Research Papers

A Multi-Objective DIRECT Algorithm Toward Structural Damage Identification With Limited Dynamic Response Information

[+] Author and Article Information
Pei Cao

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269

Qi Shuai

Department of Automotive Engineering,
Chongqing University,
Chongqing 400044, China

Jiong Tang

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jiong.tang@uconn.edu

1Corresponding author.

Manuscript received August 31, 2017; final manuscript received November 2, 2017; published online December 20, 2017. Assoc. Editor: Mark Derriso.

ASME J Nondestructive Evaluation 1(2), 021004 (Dec 20, 2017) (12 pages) Paper No: NDE-17-1084; doi: 10.1115/1.4038630 History: Received August 31, 2017; Revised November 02, 2017

A major challenge in structural health monitoring (SHM) is to accurately identify both the location and severity of damage using the dynamic response information acquired. While in theory the vibration-based and impedance-based methods may facilitate damage identification with the assistance of a credible baseline finite element model, the response information is generally limited, and the measurements may be heterogeneous, making an inverse analysis using sensitivity matrix difficult. Aiming at fundamental advancement, in this research we cast the damage identification problem into an optimization problem where possible changes of finite element properties due to damage occurrence are treated as unknowns. We employ the multiple damage location assurance criterion (MDLAC), which characterizes the relation between measurements and predictions (under sampled elemental property changes), as the vector-form objective function. We then develop an enhanced, multi-objective version of the dividing rectangles (DIRECT) approach to solve the optimization problem. The underlying idea of the multi-objective DIRECT approach is to branch and bound the unknown parametric space to converge to a set of optimal solutions. A new sampling scheme is established, which significantly increases the efficiency in minimizing the error between measurements and predictions. The enhanced DIRECT algorithm is particularly suited to solving for unknowns that are sparse, as in practical situations structural damage affects only a small region. A number of test cases using vibration response information are executed to demonstrate the effectiveness of the new approach.

