# An Extremely Close Vibration Frequency Signal Recognition Using Deep Neural Networks
## 3 The Proposed System  
Based on Figure 2, TensorFlow, a well-known framework in deep learning, develops a DNN tailored for two-dimensional (2D) vibration signal image classification tasks from a time-domain vibration signal in the sinusoidal waveform. As the vibration signal frequency is converted into 2D image data, the process of vibration signal detection inherently entails a recognition procedure. The system configuration aimed to detect the presence of a Graphics Processing Unit (GPU), optimizing computational efficiency, which is crucial for machine learning training. The dataset consisted of various MATLAB-generated 2D vibration signal frequencies, classified into fifty-one classes from the data range 0-0.5 with delta 0.01. Both sets of vibration signals are converted into 2D images [10; 38], with the simulation data employed for training DNN. The DNN parameters are shown in Table 1. These datasets are systematically divided into training and validation subsets for training purposes. To meet the model's input specifications, each image was processed to fit the required dimension of 256 \(\times\) 256 pixels, aligning with the pre-processing requirements of the ResNet50 architecture. These steps are imperative to ensure that the dataset is compatible with the model initially trained on ImageNet. Furthermore, the augmented techniques are applied to the training data, including random rotations, shifts in width and height, and horizontal flipping. These techniques introduced variation and enhanced the robustness of the dataset, simulating a broader array of training scenarios. From the whole dataset, a substantial portion of the dataset is allocated, precisely twenty percent, for validation. This division allowed for a thorough assessment of the model's performance. It enriched the training process by incorporating a diverse set of data samples. The architecture of the proposed DNN focused on the ResNet50 model, a fifty-layer convolutional neural network pre-trained on the comprehensive ImageNet dataset. This convolutional neural network pre-trained model is utilized mainly for feature extraction of 2D vibration signal images, maintaining its pre-trained weights unchanged to concentrate learning on the layers uniquely relevant to the proposed scheme. The architecture has enhanced the architecture by integrating several layers designed for our classification goals. These additions included a Global Average Pooling 2D layer, which reduced feature map dimensionality and helped prevent overfitting, a fully connected Dense layer with 128 neurons for learning significant high-level features related to our dataset, and a Dropout layer with a fifty percent rate to introduce regularization, crucial for avoiding overfitting. The architecture culminated in a Dense layer with softmax activation, intended for categorizing input images into one of fifty-one groups. Selecting the ReLU activation function for the hidden Dense layer was crucial, providing the required nonlinearity for the network to discern complex patterns in the dataset. In the training process, employing an Adam optimizer is carefully managed with an initial learning rate of 1 \(\times\) 10\({}^{-5}\), subject to dynamic adjustments. This flexible learning rate, regulated by a systematic scheduler, was vital in steering the model towards an effective weight configuration. Various callbacks were applied throughout training to refine the learning process: early stopping mechanisms to prevent excessive training, learning rate modifications for efficient convergence, model checkpointing to preserve the most effective model state, and epoch history recording for insights into training progress. In cases where an existing checkpoint was available, training recommended from that point, thus avoiding any loss of progress and enhancing training efficiency. The training process, comprising up to a hundred epochs and a batch size of thirty-two, reached a notable point in this study.