# Fault Detection in Active Magnetic Bearings Using Digital Twin Technology
## 7 Classification Algorithm  
The identification of faults in rotary equipment is a challenge in the field of pattern recognition. In addition to feature extraction, classification is another significant challenge in the field. There are many machine learning algorithms for fault diagnoses in rotary machines, such as Support Vector Machines (SVM), Artificial Neural Networks (ANN), Random Forest (RF), Hidden Markov Models (HMM), and Deep Learning Techniques (including Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Long Short-Term Memory (LSTM) [36; 37; 38; 39]. The use of deep learning models is essential in order to extract comprehensive, high-level semantic information, hence facilitating the execution of fault classification with enhanced effectiveness. The technique presented in this study incorporates CNN and its many adaptations to deal with the difficulty of  
Figure 11: The formation process of the vibration image. Figure 10: Typical vibration images produced by combining multiple channels. multiple-feature fusion. In order to achieve end-to-end learning, the vibration image is integrated with an enhanced Convolutional Neural Network (CNN). A Convolutional Neural Network (CNN) is a computational structure consisting of numerous layers that work together to analyze and extract important features from input data. The CNN architecture consists of many layers, including convolutional layers, activation functions, pooling layers, and fully connected layers. It is designed to process input data in the form of either 1D signals or 2D images. Each layer within the network performs distinct functions in the overall operations of the CNN. To execute convolutions, the input data is passed through a number of filters or kernels known as convolutional layers. Every filter is designed to extract certain characteristics by identifying and analyzing patterns and spatial data such as edges and textures in the images. Each filter produces a feature map as its output. An activation function called the Rectified Linear Unit (ReLU), which is applied after each convolutional layer, provides non-linearity to the network. Pooling layers are commonly employed following convolutional layers as a method of down sampling. Their primary purpose is to decrease the dimensionality of feature maps and spatial dimensions. This reduction in dimensionality reduces the chance of overfitting and enhances the model's robustness. Additionally, pooling layers aid in summarizing and extracting important information from the feature maps while simultaneously reducing the computational complexity of the network. There are two basic techniques for pooling layers, namely average pooling and maximal pooling. The approach most frequently applied in the suggested algorithm is maximum pooling. After the development of conventional and pooling layers, the input data's features are acquired in the form of a one-dimensional vector. The vector is then inputted into fully connected layers, which facilitate the network's capacity for advanced reasoning and allow it to provide predictions or classifications by employing the extracted features. The last layer of Convolutional Neural Networks (CNNs) is often referred to as the output layer, responsible for producing the network's predictions. The activation function used for this layer in the classification task is always softmax. The difference between the actual truth labels and the expected outputs is measured using the loss function. Cross-entropy is often used as the basis for the loss function. Stochastic gradient descent (SGD) or its derivatives, such as the Adam optimizer, are optimization techniques that are used to minimize the loss function throughout CNN training [40]. This procedure, often referred to as backpropagation, is used to modify the weights and biases of the neural network with the aim of enhancing its overall performance. Figure 12 illustrates the CNN structure.