`

POWER MANAGEMENT AND DAMAGE ASSESSMENT TECHNIQUES
FOR SELF-POWERED SENSING BASED ON PIEZOELECTRIC
TRANSDUCTION
By
Mohamed Rhimi

A DISSERTATION
Submitted to
Michigan State University
in partial fulfilment of the requirements
for the degree of
Civil Engineering- Doctor of Philosophy
2013

ABSTRACT
POWER MANAGEMENT AND DAMAGE ASSESSMENT TECHNIQUES FOR
SELF-POWERED SENSING BASED ON PIEZOELECTRIC TRANSDUCTION
By
Mohamed Rhimi
A major obstacle toward efficient health monitoring systems is the ability to accurately
predict the remaining life of the monitored components. Several commonly used remaining life
prediction models rely on empirical data which limits their applicability. Furthermore, the large
scatter in material data, i.e., fatigue, combined with limited instrumentation capabilities has
hindered the development and validation of improved prediction models. Thus, there is a need for
adequate long-term continuous monitoring techniques capable of rendering a more precise and
reliable stream of data. This would enhance the modeling proficiencies and would ultimately help
reduce maintenance cost, improve the longevity, and enhance the safety of civil infrastructures.
Wireless sensors and sensor networks are emerging as substitutes for traditional tethered
monitoring systems. A major consideration in using a dense sensor array for long term monitoring
is the power availability and management. Piezoelectric energy powering has the advantage to act
both as the sensor and as the powering means, thereby reducing the sensors’ power requirement.
Improving the efficiency of piezoelectric power harvesting from civil structures ambient
vibrations, while obeying environmental constrains (temperature variation) is the first objective of
this thesis. The application of a variable preloading condition is used as a solution to modify the
cantilever piezoelectric harvester’s properties. A generalized system model is derived. Measured
acceleration recordings from a concrete bridge decks under ambient loading and recordings from
extreme events are used to show the gain in harvested energy when the harvester is in a preloaded

configuration. The effects of temperature variations on the piezoelectric (PZT) harvested energy
from civil structures are also studied. A proposed mechanical tuning, based on the application of
an axial load using Shape Memory Alloy to compensate the temperature effect, is presented.
The work required for the deployment of a long-term piezoelectric based monitoring
system, with all necessary attributes, is also described. The calibration and installation of the sensor
is addressed. Damage prediction abilities of the long term self-powered continuous monitoring
system are evaluated considering full field data generation and interpolation issues. Sensor specific
data interpretation techniques are developed and evaluated under laboratory conditions. The
developed methods are based on tracking the variation with respect to time of the damage index,
which strongly correlates to damage evolution if the sensor is in the influence zone of the
monitored damage mechanism.

Copyright by
MOHAMED RHIMI
2013

TO MY FAMILY

v

ACKNOWLEDGEMENTS

I would like to express my gratitude to Dr. Nizar Lajnef for his guidance throughout my
study at Michigan State University and I would like to extend my appreciation to Dr. Karim Chatti
for his valuable advice and support. I also would like to thank also Dr. Tom Pence and Dr. David
Grummon for reading my thesis and for their valuable comments.
I would like to acknowledge Dr. Nicholas Brake for his assistance with damage prediction
models literature, and his concrete beam testing results.
Finally I would also like to thank all the graduate and undergraduate students at the Civil
and Environmental Engineering Department (CEE) at Michigan State University.
Research in this dissertation has been supported in part by the FHWA grant DTFH61-08C-00015.

vi

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... ix
LIST OF FIGURES .......................................................................................................................x
CHAPTER 1: INTRODUCTION.................................................................................................1
Motivation...................................................................................................................................1
Piezoelectric Energy Harvesting from Civil Structures for Self Powered Sensing .............4
Self Powered Long Term Monitoring System and Damage Prediction ................................9
Objective and Overview ..........................................................................................................11
CHAPTER 2: TUNABLE PIEZOELECTRIC ENERGY HARVESTING FROM CIVIL
STRUCTURE ...............................................................................................................................13
Introduction ..............................................................................................................................13
General Model of Axially Preloaded Bimorph Piezoelectric Energy Harvester................14
System Configuration ..........................................................................................................14
Effect of Preloading on the Harvester Governing Equations ..........................................16
Experimental Setup and Model Verification.........................................................................20
Experimental Setup .............................................................................................................20
Model Verification and Experimental Results ..................................................................22
Tunable Energy Harvesting from Ambient Vibrations in Civil Structures .......................26
Maximum Harvestable Power Using Preloaded Harvester .............................................26
Tunable Energy Harvesting from Civil Structures ..........................................................28
Conclusion ................................................................................................................................34
CHAPTER 3: PASSIVE COMPENSATION OF TEMPERATURE EFFECT ON
PIEZOELECTRIC ENERGY HARVESTING FROM VIBRATION ...................................36
Introduction ..............................................................................................................................36
Temperature effects on the response of a bimorph piezoelectric energy harvester ..........37
Effect of Temperature on the Material Properties ...........................................................37
Effect of Temperature on Piezoelectric Energy Harvesting from Vibration .................40
Temperature effects correction using axial preloading........................................................43
Experimental Setup .............................................................................................................43
Preliminary Result: Temperature Compensation Using Preload ...................................45
Passive self-tuned harvester using shape memory alloy effect ............................................47
Passive Self-Tuned Harvester Design.................................................................................47
Self-Tuned Vibration Energy Harvester ...........................................................................50
Numerical Analysis ..............................................................................................................52
Experimental Results and Validation ................................................................................56
Conclusion ................................................................................................................................57
CHAPTER 4: PIEZOELECTRIC BASED SELF POWERED SENSOR FOR STRAIN
MONITORING ............................................................................................................................59
vii

Introduction ..............................................................................................................................59
Piezoelectric floating gate Self Powered Sensor ....................................................................59
Sensor description ................................................................................................................59
Sensor Output under Service Load ....................................................................................64
Sensor Calibration and Initial Testing...................................................................................65
Sensor Calibration ...............................................................................................................65
Experimental Setup and Initial Testing .............................................................................66
Initial Fatigue Testing..........................................................................................................69
Sensor Network ........................................................................................................................70
Probability Density Function of the Loading Distribution Parameters .........................71
Results and discussion .........................................................................................................75
Conclusion ................................................................................................................................77
Chapter 5: DAMAGE PREDICTION USING PIEZOELECTRIC SELF POWERED
SENSOR........................................................................................................................................78
Introduction ..............................................................................................................................78
Damage Index Derivation .......................................................................................................78
Experimental Setup and Damage Index Distribution ..........................................................80
Experimental setup ..............................................................................................................80
Damage index distribution ..................................................................................................82
Remaining Life Prediction ......................................................................................................84
Linear Damage Accumulation ............................................................................................84
Survivability analysis ...........................................................................................................86
Probability density function of the damage index at failure ....................................... 86
Survivability function ..................................................................................................... 87
Results .............................................................................................................................. 88
Conclusion ................................................................................................................................91
CHAPTER 6: CONCLUSION AND RECOMMENDATIONS ..............................................92
BIBLIOGRAPHY ........................................................................................................................94

viii

LIST OF TABLES
Table 1. Piezoelectric properties used in simulations. ............................................................. 15
Table 2. Optimized maximum collected energy for axially loaded and unloaded beam
harvester configurations ............................................................................................................. 31
Table 3.. Material properties of the SMA wires used in the simulations. .............................. 52
Table 4. Predicted remaining life using calibrated coefficient and the sensor output. ........ 85
Table 5. Estimated remaining life using the different fitting shape function ........................ 89

ix

LIST OF FIGURES
Figure 1. Frequency Response of PZT Beam Loaded in the Strain and Vibration Modalities
......................................................................................................................................................... 6
Figure 2. Experimental results of the output voltage amplitude, versus the excitation
frequency and the temperature under 1 g base acceleration. (Mtip=3.75g, load
resistance=1MΩ, P=-2N) .............................................................................................................. 8
Figure 3. Schematic depiction of a cantilever bimorph piezoelectric vibration scavenger of
length (L), width (b), and height (h+2a), subjected to axial loading. ..................................... 16
Figure 4. (a) Test setup, loaded piezoelectric bimorph beam with attached tip mass; (b)
experimental apparatus mounted on a shaker for testing (For interpretation of the references
to color in this and all other figures, the reader is referred to the electronic version of this
dissertation). ................................................................................................................................ 21
Figure 5. Predicted and measured output voltage across a 10MΩ resistance (a)
Frequency=40Hz, axial preload=-2N, tip mass=3.75g, (b) Frequency=37Hz, axial preload=6N, tip mass=3.75g ...................................................................................................................... 23
Figure 6. Variation of the first mode damping ratio with respect to applied axial loading . 24
Figure 7. Output voltage transfer function of the transducer under different preload
conditions. Mtip=3.75g, Load resistance=10MΩ. (solid: theoretical, dots: experimental). . 25
Figure 8. Resonant frequency variation with respect to applied axial loading for different tip
mass (resistance R=10MΩ) ........................................................................................................ 27
Figure 9. Maximum generated power with respect to applied axial loading for different tip
mass (resistance R=1MΩ). ......................................................................................................... 28
Figure 10. (a) Frequency spectrum for the acceleration measurements from the deck of a
concrete bridge under traffic loading, (b) Variation of the output energy as a function of the
applied preload subject to the recorded bridge accelerations (resistance R=1MΩ)............. 30
Figure 11. (a) Acceleration time-history from the 1985 Valparaiso earthquake, (c) Output
energy with respect to tip mass for a loaded and unloaded system subject to the 1985
Valparaiso earthquake acceleration signal ............................................................................... 33
Figure 12. Average power output generated by a piezoelectric harvester (Table 1) subject to
a set of example earthquake accelerations events for both the unloaded and with applied
optimal axial loading configurations (Table 2) – 1: Llolleo, 2: Elcentro, 3: El Salvador, 4:
Northridge, 5: Uttarkashi, 6: Rapel, 7: Arthur Pass, 8: Dharmsala, and 9: Xiang. ............. 34
Figure 13. Temperature dependence of the elastic modulus of PZT-5H ............................... 38
x

Figure 14. Temperature dependence of (a) the dielectric constant of PZT-5H and PZT-5A
(Hooker, 1998), (b) the piezoelectric coefficient d31 of PZT-5H and PZT-5A (Hooker, 1998).
....................................................................................................................................................... 39
Figure 15. Test Setup: (a) loaded piezoelectric bimorph beam mounted on a shaker, with the
SMA springs, (b) experimental apparatus enclosed in an environmental chamber............. 41
Figure 16. Numerical results and experimental measurements of the output voltage
amplitude versus the excitation frequency at different temperatures, under a 1g base
acceleration. (Mtip=3.75g, load resistance=1MΩ) ................................................................... 42
Figure 17. Variation of the first vibration mode damping ratio with respect to temperature
....................................................................................................................................................... 43
Figure 18. Temperature compensation for a variation from the 20o C reference to (a) 0o C,
(b) 40o C. (Mtip=3.75g, load resistance=1MΩ) ......................................................................... 46
Figure 19. Schematic depiction of a piezoelectric beam with attached SMA axial loading
mechanism, (a) compression mechanism, (b) tension mechanism. ........................................ 49
Figure 20. SMA induced load versus temperature .................................................................. 52
Figure 21. Voltage transfer function versus temperature, (a) without SMA axial load, (b)
with an axial load compensator for a temperature increase ................................................... 53
Figure 22. Variation of the resonant frequency with and without SMA induced load (arrows
indicate the direction of temperature variations) .................................................................... 55
Figure 23. Output voltage transfer function of the transducer at 60 oC with and without SMA
induced axial loading. Mtip=3.75g, Load resistance=1MΩ. ................................................... 56
Figure 24. (a) Full sensor embedded in an epoxy package, (b) CMOS floating gate sensor.61
Figure 25. Illustration of the level crossing cumulative time counting implemented by the
sensor............................................................................................................................................ 63
Figure 26. Schematic of a piezoelectric strain scavenger of length L, width b, and height h
....................................................................................................................................................... 65
Figure 27. Voltage transfer function of a PZT piezo under 50 micro-strain loading across 50
mega-ohm load resistance .......................................................................................................... 66
Figure 28. (a) Piezoelectric transducer embedded in epoxy then bounded to concrete, (b)
Bending test setup to check the activation strain loss from a configuration to another. ..... 67
Figure 29. Cumulative distribution of strain duration expressed in term of voltage. .......... 68

xi

Figure 30.Strain distribution at different life stages: (a) at 25000 cycles, (b) at 40500 cycles.
....................................................................................................................................................... 69
Figure 31. Fitting of the sensor’s output at different life stages of the specimen: (a) at 25000
cycles, (c) at 40500 cycles. ........................................................................................................... 70
Figure 32. Pavement cross-section with sensors installed at the bottom of the HMA layer 72
Figure 33. Schematics of the likelihood maximization algorithm .......................................... 74
Figure 34. Theoretical and estimated density functions of the three parameters using the 10
sensors. (a) mean. (b) cumulative loading time ........................................................................ 76
Figure 35. Least square estimation error of each of the parameters' distributions versus
number of deployed sensors ....................................................................................................... 77
Figure 36. Test setup: the sensor is installed in the bottom of the concrete specimen to
measure the induced tensile strain. ........................................................................................... 81
Figure 37. Probability distribution of the damage coefficient versus the number of cycles of
loading .......................................................................................................................................... 83
Figure 38. (a) Variation over time of the mean of the damage index versus the exact damage
index evaluated with the COD gage, (b) Variation of the variance of the damage index
distribution. ................................................................................................................................. 83
Figure 39. Probability density function of the damage index at failure ................................ 86
Figure 40. Normalized estimated remaining life vs. normalized specimen’s lifetime using
three different methods, (a) first specimen (b) second specimen............................................ 89

xii

CHAPTER 1: INTRODUCTION

MOTIVATION
One major obstacle facing health monitoring systems is the ability to accurately predict
remaining life after structural state diagnosis. Today, many remaining life prediction models rely
on empirical data which limits their applicability. Moreover, the large scatter in material data, i.e.,
fatigue, combined with archaic instrumentation has hindered the development and validation of
improved prediction models. There is a need for long term continuous monitoring techniques
capable of rendering a more precise and reliable stream of data that would enhance the modeling
proficiencies and would ultimately help reduce maintenance cost, improve the longevity, and
enhance the safety of civil infrastructures.
In recent years, there has been an increasing interest in the adoption of emerging sensing
technologies for instrumentation within a variety of structural systems. Wireless sensors and sensor
networks are emerging as sensing paradigms that the structural engineering field has begun to
consider as substitutes for traditional tethered monitoring systems. Lynch et al., 2006, Watters et
al., 2003 and Cho et al., 2008 summarized the most newly developed and adopted wireless sensors;
where the wireless sensors are not sensors, but rather are autonomous data acquisition nodes to
which traditional structural sensors (e.g. strain gages, accelerometers, linear voltage displacement
transducers, inclinometers, among others) can be attached. However the adopted technology does
not appear to have kept pace with other technological improvement (Lajnef et al., 2011). The

