## 3 Methodology
### Theoretical Background  
Deep learning captures the higher-level representation of features and is widely used in computer vision, image classification, object detection, and pattern recognition algorithms. Convolutional neural networks are mostly adopted in many classification tasks [39]. Depending on the nature of the data, the features are learned by the convolutional layer. Different convolution operations are used for learning the weights of the convolution filter, which takes the input and generates the feature maps. The element-wise non-linear activation function is applied to the results. ReLU activation is used, which captures non-linearity in the network. The spatial size is reduced using the pooling layer, and it is placed between the convolution layers [40]. The average pooling or max pooling technique is used to reduce the number of parameters and to generate more abstract features using a hierarchical structure and a higher level of representation. Convolution and the pooling layers are followed by the flattened and fully connected layers with ReLU activation function. All the nodes can be fully connected to perform higher level reasoning. The back propagation algorithm stochastic gradient descent (SGD) is used to update the parameters and to learn new weights during training. CNN has been extensively used in estimating the tropical cyclone intensity using passive microwave imagery and the hurricane database [41]. The wind speed estimates are obtained using the linear interpolation on training images. The storm track models are developed using the maximal sustained wind speed and the spatial location information. With the available computing resources, it is difficult to train the deep CNN due to the network depth and the complexity involved in classifying the data. Graphical processing units (GPUs) are mainly used for various computer vision and image classification problems by training millions of higher resolution images [42]. We extend the past work by including the infrared satellite imagery and modifying the network architecture of CNNs. In the proposed model, max pooling layers are removed, and batch normalization layer is added after the first 2D convolution layer. With the dropout and batch normalization, the accuracy of the model is improved when compared to the existing works. The convolution operations generate the features map and apply ReLU for non-linearity, which is represented as f(x) = max(0,x). The convolution Layer l output at position (_i,j_) is represented as \(x_{ij}\) in Equation (1), where L X L is the size of the filter, \(w_{ab}\) is the weight of the kernel at position (_p,d_), the receptive field is represented as \(y^{l-1}\) (\({}_{i+p}\)) (\({}_{i+q}\)) at the position (_i+p_),(_i+q_), and \(B^{l}\) is the bias for Layer l.  
\[x^{l}_{ij}=\sum_{p=0}^{L-1}\sum_{q=0}^{L-1}w_{ab}y^{l}_{(i+p)(j+q)}+B^{l} \tag{1}\]  
Using the hyper parameters and the size of the filters, the spatial size of the output \(W_{0}\) is computed from the input \(W_{i}\), the Kernel size is denoted as \(k\) with stride s and padding \(p\) which is represented in Equation (2) as  
\[W_{0}=\frac{W_{i}-k+2*p}{s}+1 \tag{2}\]  
The normalization takes place by dividing each input \(x_{i}\) by the total samples n and is represented in Equation (3) as follows:  
\[\left(1+\frac{\infty}{n}\sum_{i}x_{i}^{2}\right)^{\beta} \tag{3}\]where \(\alpha\) and \(\beta\) are the learning parameters and RMSProp optimizer is used to minimize the loss function and to learn new weights. The learning rate is adjusted automatically using the RMSProp optimizer. For each parameter, the optimizer chooses a varying learning rate. Additionally, for each parameter, the update is done and is mathematically represented in Equations (4) and (5).