Probabilistic Approach to Structural Health Monitoring from Dynamic Testing

Abstract

The problem of updating a structural model by utilizing measured structural response is addressed, taking into account the uncertainties which arise from measurement noise, modeling errors, and an inherent nonuniqueness in this inverse problem. Using a Bayesian probabilistic fonnulation, the updated "posterior" probability distribution of the uncertain model parameters is obtained and it is found that for a large number of data points this probability distribution is very peaked at some "optimal" values of the parameters, which can be obtained by minimizing a positive-definite measure-of-fit function. The identifiability of the optimal parameters is discussed and an efficient algorithm is proposed to find the whole set of optimal models that have the same output at the observed degrees of freedom for a given input. Each of the optimal solutions has a weighting coefficient associated with it which describes the plausibililty of that optimal parameter, and which depends on the subjective prior probability of the parameter. The posterior probability distribution, specified by the set of the optimal parameters and their associated weighting coefficients, can be used for probabilistic health monitoring of a structure by detecting possible changes in its stiffness distribution.

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