1

existing monitoring approaches remain rather reactive than proactive in terms of detecting damage,
since they merely record the distress that has already appeared. They either require significant
personnel time or the use of costly equipment. Thus they can only be used cost-effectively on a
periodic and/or localized basis. The current technology does not allow for continuous long-term
monitoring and the deployment of existing systems on a network level remains infeasible due to
cost, unease of installation, and data collection techniques.
A major consideration in using a dense sensor array for long term monitoring is the problem
of providing power to the sensors. If the only way to provide power is by direct connections, then
there is no need for wireless protocols. To date, batteries have been the primary means of powering
wireless devices. Battery power can last anywhere from a few days to 10 years. For practical
infrastructure monitoring, it is desirable that the sensors last the service lifetime of the structure;
typically, a structure’s lifespan is several decades, but it can be as long as 100 years. Even with
the continued trend of decreasing the power consumption of electronics, it is likely that battery
self-discharge would limit the useful lifetime of any sensor to 10 years. In the cases of remote
structures and embedded sensors, it is impractical and costly to change batteries periodically
through the lifetime of the structure. The problems associated with powering wireless sensors have
led several research groups to investigate self-powering as a means of providing continuous power
to remote sensors (Elvin et al., 2006).
A possible solution to the problem of localized power generation is technologies that enable
harvesting ambient energy to power the instrumentation (Roundy et al., 2002; Rahimi et al., 2003;
Sodano et al., 2004; Elvin et al., 2006; Lajnef et al., 2008), where a myriad of potential selfpowering energy sources have been identified (e.g., solar power, thermal gradient, piezoelectric,
vibration and acoustic).
2

It is estimated that the amount of harvestable energy from solar and thermal gradient is not
enough to power a sensor. A piezoelectric powered sensor can, on the other hand, provide a reliable
energy source that is a function of the input mechanical loading experienced by the monitored
structure, making it a reliable embedded energy source.
As shown by Elvin et al. 2006, piezoelectric energy powering has the added advantage to
act both as the sensor and as the powering means, thereby reducing the power requirement and
cost of the sensor system. The piezoelectric transducer can generate large voltage signals (> 10 V),
but exhibit limited current driving capability (< 1μA), limiting the level of extractable power. But,
this ideally combines with the intrinsic properties of analog floating memories that can operate at
very low current levels (pico-amperes).
A CMOS floating gate is a poly-silicon gate surrounded by an insulator, which in standard
semiconductor fabrication process is silicon-dioxide. The charge on the gate can be modified using
hot electron injection or through tunneling. Injection in a pMOS transistor occurs primarily due to
hot-hole impact ionization caused by high electric fields at the edge of the drain-to-channel
depletion region. As electrons are added to the floating gate its potential decreases, thus
implementing a long term non-volatile memory.
Based on the described technology, the sensor was developed, tested and calibrated (Lajnef
et al., 2007). Measured results from a fabricated prototype in a 0.5 μCMOS process have
demonstrated that the processor can sense and measure the piezoelectric output voltage subjected
to strain loading. It measures the output voltage in a series of memory cells. Each cell records the
cumulative duration when the piezoelectric output-voltage exceed a preset level. This direct use of
the piezoelectric input signals allows the sensor to be self-powered and it can operate at very low
power levels.
3

PIEZOELECTRIC ENERGY HARVESTING FROM CIVIL STRUCTURES FOR SELF
POWERED SENSING
In order to use the existing concrete manufacturing methods to incorporate the sensor
within the structure, we have constrained the maximum volume of the sensor to be 5 cm3,
corresponding to the maximum size of a concrete aggregate that doesn't lead to a significant
weakening of the structure (Issa et al., 2000). However, when limited to 5cm3, the vibration based
piezoelectric will typically have a resonant frequency in the range 100-300Hz, while most civil
structures exhibit a fundamental vibration mode at frequencies less than 10 Hz. This mismatch
significantly limits the levels of extractable power.
Figure 1(a) shows the voltage output of a bimorph PZT (1 cm x 4 cm) subjected to variable
strain loading versus the loading frequency. The piezoelectric bimorph is mounted in patch
configuration, and subjected to the strain induced in the structure. Starting from 50 micro-strain,
which corresponds to the ultimate fatigue limit of concrete, the piezoelectric can provide enough
energy to power the floating gate sensor, covering most of the needed frequency and strain range
to sense. However when mounted in cantilever configuration used to harvest energy from vibration
(Figure 1(b)), the minimum power needed is met either at very high vibration amplitudes, 2 g and
more, or at higher frequencies. Thus improving the conversion capabilities of the piezoelectricharvester subjected to dynamic excitation, while obeying all necessary constrains, is critical toward
the successful implementation of a self-powered monitoring system.
Several external environmental effects, such as temperature variation, also alter the
performance of vibration piezoelectric harvester, and limit its longevity and its efficiency. The

4

temperature variations in civil structures varies from -20o to 50o C significantly limiting the levels
of extractable power. Several studies have been conducted to determine the effect of ambient
temperature on piezoelectric properties and the levels of extractable energy. Birman et al. 2006
evaluated the effect of uniformly distributed temperature on the vibrations of a piezoelectric rod
polarized in the axial direction. Omote et al., 1996 investigated the temperature dependence of
elastic, dielectric, and piezoelectric properties of single crystalline films of vinylidene fluoride–
trifluoroethylene copolymer. A change of more than 100% in the elastic modulus was shown in
the range 20o to 50o C, affecting the stiffness of the harvester, and reducing dramatically the level
of harvestable energy. Similar variations were observed for the dielectric constants, particularly
the piezoelectric constant d31. Mane et al., 2007 used a prestressed PZT-5A unimorph beam to
characterize the dependence of the output voltage to temperature variations in the range of 20 to
100 oC. Hooker, 1998 investigated the dependence of lead zirconate titanate (PZT)-4, PZT-5A,
PZT-5H, and lead lanthanum zirconate titanate (PLZT)-9/65/35 properties with respect to
temperature variations in the range -150 to 250 oC. Figure 2 shows the experimental results of the
voltage transfer function of a PZT bimorph mounted in a cantilever configuration subjected to base
excitation at different temperature. The base acceleration was kept constant at 1g for varying input
excitation frequency from 35 to 55 Hz (a selected range around the resonant response of the
system) and a varying temperature from -20 to 40 oC. A very pronounced effect is observed on
both the resonant frequency and the amplitude.
A variety of options for improved piezoelectric harvesters have been previously examined.
These include improvements through the optimization of the piezoelectric material, altering the
electrode patterns and system configuration, the use of a matching network, and tuning the device’s
resonant frequency for maximum response and power transfer.
5

Output Voltage (V)

25

(a)

20

100  
50  
25  

15
10
5
0
0

2

4
6
Loading Frequency (Hz)

8

10

Output Voltage (V)

25
1g
2g
3g

20
15
10
5
0

40

60

80
100
Frequency (Hz)

120

140

(b)
Figure 1. Frequency Response of PZT Beam Loaded in the Strain and Vibration
Modalities

6

Results from all these studies showed that PZT ceramic remains one of the most practical
options for energy harvesting from base excitation, primarily because of its low-cost and highcoupling characteristics.
Altering the stiffness of the vibrating device can maintain its natural frequency at the
desired spectrum. Several different designs have been proposed to achieve this tuning capability.
Leland et al., 2006 presented an analytical formulation of a tunable harvester using a simply
supported piezoelectric beam with a proof mass at its mid-span. Only the first mode was addressed.
An experimental apparatus was built, and measurements were compared with the theoretical
predictions. Eichhorn et al. 2009 designed an experimental mechanism for pre-stress bidirectional
frequency tuning on the basis of the theoretical formulation presented in Hu et al., 2007. An
adjustable link was used by Morris et al., 2008 to build a tunable frequency mechanism. Frequency
variations from 80 to 235 Hz were measured. Challa et al., 2008 and 2009 used magnetic forces to
build a tuning mechanism. It was shown that resonance tuning of 20% is achievable. Piezoelectric
actuation was also used by Peters et al., 2008 to build an electrically tunable resonator. An input
voltage variation of 5 V was shown to achieve a shift of the resonant frequency by 15%. Although
these designs were successful at adjusting the vibration response, they are impractical as energyharvesting devices because they require high input power for control, making them obsolete as
scavengers.
Eichhorn et al., 2011 proposed a design for a self-sufficient frequency-tunable harvester.
The system’s stiffness is altered to tune the resonance frequency using a piezoelectric actuator,
controlled by a self-adjusting control unit that delivers the appropriate voltage for correction. The
system converges to a stable operation mode within minutes, which is impractical for ambient

7

vibration events in civil structures. Around its optimal operational range, up to 90% of the
harvested energy can be fed to the powered electrical load.

Figure 2. Experimental results of the output voltage amplitude, versus the excitation frequency
and the temperature under 1 g base acceleration. (Mtip=3.75g, load resistance=1MΩ, P=-2N)

Stanton et al., 2010 used nonlinear systems as an alternative way to enhance the vibrator
response over a broader frequency range. A bi-stable inertial generator consisting of permanent
magnets and a piezoelectric beam was investigated. An analytical model was developed, and it
was shown experimentally that the system’s frequency response can be enhanced. Erturk et al.,
2011 introduced a non-resonant piezo-magneto-elastic energy harvester. They investigated
experimentally and analytically the high-energy orbits in the bi-stable Doffing oscillator over a

8

wide range of frequencies. It was proved that the proposed device can generate power an order of
magnitude higher than piezo-elastic devices under different excitation frequencies.

