Parameter variability estimation using stochastic response surface model updating

• Stochastic response surface models substitute FE models having uncertain parameters.
• Model reconstruction is performed during iterations for efficient updating.
• Parameter means and standard deviations are updated in a separate and successive way.
• Parameter significance is evaluated based on polynomial chaos expansions.

From a practical point of view, uncertainties existing in structural parameters and measurements must be handled in order to provide reliable structural condition evaluations. At this moment, deterministic model updating loses its practicability and a stochastic updating procedure should be employed seeking for statistical properties of parameters and responses. Presently this topic has not been well investigated on account of its greater complexity in theoretical configuration and difficulty in inverse problem solutions after involving uncertainty analyses. Due to it, this paper attempts to develop a stochastic model updating method for parameter variability estimation. Uncertain parameters and responses are correlated through stochastic response surface models, which are actually explicit polynomial chaos expansions based on Hermite polynomials. Then by establishing a stochastic inverse problem, parameter means and standard deviations are updated in a separate and successive way. For the purposes of problem simplification and optimization efficiency, in each updating iteration stochastic response surface models are reconstructed to avoid the construction and analysis of sensitivity matrices. Meanwhile, in the interest of investigating the effects of parameter variability on responses, a parameter sensitivity analysis method has been developed based on the derivation of polynomial chaos expansions. Lastly the feasibility and reliability of the proposed methods have been validated using a numerical beam and then a set of nominally identical metal plates. After comparing with a perturbation method, it is found that the proposed method can estimate parameter variability with satisfactory accuracy and the complexity of the inverse problem can be highly reduced resulting in cost-efficient optimization.