Modal updating method (ANN)

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Structural model updating by numerical optimization and artificial
neural network

Li, Chongyang (

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Li, C. (2013). Structural model updating by numerical optimization
and artificial neural network (Outstanding Academic Papers by
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STRUCTURAL MODEL UPDATING BY
NUMERICAL OPTIMIZATION AND ARTIFICIAL
NEURAL NETWORK

By
Chongyang LI

Submitted in partial fulfillment of the requirements for
the degree of Bachelor of Engineering (Honours) in Building
Engineering (Structural and Geotechnical Engineering)

Department of Civil and Architectural Engineering
City University of Hong Kong

March 2013


DECLARATION

I declare that this thesis represents my own work, except where due acknowledgement
is made, and that it has not been previously included in a thesis, dissertation or report
submitted to this University or any other institution for a degree, diploma or other
qualification.

Signed __________________________
Chongyang LI


Abstract

I

Abstract
Changes of physical properties of structure (mass, stiffness and damping ratio) can be
reflected on its dynamic characteristics. This project studied two approaches in
structural model updating utilizing measured dynamic data: Numerical Optimization
and Artificial Neural Network (ANN). Both numerical and experimental studies were
carried out on a four-story shear building model under laboratory conditions for the
demonstration and verification of these two approaches.
In the experiment, vibration responses of a shear building model were measured, for
the nominal case and 11 different additional mass cases, respectively. Then, modal
parameters (i.e., natural frequencies and respective mode shapes) were identified from
the measured vibration responses by the method of MODE-ID (Beck 1978). In each
additional mass case, different masses were added to different floors of the shear
building model. This project aims in studying the performance of the two approaches
in identifying the location and magnitude of the added mass(es).
For the purpose of structural model updating, the two approaches were implemented
separately. One is numerical optimization, which is to establish an analytical model to
match the measured dynamic structural response by minimizing the discrepancy
between the experimental measured and model-predicted modal parameters, such as
natural frequencies and mode shapes. The other approach is ANN, which is a network
of processing units. In this study, an ANN is trained by using the measured modal
parameters as inputs and the corresponding structural parameters (i.e., mass at
different floor of the shear building model in this study) as the outputs. Computer
simulated data was employed to train the ANN and experimental measured modal
parameters were used to test the performance of the trained ANN in estimating the
mass distribution of the building.


Acknowledgements

II

Acknowledgements
My deepest gratitude goes foremost to Dr. Paul H. F. Lam, my supervisor of Final
Year Project, for his patient guidance, enthusiastic encouragement and useful critiques
of this work. He has walked me through all the stages of FYP, from kicking off,
learning background knowledge, selection of methodologies, conducting experiments,
to the writing of this thesis. It is he that brought me into this new promising research
area. It is his illuminating instruction that guide and upgrade my work.
Secondly, I would like to express my sincere gratitude to Mr. Jiahua Yang, who taught
me a lot in the use of experiment instruments and computer software, as well as
theories in structural dynamics. He generously shared his expertise and experience
with me. Without his constructive advice and help, this thesis could not have reached
its present form.
Thirdly, my thanks would go to my fellow classmates, who shared their knowledge
without preservation and gave me the courage to insist throughout my university life.
Lastly, I wish to thank my beloved parents for their encouragement and support
throughout my career.


Table of Contents

III

Table of Contents
Abstract .......................................................................................................................... I
Acknowledgements ....................................................................................................... II
Table of Contents ......................................................................................................... III
List of Tables ................................................................................................................ V

