Bayesian method for force identification within transfer path analysis

In Transfer Path Analysis (TPA), accurate estimation results always rely on an appropriate treatment of the matrix inversion. While mainstream approaches, such as overdetermining the system and utilizing regularization techniques, are commonly applied, each method has its own limitations. Overdetermining the system requires additional indicators, further complicating the measurement procedure, and is impractical in scenarios with limited sensor mounting space. Regularization, on the other hand, is frequently criticized for instability. Its accuracy often depends on the specific problem, making it difficult to achieve satisfactory results without tailored approaches. This paper introduces a Bayesian framework to enhance the performance of classical TPA, offering a data-driven approach to handle the mentioned challenges. The feasibility of the Bayesian model is evaluated through both experimental setups that mimic an excitation source mounted on a suspension with resilient connections and corresponding numerical simulations. Moreover, to explore the possibility of applying TPA to smaller structures, we also assess the Bayesian TPA when relaxing the typically required overdetermined constraints. The results show that the Bayesian model can provide more insight into the uncertainty and model-appropriateness within the TPA estimation process and give more accurate and robust outputs in underdetermined system scenarios.