Optimal experimental design for structural health monitoring applications

Successful structural health monitoring and condition assessment depends to a large extent on the sensor and actuator networks place on the structure as well as the excitation characteristics. An optimal experimental design methodology deals with the issue of optimizing the sensor and actuator network, as well as the excitation characteristics, such that the resulting measured data are most informative for monitoring the condition of the structure. Information theory based approaches have been developed to provide rational solutions to several issues encountered in the problem of selecting the optimal sensor configuration. The optimal sensor configuration is taken as the one that maximizes some norm (determinant or trace) of the Fisher information matrix. Papadimitriou et al. (2000) introduced the information entropy norm as the measure that best corresponds to the objective of structural testing, which is to minimize the uncertainty in the model parameter estimates. An important advantage of the information entropy measure is that it allows one to make comparisons between sensor configurations involving a different number of sensors in each configuration. Furthermore, it has been used to design the optimal characteristics of the excitation (e.g. amplitude and frequency content) useful in the identification of linear and strongly nonlinear models. The optimal sensor placement strategies depend on the class of mathematical models selected to represent structural behavior as well as the model parameterization within the model class. However, it is often desirable to use the measured data for selecting the most appropriate model class from a family of alternative model classes chosen by the analyst to represent structural behavior. Such classes may be linear (modal models or finite element models), nonlinear elastic or inelastic, each one involving different number of parameters. Model class selection is also important for damage detection purposes for which the location and severity of damage are identified using a family of model classes with each model class monitoring a specific region in a structure (Papadimitriou & Katafy-giotis 2004) or incorporating different mechanisms of damage. The objective in this work is to optimise the number and location of sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural identification and damage detection purposes. Theoretical and computational issues arising in optimal experimental design are addressed. The problem is formulated as a multi-objective optimization problem of finding the Pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices related to monitoring multiple probable damage scenarios. Asymptotic estimates for the information entropy, valid for large number of measured data, are used to rigorously justify that the selection of the optimal experimental design can be based solely on nominal structural models associated with the probable damage scenarios, ignoring the details of the measured data that are not available in the experimental design stage. Heuristic algorithms are proposed for constructing effective, in terms of accuracy and computational efficiency, sensor configurations. Damage detection results on a shear model of a building structure are used to illustrate the theoretical developments. © 2008 Taylor & Francis Group, London.