, it is often desirable to look at small parts of the system. When the system bond graph is initially displayed, it is scaled to fit the window. The user can then change this view by zooming in on a desired portion of the graph. The view may also be changed by moving to the right, the left, up, or down. A zoom out option is also available as well as an option to frame the graph by sealing the system graph to fit the window. The subroutine “gfzoom” was used to implement these viewing features. If for some reason the graph does not look as it should, a redrawing option is available that calls the subroutine “redraw”. This subroutine redraws the system graph and the legends. In some cases it is desirable to add some things to the graph, such as causality. There are options available to the user to choose the grid visibility, the flame visibility, the causality visibility, whether to show the node color, whether to show the legends, and whether to show the connector labels. The subroutine “gfopts” in the file “ddisp4.for” sets logical variables from the user choices, which are then used by “ddcntr” to vary the display. When visible, the grid will appear as white dots on the graph. When the frame is not visible, the frames around the legends will remain, but the frame around the graph will not. The causality is shown with a causal stroke in the 3 5 same color as the bond. When the node color is shown, the node color represents the power type of the node. When the legends are shown, they will appear on the right side of the screen. The option of not showing the connector labels was provided for convenience when the system is large. Removing the connector labels can help unclutter a graph if the labels are covering up bonds, etc. Information about the nodes and connectors is available to the user during the Dynamic Display through use of the subroutine “gflist”. A list of the nodes and connectors can be shown as well as the node and connector attributes. The node- connector list displays each node and its corresponding connectors. The node attributes list displays information about the node including: its type, its power type, its location on the graph, and its visibility. The connector attributes list shows the starting and ending node of each connector, the type and power type of each connector, and the visibility of each connector. Chapter 4 Conclusions 4.1 Summary of Contributions The research work completed has significantly increased the usefulness of the PC version of Enport by tying visualization of the results to the bond graph model structure. The principal research objective of implementing a system in the PC-DOS environment that will display the dynamic response directly on the system bond graph model has been achieved. The Dynamic Display module provides the link between the system bond graph structure and the dynamic response of the system. This link allows the engineer to take advantage of the knowledge that bond graphs supply about system behavior through the visualization provided by the dynamic display. Since the whole system response can be viewed at once, model verification is easily done, as well as gaining insight about the model behavior. Complex system behaviors can be easily shown through use of this display. The primary functions implemented in the Dynamic Display module were: 1) loading of bond graph models into the Dynamic Display module; 2) loading of results 36 3 7 from results files into the Dynamic Display module; 3) multiplication of effort and flow to obtain the power when desired; 4) seven different scaling options for width; 5) constant color and width options; 6) a color by power type option; 7) bond width and color variation for a bond graph display of variables as if they were flowing on the graph; 8) time controls necessary to control the animation manually or automatically; 9) two options for handling negative values; 10) viewing controls that provide control of the size of the bond graph and what is shown on the bond graph. Two engineering system examples, a mechanical oscillator and an automobile suspension system, were developed to demonstrate the application of the Dynamic Display module. 4.2 Areas for Further Research Several areas have been identified as possibilities of firture research. Most of these pertain to improvement of the display allowing more user control and a higher quality display. The following areas warrant further research. 1. In some cases it may be desirable to have different scaling options for different power types. Some power domains, such as hydraulics, have small powers relative to the other domains. This may cause the power to be shown as close to zero on the hydraulic bonds for the entire time record. It is suggested that until this feature is implemented, choosing the bonds of only one power type at a time for display will eliminate the problem. 