Optimizing the placement of piezoelectric wafers on closed sections using a genetic algorithm - Towards application in structural health monitoring.

Sensor network design is essential to efficiently integrate Structural Health Monitoring (SHM) systems in aerospace, automotive, and civil structures. This study describes an optimization model for piezoelectric (PZT) wafer placement on curved structures and closed sections. The proposed approach relied on the transformation of any complex/closed surface regardless of the shape of its cross-section into a flat plate and imposed a set of boundary conditions to account for the wave propagation characteristics. Because the structure was continuous and the wave could propagate in every direction, for simplicity and without sacrificing accuracy, our model assumed that a pair of PZT elements communicated information in the two shortest directions. Thus, the concept of having two paths for each PZT couple was introduced to tackle this multidirectional behavior. The plate was then discretized into a set of control points that represented the structure geometry. The PZT couples covered the control points along the line of sight and in the neighborhood of their direct and indirect paths. The objective function was to maximize the number of covered points while minimizing the number of PZT wafers. The proposed model was solved using a genetic algorithm and was validated on circular and square sections. Sensors were spread on the circumference of the structure rather than mounting them in the form of rings or axial lines. The optimized PZT networks had high coverage that reached 99% in simulations. Notably, the optimized model improved the preliminary solution coverage by 14%. Experimental validation was performed on the circular section (pipe). The results demonstrated the proficiency of the developed model in distributing the PZT wafers on closed sections. The coverage was further evaluated by assessing if damaged areas on the pipe surface could be identified. Artificial damage was accurately located within 18 mm from the actual location. These results demonstrate that our model efficiently distributes PZT wafers on closed structures.