Probabilistic Optimization of Sensor Placement

This paper develops a methodology for sensor placement optimization (SPO) for structural health monitoring (SHM) systems under uncertainty. The methodology includes the following steps: (1) finite element-based modeling, (2) probabilistic analysis, (3) damage detection, and (4) SPO. The structure under consideration represents a component of a conceptual thermal protection system (TPS) for next generation hot aerospace flight vehicles. The prototype TPS consists of a network of heat resistant mechanically attached panels. An experimental setup exists at Air Force Research Laboratory (AFRL) and is currently undergoing testing. The FEM analysis is transient and includes dynamic mechanical loads consisting of sinusoidal frequency sweeps. A mode superposition (MSP) transient analysis is utilized. Probabilistic FEM analysis incorporates uncertainty via random realizations of spatially and temporally uncertain model parameters such as loading-, material-, and geometric-properties. The third step, damage detection, utilizes the results of the probabilistic FEM analysis and estimates Px, the probability of correctly classifying the structure as healthy or damaged for a given sensor layout x. This includes feature extraction, feature selection, and state classification. SPO is defined as maximizing the detection probabilityPx with respect to x and subject to x∈ [u,v], where x is continuous and [u,v] are physical constraints. This formulation is solved via SNOBFIT, an optimization scheme that is particularly useful for complex noisy objective functions with bound constraints.

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