SELF POWERED
PREDICTION

LONG

TERM

MONITORING

SYSTEM

AND

DAMAGE

The last 40 years have seen a rapid increase in the research related to damage prediction,
which can be classified to either local or global. Global methods are mostly structural response
vibration based. Doebling et al., 1996, Garden et al., 2006 and Fan et el., 2010 have provided a
review of the most common vibration-based methods and algorithms to identify global damage of
structures. They can be classified into three major categories: natural frequency-based methods,
mode shape-based methods and curvature mode shape-based methods.
Natural frequency-based methods use the natural frequency’s change as a way to identify
and predict damage. The natural frequency change is attractive because it is usually less sensitive
to experimental noise. However it has several other common limitations: low sensitivity to damage
and difficulty of measurement.
However compared to natural frequencies, using mode shapes as a basic feature for damage
detection is more advantageous: the mode shapes contain local information, which makes them
more sensitive to local damages, and less sensitive to environmental effects, such as temperature.
The disadvantages are also distinct; the measurement of the mode shapes requires more sensors;
the measured mode shapes are more susceptible to noise contamination than natural frequencies.
An alternative way of using mode shape to obtain spatial information about sources of vibration
changes is by using the shape mode derivative, such as curvature. In fact, there is a direct
relationship between curvature and bending strain for beams, plates, and shells.
9

Simultaneously, tremendous efforts have been spent on local damage investigation;
different prediction models have been developed, either based on linear fatigue damage
accumulation (LRD) accompanied with an experimentally generated log-log S-N curve (Basquin,
1910 and Coffin, 1954), or a reliability approach to predict fatigue damage accumulation (Park,
1990; Oh, 1991; Singh et al., 2001) by inserting an experimentally observed probability density
function into the LDR to express the number of cycle to fail in terms of a probability.
Several researchers proposed modifications to the original LDR approach. The double
linear damage rule (DLDR), introduced by Manson, 1966, separated the S-N curve into two
regions to represent the differences in damage accumulation rates within the crack initiation and
crack propagation stages. This method was then refined to include a damage curve function
(Manson and Halford, 1981) that allowed damage to be expressed as a non-linear power function
dependent on load-level. Oh, 1991, developed a non-linear damage rule for concrete that expresses
the damage index (D) as a load-level dependent cubic polynomial, and was able to predict the LDR
error for both L-H and H-L loading sequences. More recently, a one dimensional continuum
damage mechanics model was used to predict the load sequence effect (Lemaitre, 1992; Xiao et
al., 1998). These models associate damage directly to elastic modulus degradation and are founded
on thermodynamic principles in which the damage induced strain energy release rate is the driving
force for damage.
The piezoelectric self-powered sensor has showed significant promise toward a successful
integration of a strain sensor. However the used data management and organization protocol results
inevitably end in a considerable loss of information since it is not stored as function of real time,
but rather compressed as a function of cumulative time at each strain level. As a consequence, the

10

interpretation and usefulness of the strain histogram as a mean to predict the remaining life using
the conventionally developed methods is not possible.
OBJECTIVE AND OVERVIEW
This thesis is composite of two big chapters: (1) Improving piezoelectric power harvesting
from vibration, in order to achieve the minimum power needed for a self-powered vibration
monitoring system and (2) Successful deployment of the newly developed self-powered strain
sensing system for damage monitoring and remaining life prediction in civil structures, particularly
concrete.
The improvement of piezoelectric energy harvesting from civil structures using stiffness
control will be the focus of the first chapter; the application of a variable preloading condition is
used as a solution to modify the system’s properties. A generalized model that takes into account
all the vibration-mode shapes of the beam and the back-coupling effect is derived using the
Hamiltonian principle. Measured acceleration from a concrete bridge deck under ambient loading
and recordings from extreme events (earthquakes) are used to show the gain in harvested energy
when the harvester is in preloaded configuration.
In the second chapter, the effects of temperature variations on the piezoelectric (PZT)
harvested energy from civil structures are studied. A proposed mechanical tuning, based on the
application of an axial load using Shape Memory Alloy to compensate the temperature effect, is
presented. A fully passive temperature compensation mechanism is proposed, and numerical
analysis showing the improvement of energy conversion from civil structures is presented.
In order to select the best model that would fit the sensor output, the sensor will be
implemented, tested and its output will be defined. The work describing a fully deployed sensing
system with all the needed attributes will be presented in chapter three. The calibration and
11

installation of the sensor is addressed. Defining the sensor output from real time loading
distribution is shown. Finally the evaluation of a full field data from a limited number of randomly
distributed sensor is studied.
In the fourth chapter, the damage prediction abilities of the long term self-powered
continuous monitoring system are evaluated. The sensor is able to continuously monitor and
cumulatively record strain events experienced by the structure over extended periods given its selfpowered characteristic. A slightly modified linear damage accumulation approach is then proposed
using the damage index founded on continuum mechanics definition. The derivation of the damage
index using the sensor’s output data is detailed with results from a set of laboratory tests,
comparing the damage index prediction output from the sensor and values obtained using the
complete time history data. Finally, a projection of the remaining life of the tested specimens using
reliability analysis was computed and its accuracy was evaluated by completing the test until
failure and counting the total real observed cycles, showing very promising results for full field
deployment.

12

CHAPTER 2: TUNABLE PIEZOELECTRIC ENERGY HARVESTING
FROM CIVIL STRUCTURE

INTRODUCTION
Vibration based PZT bimorph scavenger, mounted in a cantilever configuration and with
an overall volume limited to less than 5cm3 (Issa et al., 2000; Elvin et al., 2006), will typically
have a resonant frequency in the range 100-300Hz, while most civil structures exhibit a
fundamental vibration mode at frequencies less than 10 Hz.
When excited with a frequency equal to the first vibration mode of the harvester, the
amount of harvested energy is maximum. However civil structures vibrate at lower frequency,
making the level of output voltage amplitude a hundred times less important. This mismatch
significantly limits the levels of extractable power. Therefore, improving the conversion
capabilities of these systems, while obeying all necessary constraints, is critical toward a successful
implementation for structural health monitoring.
A variety of options for improved PZT harvesters have been previously examined. These
include the altering of the electrodes patterns and system configuration (Erturk et al., 2008 and
2009; Mateu and Moll, 2005; Goldschmidtboeing and Woias, 2008; Rupp et al., 2009), the use of
matching network (Kim et al., 2007; Shu et al., 2007; Challa et al., 2011), and the tuning of the
device’s resonant frequency for maximum response and power transfer (Eichhorn et al., 2009 and
2011; Hu et al., 2007; Challa et al., 2008 and 2009).

13

The objective of the first chapter is to show that by using axial preloading as a way of
tuning the frequency response of the piezoelectric harvester the minimum output power
requirement to use the existing sensing technologies to monitor extreme events can be met. The
effect of the preload on the conversion process is analyzed. A comprehensive analytical model
based on the Hamiltonian principle is developed. The results show the effect of the preload on the
dominant frequency of the resonator. Then the experimental verification of the design is presented.
The apparatus’ response is measured in both the time and frequency domains then compared to
theoretical observations. Finally, case studies are presented. Vibration histories gathered from
published data are used to estimate the harvestable power for different axial preload configurations
in order to show the high improvement in piezoelectric energy harvesting from vibration in civil
structures.

GENERAL MODEL OF AXIALLY PRELOADED BIMORPH PIEZOELECTRIC
ENERGY HARVESTER

System Configuration
The configuration and the material properties of a bimorph piezoelectric vibration energy
harvester mounted in cantilever configuration are shown in Figure 3 and Table 1. The piezoelectric
cantilever bimorph beam is subjected to base excitation and to a permanent axial preload. The
energy method is used to derive the constitutive equation.
The basic variational indicator equation is given by:
t2

  T   U   W  dt  0

t1

14

(1)

where T is the kinetic energy and W is the work of external forces expressed as:

T

1
1
  su  x, t  u  x, t  dVs    pu  x, t  u  x, t  dV p
2V
2V
s
p

(2)

 M tipu  L, t  u  L, t 

W   u  x, t  f  t  dVs   u  x, t  f  t  dV p
Vs

Vp

(3)

 M tipu  L, t  . f  t 
and
u: deflection
ρ: density
f: base acceleration
'p': subscript which represents the PZT material
's' : subscript which represents the metallic substrate

Table 1. Piezoelectric properties used in simulations.

Properties

Values

Elastic modulus PZT CS

72 GPa

Elastic modulus substrate CE

11 GPa

Density piezoelectric ρp

7900 g/m3

Density substrate ρs

8900 g/m3

Piezoelectric constant d31

270e-12 m/V

Electrical permittivity ɛ

3500 ε0 (F/m)

Beam length, width (L,b)

(40, 10) mm

Thicknesses(a,h)

0.1 mm,0.2mm

15

Figure 3. Schematic depiction of a cantilever bimorph piezoelectric vibration
scavenger of length (L), width (b), and height (h+2a), subjected to axial loading.

Effect of Preloading on the Harvester Governing Equations
The added axial preload is incorporated in the constitutive equations of the cantilever beam
as a change in the potential energy U of the system. Since the system is under a permanent axial
16

load P, this change is due to the additional internal non-dissipative energy. The total potential
energy of the resonant system is then expressed as follow:

U

1
1
1
T
T
T
 S TdVs  2  S TdV p  2  E DdV p
2V
V
V
s

p

p

I



(4)

2

1
 u 
 P  x  dx
2L  
II

where S, T, E, D, and V are the strain, the stress, the electric field, the electric displacement,
and the material’s volume.
Incorporating the linear piezoelectricity equations into the potential energy function, yield
the following general potential form:

  S T c SdV   S T c E SdV   S T eT EdV 
s
s
p
p
V

Vp
Vp

1 s
U 

2
2
 u 
T s

 E  EdV p   P   dx
 V

x 
L 
 p


(5)

where c, ɛ and e are the modulus of elasticity, the dielectric constant and the coupling
factor, respectively. The superscripts, ()S and ()E, indicate that the parameter is estimated either at
constant strain or constant electric field.
Incorporating the variation of the external work, and the kinetic and potential energy into
equation (1), the variational indicator becomes:

17

   s u udVs    p u udV p  M tip u  L, t  u  L, t 

V

Vp
 s

-  S c SdV -  S c E SdV   S T eT EdV



s
s 
p
p

t2  V
Vp
Vp
 s
 dt  0


T
T s
t1     E eSdV p    E  EdV p -  P u u dx

Vp
L
 Vp



   s uf  t  dVs    p uf  t  dV p   u  L, t  M tip f  t  

Vp
 Vs




(6)

Assuming Euler-Bernoulli behavior for the considered cantilever beam subjected to the
external force (induced by the base excitation) as shown in Figure 3, the longitudinal strains are
deflection induced and are expressed as follows:

S  y

 2u  x, t 

(7)

x 2

The deflection and the electrical field are expressed in the modal and field coordinates as:

N

u  x, t    i  x  ri  t     x  r  t 
i 1

(8)

M

E  y, t     i  y  vi  t    y  v  t 

(9)

i 1

where ψ defines the field over the thickness of the PZT.
Substituting Equations 7, 8 and 9 into the variational indicator (Equation 6), leads to the
two coupled equations expressed as follows:

18

 M r  t    K  K  r  t   v  t   M * f  t 
T
 T
 T
 r (t )  C pv  t   q  t 


(10)

where the mass and the stiffness matrices of the system can be written as:

 M     T  x   x  dV     T  x   x  dV  M  T  L   L 
s
p
p
tip
 T V s
Vp
s

 *
 M    s   x  dVs    p   x  dV p  M tip   L 

Vs
Vp


(11)

 K  y 2 T  x " c   x " dV  y 2 T  x " c E   x " dV

s
s
p
 T 
Vs
Vp


 K  P   T  x '   x ' dx


L

(12)

where ̃ is the additional stiffness induced by the applied preload condition.
𝐾
The electromechanical coupling and the capacitance matrices are expressed as:

   y  T  x " eT  y  dV

p

Vp


C p    T  y   S  y " dV p

Vp


(13)

The mechanical damping can be evaluated for a single mode analysis as:

C  2

 KT  K  M

where the damping ratio ξ is evaluated experimentally.
For more than one mode the damping ratio can be defined as follows:

19

(14)

C    KT  K    M

(15)

Incorporating the damping into Equation (10) yields the following generalized equations
system for the studied setup:

 M r  t   Cr  t    K  K  r  t   v  t   M * f  t 
T
 T
 T
 r (t )  C pv  t   q  t 


(16)

Where q(t) is the electric charge output of the piezoelectric PZT element that can be directly
related to the power output through a load resistance R. The developed generalized model can
accommodate all vibration modes.

EXPERIMENTAL SETUP AND MODEL VERIFICATION

Experimental Setup
To check the validity of the developed model, an experimental setup was built (Figure 4).
The output voltage of the piezoelectric element was measured in frequency and time domains
under constant acceleration input and varying pre-load conditions.
The experimental results were then compared to the predictions of the theoretical model.
Variations of the voltage transfer function show the effect of the applied axial loading on the
resonance frequency and amplitude. In all the experiments, a standard commercial bimorph
piezoelectric sensor (SMBA4510T05M—from STEMINC Inc) was used. The materials’
properties are summarized in Table 1. Figure 3 shows the sensor’s geometry.
20

(a)

(b)

Figure 4. (a) Test setup, loaded piezoelectric bimorph beam with attached tip mass; (b)
experimental apparatus mounted on a shaker for testing (For interpretation of the
references to color in this and all other figures, the reader is referred to the electronic
version of this dissertation).

21

In the developed system, shown in Figure 4(a), the preload is applied using two metallic
springs connecting the tip of the beam to the base of the beam. Screws are used to adjust the
preload. High precision linear springs were used. For each desired preload level, the springs’ length
(linear with respect to the preload level) is adjusted. The Euler’s buckling load of a clamped-free
beam is expressed as:

Pcr 

 2 EI

(17)

4 L2

If over loaded, the beam buckles and the piezoelectric ceramic cracks. The maximum tip
deflection of the beam should not exceed 4mm peak-to-peak according to the manufacturer
specifications. Ensuring these conditions is critical because if over-strained, the PZT will lose a
significant fraction of its piezoelectric properties.

Model Verification and Experimental Results
The considered deflection shape mode in this work is assumed to have the following form
(Elvin and Elvin, 2009):

  2i  1  x 
i  x   1  cos 

2L



(18)

The potential function is assumed to be constant over the PZT thickness and is expressed
as follow:

h
V
h
h
V h
 a if 2  a  y  2 and  a if  a  2  y   2
 y  
h
h
0
  y

2
2

22

(19)

10

(a)

Ouput volage (V/g)

Theoretical
Experimental
5

0

-5

-10
0.5

0.55

0.6

0.65

0.7

Time (s)
10

(b)

Output Voltage (V/g)

Theoretical
Experimental
5

0

-5

-10

0.85

0.9

0.95
Time (s)

1

1.05

Figure 5. Predicted and measured output voltage across a 10MΩ resistance (a) Frequency=40Hz,
axial preload=-2N, tip mass=3.75g, (b) Frequency=37Hz, axial preload=-6N, tip mass=3.75g

23

A first set of experiments was conducted to compare the model predictions and the
collected data for the time domain response under different configurations.
Figure 5(a) shows the measured and the predicted output voltage across a 10 MΩ load
resistance for an excitation frequency of 40 Hz under a constant applied compressive axial loading
of -2N. Less than 1 second of recording is shown for clarity. Different combinations of tip mass
and axial loading conditions were tested at different excitation frequencies for accurate validation
of the developed model. Figure 5(b) shows a second case of comparison at a loading frequency of
37 Hz and applied compressive constant loading of -6N. The results match, thus confirming the
validity of the developed model.

