On statistical Multi-Objective optimization of sensor networks and optimal detector derivation for structural health monitoring

Sensor placement and structural health classifiers are fundamental components of Structural Health Monitoring (SHM) systems, as they largely define system detection (or classification) performance. Optimal sensor placement strategies are designed to maximize the ability to detect damage or to minimize lifetime costs, given limited resource availability. However, usually choosing one strategy over the other and non-optimal detector implementation may provide poorly performing solutions in terms of detection performance or total cost, even though both are critical objectives for a cost-effective SHM system implementation. The work proposes a unique and coherent framework for optimal detector and sensing network design for SHM. After an optimal detector is defined based on the Neyman-Pearson likelihood ratio test, classification performance indexes are used in a multi-objective optimization paradigm for optimal sensor placement. Specifically, the optimization considers maximizing the classification performances and, simultaneously, minimizing a measure of total cost or risk in a Bayesian sense. Even though the approach is general for any structure and sensor measurement process, the method is numerically verified with a cracked plate under tension and monitored by measurements of local strain serving as the surrogate SHM system. The results are also validated by comparing the multi-objective optimal design to engineering judgment and single-objective-based solutions in terms of probability of detection and costs. The advantages of an optimization scheme are emphasized with respect to an engineering scheme and, above all, how a multi-objective optimization strategy reflects a conjunct saving in costs and improvement in detection performances.