List of Figures ............................................................................................................ VII
CHAPTER 1: INTRODUCTION .................................................................................. 1
1.1 Project Background ................................................................................. 1
1.2 Project Description and Scope ................................................................ 2
1.3 Project Objectives ................................................................................... 3
CHAPTER 2: LITERATURE REVIEW ....................................................................... 5
2.1 Modal Frequency Changes ........................................................................ 5
2.2 Mode Shape Changes ................................................................................ 6
2.3 Model Updating Method............................................................................ 7
2.3.1 Numerical Optimization ................................................................... 7
2.3.2 Artificial Neural Network ................................................................. 9
2.4 Other issues .............................................................................................. 11
CHAPTER 3: METHODOLOGY ............................................................................... 12
3.1 Basics of Structural Dynamics................................................................. 12
3.1.1 Single Degree of Freedom System ................................................. 12
3.1.2 Multiple Degrees of Freedoms System ........................................... 13
3.2 Shear Building and Experimental Considerations ................................... 16
3.2.1 Shear Building ................................................................................ 16
3.2.2 Additional Masses .......................................................................... 19
3.2.3 Vibration Measurement and Excitation .......................................... 19
3.3 System Identification ............................................................................... 20
3.4 Structural Model Updating and Detection of Additional Mass ............... 21
3.4.1 Numerical Optimization ................................................................. 21


Table of Contents

IV

3.4.2 Artificial Neural Network ............................................................... 25

CHAPTER 4: CASE STUDY ...................................................................................... 31
4.1 Flow of the case study ............................................................................. 31
4.2 Experimental Apparatus and Setup ......................................................... 32
4.3 Additional Mass Cases ............................................................................ 38
4.4 Measurements .......................................................................................... 39
4.5 System Identification ............................................................................... 42
4.6 Structural Model Updating: Numerical Optimization Approach ............ 44
4.7 Structural Model Updating: Artificial Neural Network (ANN) Approach
56
CHAPTER 5: DISCUSSION AND CONCLUSION .................................................. 64
5.1 Overall Performance ................................................................................ 64
5.2 Evaluation of Methodology ..................................................................... 65
5.3 Comparison between Two Approaches ................................................... 68
5.4 Future work .............................................................................................. 74
REFERENCES ............................................................................................................ 76
APPENDIX A: Matlab script-Eigenvalue problem ..................................................... 79
APPENDIX B: Matlab script-function of Fast Fourier Transform ............................. 80
APPENDIX C: Matlab script-Modal Assurance Criteria (MAC) ............................... 81
APPENDIX D: Matlab function-Objective function J( ) ........................................... 82
APPENDIX E: Matalab script-Training and use of ANN ........................................... 83
APPENDIX F: Properties of accelerometer ................................................................ 86
APPENDIX G: Matlab script-MODE-ID .................................................................... 88
APPENDIX H: Identified natural frequencies ............................................................. 91
APPENDIX I: Comparison between identified mode shapes and mode shapes of
numerically updated model .......................................................................................... 95
APPENDIX J: Comparison between identified natural frequencies and calculated
natural frequencies of the numerically updated model .............................................. 101


List of Tables

V

List of Tables
Table 4. 1 Procedures of case study ............................................................................. 31
Table 4. 2 Pictures of Experimental Apparatus ............................................................ 32
Table 4. 3 Dimensions of shear building ..................................................................... 36
Table 4. 4 Physical Properties of the shear building .................................................... 36
Table 4. 5 Theoretical natural frequencies and mode shapes ....................................... 37
Table 4. 6 Additional mass cases, location and magnitude .......................................... 38
Table 4. 7 Optimal mass coefficients, J( ) and calculated natural frequencies of Case 1
(No additional mass) ............................................................................................ 45
Table 4. 8 Optimal mass coefficients, J( ) and calculated natural frequencies of Case 2
(10 kg Mass on Floor 2) ....................................................................................... 45
Table 4. 9 Optimal mass coefficients, J( ) and calculated natural frequencies of Case 3
(10 kg Mass on Floor 3) ....................................................................................... 46
Table 4. 10 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
4 (5 kg Mass on Floor 2) ...................................................................................... 46
Table 4. 11 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
5 (5 kg Mass on Floor 3) ...................................................................................... 47
Table 4. 12 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
6 (1.5 kg Mass on Floor 2) ................................................................................... 47
Table 4. 13 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
7 (1.5 kg Mass on Floor 3) ................................................................................... 48
Table 4. 14 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
8 (10 kg Mass on both Floor 2 and Floor 3) ........................................................ 48
Table 4. 15 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
9 (5 kg Mass on both Floor 2 and Floor 3) .......................................................... 49
Table 4. 16 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
10 (1.5 kg Mass on both Floor 2 and Floor 3) ..................................................... 49