0.048
Experimental Measurments

0.046

Damping Ratio ( )

0.044
0.042
0.04
0.038
0.036
0.034
0.032
0.03
-5

-4

-3
Axial Load (N)

-2

-1

Figure 6. Variation of the first mode damping ratio with respect to applied axial loading

24

The variation of the damping ratio for the first vibration mode with respect to the applied
preload was examined experimentally. The output voltage response of the system was measured
under mechanical impulse excitation at different axial load levels ranging from -1 to -5 N. The
damping ratio is then evaluated from the observed decay across a 10 MΩ load resistance. It is
assumed that the damping ratio is constant over the frequency domain. Figure 6 shows the effects
of preload on the damping ratio. It was observed that the damping ratio increases by more than
50% for a -5 N compressive loading. The measured damping ratio and the piezoelectric
capacitance are injected into the analytical model in order to increase the accuracy of the numerical
simulations.

Output Voltage Amplitude (V/g)

30
25
20

P= - 2 N
P= - 3 N
P= - 4 N
Predicted
data

15
10
5
0

35

40
Frequency (Hz)

45

50

Figure 7. Output voltage transfer function of the transducer under different preload
conditions. Mtip=3.75g, Load resistance=10MΩ. (solid: theoretical, dots: experimental).

25

The performance of the model was also evaluated in the frequency domain. The resonant
frequency and the amplitude of the response were monitored for different applied axial loading.
Figure 7 shows the measured and the computed voltage transfer functions of the resonator
subjected to a compressive axial loading varying from -2 N to -4 N. The resonant frequency shifted
from 44.5Hz to 40Hz. Only the first mode is shown in Figure 7.
As an example, it can be observed that when the energy harvester is designed for optimal
response to base acceleration excitations centered at 45 Hz, a 3 Hz mismatch will induce a 50%
reduction in the voltage response. This loss can be completely recovered through an adjustment of
axial pre-loading of around 1.5N. The maximum response is constant despite the increase of the
measured damping ratio. Experimental results shown in Figure 7 display a non-linear behavior
with a prominent effect, especially for post-resonance frequencies. The high error after resonance
can be explained by the softening nonlinearity in the piezoelectric resonator under high excitations
(Erturk et al., 2010; Stanton et al., 2010).

TUNABLE ENERGY HARVESTING FROM AMBIENT VIBRATIONS IN CIVIL
STRUCTURES

Maximum Harvestable Power Using Preloaded Harvester
Figure 8 presents a theoretical analysis of the variation in the resonant frequency response
of the cantilever system as a function of the applied axial loading for different tip mass values. It
can be observed that the effect of the axial loading on the resonant frequency (slope of the curves)
is more prominent for lower mass values. Similarly, the higher the compressive loading, the lower
is the effect of mass variations.

26

This is illustrated by the narrowing gap between the curves as the compressive loading is
increased. These effects should be carefully considered while designing an energy harvesting
resonator system.

Resoant Frequency (Hz)

45

40

Mtip= 5 g
Mtip= 7.5 g
Mtip= 10 g

35

30

25

20

15
-8

-6

-4

-2

0

Axial Loading (N)
Figure 8. Resonant frequency variation with respect to applied axial loading for different
tip mass (resistance R=10MΩ)

Figure 9 shows the maximum generated power by a piezoelectric element as a function of
the applied preload. The properties and dimensions of the piezoelectric are shown in Table 1. It is
shown that by lowering the resonant frequency response of the piezoelectric device, slightly higher
power is coupled through the system. This is also illustrated in Figure 7 (maximum voltage). It is
observed that changes in the tip mass have a more prominent effect on the increase of the output
power; this is due to the fact that a change in tip mass not only affects the resonant frequency but
also the level of input work due base acceleration (Equation 11-b). Furthermore, it is shown that
27

frequency shifts due to mismatches (mechanical, environmental, etc), can be re-adjusted by
varying the compressive loading to recover the loss in design power levels. It should be noted that
all the shown numerical simulations’ results are obtained using the material properties given in
Table 1, under a constant amplitude acceleration input loading at 1 "g".

900
Mtip= 5 g
Mtip= 7.5 g
Mtip= 10 g

Output Power (W/g 2)

800
700
600
500
400
300
200
100
-8

-6

-4

-2

0

Axial Loading (N)
Figure 9. Maximum generated power with respect to applied axial loading for different tip mass
(resistance R=1MΩ).

Tunable Energy Harvesting from Civil Structures
Typical civil engineering structures exhibit fundamental vibration frequencies in a range
below 10 Hz. The addition tip mass and axial loading shifts down the resonant frequency of a
bimorph beam scavenger from its relatively high value at 157Hz. However, the maximum tip mass
and deflections that the piezo-beam can accommodate are limited. The maximum volume of a
28

sensor node considered in this study, including the tip mass, is below 5 cm3. This relatively small
volume is approximately the size of a large concrete aggregate (Issa et al. 2000), thus making the
system suitable for embedment in, for example, concrete, without affecting the structural integrity
of the host material.
In order to show the potential advantage of preload tuning, a set of study cases were
conducted with the objective of evaluating the potential gains in harvested power under realistic
excitation conditions on a civil structure. A set of extreme events – that is, earthquake recordings
- were considered. Data were obtained from “the Earthquake Engineering Online Archive” of the
University of California at Berkeley.
The energy output from the piezo-generator across a load resistance is evaluated using the
following expression:

V 2 t 
En  
dt
R
0
tf

(20)

Acceleration recordings from the deck of a 60 foot reinforced-concrete bridge under traffic
loading (El-Borgi et al., 2005) were used as input excitation. The frequency spectrum of the
measured accelerations is shown in Figure 10(a).
Obtained simulation results are illustrated in Figure 10(b). As the resonant frequency
response of the harvester shifts closer to the dominant frequency of the bridge vibrations, more
energy content is coupled to the resonator and harvestable power output increases considerably.
For a system with a tip mass of 15 grams, the output power increases approximately a seven fold
between the unloaded configuration and a system with an applied constant axial preload of -8 N.
29

(a)

(b)

Figure 10. (a) Frequency spectrum for the acceleration measurements from the deck of a concrete
bridge under traffic loading, (b) Variation of the output energy as a function of the applied preload
subject to the recorded bridge accelerations (resistance R=1MΩ)

30

Two different optimization analyses have been conducted: first, an optimization with
respect to the tip mass and the resistive loading, and a second, analysis for the axially loaded
confirmation with respect to the tip mass, the applied mechanical loading, and the resistive loading.
The used optimization tolerances for the tip mass, the preload, and the electrical load are 0.5g,
0.1N, and 1kΩ, respectively.
Table 2. Optimized maximum collected energy for axially loaded and unloaded beam harvester
configurations

Unloaded configuration
Earthquake event

Applied axial preloading

Total output

Tip mass

Total output

Tip mass

Axial

energy (uJ)

(g)

energy (uJ)

(g)

preload (N)

Llolleo (1985)

485.18

25

5497.31

25

-8.5

El Salvador (2001)

212.88

25

1422.13

22

-7

El Centro (1940)

22.43

25

1150.38

25

-10

Northridge(1994)

8.17

25

412.25

25

-10

Arthurs Pass (1995)

8.21

25

343.46

25

-9.5

Nisqually (2001)

7.55

25

329.72

25

-10

Valparaiso (1985)

3065

17.5

8049

25

-6.8

Results for the maximum harvestable energy from different earthquake events are
presented in table 2. It is observed that the total transferred energy increases significantly with the
added axial loading. A maximum mass of 25 grams was selected so that the overall constrain on
the maximum volume can be verified. The buckling limit of the considered beam was also set as
a constraining factor.
31

The buckling limit of the considered beam was also set as a constraining factor. It is also
noted that for some cases, due to the frequency spectrum of the excitation, the response maximum
can be caught on a secondary peak thus using only a portion of the maximum allowable mass. An
example of such case can be illustrated in the response to the 1985 Valparaiso earthquake recording
shoed in Figure 11(a).
A secondary peak occurs within the range 0 to 25 grams mass, at a value of 17.5 grams as
shown in Figure 11(c). The addition of an axial loading pushes the optimal response of the beam
closer toward the main resonant component, thus resulting in a significant increase of collected
energy while obeying the same volume and mass constrains. This is shown in Figure 11(c) in the
loaded configuration response curve.
Figure 12 shows the average coupled power from different earthquake events with and
without preloading condition. The shown averaged values of power are evaluated for optimized
values of mass and axial loading. On average, the power output is 10 times more important with
an added optimal preload.
In spite of that significant increase, and even though the total harvestable energy for such
extreme events might seem to be high, the levels of continuous power remain critically low to
allow for real time continuous recording of these events while relying only on harvested power.
Only advanced, specific types of sensors, such as the data logger recently developed by the team,
would allow for a self-powered processing of the generated vibration data.

32

1.5

(a)

Acceleration (g)

1
0.5
0
-0.5
-1
-1.5
-2
0

(b
)

Output Energy (mJ)

8

20

60
40
Time (s)

100

80

25 g
8.049 mJ

Preloaded (-6.8N)
Unloaded

6

17.5 g
3.065 mJ

4

2

0
0

5

10

15

20

25

Tip mass (g)
Figure 11. (a) Acceleration time-history from the 1985 Valparaiso earthquake, (c) Output energy
with respect to tip mass for a loaded and unloaded system subject to the 1985 Valparaiso
earthquake acceleration signal

33

Output Power (W)

47.23

40

Unloaded
Applied optimal axial loading

36.89

19.1

20

14.81 14.48
9.21
4.17
0.72
0

1

2

2.86

3

8.1

7.36

6.6

0.29

0.28

0.39

0.19

0.18

0.11

4

5

6

7

8

9

Events
Figure 12. Average power output generated by a piezoelectric harvester (Table 1) subject to a
set of example earthquake accelerations events for both the unloaded and with applied optimal
axial loading configurations (Table 2) – 1: Llolleo, 2: Elcentro, 3: El Salvador, 4: Northridge,
5: Uttarkashi, 6: Rapel, 7: Arthur Pass, 8: Dharmsala, and 9: Xiang.

CONCLUSION

The above chapter focused on investigating the effect of preloading on the level of
harvestable power from piezoelectric cantilever beam subjected to base excitation, in order to
achieve a self-powered sensing system. A generalized model for a bimorph piezoelectric energy
transducer mounted in a cantilever configuration and subject to permanent axial loading has been
developed. The comprehensive model encompasses all the theoretical vibration modes of the beam
and also takes into account the back coupling effect. A testing apparatus was built and tested for
34

different conditions. Obtained measurements showing the variations of the natural frequency and
amplitude of the piezoelectric device response with varying preload validated the theoretical
results. Realistic vibration recordings from earthquakes were used. Increases by 100 times in the
output power levels were shown feasible through the application of -11 N of compressive axial
loading.
It was also shown that tuning of vibration energy harvesters through axial preloading can
be used to correct for mismatch induced effects. Such observed variations could be due to
manufacturing mismatches or environmental effects (temperature, etc). The feasibility of a passive
temperature effect compensator based on applied adjustments of an additional axial loading will
be the focus of the next chapter.

35

CHAPTER 3: PASSIVE COMPENSATION OF TEMPERATURE EFFECT
ON PIEZOELECTRIC ENERGY HARVESTING FROM VIBRATION

INTRODUCTION

Using preloading as a way of tuning the frequency response of the PZT harvester
drastically increases the level of harvestable energy from vibration. However, several other
obstacles still hinder their use in civil infrastructure. An important factor is mismatches induced
due to temperature variations, as harvesters typically operate in a range varying from -20 to 50
degree Celsius.
In this chapter, the harvester's frequency response dependence to preloading is used to
compensate for the observed temperature effects. Subsequently, we can partially recover the lost
energy due to the induced mismatches. The main purpose is to develop a self-tuned piezoelectric
energy harvester that can couple the maximum energy from vibration of civil structures in order
to provide enough power for a successful implementation of self-powered vibration monitoring.
This chapter shows that passive compensation of temperature effects on piezoelectric
vibrators is feasible using applied adjustments of axial preloading Shape Memory Alloy induced.
Numerical and experimental analyses are performed to show the effect of varying temperatures on
the voltage response of a bimorph cantilever piezoelectric energy harvester. A developed
generalized modeling scheme, which employs a combination of temperatures and preloading, is
presented. Based on this, the inclusion of shape memory alloys (SMAs) is proposed to achieve the
36

temperature correction, and thus a fully passive self-tuned vibration energy harvester. The
proposed idea relies on the temperature dependence of SMAs to counteract the variations of the
piezoelectric response induced by temperature change. SMAs are modeled using the onedimensional constitutive behavior (Brinson (1993)). A proof of concept system that uses shape
memory alloy wires is shown. Numerical analyses using optimal mechanism properties, which
achieve the desired correction effects on a bimorph cantilever PZT-5H, are presented.

