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

VIETNAM GENERAL CONFEDERATION OF LABOUR 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: Chairman Examiner Examiner Member Secretary LIST OF PUBLISHED ARTICLES ISI Journals 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 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 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 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 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 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 Dinh-Cong, D., Nguyen-Thoi, T, T., & Nguyen-Thai, D (2021) A twostage multi-damage detection approach for composite structures using MKECR-Tikhonov regularization iterative method and model updating procedure Applied Mathematical Modelling, 90, 114–130 Dinh-Cong, D., Truong, T T., & Nguyen-Thoi, T (2021) A comparative study of different dynamic condensation techniques applied to multidamage identification of FGM and FG-CNTRC plates Engineering with Computers DOI: 10.1007/s00366-021-01312-y Dinh-Cong, D., & Nguyen-Thoi, T (2021) A new efficient two-stage method for damage localization and quantification in shell structures Applied Soft Computing, 108, 107468 DOI: 10.1016/j.asoc.2021.107468 10 Dinh-Cong, D., & Nguyen-Thoi, T (2021) An effective damage identification procedure using model updating technique and multiobjective optimization algorithm for structures made of functionally graded materials Engineering with Computers, DOI: 10.1007/s00366021-01511-7 Non-ISI Journals 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 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 C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an CHAPTER 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 - detection, Level localization, Level - quantification, and Level - 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 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 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 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 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 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; Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an (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 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an CHAPTER LITERATURE REVIEW 2.1 Introduction The purpose of conducting this literature survey is to perceive the development of the techniques The review focuses on the classification based on performance levels, such as damage localization techniques and damage estimation techniques, which aims to identify their limitations and gaps 2.2 Damage localization techniques 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: Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an  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 The next chapter will cover the OSP problem for damage identification of structures Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 35 able to provide the damage locations and their levels with satisfactory accuracy and also achieve the same level of precision even under the effect of incomplete and noisy modal data Nevertheless, the LAPO algorithm always takes much less computational time than the others (iv) It must be mentioned that the availability of higher modes data is a challenging task or even not practical in engineering applications Thus, it is more realistic to utilize only a few of the lower modes of vibration of the monitored structure In this study, the proposed two damage identification strategies used only the first four/five frequencies and corresponding mode shapes Besides, considering the sufficient number of vibration modes for damage identification with limited sensors is also an important factor for the proper and efficient evaluation of damage sites (v) The influences of inevitable noise with a proper assumption in the incomplete measured modal data have been studied, and in general, the results obtained from the proposed two damage identification strategies are slightly affected In practical, however, modal information may be significantly deviated by many sources of errors In such circumstances, the polluted dynamic responses are needed to be denoised before applying damage identification processes Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 36 CHAPTER DAMAGE LOCALIZATION AND QUANTIFICATION OF A 3D FULL-SCALE STRUCTURE 6.1 Introduction In the literature, many researchers successfully implemented the approaches based on FE models and model updating strategies for damage identification of small and simple structures Nevertheless, their applications to large and complex structures are still limited because of performing structural FE analysis in MATLAB Thanks to the rapid development of modern computer and computer-aided engineering technologies, commercial FE modelling software packages such as SAP2000, ETABS, ABAQUS, ANSYS, etc., have become powerful tools in engineering applications These software packages are not only capable of analyzing large and complicated structural systems more conveniently and accurately but also allow users to link them with third-party software (e.g MATLAB) The concept has generated the motivation for the current