Table 4. 17 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
11 (10 kg Mass on Floor 2 and 5 kg Mass on Floor 3) ........................................ 50


List of Tables

VI

Table 4. 18 Optimal mass coefficients, J( ) and calculated natural frequencies of Case
12 (5 kg Mass on Floor 2 and 10 kg Mass on Floor 3) ........................................ 50
Table 4. 19 Comparison between theoretical and analytical mass coefficient and
natural frequencies for nominal case ................................................................... 51
Table 4. 20 Comparison between Actual Additional Mass and Detected Additional
Mass by Numerical Optimization Method........................................................... 53
Table 4. 21 Detected Additional Mass by ANN for Additional Mass Case 2-5........... 58
Table 4. 22 Detected Additional Mass by ANN for Additional Mass Case 6-9........... 59
Table 4. 23 Detected Additional Mass by ANN for Additional Mass Case 10-12....... 60
Table 4. 24 Comparison between Detected Additional Mass by ANN and Actual
Additional Mass ................................................................................................... 61
Table F. 1 Technical data of accelerometer .................................................................. 87
Table H. 1 Identified Natural Frequencies (Hz) of Case 1-3 ....................................... 91
Table H. 2 Identified Natural Frequencies (Hz) of Case 4-6 ....................................... 92
Table H. 3 Identified Natural Frequencies (Hz) of Case 7-9 ....................................... 93
Table H. 4 Identified Natural Frequencies (Hz) of Case 10-12 ................................... 94
Table J. 1 Comparison of calculated and identified natural frequencies of Case 1 ... 101
Table J. 2 Comparison of calculated and identified natural frequencies of Case 2 ... 101
Table J. 3 Comparison of calculated and identified natural frequencies of Case 3 ... 102
Table J. 4 Comparison of calculated and identified natural frequencies of Case 4 ... 102
Table J. 5 Comparison of calculated and identified natural frequencies of Case 5 ... 103
Table J. 6 Comparison of calculated and identified natural frequencies of Case 6 ... 103

Table J. 7 Comparison of calculated and identified natural frequencies of Case 7 ... 104
Table J. 8 Comparison of calculated and identified natural frequencies of Case 8 ... 104
Table J. 9 Comparison of calculated and identified natural frequencies of Case 9 ... 105
Table J. 10 Comparison of calculated and identified natural frequencies of Case 10105
Table J. 11 Comparison of calculated and identified natural frequencies of Case 11 106
Table J. 12 Comparison of calculated and identified natural frequencies of Case 12106


List of Figures

VII

List of Figures
Figure 3. 1: Vibration response of SDOF .................................................................... 13
Figure 3. 2: Linear combination of mode shapes in MDOF ........................................ 16
Figure 3. 3 Spring model of shear building ................................................................. 16
Figure 3. 4 Free-body diagram of shear building ........................................................ 17
Figure 3. 5: Shape of shear building ............................................................................ 18
Figure 3. 6: Measured and calculated mode shapes with J( )=0.6063 ........................ 23
Figure 3. 7: Measured and calculated mode shapes with J( )=0.0402 ........................ 23
Figure 3. 8: Typical network architecture of ANN ...................................................... 25
Figure 4. 1: Accelerometers ......................................................................................... 32
Figure 4. 2: Shear Building with additional mass ........................................................ 33
Figure 4. 3: Impact hammer hitting on the floor slab .................................................. 33
Figure 4. 4: A NI A/D card with chassis ...................................................................... 34
Figure 4. 5: A computer with LabView ........................................................................ 34
Figure 4. 6: 1.5 kg additional mass .............................................................................. 34
Figure 4. 7: 5 kg additional mass ................................................................................. 35
Figure 4. 8: 10 kg additional mass ............................................................................... 35
Figure 4. 9: Theoretical mode shapes of shear building .............................................. 37

