Uncertain Parameters Estimation using Multi-Dimensional Analysis and Stochastic Model Updating

Abstract

Stochastic model updating based on perturbation theory has been widely applied to quantify uncertain parameters in structural systems due to its simplicity and straightforward approach. Nevertheless, the significant requirements for establishing a good correlation in the initial prediction of structural responses and small perturbations in uncertain parameters have become influential in stochastic model updating. The initial assumptions of structural parameters are often unavailable to quantify the input properties due to insufficient information about the structural system. These problems contribute to large errors in initial prediction, causing ill-posedness in sensitivity matrices and convergence difficulties caused by the local minima function in the stochastic model updating approach. In these circumstances, this study attempts to propose a novel scheme to overcome the ill-posed and converging problems in the stochastic model updating by quantifying structural parameters of the assembled structure encompassing high uncertainties such as the stiffness term of the contact joint interface by using a combination of the lattice-based exploration approach and the perturbation-based stochastic model updating method. The lattice-based exploration approach is adopted for generating samples of predicted responses from the assumed initial distribution of random parameters in the interest of improving the initial correlation of the predicted responses for producing well-condition sensitivity. Responses from each sample are evaluated in light of their experimental counterparts to estimate the optimum initial distribution of the random parameters. Then, the initial statistical properties of the parameters can be estimated by rerunning the sampling approach using the optimum distribution. As a result, stochastic model updating using the perturbation approach can be applied efficiently with the new initial distribution. The proposed scheme has been demonstrated on an assembled bolted joint structure, focusing on the contact interfaces. It is found that the proposed scheme managed to produce satisfactory predictions on the distribution of natural frequencies with only 12.5 % of total errors are recorded in comparison with the experimental data.