Damage Identification in a Multi-DOF System under Uncertainties Using Optimization Algorithms

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Rio de Janeiro , Brazil

2 Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

3 Computing and Applied Mathematics Laboratory, Instituto Nacional de Pesquisas Espaciais (INPE), São José dos Campos, Brazil

Abstract

In this study, four optimization algorithms are applied to identify the damage in a multi-DOF dynamical system composed of masses, springs, and dampers. The damage is introduced artificially by choosing a lower value for the stiffness. The applied algorithms include Nelder-Mead Simplex, BFGS Quasi-Newton, interior point, and sequential quadratic programming - SQP. In addition, some different strategies to identify damage are applied. First, a deterministic analysis is performed to identify the damage; i.e, the values of the stiffnesses. Then, random forces are considered, and finally, the stiffness values are considered uncertain and the different strategies are compared.

Keywords

Main Subjects

[1] Beale, E.M.L., Numerical Methods. In: Nonlinear programming, J. Abadie, North-Holland, 1967.
[2] Byrd, R.H., Hribar, M.E., Nocedal, J., An Interior Point Algorithm for Large-Scale Nonlinear Programming, SIAM Journal on Optimization, 9, 1999, 877-900.
[3] Hall, S.R., The effective management and use of structural health data, International workshop on structural health monitoring, 1999, 265-275.
[4] Hicken, J.E., Alonso, J.J., Lecture notes from the course AA222 - Introduction to Multidisciplinary Design Optimization, Stanford, 2012.
[5] Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E., Convergence Properties of the Nelder-Mead Simplex Algorithm in Low Dimensions, SIAM Journal on Optimization, 9, 1998, 112-147.
[6] Nelder, J.A., Mead, R., A simplex method for function minimization, Computer Journal, 7, 1965, 308-313.
[7] Fletcher, R., Practical Methods of Optimization, Wiley, 2000.
[8] Ooijevaar, T.H., Vibration based structural health monitoring of composite skin-stiffener structures. PhD theses, University of Twente, 2014.
[9] Ritter, A., Vibrational Based Inspection of Civil Engineering Structures, PhD theses, Aalborg University, 1993.
[10] Castello, D.A., Ritto, T.G. Quantificação de incertezas e estimação de parâmetros em dinâmica estrutural: uma introdução a partir de exemplos computacionais, SBMAC, 2016.
[11] Wilson, R.B., A Simplicial Algorithm for Concave Programming, PhD theses, Harvard University Graduate School of Business Administration, 1963.
[12] Worden, K., Dulieu-Barton, J.M., An overview of intelligent fault detection in systems and structures, Structural Health Monitoring, 3(1), 2004, 85-98.
[13] Xiu, D., Numerical methods for stochastic computations: A spectral method approach, Princeton University Press, 2010.
[14] Lopez, R.H., Optimisation en presence d’uncertitudes, PhD theses, Insa-Rouen, France, 2010.
[15] Ritto, T.G., Lopez, R.H., Sampaio, R., Souza De Cursi, J.E., Robust optimization of a flexible rotor-bearing system using the Campbell diagram, Engineering Optimization, 43(1), 2011, 77-96.
[16] Ritto, T.G., Soize, C., Sampaio, R., Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model, Computational Mechanics, 45(5), 2010, 415-427.
[17] Cadini, F., Sbarufatti, C., Corbetta, M., Giglio, M., A particle filter-based model selection algorithm for fatigue damage identification on aeronautical structures, Structural Control and Health Monitoring, 24(11), 2017, e2002.
[18] Yin, T., Jiang, Q.-H., Yuen, K.-V. , Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique, Engineering Structures, 2017, 132, 260-277.
[19] Varmazyar, M., Haritos, N., Kirley, M., A wavelet-based Bayesian damage identification technique using an evolutionary algorithm, Australian Journal of Structural Engineering, 2016, 17(4), 225-241.