Figure 4. 10: Block diagram in LabView for shear building measurements ............... 39
Figure 4. 11: Input information to LabView file .......................................................... 40
Figure 4. 12: Match physical channels with channels in software .............................. 40
Figure 4. 13: Specify location to save measured data .................................................. 41
Figure 4. 14: Specify sampling frequency and time length of each loop .................... 41
Figure 4. 15: Time domain response of the first sensor ............................................... 42
Figure 4. 16: Frequency domain response of the first sensor ...................................... 43
Figure 4. 17: Identified mode shapes and natural frequencies..................................... 43


List of Figures

VIII

Figure 5. 1 Comparison between Detected Additonal Mass by Numerical
Optimization and ANN ........................................................................................ 69
Figure 5. 2 Percentage Detection Errors in Numerical Optimization and ANN .......... 70
Figure F. 1: Appearance and size of accelerometer ..................................................... 86
Figure I. 1 Case 1: No additional mass ........................................................................ 95
Figure I. 2 Case 2: 10 kg mass on floor 2 .................................................................... 95
Figure I. 3 Case 3: 10 kg mass on floor 3 .................................................................... 96
Figure I. 4 Case 4: 5 kg mass on floor 2 ...................................................................... 96
Figure I. 5 Case 5: 5 kg mass on floor 3 ...................................................................... 97
Figure I. 6 Case 6: 1.5 kg mass on floor 2 ................................................................... 97
Figure I. 7 Case 7: 1.5 kg mass on floor 3 ................................................................... 98
Figure I. 8 Case 8: 10 kg mass on both floor 2 and floor 3 ......................................... 98
Figure I. 9 Case 9: 5 kg mass on both floor 2 and floor 3 ........................................... 99
Figure I. 10 Case 10: 1.5 kg mass on both floor 2 and floor 3 .................................... 99
Figure I. 11 Case 11: 10 kg mass on floor 2 and 5 kg mass on floor 3 ...................... 100
Figure I. 12 Case 12: 5 kg mass on floor 2 and 10 kg mass on floor 3...................... 100

CHAPTER 1: INTRODUCTION

1

CHAPTER 1: INTRODUCTION
1.1 Project Background
In the past few decades, human’s needs of accommodation, entertainment and
communication simulated the growth of civil engineering technique. An enormous
number of large-scale civil engineering projects can be seen throughout the world,
especially on the land of Asia. However, danger coexists with success. Almost every
year in China, improper design or inferior construction lead to collapse of civil
structures, causing losses of lives. Even in developed areas, natural or non-natural
disasters, such as Great East Japan Earthquake in 2011 and Hong Kong Harbour
Grand Hotel Fire Hazard in 2012, affect the integrity of buildings, leading to huge
amount of financial and social loss.
These disasters attract public concern on safety. A very big topic after that is the
comprehensive usability study of those physically changed buildings, as well as those
unchanged ones, which are generally deemed to be safe. Therefore, a fast and safe
way to evaluate the changes caused to these buildings and the general “health
condition” of structures is badly needed, which raised the interests of many
researchers and practicing engineers.
One way of evaluating is the visual inspection with appropriate localized experiments
such as acoustic or ultrasonic tests. Local techniques often require that the existence
and approximate location of physical changes be known. In order for these local
techniques to be used, damaged members usually have to be accessed, which means
that barriers (e.g. walls) must be removed and structural use must be limited or
completely restricted. (Brandon. A. Mogan, 2005) However, due to the complexity of
the high rise hotel buildings and high level of radiation in the Fukushima Daiichi

nuclear power plant, this method is not applicable. Similar conditions are encountered
frequently in other major structures as well.


