Hybrid Sensor Placement Framework Using Criterion-Guided Candidate Selection and Optimization.

This study presents a hybrid sensor placement methodology that combines criterion-based candidate selection with advanced optimization algorithms. Four established selection criteria-modal kinetic energy (MKE), modal strain energy (MSE), modal assurance criterion (MAC) sensitivity, and mutual information (MI)-are used to evaluate DOF sensitivity and generate candidate pools. These are followed by one of four optimization algorithms-greedy, genetic algorithm (GA), particle swarm optimization (PSO), or simulated annealing (SA)-to identify the optimal subset of sensor locations. A key feature of the proposed approach is the incorporation of constraint dynamics using the Udwadia-Kalaba (U-K) generalized inverse formulation, which enables the accurate expansion of structural responses from sparse sensor data. The framework assumes a noise-free environment during the initial sensor design phase, but robustness is verified through extensive Monte Carlo simulations under multiple noise levels in a numerical experiment. This combined methodology offers an effective and flexible solution for data-driven sensor deployment in structural health monitoring. To clarify the rationale for using the Udwadia-Kalaba (U-K) generalized inverse, we note that unlike conventional pseudo-inverses, the U-K method incorporates physical constraints derived from partial mode shapes. This allows a more accurate and physically consistent reconstruction of unmeasured responses, particularly under sparse sensing. To clarify the benefit of using the U-K generalized inverse over conventional pseudo-inverses, we emphasize that the U-K method allows the incorporation of physical constraints derived from partial mode shapes directly into the reconstruction process. This leads to a constrained dynamic solution that not only reflects the known structural behavior but also improves numerical conditioning, particularly in underdetermined or ill-posed cases. Unlike conventional Moore-Penrose pseudo-inverses, which yield purely algebraic solutions without physical insight, the U-K formulation ensures that reconstructed responses adhere to dynamic compatibility, thereby reducing artifacts caused by sparse measurements or noise. Compared to unconstrained least-squares solutions, the U-K approach improves stability and interpretability in practical SHM scenarios.