Development of damage identification methods for civil engineering structures with limited sensors and noisy measurement data

Damage Assessment in Truss Structures with Limited Sensors Using a Two-Stage Method and Model Reduction.. An effective damage identification procedure using model updating technique an

TON DUC THANG UNIVERSITY INSTITUTE FOR COMPUTATIONAL SCIENCE

DINH CONG DU

DEVELOPMENT OF DAMAGE IDENTIFICATION METHODS FOR CIVIL ENGINEERING STRUCTURES WITH LIMITED SENSORS AND NOISY

MEASUREMENT DATA

SUMMARY OF DOCTORAL DISSERTATION

MAJOR: COMPUTATIONAL SCIENCE

Major code: 9460107

This dissertation was carried out at Ton Duc Thang University

Advisor: Prof Nguyen Thoi Trung ………

Prof Nguyen Thai Duc ………

This dissertation is defended at the Doctoral Dissertation Examination Committee was hold at Ton Duc Thang University on …./…/……pursuant to Decision ……./20…./QĐ-TĐT on …./…./…

Members of the Doctoral Dissertation Examination Committee:

LIST OF PUBLISHED ARTICLES

ISI Journals

1 Dinh-Cong, D., Vo-Duy, T., & Nguyen-Thoi, T (2018) Damage

Assessment in Truss Structures with Limited Sensors Using a Two-Stage

Method and Model Reduction Applied Soft Computing, 66, 264-277

2 Dinh-Cong, D., Dang-Trung, H., & Nguyen-Thoi, T (2018) An Efficient

Approach for Optimal Sensor Placement and Damage Identification in

Laminated Composite Structures Advances in Engineering Software,

119, 48-59

3 Dinh-Cong, D., Vo-Duy, T., Ho-Huu, V., & Nguyen-Thoi, T (2019)

Damage Assessment in Plate-like Structures Using a Two-Stage Method

Based on Modal Strain Energy Change and Jaya Algorithm Inverse Problems in Science and Engineering, 27(2), 166-189

4 Dinh-Cong, D., Nguyen-Thoi, T., Vinyas, M., & Nguyen, D T (2019)

Two-Stage Structural Damage Assessment by Combining Modal Kinetic

Energy Change with Symbiotic Organisms Search International Journal

of Structural Stability and Dynamics, 19(10), 1950120

5 Dinh-Cong, D., Pham-Toan, T., Nguyen-Thai, D., & Nguyen-Thoi, T

(2019) Structural Damage Assessment with Incomplete and Noisy Modal

Data Using Model Reduction Technique and LAPO Algorithm Structure and Infrastructure Engineering, 15(11), 1436-1449

6 Dinh-Cong, D., Nguyen-Thoi, T., & Nguyen, D T (2020) A FE Model

Updating Technique Based on SAP2000-OAPI and Enhanced SOS

Algorithm for Damage Assessment of Full-Scale Structures Applied Soft Computing, 89, 106100

7 Dinh-Cong, D., Nguyen-Thoi, T, T., & Nguyen-Thai, D (2021) A

two-stage multi-damage detection approach for composite structures using MKECR-Tikhonov regularization iterative method and model updating

procedure Applied Mathematical Modelling, 90, 114–130

8 Dinh-Cong, D., Truong, T T., & Nguyen-Thoi, T (2021) A comparative

study of different dynamic condensation techniques applied to

multi-damage identification of FGM and FG-CNTRC plates Engineering with Computers DOI: 10.1007/s00366-021-01312-y

9 Dinh-Cong, D., & Nguyen-Thoi, T (2021) A new efficient two-stage

method for damage localization and quantification in shell structures

10.1016/j.asoc.2021.107468

10 Dinh-Cong, D., & Nguyen-Thoi, T (2021) An effective damage

identification procedure using model updating technique and objective optimization algorithm for structures made of functionally graded materials Engineering with Computers, DOI: 10.1007/s00366-021-01511-7

multi-Non-ISI Journals

1 Dinh-Cong, D., Pham-Duy, S., & Nguyen-Thoi, T (2018) Damage

Detection of 2D Frame Structures Using Incomplete Measurements by

Optimization Procedure and Model Reduction Journal of Advanced Engineering and Computation, 2(3), 164-173