CHAPTER 1: INTRODUCTION

2

To move on from the superficial changes, applicable methodology has to go deep into
the structure, deep into the problem. The need for additional global detection methods
that can be applied to complex structures has led to the development of methods that
examine changes in the vibration characteristics of the structure. (Doebling et al. 1996)
[18] The basic idea of vibration-based methods is finding out changes in physical
properties of structure (i.e., mass, stiffness and damping ratio), by analyzing its
changes in dynamic characteristics (i.e., modal frequencies, mode shapes and modal
damping ratio).
This idea is applicable, based on an intrinsic relation between physical properties and
dynamic characteristics of a building. For instance, for an undamped free vibration of
multi-degrees of freedoms structural system, this relation can be written as Equation
1.1 (eigenvalue problem)
k

m

Equation 1. 1

in which k is the stiffness matrix of the system (physical property), m is the mass
matrix of the system (physical property),
property or called dynamic characteristic) and

n

is the nth modal frequency (modal
n

is the nth mode shape vector (modal

property or called dynamic characteristic).
Nevertheless, difficulties are encountered, mainly in two procedures: one is the
process of identifying modal properties from measured vibration response, which is
called System Identification; the other is the process of establishing the connection
between the identified modal parameters and the physical changes (additional masses
or stiffness reduction), which is called the Model Updating.
1.2 Project Description and Scope
Proceeding from the existing difficulties, this project focuses on the development and
usage of specific methodologies in System Identification and Model Updating, all of
which are designed to be achieved on computer through Matlab. In System


CHAPTER 1: INTRODUCTION

3

Identification process, modal parameter values are obtained by adopting an existing
algorithm called MODE-ID, while in Model Updating part, two approaches are
adopted. One is Numerical Optimization, in which an optimal analytical model is to
be found to match the measured vibration response by minimizing an objective
function describing the discrepancy between model-reproduced modal parameters and
identified modal parameters from the measured dynamic data. The optimized
analytical models for both nominal case and additional mass cases can be compared to

determine the existence, location and magnitude of the additional mass. The other
approach is Artificial Neural Network (ANN), which network of processing units
between the natural frequencies and physical properties (mass distribution of the
building in this case). Changes in optimal models and changes in outputs from the
ANN are the detected additional mass.
To utilize and examine the developed methodologies, impact hammer excited
vibration response of a 4-storey shear building is studied. Dynamic data taken by
accelerometer is obtained for different cases, including original shear building and
shear building with different masses added to different floors. Detection of changes in
physical properties (additional mass in this project), is the aim of this project.
1.3 Project Objectives
The ideas listed in the project description are in order to achieve the following
objectives:
(1) To measure the vibration responses of the 4-story shear building, for nominal case
and 11 different additional mass cases;
(2) To identify the modal parameters of the shear buildings in different cases based on
the measured dynamic data;
(3) To find the optimal models that match the identified modal parameters by
numerical optimization of structural model;
(4) To train an ANN that can generate output of physical properties of structures with
the input of modal parameters.


CHAPTER 1: INTRODUCTION

4

(5) In both numerical optimization and ANN, detect the location and magnitude for
the added masses in different cases.
(6) To analyze the advantages and drawbacks of the two approaches of structural

model updating.


CHAPTER 2: LITERATURE REVIEW

5

CHAPTER 2: LITERATURE REVIEW
Due to the high similarity between detection of additional mass (used to verify the
proposed methodologies in this project) and structural damage detection, some
methodologies presented in this chapter refer to damage detection techniques.
By the extent and significance of findings, structural changes detection methods are
classified into 4 levels (Rytter, 1993) [26]:
Level 1: Determination that structural changes is present in the structure
Level 2: Level 1 plus determination of the geometric location of the change
Level 3: Level 2 plus quantification of the severity of the change
Level 4: Level 3 plus prediction of the remaining service life of the structure
Generally, vibration based detection methods without a structural model, like just
considering changes in modal frequencies, can only reach the Level 1 and 2. Coupled
with a structural model, structural changes can be identified to the Level 3. Findings
in Level 4 require a complex combination of knowledge such as fatigue-life analysis
and structural design system, which are excluded in this review.
2.1 Modal Frequency Changes
In 1969, Lifshitz and Rotem

present the first journal paper proposing damage

detection method via vibration measurement. They find changes of the structures by
observing changes in dynamic moduli, which are the slopes of the extensional and
rotational stress-strain curves under dynamic loading.

