Identification of Distributed Dynamic Loads in Gradually Varying Two Spatial Dimensions Based on Discrete Cosine Transform and Kalman Filter with Unknown Inputs

Abstract

The identification of two-dimension distributed dynamic loads using partial structural responses is still challenging. In this paper, a method is proposed to identify the gradually varying spatial distribution functions and the time histories of time-space decoupled two-dimension distributed dynamic loads using partial structural responses. First, due to the properties of good decorrelation and energy compression by discrete cosine transform (DCT), two-dimension DCT is used to expand the spatial distribution functions with fewer coefficients than those by other transform such as discrete wavelet transform (DWT) in previous identification approaches. Under given DCT coefficients, the load time histories and structural responses are identified by the Kalman filter with unknown input (KF-UI). Then, the DCT coefficients are evaluated based on minimizing the errors between the estimated and measured structural responses. Finally, the spatial distribution function is reconstructed by the inverse two-dimension DCT with the estimated optimal DCT coefficients, and the load time history is identified by KF-UI accordingly. The novelty of the proposed method is that fewer DCT coefficients are involved to expand the gradually varying two spatial dimensions, which simplifies the difficulty of estimating many coefficients using partial structural responses. Numerical examples of identifying different dynamic loads verify the effectiveness of the proposed method.