## 3 Background of Study
### Proposed Intelligent Monitoring Framework
#### 3.2.2 Standard DL-Based Diagnostic/Classification Models  
Traditional classification algorithms (e.g., support vector machine, decision trees) require preprocessing in order to extract discriminative features. This often creates too much room for expensive statistical assumptions peculiar to the feature extraction method; amidst the limitations of the traditional classification algorithms. On the bright side, DL-based algorithms offer better classification accuracies, ease-of-use, and automatic feature extraction capabilities. Amongst the many standard DL algorithms, CNNs and MLPs are the most popular for accurate discriminative modeling efficiencies. While CNNs are unique for their working principle--mimicking the human visual cortex for discriminative feature extraction and identification of labels (objects, conditions, etc. ), MLPs comprise nodes/neurons that perform tasks via a feedforward activation learning process [5]. CNNs are quite popular for many diagnostic/detection problems, including, but not limited to wear detection and pattern recognition [27]. This efficiency emanates from the convolving (Conv) and pooling layers, which function as filters for high-level (automatic) feature extraction; and with the fully connected layer(s), its architecture can be modified for better diagnostic accuracies. On the other hand, MLPs comprise two or more multi-layer perceptrons--a class of feedforward artificial neural network that consists of at least three layers of nodes: an input layer, a hidden layer, and an output layer, whereby the supervised training process is achieved via a backpropagation learning process with the aid of nonlinear activation functions [5]. Given a set of one-dimensional vibration measurements as inputs-- \(X_{n}^{\prime}=\{(x_{1}^{\prime},y_{1}),\)\((x_{2}^{\prime},y_{2}),...,(x_{n}^{\prime},y_{n})\}\), where \(x_{n}^{\prime}\in R^{m}\) and \(y_{n}\in\{0,1,...,n\}\), the convolution layer performs a convolution operation on the data through a convolution kernel, and then adds a bias and activation function to finally form a corresponding convolution feature map:  
\[h_{2,j}=f(\sum_{i=1}^{r}X_{ni}^{\prime}*W_{j}+b_{j}) \tag{4}\]  
where \(X_{ni}^{\prime}\) represents the \(i\)-th channel of the input data (a total of r channels), \(W_{j}\) is a weight matrix, \(b_{j}\) is the bias, * indicates convolution operation, and \(f\) is an activation function that ranges across popular functions, such as the _Sigmoid, Tanh_, and rectified linear unit (_ReLU_) [28]. On the other hand, consider an MLP with \(l\) hidden layers with a varying real integer number of nodes in each layer such that the nodes \(a_{1}^{l-1},a_{2}^{l-1},\ldots,a_{r}^{l-1}\) are in the \(l-1 th\) hidden layer. They first receive activated outputs from the nodes in the preceding layer--\(l-2 th\) layer via a forward propagation process and compute yet another activated output to the nodes in the final hidden layer--the \(l_{th}\) hidden layer. The forward propagation continues from the input layer nodes to the nodes in the output layer \(O_{iou}\), which is then followed by a backpropagation process (by updating the weights and biases) to minimize the cost function by either a stochastic gradient descent algorithm, _Adam_[29] optimizer, and/or any of the quasi-Newton algorithms [30]. Empirically, the inputs \(O_{i_{\text{in}}}\) provided by the node \(a_{i}^{l}\) are received by the nodes \(O_{i}\) are given by the sum of the activated outputs of \(a_{i}^{l}\) multiplied by the corresponding connection weight matrix \(w_{l}\) using Equation (5). \[O_{i_{\text{in}}}=\sum_{i=1}^{r}w_{l}*A[i] \tag{5}\]  
where \(A[i]\) is the activated outputs of the nodes in the \(l_{th}\).