A substructural and wavelet multiresolution approach for identifying time-varying physical parameters by partial measurements

Abstract

Currently, most wavelet multiresolution based methods for the identification of time-varying structural physical parameters request the full measurements of all structural responses. All physical parameters including time-varying and time-invariant parameters are expanded by wavelet multiresolution, so it is only applicable to structures with a few degree-of-freedoms. In this paper, based on the substructural identification technique, a novel two-step approach is proposed to identify the time-varying physical parameters of linear structures with more degree-of-freedoms under unknown excitations using only partially measured responses. The whole structure is divided into several substructures. For a substructure concerned, the unknown interaction forces from neighboring structures are treated as ‘additional unknown inputs’ to the substructure, so the identification of complete structure can be transformed to the identification of each substructure with parallel computing in two steps. In the first step, the fading-factor generalized extended Kalman filter under unknown input algorithm is proposed to locate the time-varying physical parameters. In the second step, a synthesized method is developed for the quantitative identification of time-varying physical parameters based on the integration of wavelet multiresolution analysis and the generalized Kalman filter under unknown input. The time-varying structural physical parameters distinguished in the first step are expanded by wavelet multiresolution analysis. Then, the time-invariant physical parameters and the scale coefficients of time-varying physical parameters are identified by performing a nonlinear optimization with an objective function established by the extended Kalman filter under unknown input. Finally, the estimated scale coefficients are used to reconstruct the original time-varying structural physical parameters. Several numerical examples are used to demonstrate the effectiveness of the proposed approach.