2 Dinh-Cong, D., Vo-Van, L., Nguyen-Quoc, D., & Nguyen-Thoi, T

(2019) Modal Kinetic Energy Change Ratio-Based Damage Assessment

of Laminated Composite Beams Using Noisy and Incomplete

Measurements Journal of Advanced Engineering and Computation, 3(3),

452-462

CHAPTER 1 INTRODUCTION

1.1 Background

Structural health monitoring (SHM) has indeed emerged as an important research area in civil, mechanical, and aerospace engineering SHM provides valuable information for assessment and decision-making purposes about the health state of a monitored structural system, which aims to ensure its integrity, serviceability, and safety

It is well known that the problem of SDI is generally segmented into four levels (Doebling et al., 1998; Hu et al., 2006): Level 1 - detection, Level 2 - localization, Level 3 - quantification, and Level 4 - prediction of the remaining service life of the structure, in which a higher level always plus a previous (lower) level The core interest of SHM is at early damage identification, which not only provides cost-effective maintenance but also prolongs the service life

of the structures The research work reaches Level 3 of damage identification, which means that it provides a mean to detect, localize as well as quantify the extent of the damage in civil structures

One of the practical challenges for SDI problems is that the existing model-based techniques often require complete measurement at locations corresponding to every node/degree of freedom (DOF) in the finite element (FE) model of monitored structure (D Dinh-Cong, Dang-Trung, et al., 2018;

D Dinh-Cong, Vo-Duy, et al., 2018; Moslem & Nafaspour, 2002) Nevertheless, this is rarely possible in real-world applications because the number of available sensors is strictly constrained by instrumentation cost, measurement, and capacity installation efforts In other words, only the spatially-incomplete modal data of a damaged structure are available in experimental data acquisition The structural damage detection problem arising from a limited number of sensors has always been a hard task The

development of model-based damage identification techniques considering missing or incomplete measurements is of practical significance

The sensor system, an important component of vibration-based SHM system, is installed to measure the vibrational responses of a monitored structure In fact, owing to a limited number of sensors, the quality of vibrational response data, as well as the quality of damage identification depends much on their placement (D Dinh-Cong, Dang-Trung, et al., 2018)

As a result, an important initial step in a damage identification strategy is to solve optimal sensor placement (OSP) problem In the last few decades, various OSP techniques have been developed, which utilize the FE model simulation in their algorithm to find out the suitability of sensors' location from

a given set, such that the measured dynamic data gives the best possible information of modal identification As extensive review articles have already been published (Mallardo & Aliabadi, 2014; Yi & Li, 2012), it is found that most of the techniques focus on OSP problems without validating the optimal sensor layout for the objectives of SHM

Based on the above-mentioned problems, the research work in the

dissertation entitled “Development of damage identification methods for civil engineering structures with limited sensors and noisy measurement data” will have a significant contribution to the development and improvement

of existing SHM techniques, aiming to provide more efficient damage detection techniques that have potential applications to real SHM systems 1.2 Research motivation

There are three main motivations of this research work, which are given

as below:

 The first motivation is that the exploration of optimal sensor layout obtained by the OSP techniques for SDI problems has not yet been received enough attention Thus, the integration of a damage

identification method with an OSP strategy is necessary to make an SHM scheme suitable for practical applications

 The second motivation is that solving practical challenges related to the sources of errors (limited measurements, and noise polluted data) will provide a theoretical foundation for an effective SHM technique, which is a significant motivation

 The last motivation is related to my Vietnam country where there are many existing large-scale civil engineering structures With the expectation that in near future, this research work will contribute to promoting the task of SHM of the existing structures, which help us to avoid sudden collapses and have a safe and smart community

1.3 Research objectives

The following objectives of this present research will be undertaken: (i) Study the fundamental theory of SHM, and evaluate the limitations and applicability of existing OSP and vibration-based SHM techniques for civil engineering structures;