After Lifshitz and Rotem, people first found that changes of structural properties
could be detected by the changes of modal frequency. Cawley and Adams (1979)
employed a sensitivity based damage detection method for with the hypothesis that
frequency is dependent on the location of damage only. Theoretical frequencies for
different cases of potential damage are calculated to be compared with the measured
values. The sensitivity, which refers to the rate of change of modal parameters with


CHAPTER 2: LITERATURE REVIEW

6

the respect to the structural parameters, illuminate the development of “optimal matrix
updating” approach of damage detection. A drawback of this method is its need to
model all damage cases.
Ju and Mimovich (1986) used modal frequencies changes to locate damage in sections
of a beam, with an accuracy of 3% of the total length. In this method, damages are
represented by a ‘fracture hinge’. A limitation of the proposed method is its difficulty
on application on other complex structures.
Generally, an obvious advantage of modal frequency change is the number of required
sensors is small, and the techniques to handle the complexity of different sensors and
different modal parameters are not needed. One significant limitation is its low
sensitivity to the damage. As a result, large extent of damage is usually needed to get
an ideal detection result. Another drawback is the frequencies generally cannot
provide spatial information about structural changes. (Scott et al. 1996)
2.2 Mode Shape Changes
Later on, the monitoring of changes in mode shape for the detection of damage has
been very popular.
Idichandy and Ganapathy (1990) did direct comparison on measured mode shapes for
the detection of damage. However, it stays in the level 1, determination that damage is

present in the structure.
Allemang and Brown (1982) proposed modal assurance criterion (MAC) for checking
modal vectors. Using the mode shape changes as indicator of damage, MAC is widely
used in researches in different structures. It is also largely employed in subsequent
analytical-model based detection methods.
In methods focusing on mode shape change or modal frequency change, the generally
“direct” comparison between modal parameters needs no analytical model, which is


CHAPTER 2: LITERATURE REVIEW

7

an advantage. But low sensitivity to damage and incapability to detect damage extent
level limits their practical value.

2.3 Model Updating Method
Finite element model updating has emerged in the 1990s as a subject of immense
importance to the design, construction and maintenance of mechanical systems and
civil engineering structures. (Friswell and Mottershead 1995) Model updating method
employs an analytical structural model (containing mass, stiffness and damping ratio)
which can be updated and reproduce as closely as possible the measured static or
dynamic response (modal frequencies and mode shapes) from the data. If modal
parameters for both undamaged case and damaged case are available, the optimized
analytical models for both cases can be compared. The existence, location and extent
of damage/additional mass may be obtained after comparison. This method is also
referred as Matrix Update Methods.
Structural Model Updating method is used by in large number of researches and is
applied on different kinds of structures. Various algorithms are proposed to realize the
process of optimization. Two typical approaches are Numerical Optimization and

Artificial Neural Network (ANN).
2.3.1 Numerical Optimization
Chen and Garbat (1980) proposed a matrix perturbation method to calculate the
Jacobian Matrix and to compute the new eigendata for the parameter estimation
procedure. This method can be applied to large complex structures without knowing
the analytical expressions for mass and stiffness matrix. It is applied in the aerospace
area.
Methods based on the solution of a first-order Taylor series that minimizes an error


