Non-probabilistic uncertain inverse problem method considering correlations for structural parameter identification

This paper presents an effective sequence interval and correlation inverse strategy for the uncertain inverse problem, aiming to identify the uncertainties and non-probabilistic correlations of the structural parameters simultaneously. First, an ellipsoidal convex model is adopted to quantify the uncertainty boundary of the measured responses with limited samples. Then, the uncertain inverse problem based on the ellipsoidal convex model is decoupled into an interval inverse problem and a correlation inverse problem. For the interval inverse problem, a subinterval decomposition analysis method constrained by the ellipsoidal convex model is developed to evaluate the intervals of the structural responses with a low computational cost. For the correlation inverse problem, the correlation propagation equations are derived to calculate the non-probabilistic correlation coefficient matrix of the structural responses. After that, by using optimization algorithms to circularly reduce the errors of the intervals and the correlation coefficients between the measured responses and calculated structural responses, the intervals and the non-probabilistic correlation coefficient matrix of the structural parameters are identified effectively, and an ellipsoidal convex model of the structural parameters can be established eventually. Two numerical examples and one experimental example are investigated to verify the effectiveness and accuracy of the proposed sequence interval and correlation inverse strategy.

Automated summary

This paper proposes an effective sequence interval and correlation inverse strategy to identify uncertainties and non-probabilistic correlations of structural parameters simultaneously. By quantifying uncertainty boundaries with an ellipsoidal convex model, the uncertain inverse problem is divided into an interval inverse problem and a correlation inverse problem.