research This research work is intended for a FE model updating framework that is the integration of a commercial software package with a powerful and reliable optimization algorithm, which deals with the detection and quantification of full-scale structures with limited sensors (D Dinh-Cong et al., 2020) The main contribution of the method is shown in the following aspects: • Overcome the difficulties faced in developing the FE model in computational programs like MATLAB for damage identification problems of full-scale structures; • ESOS algorithm is exploited to further improve the performance of the original SOS algorithm for damage identification of full-scale structures; Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 37 • Develop a particularly useful tool to solve the inverse problem of damage identification of full-scale structures, which takes into account spatially-incomplete measurements and noise contamination The effectiveness and robustness of the proposed FE model updating technique are investigated through a two-story full-scale building with various possible damage scenarios 6.2 The FE model updating problem using SAP2000-OAPI The description of the FE model updating technique which is the integration of a commercial software package with an enhanced optimization algorithm is explained in the following steps: (i) A FE model of the monitored structure is first constructed in SAP2000 software Here, SAP2000 serves as a slave program for analyzing the dynamic behavior of the structure (ii) The results of the structural vibration analyses (e.g natural frequencies and corresponding mode shapes) extracted from the SAP2000 model are transferred to MATLAB to calculate the objective function using the OAPI feature of SAP2000 (iii) For finding the value of vector x (design variable vector) of Eq (4.21), the enhanced symbiotic organisms search (ESOS) algorithm (Prayogo et al., 2018), an improved version of the standard SOS algorithm (Cheng & Prayogo, 2014) is then applied to minimize the objective function This algorithm is coded in MATLAB interacting with SAP2000 through OAPI feature for automatically performing two-way data exchange (iv) The iterative optimization process is performed automatically until the convergence condition is reached The flowchart of the FE model updating process based on SAP2000OAPI and ESOS algorithm for damage assessment of full-scale structures is presented in Figure 6.1 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 38 Figure 6.1 The flowchart of the proposed FE model updating process 6.3 Description of a two-story full-scale building A two-story full-scale building, 12 m long, m wide and m high, is selected as the numerical example for investigating the performance of the proposed FE model updating technique The building has a concrete slab at each floor level and the thickness of each plate is 120 mm The SAP2000 v16 commercial software is used to create a 3D FE model of the building structure, as shown in Figure 6.2 For this investigation, six different damage scenarios are considered as listed in Table 6.1 In the example, it is also assumed that only the first five modes are available for SDI To deal with the incompleteness conditions of measured modal data, a set of selected sensors at 23 nodes are installed to provide the partial mode shapes Figure 6.3 highlights the locations of these measurement points on the plan view of the building Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 39 Figure 6.2 The FE model of two-story full-scale building and its element numbering (a) (b) Figure 6.3 Sensor layout on the two-story full-scale building: (a) first floor; (b) second floor Table 6.1 Six different damage scenarios in the two-story full-scale building Damaged elements (reduction of stiffness) Single damage on column (20%) Double damage on column and beam (30%) & (20%) Double damage on floor and column 15 (20%) & 47 (40%) Double damage on floor (stories and 2) 36 (20%) & 64 (20%) Double damage at on beam and floor 10 (20%) & 64 (20%) (25%) & 10 (20%) & Multi-damage on column, beam, floor 27 (40%) & 60 (25%) Scenario Description A B C D E F Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 40 6.4 Damage identification using incomplete and noisy modal data For predicting damage locations and their severities, the FE model updating process uses the model information (138 DOFs) from the 21 measurement points The model updating-based optimization problem is solved using the ESOS algorithm (a) (b) (c) (d) Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 41 (e) (f) Figure 6.4 Damage detection results for six damage scenarios of the two-story full-scale building: (a) Scenario A; (b) Scenario B; (c) Scenario C; (d) Scenario D; (e) Scenario E; (f) Scenario F Employing the proposed FE model updating technique, the final SDI results are shown in Figure 6.4 (a) to (e) for scenarios A to E, respectively It is evident from the figures that overall, all the true damaged positions are correctly identified in all considered scenarios Particularly, in the case of spatially-incomplete measurements with noise-free data, the proposed technique succeeds in both localization and damage quantification with high precision In the case of spatially-incomplete