Tuning-Free Bayesian Estimation Algorithms for Faulty Sensor Signals in State-Space

Sensors provide insights into the industrial processes, while misleading sensor outputs may result in inappropriate decisions or even catastrophic accidents. In this paper, the Bayesian estimation algorithms are developed to estimate unforeseen signals in sensor outputs without tuning. The optimal Bayesian estimation method is first derived by incorporating a Gaussian distribution specifying potential un-modeled dynamics into the measurement equation. Since its performance depends on tuning parameters, an iterative Bayesian estimation algorithm is developed using the variational inference technique. Specifically, an inverse Wishart distribution is introduced to describe the predicted covariance of abnormal signals. We then estimate it together with the other independent Gaussian distributions to conditionally approximate the joint posterior distribution, by which the effects of tuning parameters can be replaced adaptively. Testing the proposed algorithms through a simulated electro-mechanical brake model and a real experimental system shows that the proposed algorithm can satisfactorily estimate additive sensor faults online and services as a sensor monitor that simultaneously provides the locations and magnitudes of faulty signals without tuning.