(ii) Explore and exploit a powerful intelligent optimization algorithm, namely Lightning Attachment Procedure Optimisation (LAPO), for both OSP and damage identification problems;

(iii) Investigate different model order reduction techniques, i.e., Guyan’s method, Neumann series expansion-based second-order model reduction (NSEMR-II) method, improved reduced system (IRS) method and iterated IRS (IIRS) method for condensing a FE model

to the spatially incomplete DOFs measured by sensors installed on a structure;

(iv) Study an efficient OSP method for finding proper sensor locations installed on civil engineering structures to maximize damage detection accuracy;

(v) Develop SDI methods using incomplete modal data, which aims to validate the optimal sensor layout obtained from the proposed OSP strategy, and simultaneously show their capacity in structural damage localization and quantification This involves the following main steps:

 Apply FE methods to analyze the actual behavior of civil engineering structures;

 Formulate different objective functions that are sensitive enough

to small local damages;

 Examine various hypothetical damage scenarios with considering the problems of incompleteness, noise levels and modelling errors

in the baseline FE model

 Compare the performance of the different implemented methods

in term of accuracy, computational cost and time;

(vi) Demonstrate the reliability and efficiency of the proposed damage identification methods through various kinds of engineering structures The difficulties and promising research efforts from these investigations will also be discussed

CHAPTER 2 LITERATURE REVIEW

Structural damage localization techniques can be classified as

 VBDI techniques using basic dynamic characteristics

 Methods based on natural frequency changes

 Methods based on mode shape changes

 VBDI techniques using derived dynamic characteristics

 Methods based on derivatives of mode shape

 Methods based on flexibility matrix

 Methods based on modal strain energy

 Methods based on modal residual vector

2.3 Damage localization and quantification techniques

Structural damage localization and quantification techniques developed in this area usually fall into three groups:

 Sensitivity-based methods,

 FE model updating methods

 Combined methods called two-stage methods

2.4 Research limitations and gaps

The following major limitations and gaps from the reviewed literature can

be summarized as follows:

 The integration of a damage identification method with an OSP strategy has not received enough attention Thus, this needs to be considered further to make SHM scheme suitable for practical applications

 Although most of the techniques have been well studied, many of them require a high number of sensors installed to the monitored structure Another challenging problem is the complexity of various sources of uncertainty (i.e variable temperature conditions, noise contamination, and modelling error) affecting measured modal data

 There is a potential to further develop new damage indicator(s) by making use of more sensitive dynamic parameters, especially in the case of incomplete and noisy measurements

 It is necessary to explore and exploit powerful and reliable optimization algorithms with the aim of decreasing computational burdens and producing accurate damage prediction

 A majority of the existing techniques in the literature still focused on small and simple structures

According to the surveyed literature, this dissertation aims to reduce the current research limitations and gaps presented above This dissertation work explores FE model updating methods and two-stage methods to address these above issues, which will be presented in more detail in Chapter 4 The next chapter will cover the OSP problem for damage identification of structures

CHAPTER 3 OPTIMAL SENSOR PLACEMENT FOR DAMAGE

IDENTIFICATION OF STRUCTURES

3.1 Optimal Sensor Placement (OSP) Problem

Placing sensors at all DOFs/ nodes of a structure is impossible due to the high cost of sensors, data acquisition and data processing systems As a result,

a number of limited sensors are installed individually as separate DOFs/ nodes, and this, in turn, requires them to be placed at proper locations to provide the best dynamic information The present research focuses on finding important locations to place sensors where a pre-defined limited number of sensors should be placed at nodes to obtain the best dynamic information for damage identification To do this, a reduced-order model for sensor placement optimization, recently proposed by Dinh-Cong et al (D Dinh-Cong, Dang-Trung, et al., 2018), should be utilized for the present work Another goal is to extend the previous study for selecting optimal sensor locations in various kinds of engineering structures including frame, truss, and plate structures 3.2 Optimal Sensor Location as Optimization Problem