measurements with noisepolluted data, although several undamaged elements are falsely detected especially for multi-damage scenario F, it is still effective to localize the actually damaged elements and approximately estimate their severities These presented results also emphasize on the impact of measurement errors on the success of the FE model updating process 6.5 Concluding remarks A FE model updating technique based on the ESOS algorithm in conjunction with SAP2000 OAPI has been proposed for the detection and Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 42 quantification of full-scale structures, taking into consideration of incomplete measurements and noise In the developed technique, the commercial software SAP2000 is invoked as a slave program for FE analysis and the ESOS algorithm as a powerful optimization solver is utilized for finding the optimal solution of FE model updating problem By making use of the OAPI feature, the information exchange between MATLAB and SAP2000 has been performed automatically The numerical validation showed that even under incomplete measurements and a relatively high level of noise, the proposed technique could reliably produce the detection of true damage locations and the prediction of damage magnitudes with acceptable accuracy Such a technique can be potentially developed and applied for practical purposes Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 43 CHAPTER CONCLUSIONS For the research work presented in this dissertation, it is possible to derive the following general conclusions: 7.1 Optimal sensor placement We used the suggested OSP strategy for finding proper sensor locations to collect as much information on structural dynamic characteristics as possible The extensive application of the strategy has been investigated for various kinds of engineering structures including frame, truss, and plate structures The OSP results showed the trade-off between the number of used sensors and information quality It was identified that the OSP strategy is able to provide an appropriate configuration of sensors that have been used by the damage identification procedures for tracking structural damage This means that the cost of instrumentation and maintenance should be minimized, which has the potential to achieve cost-effective SHM on a structure 7.2 Damage localization and quantification We proposed two kinds of damage identification methods including FE model updating method and two-stage method for damage localization and quantification for civil engineering structures All the case studies indicate that the proposed method is effective for damage localization and quantification in the structures The comparison results well demonstrated that among different model-order reduction techniques studied in this dissertation, the IIRS technique is the most suitable method for model reduction and damage identification problems Whereas, the LAPO algorithm is found to be an efficient optimizer in computational cost for solving the problems of damage Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an 44 identification in comparison with four other well-known optimization algorithms (CS, BLPSO, DSA and TLBO) Next, the two-stage method based on an efficient indicator MKECR and optimization procedure of LAPO algorithm was implemented for locating and quantifying damage in a cantilever-laminated composite plate (00/900/900/00) structure The numerical validation showed that the proposed two-stage method was successful in solving the problem of damage localization and quantification in the composite structure, even under incomplete measurements with a high noise level The extensive application of MKECR, as well as LAPO to the damage detection problem of composite materials, was also confirmed in this part Finally, for damage assessment of full-scale structures, another FE model updating technique based on existing commercial software SAP2000-OAPI and ESOS algorithm was developed The results obtained from the numerical simulation on a two-story full-scale building confirmed the feasibility of the proposed technique in predicting the actual damage sites and their severities Due to the major advances in conquering the complexities of FE simulation, it makes the proposed FE model updating technique can be potentially developed for practical applications of fault diagnosis of civil engineering structures Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an REFERENCES Alkayem, N F., & Cao, M (2018) Damage identification in threedimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison Engineering Optimization, 50(10), 1695–1714 DOI: 10.1080/0305215X.2017.1414206 Bathe, K.-J., & Dvorkin, E N (1985) A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation International Journal for Numerical Methods in Engineering, 21(2), 367–383 DOI: 10.1002/nme.1620210213 Chen, X., Xu, B., & Du, W (2018) An improved particle swarm optimization with biogeography-based learning strategy for economic dispatch problems Complexity, 2018, 1–15 DOI: 10.1155/2018/7289674 Cheng, M.