A new optimal sensor placement method for virtual sensing of composite laminate

Identifying modal coordinates from output-only data is a key link of virtual sensing technology based on the modal extension method. It is also one of the goals of optimal sensor placement (OSP). Traditional OSP methods are based on the underlying assumption that the estimated values of modal coordinates are unbiased estimates of real values. However, due to uncertainty and the characteristics of an inverse problem, the unbiased estimation obtained from the outputonly data may seriously deviate from the true value. This study proposes a new OSP method for composite virtual strain sensing, which can obtain the global unbiased estimation of modal coordinates. First, a Bayesian probabilistic model for virtual sensing considering model uncertainty and measurement error is formulated. Then, the K-L divergence, which measures the reduction in utility by removing sensors from the full configuration, is used to obtain the unbiased estimation of modal parameters. Finally, using the regularization mechanism in the Bayesian method, a new variance determination method is proposed to improve the stability of the solution. Considering both unbiasedness and stability, NSGA-II multi-objective optimization algorithm and two OSP evaluation criteria are used to obtain the final optimal sensor placement. To illustrate the effectiveness of the proposed method, an example involving a laminate plate is considered, accompanied by comprehensive discussions.