Conditional information entropy based sensor placement method considering separated model error and measurement noise.

Abstract The sensor placement methods for the modal identification are usually based on the prediction error between the measured and the structural model responses. Generally, the prediction errors, which are caused by the model error and the measurement noise, are assumed to be a Gaussian random vector together. This paper proposes a conditional information entropy based sensor placement method to separately investigate the influences of the measurement noise and the model error on the sensor placement. The changes in the element stiffness matrices are used to represent the model error. To quantify the uncertainty in the modal identification result, the conventional information entropy method is not suitable, due to the uncertainty in the Fisher matrix caused by the uncertain model error. This paper proposes a conditional information entropy index to quantify the uncertainty in the modal identification result with uncertain Fisher matrices. The optimal sensor placement corresponds to the one that maximizes the conditional information entropy index value over the set of all possible sensor placements. The conventional information entropy method can be seen as a special case of the proposed conditional information entropy method. In addition, the proposed sensor placement method can be applied to the placement of the multidimensional sensors. The simply supported beam and a bridge benchmark structure are used to explain the sensor placement method, and the redundancy threshold can be set to avoid redundant information provided by closely spaced sensors. Highlights • A conditional information entropy based sensor placement method is proposed. • The model error and the measurement noise are separately considered. • The uncertainty in modal identification is quantified by the proposed CIE index. • The model error is represented by the perturbation in the element stiffness. • The proposed method can be applied to multidimensional sensors. [ABSTRACT FROM AUTHOR]