-Y., & Prayogo, D (2014) Symbiotic Organisms Search: A new metaheuristic optimization algorithm Computers & Structures, 139, 98– 112 DOI: 10.1016/j.compstruc.2014.03.007 Civicioglu, P (2012) Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm Computers and Geosciences, 46, 229–247 DOI: 10.1016/j.cageo.2011.12.011 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 DOI: 10.1016/j.advengsoft.2018.02.005 Dinh-cong, D., Nguyen-thoi, T., & Nguyen, D T (2021) A two-stage multi-damage detection approach for composite structures using MKECRTikhonov regularization iterative method and model updating procedure Applied Mathematical Modelling, 90, 114–130 DOI: 10.1016/j.apm.2020.09.002 Dinh-Cong, D., Nguyen-Thoi, T., & Nguyen, D T (2020) A FE model Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an updating technique based on SAP2000-OAPI and enhanced SOS algorithm for damage assessment of full-scale structures Applied Soft Computing, 89, 106100 DOI: 10.1016/j.asoc.2020.106100 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 DOI: 10.1142/S0219455419501207 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 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 DOI: 10.1080/17415977.2018.1454445 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 DOI: 10.1016/j.asoc.2018.02.028 Dinh-Cong, Du, Vo-Duy, T., Nguyen-Minh, N., Ho-Huu, V., & NguyenThoi, T (2017) A two-stage assessment method using damage locating vector method and differential evolution algorithm for damage identification of crossply laminated composite beams Advances in Structural Engineering, 20(12), 1807–1827 DOI: 10.1177/1369433217695620 Doebling, S W., Farrar, C R., & Prime, M B (1998) A Summary Review of Vibration-Based Damage Identification Methods The Shock and Vibration Digest, 30(2), 91–105 DOI: 10.1177/058310249803000201 Du, D.-C., Vinh, H.-H., Trung, V.-D., Hong Quyen, N.-T., & Trung, N.Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an T (2018) Efficiency of Jaya algorithm for solving the optimization-based structural damage identification problem based on a hybrid objective function Engineering Optimization, 50(8), 1233–1251 DOI: 10.1080/0305215X.2017.1367392 Friswell, M I., Garvey, S D., & Penny, J E T (1995) Model reduction using dynamic and iterated IRS techniques Journal of Sound and Vibration, 186(2), 311–323 DOI: 10.1006/jsvi.1995.0451 Friswell, M I., Garvey, S D., & Penny, J E T (1998) THE CONVERGENCE OF THE ITERATED IRS METHOD Journal of Sound and Vibration, 211(1), 123–132 DOI: 10.1006/jsvi.1997.1368 Ghasemi, M R., Nobahari, M., & Shabakhty, N (2018) Enhanced optimization-based structural damage detection method using modal strain energy and modal frequencies Engineering with Computers, 34(3), 637–647 DOI: 10.1007/s00366-017-0563-5 Gomes, G F., Mendez, Y A D., da Silva Lopes Alexandrino, P., da Cunha, S S., & Ancelotti, A C (2018) A Review of Vibration Based Inverse Methods for Damage Detection and Identification in Mechanical Structures Using Optimization Algorithms and ANN Archives of Computational Methods in Engineering, 4(1), 1–15 DOI: 10.1007/s11831-018-9273-4 Hosseini, M., Khoshnoudian, F., & Esfandiari, A (2017) Improved data expansion method used in damage detection method Journal of Civil Structural Health Monitoring, 7(1), 15–27 DOI: 10.1007/s13349-016-0205-4 Hu, S J., Wang, S., & Li, H (2006) Cross-Modal Strain Energy Method for Estimating Damage Severity Journal of Engineering Mechanics, 132(4), 429 DOI: 10.1061/(ASCE)0733-9399(2006)132:4(429) Kaveh, A., & Dadras Eslamlou, A (2019) An efficient two-stage method for optimal sensor placement using graph-theoretical partitioning and evolutionary algorithms Structural Control and Health Monitoring, 26(4), 1– 17 DOI: 10.1002/stc.2325 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Mallardo, V., & Aliabadi, M H (2014) Optimal sensor placement for structural, damage and impact identification: A review SDHM Structural Durability and Health Monitoring, 9(4), 1–32 Moslem, K., & Nafaspour, R (2002) Structural damage detection by genetic algorithms AIAA Journal, 40(7), 1395–1401 DOI: 10.2514/3.15208 Nematollahi, A F., Rahiminejad, A., & Vahidi, B (2017) A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization Applied Soft Computing, 59, 596–621 DOI: 10.1016/j.asoc.2017.06.033 Prayogo, D., Wong, F T., & Sugianto, S (2018) Enhanced symbiotic organisms search (ESOS) for global numerical optimization Proceeding ICAMIMIA 2017: International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation, 69–73 DOI: 10.1109/ICAMIMIA.2017.8387560 Rao, R V., Savsani, V J., & Vakharia, D P (2011) Teaching–learningbased optimization: A novel method for constrained mechanical design optimization problems Computer-Aided Design, 43(3), 303–315 DOI: 10.1016/j.cad.2010.12.015 Seyedpoor, S M (2012) A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization International Journal of Non-Linear Mechanics, 47(1), 1–8 DOI: 10.1016/j.ijnonlinmec.2011.07.011 Shabbir, F., Khan, M., Ahmad, N., Tahir, M., Ejaz, N., & Hussain, J (2017) Structural Damage Detection with Different Objective Functions in Noisy Conditions Using an Evolutionary Algorithm Applied Sciences, 7(12), 1245 DOI: 10.3390/app7121245 Sung, H., Chang, S., & Cho, M (2017) Structural system identification using degree of freedom-based reduction method and sensor selection algorithm AIAA Modeling and Simulation Technologies Conference, January, Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn