Optimal sensor placement for uncertain inverse problem of structural parameter estimation

Abstract This paper presents an optimal sensor placement approach for the uncertain inverse problem of structural parameter estimation, aiming to mitigate the ill-posedness problem that often exists in inverse procedures. The key idea is to select the sensor positions with the most sensitive measured responses to the structural parameters and the least correlated measured responses at the selected positions. Our optimization strategy is to convert the traditional minimum variance criterion of structural parameters to be identified into a new maximum independent mean-variance criterion of structural responses, so that the complex optimal sensor placement problem is transformed into a forward uncertainty propagation problem. Then, two orthogonal matching pursuit (OMP) methods based on Monte Carlo simulation (MCS) and dimension reduction integration (DRI) method are presented in this work, in which the MCS and the much more efficient DRI method are employed to solve the forward uncertainty propagation problem, and the OMP methods in sample form and moment form are developed to determine the optimal sensor placement for the identification procedure by considering the uncertainties in the measured responses. A Markov Chain Monte Carlo algorithm is adopted to identify the distributions of structural parameters eventually. Numerical and experimental examples are presented to verify the practicability and effectiveness of the proposed methods.