Sensor placement method for dynamic response reconstruction

Structural dynamic response reconstruction can be conducted by transforming the measured responses into responses at other selected locations of a structure. The quality of the reconstructed responses strongly depends on the quality of the measured response data, which further depends on the number and location of sensors in the structure. A new sensor placement method is proposed in this paper for better prediction of the dynamic response reconstruction.The response reconstruction is based on the transmissibility matrix between two sets of sensor locations, and a two-step sensor placement method is proposed. In the first step, the initial combination of sensor is determined based on the ill-posedness of the response reconstruction equation, which means that the rank of the Markov parameter matrix corresponding to the measurement locations must be full. The system Markov parameter matrix corresponding to the candidate sensor locations are re-assembled and singular value decomposed with One-sided Jacobi-transformation and QR decomposition method. The summations of the singular value at each time instant for each candidate sensor location are ranked and those locations with non-zero summation values are combined as the initial sensor combination. In the second step, a measurement noise effect index is defined and the number and locations for the final sensor placement can be obtained from a heuristic forward sequential sensor placement algorithm based on the minimization of the noise effect index. Numerical simulations with a plane truss structure and a three-dimensional frame structure are investigated to illustrate the performances of the proposed method. Results reveal that the sensors selected would lead to acceptable error of response reconstruction even with 5 percent measurement noise.