Utilizing available time-varying operating condition information in learning-based methods for fault diagnostics of rotating machinery

Abstract

Historical failure datasets for critical assets are rarely available. This makes it difficult to integrate condition monitoring techniques found in literature into industry, as these techniques are often either equipment-specific or highly dependent on the availability of a historical failure database. Recent research in the vibration-based condition monitoring field addressed this problem, by focusing on using unsupervised latent variable models that require only healthy data for training. By learning the distribution of the healthy data, faults can be detected and tracked when new data starts to deviate from the learned healthy distribution.

The complexity of the healthy data distribution drastically increases when machines are operated at varying rotational speeds, resulting in smearing in the frequency spectrum, amplitude modulation, and heteroscedastic noise in the data. This makes it more difficult to accurately model the healthy data distribution. Signal processing methods that incorporate available shaft speed and phase information, have been applied extensively to vibration data from varying speed conditions, to make it easier to analyse. Order tracking has been performed to convert the signals to the angle domain, and regression methods have been applied to normalize the effect of amplitude modulation. This work systematically investigates to what extent the availability of operating condition information can help to simplify the learning process for latent variable models in a semi-supervised setting. For a baseline, the operating conditions are mapped to the vibration data in a supervised setting. This is done to see how much of the variance in the vibration data can be explained by the operating conditions, and to highlight the importance of using latent variable models when the data is influenced by generative factors that cannot easily be measured or extracted from the data. Unsupervised models (that take raw unprocessed vibration data as inputs) are compared with semi-supervised models that incorporate operating condition information during data pre-processing (order tracking), and during modelling (learning distributions conditioned on the associated operating conditions).

Two latent variable frameworks that are often used for anomaly detection are investigated: Principal Component Analysis (PCA) and Variational Auto-Encoders (VAEs). This work highlights practical limitations in the PCA and VAE frameworks for condition monitoring in an unsupervised setting. It is shown that PCA can't accurately capture the heteroscedastic noise in the data, since it is formulated by assuming constant variance across the whole dataset. It is proposed that the correct variance can be learned using linear regression between either the latent space representations (unsupervised) or the available operating condition information (semi-supervised). Using the available operating condition information yielded the most robust results. For the VAE framework, it is shown that the latent space prior commonly used to facilitate disentanglement in $\beta$-VAEs, can in this case lead to posterior collapse, which leads to poor discrepancy analysis results. This occurs because of circular structures present in the underlying latent space manifold, caused by the periodic nature of vibration signals. The isotropic variance Gaussian usually used as a latent space prior is not well suited to capture these manifolds. This challenge is overcome by conditioning the prior on the associated operating condition information.

This work also provides clear insights into how linear and nonlinear models capture these distributions differently with lower and higher dimensional latent spaces, which improves the interpretability of the latent space and the associated model performance. It is shown how the size of the latent space affects whether the damage is detected in the latent space or the reconstruction space. In addition, the latent space representations can successfully be monitored for anomalies when conditioned on the available operating condition information. The latent variable models' performances are compared to traditional signal processing approaches (envelope analysis). The semi-supervised models return promising results on a dataset that is known to be difficult to analyse with traditional signal processing methods.