On the convergence of multiple excitation sources to a two‐tone excitation class: Implications for a global optimum excitation in active sensing for structural health monitoring

We showed in a recent study that the parameters of a system of ordinary differential equations (ODEs) may be adjusted via an evolutionary algorithm (EA) to produce deterministic excitations that improve damage detection in a simple computational spring–mass system. In that study, frequency considerations were found to be dominant, but the exact mechanism by which detection improvement is effected was not immediately apparent. In this work, an EA is used to shape bandlimited noise excitations in the frequency domain such that improvement is seen in the sensitivity of the detection feature. Tailored excitations generated from three bandlimited excitation sources, a multi-tone (linear sum of sinusoids) excitation source, and an ODE excitation source complement results from the previous study and help explain what excitation frequency characteristics are important for improved damage discernment. The convergence of all excitation source optimizations to similar solutions suggests the existence of a class of excitations that are globally optimal for improved damage detection sensitivity in the model application. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  Hoon Sohn,et al.  A review of structural health monitoring literature 1996-2001 , 2002 .

[3]  Jonathan M. Nichols,et al.  Structural health monitoring of offshore structures using ambient excitation , 2003 .

[4]  Louis M. Pecora,et al.  Dynamical Assessment of Structural Damage Using the Continuity Statistic , 2004 .

[5]  Michael D. Todd,et al.  Using state space predictive modeling with chaotic interrogation in detecting joint preload loss in a frame structure experiment , 2003 .

[6]  D Chelidze,et al.  Phase space warping: nonlinear time-series analysis for slowly drifting systems , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Charles R. Farrar,et al.  A summary review of vibration-based damage identification methods , 1998 .

[8]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  J. Yorke,et al.  HOW MANY DELAY COORDINATES DO YOU NEED , 1993 .

[10]  Michael D. Todd,et al.  Use of data-driven phase space models in assessing the strength of a bolted connection in a composite beam , 2004 .

[11]  J M Nichols,et al.  Use of chaotic excitation and attractor property analysis in structural health monitoring. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  P. Grassberger,et al.  A robust method for detecting interdependences: application to intracranially recorded EEG , 1999, chao-dyn/9907013.

[13]  Michael D. Todd,et al.  Sensitivity and computational comparison of state-space methods for structural health monitoring , 2005, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[14]  Michael D. Todd,et al.  Structural Health Monitoring Through Chaotic Interrogation , 2003 .

[15]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[16]  Charles R. Farrar,et al.  Improving Excitations for Active Sensing in Structural Health Monitoring via Evolutionary Algorithms , 2007 .

[17]  Michael D. Todd,et al.  Excitation considerations for attractor property analysis in vibration-based damage detection , 2003, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[18]  Michael D. Todd,et al.  A parametric investigation of state-space-based prediction error methods with stochastic excitation for structural health monitoring , 2007 .

[19]  Laura E. Ray,et al.  Damage Identification Using Sensitivity-Enhancing Control and Identified Models , 2006 .

[20]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[21]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[22]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[23]  L. Pecora,et al.  Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio , 2001 .