## 1 Introduction
For instance, there are several challenges for signal-based techniques under an unknown status [19]. Moreover, data-driven techniques have limitations related to massive datasets, while model-based approaches have difficulties in modeling a system accurately [18, 19,20]. The more robust and accurate fault diagnostics process should be considered if an uncertain situation exists [11]. To overcome the mentioned limitations and attain a more effective technique for flaw diagnosis, the hybrid method is proposed. A combination of the model-based approach, data-driven method, and signal-based approach is proposed in which diagnosis results are claimed to be less complicated, more reliable, and accurate [11]. Some examples are as follows: the combination of signal processing and deep learning techniques has been proposed in [21]. This research has two main stages. First, the hybrid feature pool was generated using envelope spectrum, time domain and wavelet packet transform. Next, the stacked autoencoder was suggested to perform fault detection and diagnosis. In this work, determining the number of features and selecting the best features are the main challenges. The combination of data-driven and modern control algorithms for fault detection and diagnosis has been presented in [22]. In this research, the second order system was modeled using the linear AutoRegressive with eXternal input (ARX)-Laguerre technique. The proportional integral (PI) observer was evaluated for the signal estimation. This technique is linear; however,for nonlinear and non-stationary signals such as vibration bearing signals, the accuracy may decrease. The combination of the modern control algorithm and deep learning approach has been proposed in [23]. In this research, the rotor signal was modeled using the ARX-Laguerre technique. The combination of the PI observer and the scalable deep neural network was also used for signal estimation and fault decision. In this work, the combination of the signal-based approach for signal modeling and artificial intelligence approaches for signal estimation, and a machine learning method for classification is recommended as a hybrid algorithm for fault diagnosis of bearing. Even though the current and voltage encompass all the information, sometimes fitting raw signals into some groups of rules and criteria for interpreting the fundamental messages that come from the signals is very difficult. This is where feature extraction methods help to dig out beneficial information purposefully from within the considered system. Using proper feature extraction techniques, researchers can obtain further knowledge on fault classification, which enables them to provide more efficient methods for this topic [21; 24]. Signal modeling is one of the critical challenges to design the modern control-based approach for fault diagnosis [25]. The challenge in nonlinear and nonstationary signal modeling was recently discussed [23; 26; 27; 28; 29]. Signal modeling can be categorized into two standard groups: modeling based on the system's dynamics [29], and data-driven modeling [18; 22; 30]. The challenge of vibration signal modeling may be solved by the mathematical-based approach and five degrees of freedom vibration bearing modeling are included [29]. In complex systems, modeling with the dynamics-based approach has the challenge of intricacy. To reduce the challenge from complexity in dynamics-based system modeling, data-driven signal modeling such as linear regression with ordinary least squares, AutoRegressive models (AR), the AutoRegressive with eXternal input (ARX) model, random forest, ARX-Laguerre, multivariate adaptive regression splines, support vector regression, the neural network, and Gaussian process regression have been suggested [31]. Specially, in [22; 30] the ARX and ARX-Laguerre methods have been used for signal modeling in second order systems. However, the accuracy of the nonlinear and nonstationary signal approximation is not good, which is the main challenge of these techniques [22; 23; 30].