Robust identification of distributed dynamic loads acting on multi-degree-of-freedom structures based on sparse measurement

Abstract

Distributed dynamic loads (DDLs) have attracted much attention due to their widespread existence in engineering. However, it remains difficult to measure them directly. Existing DDL identification algorithms have some limitations in terms of dimensionality reduction of DDLs, model order reduction, and robustness. In this study, these issues were addressed and resolved. First, the dimension of continuously DDLs was reduced by combining Lagrange piecewise linear interpolation with the finite element model (FEM), which avoids the dilemma of selecting the type and number of the basis functions. Second, the order of the original model was reduced by combining the substructure method with the complex modal analysis, which avoids the need for repeated transformation between the physical and modal spaces. Finally, with the discrete scheme of the continuous state equation as the factor to be optimized, an adaptive generalized Kalman filtering algorithm with unknown input (AGKF-UI) was derived using the principle of minimum-variance unbiased estimation (MVUE); this step improved the robustness of the identification algorithm. The effectiveness of the proposed method was verified by applying it to three examples: a 20-story shear frame structure, a three-span continuous beam and a plate shell structure. The superiority of the proposed method was demonstrated by comparing it with existing methods.