Incomplete sensed data in structures have made exact structural damage detection a serious challenge. In this paper, an effective method is presented for damage detection and estimation in structures based on incomplete modal data of a damaged structure via a pattern search algorithm. An objective function based on the condensed mass and stiffness matrices is formulated. The proposed method determines the damage to structural elements using optimization of the objective function by using pattern search algorithm. The performance of the presented method has been verified through two numerical examples, namely, a two-span continuous beam and a three-story plane frame with and without noise in the modal data containing several damages. Also, the effect of the discrepancy in mass and stiffness between the finite-element model and the actual tested dynamic system has been investigated. Furthermore, the experimental data from the vibration test of a mass–stiffness system are used for verification of the proposed approach. The results show that the presented method is sensitive to the location and severity of structural damage in spite of the incomplete modal data.
Al-SumaitJSAl-OthmanAKSykulskiJK (2007) Application of pattern search method to power system valve-point economic load dispatch. International Journal of Electrical Power & Energy Systems, 29: 720–730.
2.
AuFTKChengYSThamLGBaiZZ (2003) Structural damage detection based on a micro-genetic algorithm using incomplete and noisy modal test data. Journal of Sound and Vibration, 259: 1081–1094.
3.
BiondiTCiccazzoACutelloV (2006) Multi-objective evolutionary algorithms and pattern search methods for circuit design problems. Journal of Universal Computer Science, 12: 432–449.
4.
BoxGEP (1957) Evolutionary operation: A method for increasing industrial productivity. Journal of Applied Statistics, 6: 81–101.
5.
CarvalhoJDattaBNGuptaALagadapatiM (2007) A direct method for model updating with incomplete measured data and without spurious modes. Mech Syst Signal Process, 21: 2715–2731.
6.
ChandrashekharMGanguliR (2009) Uncertainty handling in structural damage detection using fuzzy logic and probabilistic simulation. Mechanical Systems and Signal Processing, 23: 384–404.
7.
ChenCW (2006) Stability conditions of fuzzy systems and its application to structural and mechanical systems. Advances in Engineering Software, 37: 624–629.
8.
ChenCW (2009) The stability of an oceanic structure with T-S fuzzy models. Mathematics and Computers in Simulation, 80: 402–426.
9.
ChenCW (2011) Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method. Neural Computing & Applications, 20: 527–534.
10.
ChenCWChiangWLTsaiCH (2006) Fuzzy Lyapunov method for stability conditions of nonlinear systems. International Journal on Artificial Intelligence Tools, 15: 163–172.
11.
ChenCWLinCLTsaiCH (2007) A novel delay-dependent criterion for time-delay T-S fuzzy systems using fuzzy Lyapunov method. International Journal on Artificial Intelligence Tools, 16: 545–552.
12.
ChenH (2008) Application of regularization methods to damage detection in large scale plane frame structures using incomplete noisy modal data. Engineering Structures, 30: 3219–3227.
13.
Chen PC, Yeh K, Chen CW and Chen CY (2009) Application to GA-based fuzzy control for nonlinear systems with uncertainty. In Asian Conference on Intelligent Information and Database Systems, Dong hoi, Quang binh, Vietnam, 1–3 April 2009, pp. 249–252.
14.
ChiangWLChenCWHsiaoFH (2004) Stability analysis of nonlinear interconnected systems via T-S fuzzy models. International Journal of Computational Intelligence and Applications, 4: 41–55.
15.
ChingJMutoMBeckJL (2006) Structural model updating and health monitoring with incomplete modal data using Gibbs sampler. Computer-Aided Civil and Infrastructure Engineering, 21: 242–257.
16.
CoelhoLSMarianiVC (2006) Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Transactions on Power Systems, 21: 989–996.
17.
Doebling SW, Farrar CR and Prime MB (1998) A summary review of vibration-based damage identification methods. The Shock and Vibration Digest 30: 91–105.
18.
DuanZYanGOuJSpencerBF (2007) Damage detection in ambient vibration using proportional flexibility matrix with incomplete measured DOFs. Structural Control & Health Monitoring, 14: 186–196.
19.
Duffey TA, Doebling SW, Farrar CR, et al. (2001) Vibration-based damage identification in structures exhibiting axial and torsional response. Journal of Vibration and Acoustics 123(1): 84–92.
20.
GuyanRJ (1965) Reduction of stiffness and mass matrices. AIAA Journal, 3: 380–387.
21.
HookeRJeevesTA (1961) Direct search solution of numerical and statistical problems. Journal of the ACM, 8: 212–229.
22.
HsiaoFHChiangWLChenCW (2005) Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13: 281–296.
23.
HuajunLFushunLJamesHS (2008) Employing incomplete complex modes for model updating and damage detection of damped structures. Science in China Series E – Technological Sciences, 51: 2254–2268.
24.
KoldaTGLewisRMTorczonV (2003) Optimization by direct search: new perspectives on some classical and modern methods. SIAM Review, 45: 385–482.
25.
LawSSShiZYZhangLM (1998) Structural damage detection from incomplete and noisy modal test data. Journal of Engineering Mechanics, 124: 1280–1288.
26.
LewisRMTorczonV (2002) A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM Journal on Optimization, 12: 1075–1089.
27.
LewisRMTorczonVTrossetMW (2000) Direct search methods: then and now. Journal of Computational and Applied Mathematics, 124: 191–207.
28.
LiHWangJHuSJ (2008) Using incomplete modal data for damage detection in offshore jacket structures. Ocean Engineering, 35: 1793–1799.
29.
Mathworks (2008) MATLAB User Manual. Lowell, MA: Mathworks Inc.
30.
PawarPMGanguliR (2007) Genetic fuzzy system for online structural health monitoring of composite helicopter rotor blades. Mechanical Systems and Signal Processing, 21: 2212–2236.
31.
RahaiABakhtiari-NejadFEsfandiariA (2007) Damage assessment of structure using incomplete measured mode shapes. Structural Control & Health Monitoring, 14: 808–829.
32.
SwannWH(1972) Direct search methods. In: MurrayW (eds) Numerical Methods for Unconstrained Optimization, pp. New York: Academic Press.
33.
TokanFGunesF (2011) Interference suppression by optimizing the positions of selected elements using generalized pattern search algorithm. IET Microwaves, Antennas & Propagation, 5: 127–135.
34.
Yeh K, Chen CW, Lin SH and Chen CY (2009) Stability analysis of time-delay fuzzy systems using fuzzy Lyapunov method. In Asian Conference on Intelligent Information and Database Systems, Dong hoi, Quang binh, Vietnam, 1–3 April 2009, pp. 243–248.
35.
YehKChenCYChenCW (2008) Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method. Applied Mathematics and Computation, 205: 568–577.
36.
YuenKBeckJLKatafygiotisLS (2006) Efficient model updating and health monitoring methodology using incomplete modal data without mode matching. Structural Control &Health Monitoring, 13: 91–107.
