Optimum sensitivity-based statistical parameters estimation from modal response

Based on the concept of optimum sensitivity, we present a method for estimating the mean and covariance of parameters of a mechanical system from the statistics of its measured modal response. The:optimum sensitivity, defined as the sensitivity of system parameters with respect to observed output, is obtained by direct differentiation of the Kuhn-Tucker optimality criteria for a nonlinear least-squares output error estimator. With the optimum sensitivity derivatives up to the second order, we can estimate the second-order approximation of both the mean and covariance of the system parameters by applying methods developed originally for evaluating the output of uncertain systems based on the more conventional notion:of sensitivity, the sensitivity of system response:with respect to system parameters. The present approach allows us to assess the bias due to nonlinearities in the least-squares estimator whereas conventional sensitivity-based methods do not. Furthermore, the present method is generally much more efficient than Monte Carlo simulation because nonlinear optimization is performed only once. We demonstrate through example problems that, compared to the conventional sensitivity-based methods, the present method provides statistical indices that are more consistent with those obtained by Monte Carlo simulation.