Mathematically, the OSP problem can be formulated as a constrained optimization problem in which the sensor positions are considered as the discrete design variables and the constraint is typically a given limited number

of sensors The objective function, usually based on the dynamic characteristics of a structure, can be maximized or minimized to determine the optimal locations from all feasible sensor configurations Thus, the mathematical model of the OSP problem can be described by the following optimization equation (D Dinh-Cong, Dang-Trung, et al., 2018)

S S S

(2.1)

where f is the objective function; S( , , ,s s1 1 s n) is denoted as the candidate

sensor locations placed at nodes/ DOFs of the FE structural model; n is the

given limited number of sensors; lb

S and ub

S represent the vectors of lower and

upper bound of S , respectively; and is the set of positive integers

The MAC criterion (Kaveh & Dadras Eslamlou, 2019; Tong et al., 2014;

Yi et al., 2014; Zhou et al., 2015) can be utilized to estimate the correlation between the flexibility matrix obtained from an original FE model and the corresponding one calculated from IIRS method Based on the idea, Dinh-Cong et al (D Dinh-Cong, Dang-Trung, et al., 2018) presented an objective function for OSP by using the diagonal terms of the flexibility matrix, which can be expressed as follows

CHAPTER 4 STRUCTURAL DAMAGE DIAGNOSIS TECHNIQUES USING INCOMPLETE MEASURED VIBRATION

DATA

4.1 Introduction

The finite element (FE) model updating technique which serves wide applications to civil engineering structures belongs to the broad category of inverse problems of applied mechanics (D Dinh-Cong, Vo-Duy, et al., 2019) One of its most prominent research and application areas is found in the field

of structural damage identification (SDI) In general, the FE model updating technique for SDI is usually formulated as an optimization problem, which can provide an efficient way of not only locating damage but also quantifying its severity The main concept of the technique is to modify the structural parameters related to the FE model of a structure in order to obtain a good agreement between analytical and experimental modal data

In this present work, an FE Model Updating method based on a combination of a powerful optimization tool named LAPO algorithm and IIRS technique is proposed for damage identification of 2D frame, truss, and plate structures The major contribution of the method is as follows:

• Provide a model updating-based damage detection method that takes into account both spatially-incomplete measurements and noise contamination;

• Introduce for the first time the extension of a recently developed optimization algorithm, Lightning Attachment Procedure Optimisation (LAPO) algorithm (Nematollahi et al., 2017), to the field of SDI with the purpose of reducing the computational cost 4.2 FE Model updating technique with powerful meta-heuristic algorithms

Generally, the optimization problem of FE model updating for SDI is composed of the general form as follows

where ( )x is the objective function that has to be minimized; x i is the

location and magnitude of the ith elements; and n is the total number of design

variables that is usually equal to all discretized elements used in the FE model With the purpose of finding forms of distinctive objective functions,different combinations of two or more residuals of dynamic characteristics have been formulated by researchers (Alkayem & Cao, 2018; Du et al., 2018; Gomes et al., 2018; Shabbir et al., 2017) In this regard, a combination of the modal flexibility and Modal Assurance Criterion (MAC) sub-objectives is presented here, which is expected to generate a proper objective function for tracking structural damage The two forms of the residuals are given as follows

For the purpose of finding the value of vector x (design variable vector) of

Eq Error! Reference source not found., A recently developed optimization

algorithm, named LAPO (Nematollahi et al., 2017) is applied to the damage identification problems

In addition, in real-world applications, due to a limited number of sensors available for instrumentation, the damage detection problem based on FE model updating has become more challenging It has been revealed that the

strategy using mode shape expansion techniques can aggregate additional errors (i.e modeling error and other sources of uncertainties) (Hosseini et al., 2017; Zare Hosseinzadeh et al., 2014), which can lead to unreliable damage detection results, especially for large-scale structures While the model reduction techniques can be considered as a more practical and workable alternative to the problem (D Dinh-Cong et al., 2021; D Dinh-Cong, Vo-Duy,

et al., 2018; Sung et al., 2017) For this reason, a well-known reduced-order model named IIRS technique (Friswell et al., 1995, 1998) is adopted in this work