38 2. It would be desirable to only redraw the bonds that change for each time step. This is especially desirable for large systems where the redrawing of the system is most noticeable. In the Dynamic Display module, the entire visible graph is redrawn at each time step. Reducing the number of items to redraw at each time step would decrease the minimum time step possible, since the minimum time between frames is limited by the time it takes to draw the system. 3. Logarithmic scaling would be usefirl for systems whose results’ magnitudes are logarithmically spaced. In these cases, a linear scale tends to make most of the results that are smaller than the maximum value appear close to zero. 4. Signal variables are not displayed in this module. However, there is code available in the subroutine “drarow” in the file “ddisp2.for” to generate signals of differing width and color, just as the code to generate bonds does. The only difference between the signal and bond drawing techniques is that a signal can never switch directions and therefore negative signal data is always indicated by a negative sign in front of the signal name. 5. In the future, it would be desirable to allow the user to edit the bond graph in the Dynamic Display module. Utilities could be created to allow the user to move or delete the legends and the connector labels. Another feature that would be useful would be to allow the user to move the nodes without removing the connectors, or to 39 add interior points to a connector. These features would be especially useful for large systems where the dynamic display may be very cluttered. 6. Allowing the user to select subsets of the time record for display would be useful as well as allowing the user to choose the time step between displayed results. Without forcing the solution to be calculated in the Dynamic Display module, these features could be implemented if the user was limited to pick an initial and final time that was in the time record saved and a time step that was an integer multiple of the time step between saved results. 7. It would be very desirable to allow the user to click on a connector with the mouse and display the exact value of the variable being displayed at that time. This would greatly improve the quantitative information given by the dynamic display. Other options such as some type of indication of when a connector reached its maximum value would be desirable also. 8. Allowing the user to select the number and order of colors in the color legend would be useful since there is not an obvious order of colors that makes sense. Graphic tools could be implemented that would allow the user to select from a wide range of colors, including shades of the same color. APPENDICES Appendix A User's Guide The following section can be used as reference for running the dynamic display environment. Information on the functions available is located under the appropriate headings. Most selections may be made with either the mouse or with keyboard strokes. Starting the Dynamic Display Module. The Dynamic Display Module can be loaded by typing "DD” and pressing “Enter” at the DOS prompt in the "Enptdev" directory. Pressing any key will cause the Enport logo screen to disappear and the main screen to appear with the line menu at the t0p of the screen as shown in Figure A-l. The menu at the top of this screen provides the functions of loading model and results files, setting the controls for the display, and opening the graphical display screen. The last line of the screen shows the option keys and their functions. These keys work almost everywhere in the Dynamic Display Module. M Figure A-l. Main Menu for Dynamic Display 40 41 Importing of Enport Files In order for a dynamic display to be made, a model and the corresponding results file is needed. The model file is imported from the Model Builder Module and the results file from the Solver Module of Enport. Model Files Operations. Selecting ”Model File" from the top line of the main screen will bring up a window containing model file options as shown in Figure A-2. The ”Load a file" option opens a window containing the names of the files currently available. To view the file without loading it, select the "Show file contents" option and the list of the available files will appear. If the desired file is not on the list, select "Add a file" to add the filename to the list. There will be a prompt for the path and the filename, which must have the suffix ”.enp". The "Delete file" option allows the user to remove a filename from the list. To exit the model file options menu, select "Return" or press the function key “F2”. Figure A-2. Model File Options Menu 42 Results File Options. Selecting "Results file" from the top line of the main screen will bring up a window containing results file options as shown in Figure A-3. The "Load variables" option