A Novel Stochastic Finite Element Model Updating Method Based on Multi-Point Sensitivities

A novel stochastic finite element model updating method based on multi-point sensitivities is proposed to improve the reproduction and prediction ability of finite element models for experimental data. Drawing upon the theory of small perturbations, this approach employs the sensitivity matrix in conjunction with the probability distribution of responses evaluated at multiple parameter points to determine the probability density associated with each parameter point and to estimate the statistical properties of the parameters. To achieve this objective, principal component analysis is employed to unify the dimensionality of the parameters and the responses; the least squares method was used to estimate the characteristics of the parameters. The reliability and validity of this method were confirmed through experimentation with a 3-degree-of-freedom spring-mass system and an aerospace thermal insulation structure. A comparison of this method with classical methods reveals significant advantages in terms of robustness across varying computational scales. Notably, it attains superior accuracy with smaller sample sizes while maintaining precision comparable to conventional methods with large samples. Consequently, this characteristic confers upon the method a distinct advantage in scenarios where the costs of finite element computation are prohibitively high.