Rotating machines are widely used in manufacturing industry, where sudden failures of key components such as bearings may lead to unexpected breakdown of machines and cause economic loss and human casualties. In addition, machines usually are operating under variable working conditions leading to the dynamic changes of fault characteristic, thus presenting big challenges of reliable and accurate fault diagnosis. Data-driven based deep learning fault diagnosis methods are powerful tools to capture hierarchical features from raw input to classify fault patterns by stacking multiple non-linear transformation layers. Deep models are constructed and trained, relying on huge historical data and requiring less expert knowledge to obtain decision-making. These techniques present high effectiveness and advantages in many intelligent fault diagnosis tasks. However, deep learning algorithms require a large amount of training data to fit on multiple non-linear functions, which often makes the trained network, in general, prone to over-fitting on small datasets. The models tend to perform well on the training data, but not so well on the testing data. Moreover, those methods utilize single point-estimates as weights to implement classification, in which, the distributions of weight parameters through the neural network layers are unknown. Thus they usually provide normalized score vectors and are unable to reveal the model uncertainty [1], which is important for accurate and reliable diagnosis and decision making in the field of condition monitoring. In this paper, a cyclostationary-based tool is combined with a Bayesian Convolutional Neural Network in order to tackle these problems. Firstly, the Cyclic Spectral Correlation (CSC) is adopted to capture correlation features of periodic phenomenon in the frequency domain. CSC is a bi-variable map of two frequency values, which is sensitive to the level of cyclostationary [2-3]. This 2D matrix can be used to enhance/reveal the cyclostationary nature of the signature masked by strong noise, characterizing the fault vibration signals obtained from rotating machinery operating under varying conditions. Moreover the Bayesian Convolutional Neural Network, which is a variant of Convolutional Neural Network, is proposed in order to process the uncertainty and to predict the output distribution for each class. The Bayesian Convolutional Neural Network integrates the prior probability distribution to the weights of all convolutional and fully-connected layers, obtaining the epistemic uncertainty, by capturing the weights variation for given input data and the aleatoric uncertainty estimated over the output of the model [4]. The model can be effectively updated to learn feature representations and obtain predictions according to Bayes' theorem with variational inference. The proposed method is tested and evaluated on an experimental study of rolling element bearing fault diagnosis, where datasets have been collected under variable working conditions. The results demonstrate that the proposed method achieves good classification performance and superiority compared with other state of the art approaches.

Keywords:  Fault diagnosis; Cyclic Spectral Correlation; Bayesian Convolutional Neural Network; Rolling element bearings

References:

[1] Kendall, A., & Gal, Y.. What uncertainties do we need in bayesian deep learning for computer vision?. In Advances in neural information processing systems, pp. 5574-5584 (2017

[2] Antoni, J., Cyclic spectral analysis in practice, Mechanical Systems and Signal Processing, 21, 597 – 630 (2007).

[3] Mauricio, A., Qi, J., Gryllias, K., Sarrazin, M., Janssens, K., Smith, W., & Randall, R. Cyclostationary-based bearing diagnostics under electromagnetic interference. In 25th International Congress on Sound and Vibration 2018, ICSV 2018: Hiroshima Calling, Vol. 5, pp. 2860-2867 (2018)

[4] Shridhar, K., Laumann, F., & Liwicki, M. A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference. arXiv preprint arXiv:1901.02731 (2019)