opens a window listing the results files currently available. When a file is selected from the list, a window with the variables saved in the file appears. All desired results for display purposes should be selected from this list. The "Scan file" option allows a results file to be chosen from the current list for scanning purposes. The information that will be shown includes: information about the file and what model it pertains to, solution control information, and a list of the saved variables. When one of these files is selected, the results file will be displayed on the screen. If the desired file is not on the list, select "Add a file" to add the filename to the list. A prompt will appear for the path and the filename of the file. The filename must have the suffix '.bdt' to indicate it is a results file. The "Delete file" option removes a filename from the file list. To exit the "Results File Options" menu, select " Return" . Figure A-3. Results File Options Menu 43 Setting the Display Configuration Display configurations may be created or they may be loaded from a file. If no configuration is chosen, the default configuration will be loaded at display time. Loading 0 Configuration File. Selecting "Display Options” from the main screen will bring up a window displaying the configuration file options for the display. The configuration may be loaded from a file or selected by several menu choices. The ”Load file" option opens a window listing the configuration files currently available. Selecting a file causes the file to be loaded. Making a New Configuration. Select "Show configuration” from the "Display Options” menu to display the current configuration as shown in Figure A-4. If no file has been loaded, the default configuration will be shown. Move through the configuration menu using the "Tab" key to go forward or both the ”Shift" and "Tab" keys to go backwards. The mouse can also be used to select a field. To leave the configuration window and save the changes, select "Done". Select "Cancel" to exit the configuration window without saving the changes. To reset the configuration to the original configuration, select ”Reset". Figure A-4. Display Configuration Window Width Options. The "Width by:" option in the "Show configuration" window allows for specification of whether the width of the bonds will represent effort, flow, power, or be constant. The selected option is displayed. To see another selection, move through the options using the up and down arrows on the keyboard. To choose a menu item, press “Enter” or click on it with the mouse. If constant width is chosen, the desired width can be set to integer values between 1 and 8 pixels with the "Width (if const):" option. Ifthe width is not constant, the maximum width can be set to and integer between 2 and 8 pixels using the "Maximum Widthz" option. Color Options. Selecting the "Color by:" option from the "Show configuration" window allows for the specification of whether the color will represent power type, effort, flow, power, or be constant. If the width was not constant, the 45 user will be limited to choose color to either represent the same variable as width, the power type, or remain constant. When the color is chosen to be constant, the color may be selected with the "Color (if const):" option. Negative Data Handling. To choose how negative results should be represented, select ”Direction" or ”Negative Sign” from the "Negative Dataz" option in the "Show configuration” window. If "Direction” is chosen and the data is negative, the direction of the bond will change. If "Negative Sign” is chosen, negative data will be indicated by a negative sign in front of the bond label. Timing Options. The "Frame Advancement” option from the "Show Configuration" window allows for the choice of ”Automatic" or ”Manual” frame advancement. When ”Automatic” frame advancement is chosen, the time between frames should be entered from the keyboard at the ”Tirningz" prompt. The value is entered in seconds and hundredths of a second. Values between 0 and 9.99 seconds are allowed. Saving 0 Configuration to a File. Selecting "Save to file” from the "Display Options" menu allows the user to save the current configuration to a file. The user will be prompted for a path and filename. The filename must be 8 characters or less with the suffix '.cfg' to indicate that it is a configuration file. Selection of the ”Save as 46 Default” option will cause the current configuration to be saved to a file called 'Defaultcfg'. This will overwrite the existing default file. Adding and Deleting Configuration Files. Select "Add a file" to add a filename to the current configuration file list. There will be prompts for the path and the filename of the file. The filename must have the suffix '.cfg' to indicate it is a configuration file. When "Delete file" is selected, the current list of