CHAPTER 2: LITERATURE REVIEW

8

function of the matrix perturbations are known as sensitivity-based update methods.
Hemez (1993) presents a sensitivity-based matrix update procedure which formulates
the sensitivities at the element level.
Teughels et al. (2002) presented a sensitivity-based finite element (FE) model
updating method using experimental modal data. Such a procedure aims to adjust the
uncertain properties of the FE model by minimising iteratively the differences
between the measured modal parameters (natural frequencies and mode shapes) and
the corresponding analytical predictions. The updating parameters are the
multiplication factors of the damage functions. This method is demonstrated on a
reinforced beam, which is limited to a structural member level.
Lam et al. (2003) employed a statistical model updating methodology by identifying a
set of optimal model parameters based on maximizing the posterior probability
density function (PDF) of the modal parameters given measured ambient response
data is derived. The methodology did not fail to detect damage in any of all the 6
cases of Phase I of a SHM benchmark study set up by the IASC-ASCE Task Group.
Lam et al. (2007) proposed a methodology that successfully identified the number

location and depth of cracks on an aluminum beam characteristics. The posterior
probability density function (PDF) of crack characteristics (i.e., the crack locations
and crack depths) is determined by the Bayesian model updating method.
Kolakowski et al. (2006) [proposed a virtual distortion method (VDM), which is a
model-updating method of damage assessment, utilizing gradient-based optimization
techniques to solve the resulting inverse dynamic problem in the time domain.
Numerical Optimization method presents encouraging result, especially in the
detection of extent of structural changes. However, due to the imperfection in
analytical model in updating process, noise in ambient vibration data and amount of
available data, this inverse problem sometime gives non-unique solutions, though


CHAPTER 2: LITERATURE REVIEW

9

these problems are partly solved by the employment of a Bayesian probabilistic
framework developed by Beck and Katafygiotis (1998).
2.3.2 Artificial Neural Network
In recent years, Artificial Neural Network (ANN) raised the interests of many
researchers, for their application on structural changes detection in complicated
structures.
Lam (2003) presented a typical procedure of usage ANN in function approximation in
Matlab, using the Matlab® Neural Network Toolbox:
1. ANN design:
a. Design the integration and activation functions of neurons
b. Design the number of layers and the number of neurons for each layer
2. ANN training
a. Selection of training method
b. Selection of training input-output data

3. ANN checking
Check the accuracy of the trained function with data other than the training data
This procedure is found simple and effective, which can be adopted in the
methodology of this project.
Rhim and Lee (1995) verified the feasibility of using artificial neural network in
conjunction with system identification techniques to detect the existence and to
identify the characteristics of damage in composite structures.
Zang and Imregun (2000) used measured frequency response function (FRFs) as input
data to ANN, successfully distinguish between the healthy and damaged states of a
railway wheel with very good accuracy and repeatability. An advantage of this


CHAPTER 2: LITERATURE REVIEW

10

particular approach was found to be the ability to deal with relatively high
measurement noise.
Lam et al. (2006) presented an ANN based pattern recognition approach for structural
health monitoring (SHM) that uses damage induced changes in Ritz vectors as the
features to characterize the damage patterns defined by the corresponding locations
and severity of damage. A design method of ANN based on a Bayesian probabilistic
approach for model selection is proposed.
However, uncertainties existing in the structural model adopted and the measured
vibration response may lead to unreliable output result from such networks. Bakhary
et al. (2006) proposed a statistical approach to take into account the effect of
uncertainties in developing an ANN model. By applying Rosenblueth’s point estimate
method verified by Monte Carlo simulation, the statistics of the stiffness parameters
are estimated
ANN based methods show a great advantage because Level 3 of damage detection,

which is damage extent, is reached. In the meantime, no complex model is essential
for in the whole process. One drawback is the different selections of neural network
type can affect the results a lot, and sometimes, input in the training data is repeated,
causing problem that ANN does not know which output should be given.
There are three common forms of modeling error which may raise the inaccuracy in
the model predictions (Mottershead and Friswell 1993):
1) Model structure errors, which are liable to occur when the governing physical
equation are uncertain
2) Model parameter errors, which would typically include the application of
inappropriate boundary conditions and inaccurate assumptions used in order to
simplify the model
3) Model order errors, which arise in the discretization of complex systems


CHAPTER 2: LITERATURE REVIEW

11

2.4 Other issues
Placement of sensors can influence the study of structure’s dynamic behavior a lot.
Sensors should be optimized to the key locations to get ideal detection result
Shi et al. (2000) presented a method of optimizing sensor locations and detecting
damage in a structure using the collected information. In this approach, the sensor
locations are prioritized according to their ability to localize structural damage based
on the eigenvector sensitivity method.
In this project, as the lumped mass are concentrated on floor slab in shear building
model, so the sensors should be placed accordingly.


