Dynamic load localization and time history identification using blind source separation and structural modal shape matching

Abstract

Accurate knowledge of dynamic load locations and time histories is a critical input for structural design but is often infeasible to measure directly. While numerous load identification methods exist, they predominantly address the localization and time-history reconstruction separately, relying on the prior assumption that one of the two is known. This paper introduces a novel and efficient integrated approach that combines Blind Source Separation (BSS) with Structural Modal Shape Matching (SMSM) to concurrently identify both the spatial location and temporal profile of dynamic loads. The proposed methodology is founded on the principle that modal loads and physical loads are mutually convertible. Initially, truncated modal loads are stably reconstructed in the modal space using a shape function method with Tikhonov regularization. These recovered modal loads are then interpreted as blind mixtures of the unknown physical load source signals, with the structural modal shape coefficients acting as the mixing matrix. BSS is subsequently employed to separate the equivalent load time histories and estimate the mixing matrix. Since the mixing coefficient vector is linearly related to the structural mode shape vector at the load application point, SMSM is implemented by quantifying the intersection angles between the estimated mixing vectors and candidate modal shape vectors to pinpoint the most probable load locations. Finally, the actual load time histories are accurately retrieved using the reconstructed modal loads and the identified modal shape matrix. The efficacy of the proposed method is rigorously demonstrated through two numerical examples involving a complex ropeway tower and a rectangular plate.