Probability assessments of identified parameters for stochastic structures using point estimation method

In this paper, a kind of inverse problem for assessing the probabilities of identified parameters with uncertainties in structural parameters and limited experimental results is investigated. The point estimation method and maximum entropy principle are adopted to efficiently evaluate the effect of uncertain parameters on the identified parameters. First, the probability distribution function of each uncertain parameter can be approximately represented by several nodes. Thus, the uncertain inverse problem can be transformed into several deterministic inverse problems through multivariate Taylor expansion and point estimation method. Then, to obtain the moments of identified parameters, the deterministic inverse process for each selected node with concentrated probability are conducted by the genetic algorithm. Finally, the probability distribution functions of the identified parameters can be assessed by the obtained moments based on the maximum entropy principle. The proposed method effectively avoids the low efficiency of uncertain inverse problem, which commonly involves a double-loop procedure with uncertainty propagation and inverse calculation. Numerical examples and the engineering application demonstrate the feasibility and effectiveness of the proposed method.