On the Performance of Online Parameter Estimation Algorithms in Systems with Various Identifiability Properties

Abstract

In recent years, Bayesian inference has been extensively used for parameter estimation in non-linear systems; in particular, it has proved to be very useful for damage detection purposes. The problem of parameter estimation is inherently correlated with the issue of identifiability, i.e., is one able to learn uniquely the parameters of the system from available measurements? The identifiability properties of the system will govern the complexity of the posterior probability density functions (pdfs), and thus the performance of learning algorithms. Offline methods such as Markov Chain Monte Carlo methods are known to be able to estimate the true posterior pdf, but can be very slow to converge. In this paper, we study the performance of online estimation algorithms on systems that exhibit challenging identifiability properties, i.e., systems for which all parameters cannot be uniquely identified from the available measurements, leading to complex, possibly multimodal posterior pdfs. We show that online methods are capable of correctly estimating the posterior pdfs of the parameters, even in challenging cases. We also show that a good trade-off can be obtained between computational time and accuracy by correctly selecting the right algorithm for the problem at hand, thus enabling fast estimation and subsequent decision-making.

Real‐time anomaly detection with Bayesian dynamic linear models

“…The main idea of RBPF is to estimate analytically the posterior PDF for hidden state variables using Kalman filter equations and approximate the posterior PDF for the model parameters using sampling. The RBPF has been applied to problems such as robot localization, visual objection tracking, online parameter estimation, and anomaly detection for environmental data . The contribution of this paper is to enable the existing BDLMs (a) to perform anomaly detection in real time and (b) to provide the real‐time estimation of the hidden state variables and the model parameters.…”

A Discontinuous Unscented Kalman Filter for Non-Smooth Dynamic Problems

“…While this holds true for smooth systems, the same does not apply for their non-smooth counterpart, which pertains to systems that are described by non-differentiable statespace equations (Chatzis et al, 2014;Olivier and Smyth, 2017a). Nonetheless, the simulation and tracking of non-smooth systems is essential for numerous engineering problems, since these are by default tied to manifestations of damage and failure.…”