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Michaels, J. E. , and Michaels, T. E. , 2007, “ Guided Wave Signal Processing and Image Fusion for In Situ Damage Localization in Plates,” Wave Motion, 44(6), pp. 482–492. [CrossRef]
Harley, J. B. , and Moura, J. M. F. , 2014, “ Data-Driven Matched Field Processing for Lamb Wave Structural Health Monitoring,” J. Acoust. Soc. Am., 135(3), pp. 1231–1244. [CrossRef] [PubMed]
Cawley, P. , and Simonetti, F. , 2005, “ Structural Health Monitoring Using Guided Waves–Potential and Challenges,” Fifth International Conference on Structural Health Monitoring, pp. 503–510.
West, H. H. , and Mafi, M. , 1984, “ Eigenvalues for Beam-Columns on Elastic Supports,” J. Struct. Eng., 110(6), pp. 1305–1320. [CrossRef]
Kim, J. T. , and Stubbs, N. , 2003, “ Crack Detection in Beam-Type Structures Using Frequency Data,” J. Sound Vib., 259(1), pp. 145–160. [CrossRef]
Annamdas, V. G. M. , and Radhika, M. A. , 2013, “ Electromechanical Impedance of Piezoelectric Transducers for Monitoring Metallic and Non-Metallic Structures: A Review of Wired, Wireless and Energy-Harvesting Methods,” J. Intell. Mater. Syst. Struct., 24(9), pp. 1021–1042. [CrossRef]
Shuai, Q. , Zhou, K. , Zhou, S. , and Tang, J. , 2017, “ Fault Identification Using Piezoelectric Impedance Measurement and Model-Based Intelligent Inference With Pre-Screening,” Smart Mater. Struct., 26(4), p. 045007. [CrossRef]
Cao, P. , Shuai, Q. , and Tang, J. , 2017, “ Structural Damage Identification Using Piezoelectric Impedance Measurement With Sparse Inverse Analysis,” eprint arXiv:1708.02968. https://arxiv.org/abs/1708.02968
Kim, J. , and Wang, K. W. , 2014, “ An Enhanced Impedance-Based Damage Identification Method Using Adaptive Piezoelectric Circuitry,” Smart Mater. Struct., 23(9), p. 095041. [CrossRef]
Hao, H. , and Xia, Y. , 2002, “ Vibration-Based Damage Detection of Structures by Genetic Algorithm,” J. Comput. Civil Eng., 16(3), pp. 222–229. [CrossRef]
Villalba, J. D. , and Laier, J. E. , 2012, “ Localising and Quantifying Damage by Means of a Multi-Chromosome Genetic Algorithm,” Adv. Eng. Software, 50, pp. 150–157. [CrossRef]
Seyedpoor, S. M. , 2012, “ A Two Stage Method for Structural Damage Detection Using a Modal Strain Energy Based Index and Particle Swarm Optimization,” Int. J. Nonlinear Mech., 47(1), pp. 1–8. [CrossRef]
He, R.-S. , and Hwang, S.-F. , 2006, “ Damage Detection by an Adaptive Real-Parameter Simulated Annealing Genetic Algorithm,” Comput. Struct., 84(31), pp. 2231–2243. [CrossRef]
Seyedpoor, S. M. , Shahbandeh, S. , and Yazdanpanah, O. , 2015, “ An Efficient Method for Structural Damage Detection Using a Differential Evolution Algorithm-Based Optimisation Approach,” Civil Eng. Environ. Syst., 32(3), pp. 230–250. [CrossRef]
Messina, A. , Williams, E. J. , and Contursi, T. , 1998, “ Structural Damage Detection by a Sensitivity and Statistical-Based Method,” J. Sound Vib., 216(5), pp. 791–808. [CrossRef]
Cao, P. , Yoo, D. , Shuai, Q. , and Tang, J. , 2017, “ Structural Damage Identification With Multi-Objective DIRECT Algorithm Using Natural Frequencies and Single Mode Shape,” Proc. SPIE, 10170, p. 101702H.
Jones, D. R. , Perttunen, C. D. , and Stuckman, B. E. , 1993, “ Lipschitzian Optimization Without the Lipschitz Constant,” J. Optim. Theory Appl., 79(1), pp. 157–181. [CrossRef]
Fan, W. , and Qiao, P. , 2011, “ Vibration-Based Damage Identification Methods: A Review and Comparative Study,” Struct. Health Monit., 10(1), pp. 83–111. [CrossRef]
Nobahari, M. , and Seyedpoor, S. M. , 2011, “ Structural Damage Detection Using an Efficient Correlation-Based Index and a Modified Genetic Algorithm,” Math. Comput. Modell., 53(9), pp. 1798–1809. [CrossRef]
Shubert, B. O. , 1972, “ A Sequential Method Seeking the Global Maximum of a Function,” SIAM J. Numer. Anal., 9(3), pp. 379–388. [CrossRef]
Finkel, D. E. , 2005, “ Global Optimization With the DIRECT Algorithm,” Ph.D. dissertation, North Carolina State University, Raleigh, NC. https://dl.acm.org/citation.cfm?id=1087602
Cao, P. , Fan, Z. , Gao, R. , and Tang, J. , 2016, “ Complex Housing: Modelling and Optimization Using an Improved Multi-Objective Simulated Annealing Algorithm,” ASME Paper No. DETC2016-60563.
Wang, L. , Ishida, H. , Hiroyasu, T. , and Miki, M. , 2008, “ Examination of Multi-Objective Optimization Method for Global Search Using DIRECT and GA,” IEEE Congress on Evolutionary Computation (CEC), Hong Kong, China, June 1–6, pp. 2446–2451.
Al-Dujaili, A. , and Suresh, S. , 2016, “ Dividing Rectangles Attack Multi-Objective Optimization,” IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, Canada, July 24–29, pp. 3606–3613.
Wong, C. S. Y. , Al-Dujaili, A. , and Sundaram, S. , 2016, “ Hypervolume-Based DIRECT for Multi-Objective Optimisation,” Genetic and Evolutionary Computation Conference Companion (GECCO), Denver, CO, July 20–24, pp. 1201–1208.
Deb, K. , Pratap, A. , Agarwal, S. , and Meyarivan, T. A. M. T. , 2002, “ A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Computation, 6(2), pp. 182–197. [CrossRef]
Guo, H. Y. , and Li, Z. L. , 2009, “ A Two-Stage Method to Identify Structural Damage Sites and Extents by Using Evidence Theory and Micro-Search Genetic Algorithm,” Mech. Syst. Signal Process., 23(3), pp. 769–782. [CrossRef]


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Fig. 1

Initial minimum estimation of f(x) by Lipschitz optimization

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Fig. 2

The Shubert's algorithm

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Fig. 3

Initial minimum estimation of f(x) by center point sampling

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Fig. 4

Subdivision routine of DIRECT

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Fig. 5

Determine the potentially optimal intervals in 1D

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Fig. 6

Sampling and dividing of the decision space: (a)–(d) 2D example and (e) three-dimensional example (Adapted from Ref. [21])

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Fig. 8

Rank based on objective values

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Fig. 9

Comparison of two strategies on selecting potentially optimal rectangles: (a) our strategy and (b) strategy from Ref.[23]

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Fig. 7

Determine the potentially optimal rectangles

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Fig. 12

Optimization results of case 2: (a) in objective space, (b) Box plot, (c) mean value, and (d) after a posterior articulation

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Fig. 18

Strategy comparison of multi-objective DIRECT algorithms

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Fig. 13

Convergent history of case 2

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Fig. 14

Optimization results of case 3: (a) in objective space, (b) Box plot, (c) mean value, and (d) after a posterior articulation

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Fig. 15

Convergent history of case 3

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Fig. 10

Optimization results of case 1: (a) in objective space, (b) Box plot, (c) mean value, and (d) after a posterior articulation

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Fig. 11

Several iterations of multi-objective search in objective space (x-axis: d; y-axis: R) (◊: potentially optimal rectangles; *: rectangles)

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Fig. 16

Optimization results of case 4: (a) in objective space, (b) Box plot, (c) mean value, and (d) after a posterior articulation

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Fig. 17

Optimization results of case 5: (a) in objective space, (b) Box plot, (c) mean value, and (d) after a posterior articulation



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