4.3 A two-stage damage identification approach

It is a well-known fact that the complication of the optimization-based damage identification methods increases with the dimension of search space, which can impose a high computational cost for damage identification process (D Dinh-Cong, Nguyen-Thoi, et al., 2019; D Dinh-Cong, Vo-Duy, et al., 2018; Dinh-cong et al., 2021; Du Dinh-Cong et al., 2017) In this context, the damage detection procedure using two-stage approach provides a useful way

to reduce the dimension of search space for the model updating-based SDI problem In this approach, one method is implemented for damage localization

in the first step and another method is considered for damage severity evaluation in the second step after the suspected damage regions have been preliminarily determined Its significant advantage lies in the fact that by eliminating a large number of healthy elements in the first step, the two-stage approach help to reduce the computational effort to the damage severity evaluation and subsequently increase the computing accuracy

So far, there have been only a few attempts conducted in this direction for the identification of damage in structures with limited sensors Therefore, a two-stage damage detection approach for composite structures by using MKE change ratio (MKECR) and an FE model updating technique is proposed in the present study, taking into consideration of both spatially-incomplete

measurements and noise (Dinh-cong et al., 2021) First, a Tikhonov regularization-based iterative technique (Wang et al., 2019) is introduced to solve the set of linear equations constructed by MKECR-based method, aiming

to find out the most potentially damaged sites After that, the LAPO algorithm

as a powerful optimization solver is applied to update the FE model for the detection of true damage locations and corresponding severities For consistency, the cost function for the FE model updating is also based on MKE-based residual

Figure 4.1 The flowchart of the two-stage approach based on LAPO algorithm and MKECR-Tikhonov regularization iterative method

The major contribution of the two-stage method is highlighted in the following aspects:

 Extend the damage indicator MKECR to damage detection in composite plate structures is studied through numerical simulation;

 Extend the applicability of the LAPO algorithm to estimate the magnitude of damage(s) in composite material;

 Propose for the first time the objective function based on MKE feature for structural damage identification

Figure 4.1 shows the flowchart of the two-stage approach which combines the LAPO algorithm and the MKECR-Tikhonov regularization iterative method to multi-damage detection for composite structures

CHAPTER 5 DAMAGE LOCALIZATION AND QUANTIFICATION

OF 2D TRUSS, FRAME, AND PLATE STRUCTURES

The section exhibits a FE model updating-based damage identification procedure using a combination of a powerful optimization tool and a model reduction technique for damage localization and quantification with a limited number of sensors installed on structures To illustrate the performance of the proposed damage identification procedure, three types of structures, including

a 31-bar 2D truss, a 4-storey (3 Bay) steel 2D frame and a concrete plate are investigated

5.1 A damage identification method based on model reduction technique and optimization procedure

5.1.1 31-bar 2D truss

The first numerical example considers a 31-bar planar truss referred to the works of Ghasemi et al., (2018) and S M Seyedpoor (2012), as shown in Figure 5.1

Figure 5.1 Schematic of a 31-bar planar truss

5.1.1.1 Optimal sensor placement

First, the OSP strategy is used for finding proper sensor locations from a set of possible positions Table 5.1 reports the OSP results of the truss structure with 4, 5 and 6 sensors The MAC values of the selected first ten modes are shown in Figure 5.2 As can be seen in the figure, the number of identified modes is increased when more sensors are properly added

Table 5.1 Various sensor placements obtained by the OSP strategy

for the truss structure

(c) MAC values obtained using 6 sensors

Figure 5.2 The MAC values of the first ten modes obtained by the OSP

strategy for the truss structure with three sets of sensors

5.1.1.2 Comparison of different model-order reduction techniques

Table 5.2 reports the results of the first five natural frequencies of the planar truss obtained by five model-order reduction techniques As can be seen,

the model reduced using the IIRS technique is completely accurate for all thesemodes Therefore, the IIRS will be used to reduce the FE model for the model updating procedure of damage identification

