# Rolling-Element Bearing Fault Diagnosis Using Advanced Machine Learning-Based Observer
## 1 Introduction
The chattering phenomenon (high-frequency oscillation) is one of the significant disadvantages of SMO. The main effect of this challenge is the increase of some serious mechanical obstacles such as heats the mechanical components and saturation. To decrease the chattering, the higher-order SMO (HSMO) is presented and reported in [25; 26]. To increase the performance of the HSMO, different techniques, such as the quasi-continuous (QC) algorithm [27], suboptimal (SO) method [28], and twisting technique (TW) [29], have been introduced. The main challenge of the QC-HSMO, SO-HSMO, and TW-HSMO approaches is the first-order derivative of the sliding variable. To address this issue, a higher-order super-twisting (advanced) SMO (ASMO) for measurable and unmeasurable state observer has been reported [6]. Apart from the stability, robustness, and chattering attenuation in the ASMO, this method suffers from a somewhat reduced fault estimation accuracy. Therefore, in this research, the fuzzy technique is applied to the ASMO to increase the estimation accuracy and design AFSMO. Once the observer is designed, the decision regarding the REB condition should be made. There are various conventional techniques that can be applied for the decision-making, such as decision tables, rule-based reasoning, and case-based reasoning [30]; however, recently the solutions provided by artificial intelligence (AI) are frequently applied to resolve the problems of fault diagnosis. Machine learning (ML) is one of the fields of AI that introduces some of the most popular techniques for decision-making, such as support vector machines (SVMs) [31] and artificial neural networks (ANNs) [32; 33]. To make a decision on the particular faulty condition, the SVM first attempts to find an optimal hyperplane that best separates the feature parameters corresponding to data instances of different classes. Then, when the new data sample appears, the SVM determines on which side of the hyperplane the sample lays and assigns a class corresponding to the location. When an ANN is used in fault identification, the network learns the optimal weights of its neurons during the back-propagation procedure to minimize the loss function and meet the target values given a set of input attributes (i.e., feature set) corresponding to different faulty conditions. These days, the trend in AI applications have shifted toward the deep learning (DL) approach, which focuses on learning data representations to achieve the target goals. This shift is primarily enabled by the significant increase of computational capabilities of modern computer systems. The most popular DL-based solutions used for solving different problems in condition monitoring are convolutional neural networks [34] (fault diagnosis), autoencoders [19] (fault diagnosis, feature extraction, and data augmentation), generative adversarial networks [35] (data augmentation), and recurrent neural networks [36] (fault prediction). The principles of DL-based solutions are similar to those of the ANN; they adapt the weights of neurons and tune the hyperparameters to meet the requirements according to the task. However, unlike ANNs, the deep networks are characterized by a large number of hidden layers and nodes, which necessitate the application of huge datasets to achieve a good generalization by these networks. Also, the computational time of DL-based methods significantly increases in comparison with the conventional ML-based approaches. In this work, we employ an ML-based classification technique called a decision tree (DT) [37; 38; 39] to complete the proposed fault diagnosis methodology and implement the decision-making procedure for REB fault detection and identification. During training, the conventional DT [40] algorithm relatively fastly learns and derives the logical set of easily interpretable rules that can be used for decision-making regarding the REB faulty conditions, while providing insights into the quality of the fault estimation procedure performed by the advanced fuzzy SMO (AFSMO) in the previous step.