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

In recent years, Bayesian inference has been extensively used for parameter estimation in nonlinear 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. Off-line 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 on-line estimation algorithms on systems which exhibit challenging identifiability properties, i.e., systems for which all parameters cannot be uniquely identified from the available measurements, leading to complex, possibly multi-modal posterior pdfs. We show that on-line 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.