TEMPERATURE EFFECTS ON THE RESPONSE OF A BIMORPH PIEZOELECTRIC
ENERGY HARVESTER

Effect of Temperature on the Material Properties
The stiffness matrix of the piezoelectric energy harvester shown in Equation (12) depends
mainly on the elasticity modulus of the PZT material which varies with respect to temperature.
Figure 13 shows the dependence of the elastic modulus on temperature for PZT-5H. It can
be seen that an increase in temperature will result in a decrease of the material’s modulus. This
relative softening of the material will induce a shift of the resonant frequency toward lower
frequencies. Additionally, the overall response of the system also depends on the variations of the
electrical properties and the mechanical-to-electrical coupling variables.
The dielectric constant varies with temperature (significant variations are observed for
PZT-5H), which accounts for the strong dependence of the piezoelectric capacitance to
temperature.

37

Figure 14(a) shows experimentally evaluated data of the dielectric constant variations for
PZT-5H and PZT-5A piezoelectric ceramics. For PZT-5H, a variation of more than 50% is shown
within the considered temperature range.

Elastic Modulus (GPa)

90
85
80
75
70
65
60
-20

-10

0

30

20

10

40

50

o

Temperature ( C)
Figure 13. Temperature dependence of the elastic modulus of PZT-5H

Furthermore, in the considered cantilever configuration, the electromechanical coupling
coefficient ϴ is linearly dependent to the transverse strain constant d13 , which has a strong
dependence to temperature as shown in Figure 14(b). A variation of more than 25 % of d13 is
observed. The shown plots in Figure 14(a, b) were redrawn with parameters from experimental
data obtained by Hooker, 1998.

38

(a)

Dielectric Constant

6000
5000

PZT-5H
PZT-5A

4000
3000
2000
1000
0

-50

0

50

100

Temperature (oC)
500

PZT-5H
PZT-5A

(b)

-d31 (10

-12

m/V)

450
400
350
300
250
200
150
100

-50

0

50

100

o

Temperature ( C)
Figure 14. Temperature dependence of (a) the dielectric constant of PZT-5H and PZT-5A
(Hooker, 1998), (b) the piezoelectric coefficient d31 of PZT-5H and PZT-5A (Hooker, 1998).

39

Effect of Temperature on Piezoelectric Energy Harvesting from Vibration
An experimental apparatus was built to check the validity of all the models used in this
work. The setup is shown in Figure 15. The tested system geometry is shown in Figure 3. The first
set of experiments was designed to determine the effect of temperature on the frequency response
of the system. The output voltage transfer function of the piezoelectric element was measured
under a constant applied acceleration at different temperatures.
Measurements were taken across a load resistance of 1MΩ. The base acceleration was kept
constant at 1 g for an excitation frequency varying from 35 Hz to 55 Hz (a selected range around
the resonant response of the system), and varying temperature from -20 oC to 40 oC.
A very pronounced effect is observed (Figure 16), on both the resonant frequency and the
amplitude. An increase in temperature lowers the resonant frequency (material softening) and also
lowers the maximum peak voltage amplitude at resonance, due to variations of the electrical and
coupling properties. A resonance frequency shift between 41 and 49 Hz was observed for the
considered temperature range. This shift, purely due to temperature, will induce practically a
complete loss of the output amplitude for a resonating system tuned to respond around the peak at
a selected temperature. This is due to the narrow-band response characteristic inherent to
piezoelectric vibration harvesting devices.
Furthermore, it was observed that the damping ratio of the vibrator is affected by
temperature. In fact, the temperature variation affects the elastic modulus of the material, leading
to a change of the contact zone pressure between the piezoelectric beam and the base.

40

(a)

(b)

Figure 15. Test Setup: (a) loaded piezoelectric bimorph beam mounted on a shaker, with the
SMA springs, (b) experimental apparatus enclosed in an environmental chamber

41

35

Output Voltage Amplitude (V/g)

40 oC
30
25

20 oC
0 oC
-20 oC
Numerical Results

20
15

10
5

0
35

40

45

50

55

Frequency (Hz)
Figure 16. Numerical results and experimental measurements of the output voltage amplitude
versus the excitation frequency at different temperatures, under a 1g base acceleration.
(Mtip=3.75g, load resistance=1MΩ)

Figure 17 shows this effect measured experimentally for the first vibration mode of the
cantilevered beam. It was shown that the damping ratio increases by about 40% for a temperature
change from -20 oC to 40 oC. This increase and the observed peak amplitude decrease, induced by
the material’s properties changes, combine to further reduce the obtained output response. The
experimental measurements of the damping were injected into the analytical model in order to
enhance the accuracy of the implemented numerical simulations.

42

0.038

Damping Ratio 

0.036
0.034
0.032
0.03
0.028
0.026
0.024
-20

-10

0

30

20

10

40

50

o

Temperature ( C)
Figure 17. Variation of the first vibration mode damping ratio with respect to temperature

TEMPERATURE EFFECTS CORRECTION USING AXIAL PRELOADING

Experimental Setup
In this section, the alteration of stiffness of the vibrating device is studied to in order to
counteract the observed effects due to temperature variations. . The objective is to maintain the
natural frequency of the system around a desired spectrum for varying temperatures in the
considered range. A mechanical tuning mechanism is considered. The principle is based on the
application of a variable axial loading, which will change the beam stiffness and subsequently
affect the resonant frequency of the piezoelectric transducer. The technique employs the effect of

43

these mechanical adjustments in order to compensate for the observed deviations due to
temperature.
The obtained results from the previous chapter clearly show that by applying either
compressive or tension axial loading, it is possible to regulate the frequency response of the
vibrator and tune its resonant response to a desired range. Capitalizing on this effect, it is deduced
that the observed deviations due to variations of the ambient temperature can be compensated. The
natural resonance characteristic can be re-shifted to match the input excitation spectrum as the
temperature tries to push it away.
In the shown results, 20 degrees Celsius is selected as a reference temperature. A decrease
in temperature will stiffen the PZT and shift the cantilever resonant frequency toward higher
frequencies, a compressive axial loading is then needed to shift it back to lower values. On the
other direction, an increase in temperature shifts the cantilever resonant frequency toward lower
frequencies, and a tensile axial load will regulate it back toward higher values.
A second set of experiments were conducted to validate the updated model (including the
mechanical loading) and to verify the correction effect. The setup is shown in Figure 3. A set of
springs connect the tip mass to the base of the vibrator. Adjustable screws are used to vary the
tension in the spring and induce a tunable axial loading in the system. The resonant frequency at
the selected reference temperature of 20 oC, corresponding to the used system (Table 1), was
measured to be 45 Hz for a system subjected to an initial compressive axial preloading of 2 N.

44

Preliminary Result: Temperature Compensation Using Preload
In the first run, the temperature was decreased to 0 oC. The resonant frequency shifted to
47.6 Hz inducing more than a 40% reduction in the output voltage response evaluated across a 1
MΩ load resistance. Measured transfer functions (Figure 18(a)) show that the temperature induced
shift of the resonant frequency can be corrected, meaning an adjustment of the axial loading
through the application of an additional 1.2 N compressive axial loading, thus increasing the total
load to 3.2 N and counteracting the temperature effect. Furthermore, the voltage loss can be
completely recovered. The additional compressive loading reduces the overall stiffness of the
system, hence allowing for increased maximum deflections and peak response voltages.
For the second considered case, the temperature was increased to 40 oC starting from the
same reference point at 20 oC. The heating induced a decrease of the resonant frequency response
to 42 Hz. Figure 18(b) also shows that a reduction of the applied axial force by 1.2 N to a new
tuning point at 0.8 N compressive force (the initial reference point was at 2 N applied compressive
loading) induced a total resetting of the resonant frequency response. But in this case, only a
portion of the loss in the amplitude voltage is recovered since the tuning increased the stiffness
and in turn affected the allowable maximum deflection range under the same input excitation force.
Figures 18(a) and (b) present both experimental measurements and theoretical results
obtained using the model developed above. These experiments prove the validity of the tuning
concept and verify the accuracy of the considered models

45

Output Voltage Amplitude (V/g)

35
T = 20o C

30

T = 0o C

25

T = 0o C
with compensation
Theoretical

20
15
10
5
0
35

40

45

50

55

Ouput Voltage Amplitude (V/g)

Frequency (Hz)
30
T = 20o C
T = 40o C

25

T= 40o C
with compensation
Theoretical

20
15
10
5
0
35

40

45

50

55

Frequency(Hz)
Figure 18. Temperature compensation for a variation from the 20o C reference to (a) 0o C, (b)
40o C. (Mtip=3.75g, load resistance=1MΩ)

46

As observed in Figures 18(a) and (b), under certain configurations the loss due to
temperature cannot be completely recovered by varying the load. In fact, a temperature increase
induces an amplitude decrease in addition to the frequency shift. Furthermore, when trying to
correct for the shift, the needed stiffness increase will also reduce the maximum response. This
effect is illustrated in Figure 18(b). In spite of this behavior, it is shown in the conducted
experiment that up to 60% of the amplitude is recovered. The effects are exactly the opposite for
a decrease of temperature compared to the reference point.
This explains the measured peaks in Figure 18(a), which are higher after tuning than the
original reference. Following these observations, it is concluded that the selection of the initial
reference, the one at which the system is designed, is critical toward efficient correction. For
example, the reference temperature should be the highest in the considered range for a piezo that
softens when temperature increase (PZT-5H), and the lowest for a piezo material that exhibit an
opposite behavior. Further analyses are required to establish proper design guidelines.

PASSIVE SELF-TUNED HARVESTER USING SHAPE MEMORY ALLOY EFFECT

Passive Self-Tuned Harvester Design
As previously discussed, systems that require constant corrections, either through
mechanical or electrical input, are impractical as energy harvesting modules. The need for a
external power in order to adjust the control mechanism makes it impractical. In this section, I
propose a method to design a self-correcting energy harvester. The method combines shape
memory alloys (SMAs) with the active piezoelectric transducer. It relies on the temperature effect
in these SMAs to counteract the variations induced in the piezoelectric device.
47

Inherent characteristics found in Shape memory alloys allow them to exhibit large strains
deformation under temperature variation. This behavior is reversible when the applied stress in the
material is kept above a critical limit defined by the material properties. The described concept
here is to adjust the frequency response shifts observed in the piezoelectric vibrator under varying
temperature, meaning an applied axial loading generated by deformations in a set of SMA wires
that are induced by the same temperature variations. The tuned system then exhibits a fully-passive
self-correcting behavior. Obtained results using the presented preliminary experimental setup
show that the temperature effects are not fully recovered. This is due to the hysteresis nature of the
SMA, and the fact that simple, commercially available SMA springs were used in the proof of
concept setup. But, it is also shown that the properties of the alloy can be optimized to match the
used piezo material characteristics, and achieve then an optimal loss recovery.
Figure 19 shows the considered configurations. The SMA wires are initially pre-stressed.
When the temperature changes, the wires induce large strains satisfying the following equation:

 i    A    i  LK  0
 i    A    i  LK  0

Compressive mechanism (Figure 19(a))

(21-a)

Tensile mechanism (Figure 19(b))

(21-b)

where 𝐴 is the wire cross section, 𝐿 is the wire length, 𝐾 is the spring stiffness, 𝜎 and 𝜀 are
respectively the stress and strain within the wire, and the subscript 𝑖 refer to the initial condition.
The one dimensional constitutive model (Funakubo, 1987) is used in this study. The
mechanical behavior of the SMAs is described by the following system of equations:

   0  D      0       S   S 0    T  T0 

48

(22)

(a)

(b)

Figure 19. Schematic depiction of a piezoelectric beam with attached SMA axial loading
mechanism, (a) compression mechanism, (b) tension mechanism.

