## 4 Result Analysis and Discussion
### Training and Verification of the Proposed LSTM Neural Network  
The training and verification of the proposed long short-term memory (LSTM) neural network were conducted to ensure its effectiveness in accurately diagnosing faults in the power transformer. A comprehensive dataset, which included various fault scenarios and conditions, was utilized for this purpose. As discussed in the preceding section, a power transformer with specifications (132/33 kV, 63 MVA, 50 Hz) configured as YnD11 was used to validate the proposed inner fault detection methodology. The discussion of the RBSWT-LSTM model's results is based on testing the model across multiple fault and inrush current scenarios. The model's performance was evaluated by training it on the proposed deep learning framework, using a total of 2000 cases segregated into four groups: inrush current, internal defects, external faults, and internal faults with CT saturation. The proposed methodology initially extracted features from the differential current using wavelet transform and subsequently computed the mean value of each detail coefficient level of the signals. As previously mentioned, spectral analyses were conducted for each of the four cases, with each case demonstrating unique characteristics, highlighting the effectiveness of the deep learning model in accurately recognizing various fault conditions. The training phase involved feeding the LSTM network with a diverse set of faulted and normal operation signals, allowing the network to learn the underlying patterns and characteristics associated with each condition. The wavelet-decomposed signals, as shown in Figures 11-14 were particularly useful in extracting the component levels of the faulted signals, providing the LSTM with detailed information for analysis. During the verification phase, the performance of the LSTM network was rigorously tested against a separate validation dataset. This dataset included signals not previously seen by the network, ensuring an unbiased evaluation of its diagnostic capabilities. The results demonstrated that the LSTM network could accurately identify and classify different types of faults, including external faults, internal faults, inrush currents, and internal faults with CT saturation. Overall, the training and verification process confirmed the robustness and reliability of the proposed LSTM neural network in diagnosing transformer faults, making it a valuable tool for enhancing the protection and monitoring of power systems. In this analysis, MATLAB 2024a programming software is utilized to conduct experiments using data obtained from model tests comprising 2000 cases, each representing a specific type of fault. The collected vibration time-series data were segmented into brief intervals of 0.02 s using the current method. Each segment contained 60 consecutive sample points, with the original time series sampled at a consistent rate of 3 kHz. For this study, the observations were shuffled, and 25% of the observations for each load current were reserved as a validation set for model selection. The analyses in this study are based on a thoroughly researched dataset. The LSTM network, as it gains experience, learns to identify patterns and temporal dependencies within input sequences by adjusting its weights and biases to minimize prediction errors. This capability is facilitated by the unique LSTM architecture, which incorporates cell state mechanisms and gating functions. The model's outputs are the raw numerical predictions, and the network is trained to make accurate forecasts. The training process spans 200 epochs, with the learning rate gradually decreasing from an initial value of 0.01. By specifying validation data and frequency, the accuracy of the network is verified, and the algorithm continuously assesses the validation data's accuracy during training. The model's performance is evaluated using the root mean square error (RMSE) of the predicted values and the proportion of predictions within an acceptable error margin.