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Stability analysis and multi-sensor placement optimization for dynamic load identification using the Kalman filter method
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DOI：10.1016/j.ymssp.2026.114497.png)
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Abstract
En 中文
Dynamic load identification is an inverse problem in structural dynamics aimed at recovering the loads acting on a structure. Determining sensor locations to ensure stable and accurate identification has long been an important research topic. Kalman-filter-based methods can identify dynamic loads while simultaneously estimating the state vector, enabling online identification from multiple types of sensor measurements. Although these methods offer clear advantages over traditional approaches, they also place stricter demands on algorithmic stability-a fundamental requirement for reliable performance. However, the algorithmic stability from the perspective of sensor placement has not been systematically investigated. This paper presents a theoretical derivation of practical and easy-to-implement stability criteria in both the physical and modal state-space frameworks. Then, an optimal sensor placement (OSP) strategy is proposed, which explicit clarifies the different roles of sensor types in the adopted estimation algorithm. Infeasible sensor configurations are first excluded according to the invertibility and stability requirements, and the optimal configuration is then selected from the remaining feasible candidates by minimizing the trace of the input covariance matrix. Simulation studies verify that the proposed OSP strategy can determine the optimal sensor layout under single-point excitation, multi-point excitation, and complex structural systems, while exhibits a certain degree of robustness. Finally, dynamic load identification experiments on a simply supported beam are conducted, and the accurate identification results further demonstrate the effectiveness of the proposed OSP strategy.
Keywords:
Dynamic load identification
Kalman filter
Stability criteria
Optimal sensor placement
Input covariance matrix
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