# Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning
###### Abstract
The applications of the neural network such as multilayer perceptron (MLP) and radial bases neural network for approximation of the system/signal have been proposed in [15]. In recent years, the application of machine and deep learning for function approximation has increased sharply. The application of a machine learning-based approach such as support vector regression for signal approximation has been introduced in [16]. Recently, deep learning methods such as convolutional neural networks [17], recurrent neural networks [18], generative adversarial networks [19], self-organizing maps [20], Boltzmann machines [21], deep reinforcement learning [22], and autoencoders [23] have been highly recommended for function approximation. The next algorithms for function approximation are identification techniques. These techniques work based on the combination of modern control algorithms and regression techniques. The identification algorithms are categorized into two groups: a linear approach and a nonlinear approach [24]. In the linear based identification technique, the linear function based on the regression technique is used to approximate the function of systems. In the nonlinear-based identification technique, the nonlinear functions based on a combination of the identification algorithm, artificial intelligence, and modern control algorithm are used to approximate the function of systems [17]. In this research, a combination of mathematical-based modeling and a nonlinear-based identification algorithm for modeling the DT of the bearing is recommended. To increase the accuracy of modeling in DT, various techniques can be used such as observation techniques and the Kalman filter method [25]. The observation techniques are categorized into two general groups: (i) linear observers such as proportional-integral (PI) observer [26] and proportional multi-integral (PMI) observer [27]; (ii) nonlinear observers such as sliding mode observer (SMO) [10; 28], feedback linearization observer (FLO) [29], backstepping observer (BSO) [30], fuzzy observer (FO) [31], neural network observer (NNO) [32], and Lyapunov observer (LO) [33]. However, the main advantage of the linear observer is simplicity, while accuracy is the main challenge of this algorithm. The FLO and the BSO have solved the challenge of estimation accuracy, but robustness was the challenge in these techniques. To reduce the challenge of robustness, SMO and LO have been used in different applications. The challenge of classical SMO is the chattering phenomenon. The LO also has the challenge of complexity. The FO and the NNO have the challenge of reliability for signal estimation. The second way to estimate the signal is the Kalman filter (KF) technique. The KF assumes that the noise is distributed Gaussian, and the signal observation models are linear [34]. Nevertheless, the filter gives the succeeding conditional probability estimate in the particular case where the errors follow a Gaussian distribution. The main drawback of the KF for signal estimation is the performance of this algorithm against nonlinear signals. Over the years, generalizations and extensions to this method have been established, such as the unscented Kalman filter (UKF) and the extended Kalman filter (EKF) in which both techniques are worked based on a linearization algorithm [35]. The extended Kalman filter is the most widely used estimation algorithm for nonlinear systems based on a linearization algorithm [33]. In the linearization technique, the accuracy of signal estimation is not accurate enough for signal estimation for fault pattern recognition and crack size identification (FPRCI). To develop the performance of signal estimation including reducing the estimation error in normal conditions and increasing the level of separability for FPRCI, the hybrid-based Kalman filter (HBKF), which is a combination of the Kalman filter, a high-order variable structure uncertainties estimator, hybrid-based signal modeling, and adaptive neural-fuzzy technique, will be introduced here.