Expert Knowledge Induced Logic Tensor Networks: A Bearing Fault Diagnosis Case Study

In the recent past deep learning approaches have achieved some remarkable results in the area of fault diagnostics and anomaly detection. Nevertheless, these algorithms rely on large amounts of data, which is often not available, and produce outputs, which are hard to interpret. These deficiencies make real life applications difficult. Before the broad success of deep learning machine faults were often classified using domain expert knowledge based on experience and physical models. In comparison, these approaches only require small amounts of data and produce highly interpretable results. On the downside, however, they struggle to predict unexpected patterns hidden in data. Merging these two concepts promises to increase accuracy, robustness and interpretability of models. In this paper we present a hybrid approach to combine expert knowledge with deep learning and evaluate it on rolling element bearing fault detection. First, we create a knowledge base for fault classification derived from the expected physical attributes of different faults in the envelope spectrum of vibration signals. This knowledge is used to derive a similarity function for comparing input signals to expected faulty signals. Afterwards, the similarity measure is incorporated into different neural networks using a Logic Tensor Network (LTN). This enables logical reasoning in the loss function, in which we aim to mimic the decision process of an expert analyzing the input data. Further, we extend LTNs by weight schedules for axiom groups. We show that our approach outperforms the baseline models on two bearing fault data sets with different attributes and directly gives a better understanding of whether or not fault signals are influenced by other effects or behave as expected.