Prediction for the structural response with multi-extreme points based on the third-order Taylor series expansion subinterval method

Uncertainties are ubiquitous in structural systems, and it is essential to assess their influence on structural response. In this paper, uncertainties are treated as interval parameters, and the upper and lower bounds of structural response are predicted by Taylor-series-based method. In certain scenarios, the structural response exhibits a nonlinear variation with respect to uncertain parameters. Moreover, multiple extreme points may even emerge. In view of this, an interval analysis method of multi-extreme points third-order Taylor series expansion based on subinterval-sensitivity approximate prediction (SSA-METTEM) is proposed to obtain the bounds of the structural response. The novelty of the method proposed in this paper is mainly in the following two aspects. Firstly, the idea of sensitivity approximate prediction is proposed. By leveraging high-order sensitivity analysis, the two extreme points within the response interval can be predicted. Secondly, multiple extreme points in the response interval are predicted by dichotomizing the subintervals. This interval analysis method is committed to achieve an optimal trade-off between computational efficiency and the accuracy of results. The accuracy and efficiency of the proposed method are verified by three numerical examples. Finally, several valuable conclusions are drawn.