Real-time monitoring and diagnosis in dynamic systems using particle filtering methods-Edición Única

Abstract

Fault diagnosis is a critical task for many real-world processes. The diagnosis problem is that of estimating the most probable state of a process over time given noisy observations. For many applications, the complex dynamics of the process requires reasoning with both discrete and continuous variables, so a hybrid model such as the jump Markov linear Gaussian (JMLG) model is needed. The JMLG model has a set of discrete modes to represent the fault states and a set of continuous parameters for the continuous variables. Although diagnosis is a simple procedure in principie, it is quite costly even for processes that are compactly represented, because the belief state is typically exponential in the number of state variables. Computing exact diagnosis is an intractable problem. Therefore, we must use numerical approximation methods such as Particle Filtering (PF). PF is a state-of-the-art Markov chain Monte Cario method which can diagnose dynamic systems by approximating the belief state as a set of particles. PF sequentially computes an approximation to the posterior probability distribution of the process states given the observations. This nonparametric approach has several advantages; it can approximate any probability distribution and consequently can be used to monitor systems with changing or uncertain structure. Rao-Blackwellized Particle Filtering (RBPF) is a Particle Filtering variant that combines a PF for sampling the discrete modes with Kalman Filters for computing the distributions of the continuous states. This reduces the computational cost because the continuous states are represented by the sufficient statistics of the continuous distributions. In this research, we show that it is possible to enhance the RBPF algorithm to sample the discrete modes directly from the posterior probability distribution. It is also possible to select the futes! particles before the sampling step. These improvements result in a more efficient algorithm, look-ahead Rao-Blackwellized Partióle Filtering (la-RBPF). La-RBPF essentially performs one-step look-ahead to select good sampling regions. We show that the overhead of the extra processing per particle is more than compensated for by the decrease in diagnosis error and variance. La-RBPF provides several additional advantages. It requires fewer particles to achieve the same approximation accuracy. Moreover, because the discrete modes are sampled from the posterior probability distribution, if a fault state appears, la-RBPF will detect the fault no matter how low its prior probability distribution. Another additional result of this research is a leaming method for the JMLG parameters. This modelling procedure combines the Least Squares Estimation and Expectation-Maximization algorithms. The proposed algorithms were intensively tested in several real-world systems having industrial characteristics, and compared with the existing PF and RBPF algorithms. The results consistently demonstrated la-RBPF's advantages.