Generalized Likelihood Ratio Procedures for Early Detection of Machine Faults

Abstract

Condition monitoring of industrial machinery is an important example of a cyber physical system (CPS), in which measurements on a machine, transmitted over a wireless network, are used to make inferences about the health of the machine. Our work is motivated by machines with rotating element bearings, which are monitored by vibration sensors. Continuous monitoring of machines by vibration sensors mounted on equipment is now possible due to the advances in low power electronics, new sensing technologies, and low power wireless communications. In this study, we focus on the early detection of defects in rolling-element bearings by processing the signals from machine-mounted vibration sensors.

Since manufacturing processes on a modern shop-floor are highly interdependent, the undetected failure of a single bearing in an important machine can bring the entire assembly line to a halt resulting in heavy losses. On the other hand, if a trend to failure is detected before an actual failure occurs, the component may be replaced or repaired during routine maintenance. Existing techniques for the detection of defects in bearings typically utilize only a fixed window of samples, which does not make effective use of accumulated evidence over time. Hence, such techniques have a long detection delay for a given false alarm rate. We study sequential algorithms, which can provide lower detection delay for the same false alarm rate. Since process measurements may be transmitted by the sensors to central controllers over a lossy wireless link, we also explore quickest change point (QCD) detection techniques over lossy links.

This thesis consists of two parts. In part one of the thesis, motivated by the early detection of bearing faults, we study a non-Bayesian quickest change detection problem, from a known pre-change distribution to an unknown post-change distribution whose parameters belong to a known set. We then utilize a computationally efficient generalized CUSUM algorithm, derived from the Generalized Likelihood Ratio principle, and provide analytical bounds on the probability of false alarm and the expected detection delay for a general class of probability distributions.

We propose a simple statistic based on the instantaneous power spectral density of the bearing vibration signal to detect, sequentially, early bearing faults and conclude its ineffectiveness in real-world noisy vibration signal circumstances. Recognizing the cyclostationary nature of vibration signals from rolling element bearings with surface defects, we construct two statistics that detect cyclostationarity in the vibration signal.

We evaluate the performance of the cyclic spectrum-based generalized CUSUM algorithms, first using a synthetic dataset and then using two publicly available bearing vibration datasets. We then compare, on these two datasets, the performance of our proposed algorithm with the performance of algorithms studied in the literature. We find that our sequential algorithms, based on spectral correlations induced by post-defect cyclostationarity, can detect small changes with a reasonable delay to detection and a low false alarm rate at SNRs as low as -40dB, while being computationally simple to implement.

In the second part of the thesis, we study sequential change point detection in a setting in which the sensor measurements are transmitted to the decision maker (DM) over a wireless communication link with a positive probability of packet loss. We consider a slotted model, each slot corresponding to the transmission of a packet over the link. In each slot, the sensor device takes a measurement sample with a certain probability, and inserts a packet carrying this sample into the queue of the communication link. The transmitter uses various transmission policies which may lead to delays in the delivery of measurements at the DM. A packet transmission is attempted in a slot, and the packet could be lost with a probability known to the DM. We pose the QCD problem in the non-Bayesian setting under the framework introduced by Lorden and derive a CUSUM algorithm. By defining a suitable Markov process, involving the measurements at the central controller and the transmit queue length process, we show that the problem reduces to QCD of a Markov process. Using an asymptotic analysis, we prove the asymptotic optimality of our algorithm, when the false alarm rate tends to zero. Further, we extend our analysis to include cases when the central controller receives incomplete data due to loss of measurements over the lossy link. Motivated by the possibility of reducing the detection delay for a given false alarm rate, we also discuss the effect of using different transmit queue disciplines at the transmitting sensor leading to re-ordering of measurement packets at the central controller. We show that, for a fixed false alarm rate, and over the class of work conserving disciplines, the first-come-first-serve transmit queue discipline and the last-come-first-serve transmit queue discipline provide the stochastically largest and stochastically smallest detection delays, respectively. Finally, we provide a numerical analysis of the non-asymptotic performance of our QCD algorithms.