49

Ω is the transformation tensor, Θ is related to the thermal coefficient of expansion of the
SMA, ξ is the martensite fraction of the material, ξS denotes the stress induced single martensitic
variant fraction, and D is the modulus of the SMA material which is defined as follows:

D    Da    Dm  Da 

(23)

where Da is the modulus of the SMA at 100% martensite and Dm is the modulus at 100%
austenite. The detailed phase’s transformations equations can be found in Brinson (1993).
In the experimental setup, the SMA wires are initially pre-stressed using the springs beyond
the critical stress needed so that they will exhibit reversible transformations with the temperature
changes according to Funakubo, 1987. This parameters are material property (Brinson, 1993).
When the temperature varies, the strain ε within the wire is evaluated using equations (21), (22),
(23) and the model’s specific phase transformations equations. The total induced axial load is then
evaluated as function of temperature as follow:

P T    A   LK

(24)

Self-Tuned Vibration Energy Harvester
The induced change in the piezoelectric beam stiffness due to applied axial load is
calculated using Equation (12). Finally, the modified voltage transfer function is evaluated, as
shown in the model described in section 2. For design purposes, once the dependence of the
piezoelectric to temperature is known, the SMA parameters can be optimized and ultimately
tailored in order to minimize the total stiffness change and the shift of the resonant frequency.
Commercial SMA Springs were used without an optimization of their parameters. The objective

50

of the simplified setup is to prove that the changes in the frequency response of the piezoelectric
vibrator using the SMA springs, due to temperature, can be predicted and controlled.
When the temperature increases, the SMA wires shorten, inducing compressive or tensile
axial loading depending on the adopted configuration (Figure 19(a, b)). If PZT-5H is used as the
transducer, it will soften during an increase in temperature thus causing a shift of the system’s
resonant frequency toward lower level. Based on the SMA behavior described above, if mounted
in the tensile configuration (Figure 19(b)), the induced axial load will shift it back, recovering most
of the observed losses. Other piezo materials can also be used, such as the hard PZT (EC-69).
These materials will harden under a temperature increase in the considered range. Their elastic
compliance decreases by as much as 25% for an increase in temperature from -20 oC to 40 oC
(Sabat et al., 2007). This behavior will shift the resonant frequency toward higher levels. The
compressive mechanism (Figure 19(a)) is then needed to use the stresses in the SMA wires and
shift the resonance point back to around its initial reference level.
As discussed, simple SMA wires were considered in the work reported. Thus, only an
optimization with respect to the spring stiffness, the length, and the cross section of the wires, and
also the transformation temperature, were considered. The transformation constants, CM and CA ,
are assumed to be equal. All of the other material properties used in the simulations are defined in
Table 3. PZT-5H piezoelectric is also considered for this study. As previously discussed, the tensile
configuration is used for temperature compensation in all the simulations. To demonstrate this
combined effect, a reference temperature at -20 oC is selected. The resonant frequency at the
reference frequency for the used system is 49.5 Hz. For a free piezoelectric vibrator transducer (no
SMA loading), the resonant frequency shifts down to 40.9 Hz at 50 oC, inducing a 90% reduction
in the output voltage response evaluated across a 1 MΩ load resistance at that temperature.
51

Numerical Analysis
Figure 20 shows the variation of the optimum calculated axial load (tension) as a function
of temperature using two SMA wires, which have the properties shown in Table 3, and a spring of
stiffness 1900N/m.
Table 3. Material properties of the SMA wires used in the simulations.

Transformation temperatures

Transformation constants

Mf=-37 oC

Cm=13.88 MPa/ oC

Ms=-22 oC

Ca=13.8 MPa/ oC

As=-21 oC

σscr=100 MPa

Af=6 oC

σfcr =170 MPa

Da=67 MPa

εL=0.067

Dm=26.3 MPa

Length L=0.03 m

Ω=0.55 MPa/ oC

Cross section A=10 µm

Tensile Axial Loading (N)

4
3.5
3
2.5
2
1.5
1
0.5
0
-20

-10

0

10

20

30
o

Temperature ( C)
Figure 20. SMA induced load versus temperature

52

40

50

50
25

30

20

o

Temperature ( C)

40

(a)

20
15
10
10

0
-10
-20
35

5

50

45

40

55

60

Frequency (Hz)
50
25

30

20

o

Temperature ( C)

40

(b
)

20
15
10
10

0
-10
-20
40

5
45

50

55

60

Frequency (Hz)
Figure 21. Voltage transfer function versus temperature, (a) without SMA axial load, (b) with an
axial load compensator for a temperature increase

53

Figure 21 (cont’d)
50
25

30

20

o

Temperature ( C)

40

(c)

20
15
10
10

0
-10
-20
40

5
45

50

55

60

Frequency (Hz)

Figure 21(a) shows the voltage transfer function versus temperature for a system without
SMA loading.
Figure 21(b) clearly shows the effect of an added SMA compensation mechanism, for a
decreasing temperature in Figure 21(b) and for a temperature variation from low to high in Figure
21(c). It is noted that the compensation is not perfect due to the hysteresis behavior that the SMA
exhibit. However, it is anticipated that by a better tailoring of the SMA material and the use of
wires that have different properties, this effect can be reduced.
Figure 22 shows the variation of the resonant frequency of the harvester with and without
the SMA induced axial loading effect. The arrows indicate the direction of the temperature
variations. It is clearly observed that the temperature variation in the considered range pushes the
resonant point up and down within a frequency range of about 10Hz for an uncorrected system.
54

Resonant Frequency (Hz)

52
50
48
46
44
42
40
-20

With Compensation
Without Compensation
-10

0

30

20

10

40

50

o

Temperature ( C)
Figure 22. Variation of the resonant frequency with and without SMA induced load
(arrows indicate the direction of temperature variations)

Such a huge variation naturally induces a high loss in the output of an energy harvesting
module designed to operate in a predefined spectrum. The added correction mechanism restricts
these oscillations within a narrow band of about 2 Hz. As mentioned, this band can be further
reduced using optimized tailored SMA properties.
Simplified experiments were performed as a proof of concept for the described effects.
Standard Nitinol extension springs from ‘Images SI, Inc’ were used. Only the tuning ability with
temperature change is shown. An advanced materials matching was not performed. In the used
configuration, the axial load is applied using two SMA springs connecting the tip of the beam to
the base.

55

Experimental Results and Validation
The output voltage transfer function of the piezoelectric element was measured under a
constant applied acceleration for different temperatures. At each temperature, the piezoelectric
properties are extracted from the data shown in Figures 12 and 13, then incorporated into the
response model (Equation 10) and used to evaluate the transfer function in the non-tuned
configuration (at the initial preload reference point of 2 N compressive loading). The model output
is compared to the measured results. The SMA springs are then attached to the setup. Using the
manufacturer charts for the springs, the induced additional axial loading at a given temperature is
evaluated.

20

Output Voltage Amplitude (V)

18
16
14
12
10
8
6
4
2

60o C with shape memory alloy preloading (Experimental)

0

60o C without preloading (Experimental)
Theoretical

-2
30

35

40

45

50

Frequency (Hz)
Figure 23. Output voltage transfer function of the transducer at 60 oC with and without SMA
induced axial loading. Mtip=3.75g, Load resistance=1MΩ.

56

The total loading value is injected into the model described into section 3 and the resulting
voltage transfer function is compared to measurements obtained for the SMA-tuned configuration.
Figure 23 shows the measured and the computed voltage transfer functions of the resonator at 60
o

C with and without the shape memory alloy loading effect.
It can be clearly seen that the added SMA springs shift down the resonant frequency. Using

the manufacturer chart of stiffness versus temperature for the SMA springs, it is determined that
an added 0.7N loading shifted the resonant frequency from 39Hz to 37Hz. The preliminary
experimental results prove that SMAs can be used to induce a variable axial loading dependent on
temperature changes. This variation induces a change of the vibrator’s stiffness, leading to an
adjustable shift in the frequency response.

CONCLUSION
The presented study in this chapter showed that mechanical tuning of vibration energy
harvesters through axial loading can be used to balance the effects induced by temperature
variations. It was also shown that fully-passive temperature compensation, requiring zero input
power for tuning, is feasible in piezoelectric energy harvesters. Experiments to evaluate the effect
of temperature on the frequency response of a PZT-5H piezoelectric cantilever beam under base
acceleration were first conducted. A generalized model for an axially loaded bimorph piezoelectric
subject to temperature variations was presented. The model also describes the correction effect.
Experimental results showing the combined axial load-temperature interactions were also shown.
The model was also extended to describe the overall behavior of a transducer mounted in
a cantilever configuration and subject to axial preloading induced using temperature generated
shape memory alloy deformations. Numerical simulations were conducted to evaluate the
57

variations of the SMA induced load with respect to ambient temperature. Preliminary
optimizations, performed in these simulations, showed that the resonant frequency shifts in the
piezoelectric system can be compensated. A test apparatus was built as a proof of concept
prototype. Initial measurements compared the variations of the device’s frequency response for an
unloaded configuration and a SMA loaded system.

58

CHAPTER 4: PIEZOELECTRIC BASED SELF POWERED SENSOR FOR
STRAIN MONITORING

INTRODUCTION
While the focus on piezoelectric energy harvesting from vibration was about increasing the
level of harvestable power in order to achieve the usability of the CMOS floating gate sensors for
vibration monitoring, piezoelectric energy harvesting from strain seems to provide enough energy
to power the sensor (Lajnef et al. 2008). Piezoelectric harvester with properties in Table 1 can
provide the minimum power requirement at a strain level of 25 µɛ. The sensor is then capable of
measuring and storing data using only the self-generated electrical energy harvested directly from
the sensing signal using the piezoelectric patch. The work depicting a fully deployed strain sensing
system with all the needed attributes is presented in this chapter. The calibration and installation
of the sensor is addressed. The sensor output is defined and the evaluation of a full field data from
a limited number of randomly distributed sensor is studied.

PIEZOELECTRIC FLOATING GATE SELF POWERED SENSOR

Sensor description
A CMOS floating gate is a poly-silicon gate surrounded by an insulator, which in standard
semiconductor fabrication process is silicon-dioxide. The charge on the gate can be modified using
hot electron injection or through tunneling. Injection in a pMOS transistor occurs primarily due to

59

hot-hole impact ionization caused by high electric fields at the edge of the drain-to-channel
depletion region. As electrons are added to the floating gate its potential decreases, thus
implementing a long term non-volatile memory. This low power operation makes it possible to
have a self-powered sensor that can monitor mechanical loading through a piezoelectric harvester.
In addition, a wireless communication capability was added to the sensor enabling the transmission
and the reception of the data.
This module still needs further development to optimize its performance. Figure 24(a)
shows the complete self-powered wireless strain sensor with attached antenna, and embedded into
an epoxy packaging.
To ensure a good contact, most of the marketed packaged strain gages are “H-shaped”.
Therefore, to ensure the most accurate strain measurements the sensor has been packaged in the
same commercial "H-shaped" packaging, where the piezoelectric transducer is emerged at the core
of the reinforced epoxy. It should be noted that there is a need for thermal protection for certain
applications, such as pavement monitoring. For concrete monitoring, the thermal protection is not
needed.
The envisioned monitoring system would consist of a network of low cost sensors
distributed along the monitored structure. Each sensor node would be self-powered and capable of
continuously monitoring and storing the dynamic strain levels. The data from all the sensors would
be periodically uploaded wirelessly to a central database. The sensor will be read through standard
radio-frequency (RF) transmission using a RF reader either manually operated or mounted on a
moving vehicle.

60

Antenna
Sensor

(a)
Wires connected to the piezotransducer

(b
)

Figure 24. (a) Full sensor embedded in an epoxy package, (b) CMOS floating gate sensor.

Connected to the piezoelectric, the sensor is capable of continuously monitoring local
strains within the host structure, implementing a level-crossing cumulative time counting as shown
61

in Figure 25. A series of memory cells (Si) cumulatively store the duration of strain events, at a
preselected level, experienced at the sensing node location.
The system measures the duration of events when the amplitude of the input signal coming
from the piezo exceeds s specific threshold. For the used version of the sensor in this work, the
piezoelectric transducer has to generate a voltage pulse with a minimum amplitude of 5.15 V to
power the sensor. The minimum required voltage should be generated at a strain amplitude equal
to the lowest fatigue (endurance) limit of the material, corresponding to the minimum strain
amplitude that can lead to damage.
The upper voltage limit able to be measured by the sensor is 10 V. Since the output voltage
of the piezo is linearly dependent to strain/vibration amplitude level, the measurable upper
strain/vibration level is almost twice the minimum selected strain/vibration limit. Once the
minimum level is selected depending on the strain range to be measured, the maximum level
needed to be monitored will identify the number of sensor modules required. By stacking these
modules, the covered strain spectrum can be extended depending on the specific application need.
The number of modules is easily defined by the minimum natural number satisfying the equation
below:

 max
 2n
 min

(25)

where εmax and εmin are respectively the maximum and the minimum strain amplitude.

62

S7
S6
S5
S4
S3
S2
S1

(a)

Voltage Amplitude

?

Time

(b
)

Cumulative Loading Time

8

Δ1(i)
S1

6

S2

Δ2(i)

S3

4

S4
S5

2
0

Δ7(i)

S6
S7

Discrete Strain Levels

Figure 25. Illustration of the level crossing cumulative time counting implemented by the sensor

63

Sensor Output under Service Load
In order to select the best damage prediction model that fits the sensor output, the sensor
output should be defined. The sensor measures the cumulative time of load experienced at the
hosting node at preselected discrete levels.
The sensor output is then the summation of the cumulative loading time distributions: the
cumulative distribution, and the cumulative loading time versus load (strain/vibration) level
distribution. When monitoring vibration, the sensor-output is the cumulative vibration induced
spectrum of the structure at the sensor node. When used for strain monitoring, it is the cumulative
induced strain spectrum.
Service loads and the loading frequencies usually follow a Gaussian distribution. Since the
summation of Gaussian distributions can be assumed by a Gaussian distribution, the sensor output
can be defined by the cumulative function of a Gaussian distribution:

F   



  -  

1- erf 
2
  2 

(26)

where μ is the mean of the strain distribution, σ is the standard deviation that account for
the load and frequency variability, and α is the total cumulative time of the applied strain.
The sensor output data will be defined by the three parameters of Equation 26 obtained by
fitting the function to the sensor output distribution collected from all of the memory cells.

