Identifying Distributed Dynamic Loading in One Spatial Dimension Based on Combing Wavelet Decomposition and Kalman Filter with Unknown Input

The identification of distributed dynamic loads is an important but challenging task because a distributed dynamic load is composed of both time and space functions. This paper proposes a novel method for the identification of distributed dynamic loading in one spatial dimension using only partial structural responses. The method is based on combing wavelet decomposition of space functions and the identification of time function by the improved Kalman filter with unknown input (KF-UI) developed by the authors. First, the unknown load space function of a distributed dynamic loading is approximated by wavelet decomposition with unknown scale coefficients. Under the given values of wavelet scale coefficients, the spatial information and the equivalent nodal loads of a beam-type structure can be estimated by finite-element modeling. Structural nodal responses in time-domain and the unknown load time function can be identified based on the improved KF-UI using data fusion of partial measurements of structural acceleration and strain responses. Finally, the objective function is established utilizing the error between the calculated and measured responses, and the optimal wavelet coefficients are estimated by minimizing the objective function. Therefore, the unknown distributed dynamic loading can be estimated by combing the reconstructed load space function from the optimal wavelet coefficients and the identified load time function. Numerical simulations of a simply supported beam under different unknown distributed loading verified the effectiveness of the proposed method.