# Detecting Failures in Rotating Machines

### Krishna Chaythanya KV

Inference problems in fault detection of machines are of current importance in the context of industry 4.0. We consider a networked factory where sensors used to monitor the parameters of rotating machines communicate their measurements to a central controller over a wireless network that is prone to congestion and packet drops. The controller then makes decisions on the health of the machines. Since manufacturing processes are usually highly coupled, the failure of one component may bring the entire assembly line to a halt and incur high losses. Early detection of trends to failure before the actual failure happens allows for the component to be replaced/repaired during regular maintenance schedules. In our work, we attempt to solve problems related to the detection of failures in rotating machines in the setting described above. We want to design algorithms that detect incipient failures with minimum delay and perform well in a decentralized decision making setting. We model the transition of a rotating machine to a faulty state as a change point problem and design optimal procedures to detect the change. Once the theory for a single process’s change is in place, we plan to study a multiplicity of such change detection problems in a networked factory setting described above where we will address the network/signal processing trade-off. In our work, we study the mechanical vibrations from rolling element bearings since faults in bearings is the most common cause of failures in rotating machines. We consider various parametric models that describe the vibration signals from the bearings. The parameters of the model undergo a change at a random time when the bearing transits to a faulty state from a normal state. We develop sequential parametric change detection tests for each of these models which are optimal in the sense of minimizing the detection delay subject to a false alarm constraint. We construct sufficient statistics and analyze the performance of the tests by a simulation study. We also compare the performance of these tests against existing methods in literature that use other metrics such as kurtosis and mahalanobis distance using real world datasets from bearings. The various parametric

models that we analyze in our work are listed here:

- First, we assume that the vibration signals are i.i.d. with a unknown distribution prior to the change and are i.i.d with a different unknown distribution after the change. We further assume a conjugate prior density on the pre-change and post-change distribution sets and estimate the parameters of the model from the signals.
- Next, we consider a model where the pre-change and post-change parameters are picked from disconnected sets and obtain a detection procedure that consider the worst case pre– and postchange parameters.
- We then construct a model that explains the correlation structure that is observed in vibration signals from real-world datasets. In this model, we obtain blocks of vibration signals; the samples within each block have a correlation structure, but the blocks are i.i.d. with unknown parameters pre– and post-change. We assume a conjugate prior density on the parameters and then exploit the sparse power spectral density of the samples to estimate the parameters of the pre– and post-change distributions and setup sequential detection techniques for quickest change detection.