Sensor Placement Optimization for Shape Sensing of Plates and Shells Using Genetic Algorithm and Inverse Finite Element Method

This paper reports the first investigation of the inverse finite element method (iFEM) coupled with the genetic algorithm (GA) to optimize sensor placement models of plate/shell structures for their real-time and full-field deformation reconstruction. The primary goal was to reduce the number of sensors in the iFEM models while maintaining the high accuracy of the displacement results. Here, GA was combined with the four-node quadrilateral inverse-shell elements (iQS4) as the genes inherited through generations to define the optimum positions of a specified number of sensors. Initially, displacement monitoring of various plates with different boundary conditions under concentrated and distributed static/dynamic loads was conducted to investigate the performance of the coupled iFEM-GA method. One of these case studies was repeated for different initial populations and densities of sensors to evaluate their influence on the accuracy of the results. The results of the iFEM-GA algorithm indicate that an adequate number of individuals is essential to be assigned as the initial population during the optimization process to ensure diversity for the reproduction of the optimized sensor placement models and prevent the local optimum. In addition, practical optimization constraints were applied for each plate case study to demonstrate the realistic applicability of the implemented method by placing the available sensors at feasible sites. The iFEM-GA method's capability in structural dynamics was also investigated by shape sensing the plate subjected to different dynamic loadings. Furthermore, a clamped stiffened plate and a curved shell were also considered to assess the applicability of the proposed method for the shape sensing of complex structures. Remarkably, the outcomes of the iFEM-GA approach with the reduced number of sensors agreed well with those of the full-sensor counterpart for all of the plate/shell case studies. Hence, this study reveals the superior performance of the iFEM-GA method as a viable sensor placement strategy for the accurate shape sensing of engineering structures with only a few sensors.