Table 5.2 The first five natural frequencies (rad/s) of the truss

structure calculated by various reduced models

Unreduced model

(28 DOFs) 299.99 634.05 973.18 1294.07 1605.54 Guyan method

(12 DOFs) 301.62 645.57 1009.49 1370.26 1777.81

(0.54%) (1.82%) (3.73%) (5.89%) (10.73%) NSEMR-II

(12 DOFs) 299.99 634.05 973.19 1294.19 1606.11

(0.00%) (0.00%) (0.00%) (0.01%) (0.04%) IRS method

(12 DOFs) 299.99 634.06 973.50 1297.14 1615.62

(0.00%) (0.00%) (0.03%) (0.24%) (0.63%) IIRS method

of 6 sensors are used in the damage identification process for all the damage scenarios In addition, it is assumed that only the first five modes are available for the objective function provided in Eq (4.22)

To illustrate the efficiency and accuracy of the proposed method, comparisons between the present LAPO algorithm and other four well-known algorithms such as cuckoo search (CS) (Yang & Suash Deb, 2009),

biogeography-based learning particle swarm optimization (BLPSO) (Chen et al., 2018) and differential search algorithm (DSA) (Civicioglu, 2012) and teaching–learning-based optimization (TLBO) algorithms (Rao et al., 2011) are conducted for all damage scenarios with and without measurement noise

Table 5.3 Three different damage scenarios in the truss structure

Scenario 1 Scenario 2 Scenario 3

Element No Damage

ratio Element No

Damage ratio Element No

Damage ratio

(a)

(b)

Figure 5.5 Comparison of damage identification results obtained from different optimization algorithms for scenario 3 of the truss structure:

(a) noise-free; (b) measurement noise

Figure 5.6 The comparison results between five optimization

algorithms in terms of computational time

5.1.2 A 4-storey (3 Bay) steel 2D frame

Figure 5.7 Schematic of a 4-storey frame structure

(*): noise condition

In the second example, we consider a 4-storey 2D frame structure (3-bay),

as shown in Figure 5.7

5.1.2.1 Optimal sensor placement

Figure 5.8 shows the MAC values of the first ten modes obtained by the OSP strategy for the steel 2D frame structure with three sets of sensors From the figure, one can observe that: (1) there are good agreements for the first four fundamental modes, (2) when more sensors are properly added, the number of identified modes is slightly increased Nonetheless, for this case, only the first four mode shapes are generally applicable for the purpose of damage identification

Table 5.4 Various sensor placements obtained by the OSP strategy

for the steel 2D frame structure

(c) MAC values obtained by using 8 sensors

Figure 5.8 The MAC values of the first ten modes obtained by the OSP strategy for the steel 2D frame structure with three sets of

sensors

5.1.2.2 Comparison of different model-order reduction techniques For comparison purposes, four different model-order reduction techniques are applied to the steel 2D frame structure with 8 candidate sensor locations shown in Table 5.5 Again, the IIRS method is the best method to condense structural physical properties among them

Table 5.5 The first five natural frequencies (rad/s) of the steel 2D

frame structure calculated by various models

Unreduced model (60 DOFs) 22.25 70.38 125.42 177.91 363.41 Guyan method (16 DOFs) 22.26 70.58 126.34 181.48 478.45

(0.04%) (0.28%) (0.74%) (2.01%) (31.65%) NSEMR-II (16 DOFs) 22.26 70.39 125.48 178.00 401.26

(0.00%) (0.00%) (0.02%) (0.05%) (10.41%) IRS method (16 DOFs) 22.25 70.38 125.42 177.91 377.62

(0.00%) (0.00%) (0.00%) (0.00%) (3.91%) IIRS method (16 DOFs) 22.25 70.38 125.42 177.91 365.54

(0.00%) (0.00%) (0.00%) (0.00%) (0.59%)

5.1.2.3 Damage identification using incomplete modal data obtained

from optimal sensors

The details of the three damage scenarios are listed in Table 5.6 Here, a distributed set of 8 sensors are utilized in the damage identification process for all the damage scenarios

Table 5.6 Three different damage scenarios in the frame structure

Element No Damage

ratio Element No

Damage ratio Element No

Damage ratio