64

SENSOR CALIBRATION AND INITIAL TESTING

Sensor Calibration
The system’s configuration of the piezoelectric harvester subjected to axial strain loading
is shown in Figure 26. The governing equations of strain sensor configuration are given by:

 Kr  t   v  t   F (t )

 T
 r (t )  C pv  t   q  t 


(27)

where the stiffness matrix, the electromechanical coupling matrix and the capacitance
matrix are defined in chapter two, equations (12) and (13).

F

b
h
L
Figure 26. Schematic of a piezoelectric strain scavenger of length L, width b, and height h

F is the applied load induced by the axial strain expressed as following:

F SE

(28)

where S and E are respectively the load strain and the elastic modulus of the piezoelectric
q(t) is the current output of the piezoelectric PZT element and can be directly related to the power
output through a load resistance R.
65

Figure 27 shows the voltage transfer function of piezoelectric harvester having the
properties given by table 1 subjected to 25 micro-strain across 50 mega-ohm resistance, equivalent
to the sensor impedance. The ultimate strain limit, which is the minimum strain that causes material
damage, should correspond to the minimum strain that causes the piezoelectric transducer to
generate enough voltage. The minimum needed voltage for the sensor is estimated to be 5 volts.
The dimensions of the piezoelectric generator is then the minimum width that generates 5 Volts
across a 50 mega ohm load resistance subjected to the ultimate strain limit.

6

Output Voltage (V)

5

4

3

2

1
0

2

4
6
Loading Frequency (Hz)

8

10

Figure 27. Voltage transfer function of a PZT piezo under 50 micro-strain loading
across 50 mega-ohm load resistance

Experimental Setup and Initial Testing
A total of 2 mounted sensors were tested on concrete specimens (four point bending
fixtures): two steel-reinforced specimens that had a span of 400 mm, a depth of 100 mm (S/D=4),
and a width of 100 mm.
66

(a)

(b)

Figure 28. (a) Piezoelectric transducer embedded in epoxy then bounded to concrete, (b) Bending
test setup to check the activation strain loss from a configuration to another.

67

A COD gage was also used to measure the strain and was attached to a pair of knife edges,
which were mounted to the bottom face of the beam by a fast drying epoxy resin.
The COD gage is used to control strain and to check the validity of the measurement of the
sensor. The width of the piezoelectric transducer is 5 mm, giving 5 volts under 200 micro-strain.
Three sensors were calibrated and used (using Equation 23) to track a strain spectrum 200 to 1600
micro-strain.
The sensor was mounted at the bottom face of the beam (Figure 28(b)). Each specimen was
subjected to a 5 Hz cyclical load; readings were taken every 10000 cycles. Figure 29 shows the
measured cumulative loading distributions from the sensor at different stages of life of the steel

Output Voltage Measured from the Sensor

reinforced beam.

10000 Cycles
30000 Cycles
50000 Cycles
70000 Cycles
90000 Cycles
120000 Cycles
data 28
data 29
data 30
data 31
data 32
data 33

5
4
3
2
1
0
700

800

900

1000 1100
Induced Strain

1200

1300

Figure 29. Cumulative distribution of strain duration expressed in term of voltage.

68

1400

The results were compared to the COD gage measurements; error was very low, and results
looked very promising. The prediction error will be discussed in more detail in chapter 5.

Initial Fatigue Testing
The sensor has been mounted and tested over the life span of other different concrete
specimens (with the same dimension, but notched) with random (Gaussian) loading.
Figure 30 shows the strain distribution induced at the bottom of the concrete specimen.
Figure 31 shows the cumulative strain distribution measured by the sensor at different life stage of
the specimen. Then the measured output fitted using equation 26.

400
350

(a)

Frequency

300
250
200
150
100
50
0
1

2

3

4
5
6
Strain Amplitude ( )

7
x 10

-4

Figure 30.Strain distribution at different life stages: (a) at 25000 cycles, (b) at 40500 cycles.

69

Cumulative Time (second)

(a)

5000
4000
3000
2000
1000

(b
)

Cumulative Time (second)

0

2

6
4
Strain Level (10 -4  )

8

4
6
Strain Level (10 -4  )

8

10000
8000
6000
4000
2000
0

2

Figure 31. Fitting of the sensor’s output at different life stages of the specimen: (a) at
25000 cycles, (c) at 40500 cycles.

The shift of the strain distribution over time is due to the loss of material stiffness caused
by damage to the beam, which validates the output cumulative distributing measured by the sensor.
70

SENSOR NETWORK
Given that only a limited number of sensors can be deployed, it is critical to estimate the
full-field measured strain distributions from a minimum number of sensors. The objective of this
section is to study the prediction of full field sensor output data from a minimum number of
equidistant sensors. Only the 1 D case has been considered. Its direct application is pavement
monitoring, where the number of sensors installed to monitor strain are limited. The case of sensor
network for pavement monitoring has been studied.

Probability Density Function of the Loading Distribution Parameters
The objective is to recreate the measured distribution induced by all the loading events at
all locations using only a finite number of sensors implemented at determined node locations.
Figure 32 shows a pavement cross section with N sensors distributed along the section to
monitor the longitudinal and transverse strain. The sensors are equidistant. The strain response of
the pavement to traffic is the input to the sensors. The cumulative strain data induced by randomly
generated truck traffic distributions were compressed into probability mass function histograms
using the piezoelectric generator and the sensor models. Then the distribution parameters are
evaluated (µ, σ and α).
The 3D response of a layered pavement system under a moving load with static and
dynamic components has been modeled. The properties of the used layered system were obtained
from Chabot et al. (2010). This three-layer system consists of a top viscoelastic layer modeled
through the Huet–Sayegh model (Huet, 1963 and 1999; Sayegh, 1965), a road base (0.08 m in

71

thickness), and a sub-base layer (0.42 m in thickness) both assumed to be elastic and dependent on
thermal and moisture characteristics. Detailed properties are given in Chabot et al. (2010) and
Nilsson et al. (2002).
Traffic distributions were generated and applied as input loading to the pavement structure.
Four different types of trucks were considered in the analysis: class 9, class 11, class 5, and class
16 (Chatti et al., 2009). One thousand passing truck events were simulated. Each event corresponds
to a randomly selected truck type passing at a randomly selected position within the wheel path.
The loading per axle as applied in this analysis was as follows: steering axle 68,500 N, single axle
80,070 N, tandem axle 71,170 N, and tridem and higher axles 57,830 N.

Figure 32. Pavement cross-section with sensors installed at the bottom of the HMA layer

If a model of a probability distribution "Px" describing of the variation of the parameters
of the distributions measured by the sensors along the transverse coordinate, all the missing values
would be estimated.
Assuming that the transverse coordinate is a random variable and the parameters read from
the sensors are the frequency of an observation of the transverse coordinate, then the variation of

72

each of the parameters α, µ and σ represents a probability density function of the "transverse
coordinate".
The objective then would be to estimate the probability density functions described by each
of the parameters. The log likelihood function of each probability density function can be written
as:

Log L  (log P  yi   log P( xi | yi ))
i

(29)

where yi is all the possible transverse coordinates of the sensors, and 𝑃(yi ) is its probability
density. xi is the observed data corresponding to the longitudinal coordinate of the sensor, and its
probability density is defined by the normalized values of the parameters.
If the data is complete, the likelihood can easily be maximized. However, because the
incompleteness of the data, there is a summation inside the log, which makes the optimization
much harder. So in the case of missing values, the values are estimated based on the current
probability parameters.
The probability distributions are assumed to follow a Gaussian mixture. The objective
would be to evaluate the parameters of the mixture, namely the number of distribution in the mix,
the means, and the standard deviations.
The most prominent method is known as Expectation Maximization. The data set is
modeled with a fixed (to avoid over-fitting) number of Gaussian distributions that are initialized
randomly and with parameters that are iteratively optimized.

73

Set n=0
Initialize Parameters θ
Set Q(θ0| θ-1) = -∞

E-Step
Compute the expectation of the
log likelihood function Q(θ| θn)

n = n+1

M-Step
Compute θ* = arg max(Q(θ| θn))

N
Q(θn+1 | θn ) - Q(θn | θn-1 ) < ɛ

Y

θF = θn+1
Figure 33. Schematics of the likelihood maximization algorithm

Figure 33 shows the schematic of the EM algorithm, and the missing values are filled based
on the current parameters of the probability function (the parameters of the mixture) θn, and then
74

the new parameters are computed in the M step, which maximizes the likelihood of the completed
data. If the relative error between two iterations is more than a given tolerance, continue running
- otherwise the optimum parameters are reached.

Results and discussion
Figure 34 shows the estimated and theoretical probability density function of each of the
parameters of the distributions read from the sensors. For pavement application, three components
give the best description and the least error for the estimation of the density function of each of the
parameters. Once the distribution is estimated, the output can be estimated at any point of the
pavement cross section.
Using two Gaussian mixture components, the least square error of the full field estimation
versus the number of sensors deployed in the pavement cross section has been computed and
presented in Figure 35. Starting from 11 sensors, the error is almost the same, thus making 11
sensors enough to monitor the whole pavement cross section.
Results show that the parameters of a sensor’s network output used for pavement
monitoring can be described by a Gaussian mixture model making it possible to evaluate the full
field cumulative strain measured in a hosting structure based on limited number of sensors.
However, it should be noted that these observations are made for a linear elastic material behavior
with no damage.

75

(a)

Mean Density

0.4
0.3
0.2
0.1
Exact Valus
Two Components
Three Components

0
-0.1

-2

-1

0

1

2

1

2

(b
)

Cumulative Loading Time Density

Coordinate (m)

Exact Values
Two Components
Three Components

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-2

-1

0

Coordinate (m)
Figure 34. Theoretical and estimated density functions of the three parameters using the 10
sensors. (a) mean. (b) cumulative loading time

76

16
Exact Error
Quadratic Fitting

Least Square Error (%)

14
12
10
8
6
4
2
4

6

8
10
Number of Sensors

12

14

Figure 35. Least square estimation error of each of the parameters' distributions versus number
of deployed sensors

CONCLUSION

In this chapter, the development and implementation of a piezoelectric self-powered sensor
has been presented. Application of the sensor for concrete monitoring was developed and
discussed. The feasibility of sensor network based on limited number has been addressed;
however, the effects induced by the data compression format rendered by the sensor on the fatigue
prediction capabilities of the system still need to be addressed.

77

CHAPTER 5: DAMAGE PREDICTION USING PIEZOELECTRIC SELF
POWERED SENSOR

INTRODUCTION
One major obstacles facing health monitoring systems is the ability to accurately predict
damage after structural state diagnosis. The objective of this chapter is to investigate the
performance of the smart sensor and the usability of its output as a means to measure local damage
and study remaining life prediction using a sensor node. First, the derivation of the damage index
from the sensor’s output data is detailed with results from a set of laboratory tests, comparing the
damage index prediction between using the sensor output and the prediction using the complete
time history data. Then, a projection of the remaining life of the tested specimens, using first a
linear damage accumulation rule and then a survivability analysis, was computed and the accuracy
was evaluated by completing the test until failure and counting the total real observed cycles.

DAMAGE INDEX DERIVATION
Damage, as defined in both damage and fracture mechanics, is the irreversible dissipation
of strain energy caused by some external or internal applied force, ultimately manifesting into a
loss of material stiffness (Schapery, 1990; Lemaitre, 1992). In one-dimension, damage can simply
be defined by the degradation of the elastic modulus, E, as shown in equation (30).
D

E
E0

(30)

78

D is the damage variable, defined from 1 to 0, and E and E0 are the current and initial elastic
modulus. Failure will occur at a value Df which is a material property (Lematire, 1992). In fatigue,
the loss of material stiffness (or Elastic Modulus, E) can be assessed using variations of the peak
to peak strain data (Subramaniam et al., 2000). Under constant amplitude loading, the ratio
between the modulus at any given time (E) and initial elastic modulus (E0) is equal to the inverse
of the ratio of the initial (Δɛ0) and instantaneous (Δɛ) peak to peak strain levels. Thus, the damage
variable D can be written in terms of Δɛ and Δɛ0 as shown in equation (31).

D

 0


(31)

The fitting parameters of the sensor output, the cumulative loading time, the mean and the
standard deviation, can be written as a function of the parameters of the strain distributions:
N

  i

(32)

i
N

   i i
i 

(33)

1/2

N

    i  i2 
 i 


(34)

where N correspond to the latest loading time period between the two last reading. Using
equations (33) and (34), the mean and the standard deviation of the latest applied strain distribution
at a time t can be evaluated from two consecutive readings, expressed by the following equations:

79

N 

   


 

   2
N 
 



(35)
1/2







(36)

Once the mean and the standard deviation of the strain distributions are evaluated, using
the Taylor series with exact derivation, the mean and the variance of the damage coefficient are
derived, given by the two equations below:

E  D 

Var  D  

2
0
2
N

0
N


(37)

2 2
0  N
4
N

(38)

where the subscript 0 correspond to the first loading time period.