configuration files will appear. To delete a file, select the file to be deleted and press return. Viewing the Dynamic Display When "Graph" is selected from the menu line at the top of the screen, the bond graph model will appear on the screen as shown in Figure A-5. Power type will be shown by the color of the bonds and the bond width will be 1 pixel. The Dynamic Diplay will be started by selecting “Start” or “Forward” from the line menu below the graph. The following legends are shown on the screen with the dynamic display: a color legend, a width legend, and a time legend. The color legend displays what the color represents and shows the maximum and minimum values of the data for cases where the color represents effort, flow, or power. The width legend shows what width represents and the maximum and minimum values of the data for 47 cases where the width is not constant. The time legend shows the current time and the time step size once the dynamic display has begun. COLOR KEY: POWER TYPE SE C1 4 1 MOTH KEY 7 2 Whlscmstn 1V————-‘C2 5 3 y TIME LEGEND: TIME: 0.01%!) STEP. 010e+00 GRAPH: iForuard Back Uicu Redraw Options List File Return Figure A-S. Initial Screen of the Dynamic Display Module Automatic Frame Advancement. If automatic frame advancement was chosen, the menu at the bottom of the screen will appear and include the following options: "Start", ”View", "Redraw", "Options", "Lists", "File", and "Return". Selecting "Start" will cause the dynamic display to begin. The results will be displayed at the user specified rate. However, if the user specified rate cannot be achieved, the program will display the results as fast as possible. At any point during the automatic advancement, the display may be canceled by pressing "Escape". When the final time 48 is reached, the manual frame advancement menu will appear. The user may then select ”Return" to leave the display or choose among the menu items. Manual Frame Advancement. If manual frame advancement was chosen, the list of options will be the same as for automatic frame advancement except that "Forward" and "Backward" will appear instead of "Start". "Forward" is selected to advance manually through the results by the specified time step. "Backward" allows the user to go back steps in increments equal to the time step. At any point during the display, the user may select any of the other menu items. View Options. When ”View" is chosen from the line menu displayed below the graph, a new menu will appear. The user can then choose to zoom in on a specific area, zoom out to see more of the graph, or adjust the view up, down, right, or left. Display Options. Selecting "Options" from the menu causes a list of options to appear. These options include: "Grid visible", ”Frame visible", "Causality visible", "Show node color", "Show legends", and "Show conn label". They may be chosen by entering an "x” in front of ”Y" for yes or ”N” for no. List Features. Several lists are available for view when "List" is chosen. These lists include: ”Node-connector list”, "Node attributes", and "Connector attributes". When one of these lists is chosen, a window will appear that contains the list. 49 Leaving the Dynamic Display Module The Dynamic Display module must be exited from the main screen. Selecting "Leave” from the top line menu or pressing the ”F2” function key will cause exiting fi'om the module. Appendix B Program Code The software developed for this application is stored in several files in the directory “c:\enptdev\jlo\dddev\src\dd”. It is necessary to compile this code along with the ENPORT library routines. What follows is a listing of the FORTRAN language code used to implement the Dynamic Display module. 50 51 mozxmo I QOEmDU “DozxmovaOZOmQH>Hmm u me ecu enaaofluficH Intro 0 h n 0H3m mH 02m .0. n muozox mmam .m. H ,n—‘HUZOZ ZmEP A anAOUDOAthVV + .Qz<. Adquuxzmm .mz. AmOaHZOZ.U>hxva + .DZfl. AmOJOUm .mz. AkaHZOZ.U>hxwvv v mH mH sz xoqoommmmm n DOmeD .(Om. I mswzoz mmqm moqooofimmd>m u QOZXmU .. u dHHZOZ 2mmh Am .Om. Amm9m4Q4.U>kav V mm omoexmhw u oozhxe .mm44u. u AmemO .mqum. B ogmomo m n HHZDmm auoU Mmzxoo 050m DCfiMWQ IIIIU U mH QZm EquOHQ oucc«2uow m com 0900 cyan: so asam m “om.H.H.n.fl.m4mmmxvqumpmmeHmz qqHOE..H.VFZOWBMW fl WDH.H.uammmzvqumemmeH¢3 gqmV.mz.AmmHmHxavv + .Qz<. 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Improving Engineering System Design Through Scientific Visualization Methods. Ph. D. Thesis. Michigan State University: East Lansing, MI, 1994. Rosenberg, R. C. and D. C. Kamopp. Introduction to Physical System Dynamics. New York, NY: McGraw-Hill, 1983. Rosenberg, RC. and T. Zhou. “Power-Based Model Insight.” Presented at the Winter Annual Meeting of ASME, Chicago, IL, Nov. 27 - Dec. 2, 1988. Zhou, T. Improving Design Assessment and Simulation of Large-Scale Dynamic Systems. Ph. D. Thesis. Michigan State University: East Lansing, MI, 1988. 161