CHAPTER 3: METHODOLOGY

12

CHAPTER 3: METHODOLOGY
3.1 Basics of Structural Dynamics
Structural dynamics problem differs from static load problem mainly in two aspects:
one is time varying nature, meaning load acting on a structure and the response of the
structure can vary with time; the other is inertia force, which resists the acceleration
and affect the response.
To facilitate the introduction of methodology used in this project, basic parameters,
theoretical model and dynamic response characteristics of different structural systems,
which are the basics of structural dynamics, are introduced in this chapter. (Chopra, A.
K. 2007)
3.1.1 Single Degree of Freedom System
For ease of explanation, single degree of freedom (SDOF) system is introduced first.
SDOF model is idealized as a concentrated mass m supported by a massless structure
with stiffness k in lateral direction, with a viscous damper c (also known as a dashpot)
that dissipate vibrational energy of the system. Equation of Motion (EOM) of this
SDOF can be written as:
Equation 3. 1

in which u represents the displacement of the mass, p(t) represents the time-varying
external force acting on that mass. General solution of EOM of SDOF consists of two
parts: one part is free-vibration response which is the solution to homogeneous
equation.
the dynamic loading

; The other part is the particular solution generated by
.

In this project, the vibration is excited by an impulse and no external excitation forces
are added after it, so the motion can be treated as a free-vibration response only with
an initial velocity. Therefore, only the solution to equation “

” is


CHAPTER 3: METHODOLOGY

13

valuable in this discussion. In structural dynamics,
m

frequency.

is the angular

is the critical damping.

is the damping ratio. Due

to different values of damping ratio , there are three different cases of the vibration
response. In most of the structures,

is in the range of 2 to 20%, which is less than

one.
As a result, normal systems under vibration are in the situation of under-damped. The
under-damped system oscillates about neutral position with a constant damped

For an under-damped system, the vibration

circular frequency
response can be written as
u t

e

sin

where u t is the displacement at time t,

Equation 3. 2

represents the velocity at t=0s, and

represents acceleration at t=0s. Therefore, the changing of displacement with

time can be shown as

Vibration response of SDOF

0.6

u (t) (m/s)

0.4
0.2
0
-1

-0.2

1

3

5

7

9

11

13

15

-0.4
-0.6

time (s)
Figure 3. 1: Vibration response of SDOF

3.1.2 Multiple Degrees of Freedoms System
In general, normal structures, which are structural systems of interest, have multiple
degrees of freedom (MDOF). Though some systems are adequately enough to be
described as SDOF, the analysis of MDOF system is necessary sometimes to get

CHAPTER 3: METHODOLOGY

14

meaningful findings at some particular locations. Information for particular location is
necessarily needed, for the determination of location and extent of the physical
property changes.
Motions of structure can be defined by displacements of a set of discrete points. Like
static analysis, dynamic analysis, stiffness matrix and mass matrix are also used to
describe the structure. Equation of motion in matrix form for a MDOF system with N
degrees of freedom may be written in the same manner as SDOF system:
Equation 3. 3

in which

is displacement vector (N×1),

matrix (N×N),

is mass matrix (N×N),

is stiffness matrix (N×N), and

is damping

is force vector (N×1).

If we ignore damping, by analogy with the behavior of SDOF systems, it will be
assumed that the free-vibration motion of MDOF is simple harmonic, i.e.
u t

usin

Equation 3. 4

i.e.

in which

represents the shape of the system (which does not change with time;

only the amplitude varies with time) and

is a phase angle.

Upon differentiating equation 3.4 twice with respect to time
u t

usin

Equation 3. 5

and substituting into the equation of motion gives
usin

sin

after omitting the sine term, the equation 3.6 can be written as

Equation 3. 6