Entropy-Based Optimal Sensor Placement for Model Identification of Periodic Structures Endowed with Bolted Joints

The number of sensors and the corresponding locations are very important for the information content obtained from the measured data, which is a recognized challenging problem for large-scale structural systems. This article pays special attention to the sensor placement issues on a large-scale periodically articulated structure representing typical pipelines to extract the most information from measured data for the purpose of model identification. The minimal model parameter estimation uncertainties quantified by the information entropy (IE) measure is taken as the optimality criterion for sensors placement. By utilizing the inherent periodicity property of this type of structure together with the Bloch theorem, a novel tailor-made modeling approach is proposed and the computational cost required for dynamic analysis to form the IE with respect to the entire periodic structure can be dramatically reduced regardless of the number of contained periodic units. In addition, to avoid the error of dynamic modeling induced by conventional finite element method based on static shape function, the spectral element method, a highly accurate dynamic modeling method, is employed for modeling the periodic unit. Moreover, a novel discrete optimization method is developed, which is very efficient in terms of the number of function evaluations. The proposed methodology is demonstrated by both numerical and laboratory experiments conducted for a bolt-connected periodic beam model.