Optimal sensor configuration for structural response prediction by a modified Nelder–Mead simplex method

Abstract

The optimal configuration of the sensor system is extremely critical to effectively control the test cost and ensure the quality of the collected data for structural health monitoring (SHM) system. Different from the traditional sensor configuration criterion, the information entropy measure aims to minimize the uncertainty of structural model parameters to be identified, which can ensure that the collected data provides the maximum amount of information for the model identification. However, most of the current researches within the framework of entropy measure are aimed at the model identification, while studies that consider response prediction are still rare. In this paper, by constructing the posterior predictive distribution function of the frequency response functions (FRFs) at the unmeasured positions of structures and also the corresponding information entropy representation, the optimal sensor configuration problem for the purpose of structural response prediction at the unmeasured position is studied. A modified bound-constrained Nelder–Mead simplex method to handle the binary encoded optimization variables is also proposed, which can effectively solve the combinatorial optimization problem in the optimal sensor configuration. The methodology proposed is validated by a forced vibration study conducted for a laboratory rectangular cantilever plate. The obtained results show that the prediction error and uncertainty of the higher-order modes of the FRFs at the unmeasured positions is generally larger than that of the lower ones. Also, by comparing the performance of worst and optimal sensor layouts, the importance of the optimal configuration for response prediction at unmeasured locations is clearly revealed especially for a small number of sensors.