A novel triple-structure coding to use evolutionary algorithms for optimal sensor placement integrated with modal identification

Optimal sensor placement (OSP) is a challenging combinatorial problem commonly addressed using Genetic algorithms (GAs), which are well suited to discrete problems. However, coding the problem can be difficult and often requires manual modifications during optimization. On the other hand, applying optimization methods designed for continuous problems to OSP is problematic due to its discrete nature. In this study, we propose a novel triple-structure coding approach that transforms OSP into a permutation and then a continuous optimization problem. This solves gene duplication in GAs and enables direct employment of all suitable methods for continuous problems in sensor placement optimization without any manual intervention. We evaluated the proposed method by implementing the encoding scheme with GA and mutated particle swarm optimization (MPSO) algorithms, two of the most renowned evolutionary algorithms. Additionally, we integrate modal identification within the optimization process for addressing the practicality of mode shape identification in a high-rise structure and a steel dome truss. The proposed coding reduces the cost of GA by 7 to 10 percent and MPSO by 25 to 54 percent, showcasing advancements in cost reduction within the context of sensor placement optimization. Moreover, the percentage of shared nodes in placements obtained from analytical and modal identification dropped to 34% in certain scenarios for the high-rise structure and 26% for the steel dome truss. This emphasizes the substantial distinctions in placements resulting from modal identification using structural responses compared to those obtained exclusively from analytical mode shapes.