EXPERIMENTAL SETUP AND DAMAGE INDEX DISTRIBUTION

Experimental setup
To check the capabilities of the sensor for damage variable evaluation, twenty-three plain
PCC three-point single edge notched beam specimens (TPB-SEN) were tested under constant and
variable amplitude fatigue loading. Two beam sizes were considered: (1) The large specimens,
which had a span of 400 mm, a depth of 100 mm (S/D=4), and a width of 100 mm and (2) The
80

small specimens, which had a span of 200 mm, a depth of 50 mm (S/D=4), and a width of 50 mm.
The notch to depth ratio for each specimen was 0.35. A Crack Opening Displacement (COD) gage
was used to measure the crack mouth opening and was attached to a pair of knife edges which
were mounted to the bottom face of the beam by a fast drying epoxy resin, as recommended by
RILEM (Shah, S.P., 1995). Each specimen was subjected to a 2 Hz cyclical load. Ten specimens
were subjected to constant amplitude loading using a stress ratio (max load/peak load) of 0.85 (5)
and 0.95 (5).

Figure 36. Test setup: the sensor is installed in the bottom of the concrete specimen to
measure the induced tensile strain.

81

The other specimens were subjected to variable loading in which both the R ratio (min/max
load) and the stress ratio were varied at several stages throughout the test. A reading was taken
every 200 cycles.
The concrete mix used in this research consisted of ASTMC-150 Type I cement, natural
sand, and limestone coarse aggregate (nominal maximum size of 25 mm). The water to cement
ratio was 0.45 and the air content was 6.5%. The unit weight was 2274.62 kg/m3. The average 28
day Modulus of Rupture (MOR) and the split tensile strength, f’t, were 5.23 and 2.89 MPa,
respectively. The 28 day compressive strength was 25 MPa. The specimens were cured for one
year inside of a humidity room and then placed in ambient temperature for one more month to
ensure minimal strength gain during fatigue testing.

Damage index distribution
Figure 37 shows the variation of the damage index distribution over the entire life span of
a concrete specimen. It shows that the mean damage index is decreasing over time. The standard
deviation of the index is, on the other hand, nearly constant over the life of the specimens.
The prediction’s relative error of the damage index mean is relatively low (Figure 38); less
than 20%. The prediction error is taken into account by the standard deviation.
At the initial stage of the beam, there is a fast change of the induced strain amplitude,
causing a fast variation of the damage index and a higher standard deviation.
Besides the prediction error, the standard deviation takes into account all the missed
information that the sensor can't sense, such as the load distribution, the induced strain sequence,
and the loading frequency.
82

Probability Density

10

5
1
0.8

0
0.4

0.6
0.4

0.6
0.2

0.8
1

0

Normalized Time

Damage Index

(a)

Mean of the Damage Index Distribution

Figure 37. Probability distribution of the damage coefficient versus the number of cycles of
loading

1
Using the Sensnor
Evaluated Using the COD Gage

0.9
0.8
0.7
0.6
0.5
0.4

0.2

0.4
0.6
Normalized Time

0.8

1

Figure 38. (a) Variation over time of the mean of the damage index versus the exact damage index
evaluated with the COD gage, (b) Variation of the variance of the damage index distribution.

83

REMAINING LIFE PREDICTION

Linear Damage Accumulation
Equation 39 and 40 show the linear damage accumulation rule that is used in the MEPDG
and adopted in this work in order to predict the remaining life of the concrete specimens. The
coefficients βi, in equation 40 were calibrated for every specimen using the sensor reading.
Subramaniam et al. (2000) observed that under constant amplitude loading, the inflection point
between the deceleration and the acceleration cracking region occurs at approximately 40 to 50%
of the total life of the specimen. Thus, the coefficients pertaining to the first half of the specimen’s
life should be similar to the second half. Once the coefficients are known, a remaining life
prediction can be made.

D

 

1
Nf

(39)

 1 
Log N f  0 

 SR 

1

 2

(40)

For every specimen using the sensor’s output, the linear damage accumulation equation
function is fitted and the coefficient βi are evaluated, then used to predict the remaining life of the
specimen. The fitting parameters usually converge (stabilize) when the inflection point of the
damage index is reached.
Table 4 shows the predicted remaining life using the described method based on the sensor
output and the calibrated coefficient for different tested specimens. The loading of the specimens
was stopped, and the remaining life was estimated and compared to a standard calibrated equations
estimation. The tests were then continued until failure in order to record the actual remaining life.

84

As observed in the results for the considered cases, the predictions evaluated using the
localized sensor data are closer to reality than the standard calibrated equation predictions.
Table 4. Predicted remaining life using calibrated coefficient and the sensor output.

Predicted
Exact remaining

remaining life

Relative error

life

using standard

(%)

equation

Predicted
remaining life
using the sensor

Relative error
(%)

391

709

81.3299

325

16.8798

20527

716

96.51191

5873

71.3889

420

835

98.8095

425

1.19048

9350

902

90.35294

7125

23.79679

7022

922

86.86984

11048

57.3341

10980

990

90.98361

23011

109.572

The standard calibrated equation does not differentiate between the specimen’s specific
properties; the predicted values are almost constant. However, the predictions of the calibrated
equation using the sensor’s output are more accurate since the sensor’s output is very specific to
each specimen.
It should be noted that the damage index at failure is considered a random variable that
depends on the material properties. However when installed, the only information that the sensor
provides is the cumulative strain distribution and the damage index distribution, which gives no
information about the index at failure.

85

Survivability analysis
Since the damage index at failure is a random variable that depends only on the material
properties, the prediction of the remaining life by assuming it as c constant will not improve the
prediction. The idea is to use the sensors output to construct a probability density function of the
damage index at failure in order to improve the prediction over time.
Probability density function of the damage index at failure
Reliability engineering and survival analysis mostly deal with a positive random variable
called “lifetime”. The lifetime is manifested by a failure or other “end event

3.5
Measurments
Fitted Distribution

3

Density

2.5
2
1.5
1
0.5
0
0

0.2

0.4

0.6

0.8

1

Damage Index at Failure
Figure 39. Probability density function of the damage index at failure

”. In this particular case, the failure is defined by the total break of the beam, and the
lifetime variable is the time T, at which the failure occurs with a cumulative distribution function
86

F(T), which here is defined by the probability of the damage index at time T being higher than the
damage index at failure:



F  D T    Pr D f  D T 



(41)

Figure 40 shows the density function of the damage coefficient at failure. A total of 23
specimens have been tested and the index has been measured using the COD gage. The fitted
distribution is a logit-normal.
The objective is to evaluate the survival probability function of the specimen based on the
evaluated damage index using the sensor and the probability density function of the index at
failure.
Survivability function
The remaining lifetime cumulative density function is defined using the law of conditional
probability, the condition that the beam didn’t fail at time t = x:

P  x  T  x  t  F  x  t   F  x
Fx  t   r

Pr  x  T 
1  F  x

(42)

The corresponding survival probability function of the beam is given by:

Fx  t  

1 F  x  t F  x  t

1  F  x
F  x

(43)

The remaining life at a time T is estimated to be the expectation of the survival probability
function:
87

Re m  E T  



T F  x(t )  dt
F  x(T ) 

(44)

However, the lifetime probability function is not defined; the remaining lifetime should be
expressed as function of the damage index probability function, as it is the only information that
the sensor can provide. Using a change of variable, equation 42 can be expressed as a function of
the damage index:


F  D

 DT  dD
Re m  E T  
where

dD
dt

T 
dt
F  D T  

dD
(45)

is the variation of the damage index with respect to time, evaluated by fitting a

shape function to the damage index variations values evaluated using the sensor at different life
stage of the specimen.
Results
The assumed shape functions are linear and arcsine. Figure 41 shows the normalized
predicted remaining life (41) using the described method. The specimen lifetime is normalized, as
well as the prediction remaining life. The normalized lifetime goes from zero to one, one meaning
failure; however, the predicted remaining life goes from 1 to 0, where 0 remaining life also means
failure.
As the specimen approaches failure, the more fitting points are available, and the more
accurate the prediction is. It should be noted that the fitting stabilizes when the inflection point of
the damage index variation is reached.
88

0.7
Linear
Arcsine
Deterministic

(a)

Predicted Ramining Life

0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.2

0.4
0.6
Normalized Remaining Life

0.8

Figure 40. Normalized estimated remaining life vs. normalized specimen’s lifetime using three
different methods, (a) first specimen (b) second specimen.

As shown in figure (40), the prediction using the survivability function is not always better
than the linear accumulation rule function. Two cases should be noticed: if the damage index at
failure is a higher value (higher than the mean of the distribution or at least close) then the
survivability method gives better results. Otherwise the accuracy of the results is similar. Besides
having the advantage of long-term capabilities that help give better remaining life prediction using
the linear accumulation damage rule, the sensor also gives the advantage of using a survivability
analysis that helps the predictions accuracy by providing a data base of the damage index at failure.
The probability of the remaining lifetime is a good indicator of how reliable the prediction
is. As shown in Table 5, starting from a probability of 0.6, the relative error of the predicted
remaining life is less than 50%. When installed in the real field, by evaluating the lifetime
89

probability it is able to decide how reliable the predictions are. Tables 5 compares the predictions
using a survivability analysis and the prediction using a linear damage accumulation rule.
The predictions using survivability analysis are more accurate simply because the material
properties have been considered by taking into account the probabilistic nature of the damage
index.
The probabilistic method is a powerful tool to deal with lack of information in order to
predict the remaining life of structures. When the sensor is in the field, this method has many
advantages over the linear damage accumulation method: it does not require any estimation of the
material properties. For example, the resilient modulus for concrete, and it is very convenient with
the sensor functionality, with two successive readings the estimated remaining life of the hosting
structure can be estimated. This method is more realistic since it covers the lack of data and
information about the structure such as the load distributions and the loading frequencies.

Table 5. Estimated remaining life using the different fitting shape function

Exact

Linear Shape Function

Arcsine Shape Function

Remaining
Life (RL)

RL

Prob

RL

Error

Error

(%)

Prob

(%)

Linear damage
accumulation
RL

Error (%)

0.5

0.3881 0.5988

22

0.6959

13.71

14

0.73

46

0.4

0.3481 0.6436

12

0.717

5.04

5

0.51

27

0.3

0.3115 0.6784

3

0.735

3.68

4

0.48

60

0.2

0.2836 0.7218

41

0.7575

12.87

13

0.40

100

0.1

0.2525

152

0.7748

21.71

22

0.40

300

0.757

90

CONCLUSION

The presented study in this chapter showed that remaining life of structures can be
predicted with a better accuracy using a long-term monitoring self-powered sensor. A model for
damage index derivation from cumulative load distribution was presented. The model takes into
account the missing data. It was tested on concrete samples, and the damage index evaluation
results looked very prominent.
It was also shown that probabilistic method is more practical and reasonable to use in the
field, as it is a powerful tool to deal with a lack of information and can predict the remaining life
of structures. It doesn’t require any estimation of the material properties and the remaining life of
the structure can be estimated at any time of its lifetime.

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CHAPTER 6: CONCLUSION AND RECOMMENDATIONS

Over the last four decades, a significant interest has been placed on research related to
damage prediction for the purpose of structural health monitoring. In order to improve the
predictive capabilities of these methods, new emerging sensing technologies, more adapted to the
SHM issues, are being developed. These systems are able to better measure and identify the
parameters relevant to the health state of the structure. Global methods are the most commonly
used structural health monitoring techniques. Measurement of the acceleration response of
structure is the most relevant information needed in order to use these methods. However, it has
been shown that methods are very sensitive to environmental changes (moisture content,
temperature variation, etc). In addition, the large scatter in material data, i.e., fatigue, combined
with limitations on the number of sensors that can be deployed, have hindered the development
and validation of improved prediction models.
The work aiming at developing a fully deployed piezo-based self-powered SHM sensor
has been presented in this thesis. The new type of data generated by the sensors, presented the
challenge of developing and validating new adapted models for local and global damage
prediction. The sensing system consist of a self-powered computation and non-volatile storage: it
uses the physics of floating gate transistor injection principles to compute cumulative voltage
output of a piezoelectric generator at preselected discrete levels. The wireless operating of the
sensor allows also for longer lifetimes compared to conventional strain gauges since there is no

92

risk of wire damage. In addition, extensive sensor networks could be deployed for structural
monitoring.
The major problem toward achieving long term self-powered monitoring was providing
power. Piezoelectric harvesters were used as both the sensor and the power transducers. Mounted
in cantilever configuration and subjected to ground vibration or mounted in a patch configuration
and subjected to strain loading, a piezoelectric transducer is capable of generating a monitoring
signal that is proportional to local vibrations/or strains within the hosting structural element.
The improvement of the energy harvesting using piezoelectric from vibration has been
targeted to increase the level of harvestable power. Analysis of the variations of the frequency
response, amplitude, damping ratio, and efficiency of the device with respect to the preload has
showed that stiffness tuning of the PZT harvester increases the average harvested power by a one
order of magnitude. It was also shown that the tuning through axial preloading can be used to
correct for mismatch induced effects. Combined with Shape Memory Alloy, piezoelectric
harvesters provided enough power for vibration monitoring under varying external temperature.
The frequency response shifts observed in the piezoelectric vibrator under varying temperature,
have been adjusted meaning an applied axial loading generated by deformations in a set of SMA
wires that are induced by the same temperature variations.
The second main challenge was due to the fact that the data generated by these novel seflpowered modules, is different from any data used in conventional methods. The information is
compressed and integrated in time, then reported as a cumulative histogram of a combined number
of events repetitions times the duration versus the input strain amplitude. Adequate data
interpretation techniques were developed with the purpose of extracting the variations over time
of the damage index. The issues of missing data and full field generation were also addressed.
93

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