Regularization method for load reconstruction with hybrid uncertainties based on interval theory and convex model theory

Abstract

Inevitably, load reconstruction involves uncertainties in structural responses and sensor measurements arising from test conditions, material parameters, modelling simplifications, and so on. This paper presents a method using the Green's kernel function (GKFM) to establish a linear time-domain mapping between loads under uncertain circumstances and sensor responses. We develop a regularization framework based on interval analysis and convex modelling to characterize these hybrid uncertainties. Existing non-probabilistic load reconstruction methods typically quantify hybrid uncertainties using a single model (pure interval or pure convex), which may overlook the unique characteristics of different uncertainty sources. This could have an adverse effect on the accuracy of load boundary reconstruction and the robustness of regularization parameter selection. In contrast, this method avoids probabilistic distribution assumptions. By effectively integrating interval analysis and convex modelling, it solves the boundary-value problem for load reconstruction under limited data, refining the upper and lower bounds of the reconstructed load. Crucially, this paper proposes a robust multi-objective regularization parameter optimization strategy to dynamically balance stability and accuracy under the combined influence of hybrid uncertainties. Compared with methods that treat uncertainties homogeneously, this integrated approach provides more compact and reliable estimates. Validation is performed using a space capsule numerical case study.