A novel interval model updating framework based on correlation propagation and matrix-similarity method

Abstract

Model updating techniques have achieved extensive applications in numerical models with uncertainties inherently in practical systems, whereas the stochastic theory is ineffective under insufficient knowledge. Additionally, model updating in the face of correlated uncertainties and complex numerical models remains challenging. In the present study, a novel interval model updating framework was proposed to tackle down the correlated uncertainties with limit samples. Such a framework has the advantage that parameters can be updated with high precision regardless of whether the relationship between input and output is linear or nonlinear. To achieve this advantage, the convex modelling technique and the Chebyshev surrogate model were employed for uncertain parameter quantization and numerical model approximation, respectively. Subsequently, the matrix-similarity method considering correlation propagation was developed to build the two-step interval model updating process, which was converted into a deterministic model updating problem. The mentioned process simplified the model complexity, while improving the accuracy of the updated results. Notably, three examples verified the effectiveness and superiority of the proposed framework in both linear and nonlinear relationships. As revealed from the results, the proposed interval model updating framework in the present study is suitable for coping with the updating problems of the parameter’s bounds and their correlations.