## 2 TCN-BiLSTM Predictive Model
### TCN-BiLSTM Prediction Method  
The structure of the TCN-BiLSTM model is mainly divided into three components: the data preprocessing module, the TCN layer, and the BiLSTM layer. The detailed architecture of the model is illustrated in Figure 4.  
Figure 4: TCN-BiLSTM architecture diagram. Figure 3: BiLSTM architecture diagram. In practical industrial applications, the predictive phase of a model often encounters challenges such as unmodeled noise, observational errors, and uneven data distributions in industrial sensor data. The proposed model, through its design and mechanisms, not only enhances its capability during the modeling phase but also improves its robustness during the predictive phase. The TCN layer serves as the first core component of the model, specifically designed for feature extraction from time-series data. To enhance the model's performance, the TCN layer adopts the following technical designs:  
* Causal Convolution: Causal convolution in TCN is one of its core features, ensuring that the output at each time step only depends on the current and past time steps. This means that future time steps (potential sources of noise) do not influence the prediction of the current time step, thereby preventing future information from interfering with the model's training and reducing the risk of noise propagating to subsequent time steps. * Dilated Convolution: Dilated convolution increases the receptive field of the convolution, enabling the model to capture longer temporal dependencies without adding more parameters. Dilated convolution helps reduce the impact of noise on short time scales, thereby allowing the model to more stably capture key dynamic changes in long time series. When dealing with industrial time-series data, noise typically manifests as high-frequency signals. Dilated convolution effectively diminishes the interference of high-frequency noise, allowing the model to focus more on the long-term trends of the sequence rather than on local random fluctuations. * Leaky ReLU Activation Function: Compared to the traditional ReLU activation function, the Leaky ReLU activation function maintains a small slope for negative inputs, effectively preventing the \"dying neuron\" problem. Noisy data often contain negative values, and Leaky ReLU can effectively mitigate the impact of noise on the network, allowing the neural network to continue training effectively even in the presence of noise. This enhances the model's robustness and its ability to capture nonlinear features. * Dropout: By randomly dropping out a portion of neurons during training, dropout effectively combats overfitting and enhances the model's generalization capabilities. This technique \"turns off\" a random subset of neurons during each iteration, reducing dependencies between neurons and improving the model's ability to adapt to unseen data. Dropout is a simple yet powerful regularization method commonly used in deep neural networks, particularly in deeper architectures, to significantly boost performance. * Batch Normalization: Batch normalization normalizes the inputs to each layer by adjusting their mean to 0 and variance to 1, thus mitigating the internal covariate shift and improving model stability. This technique accelerates convergence during training, alleviates the vanishing gradient problem, and enhances the stability of the training process. Additionally, batch normalization can act as a form of regularization, reducing the risk of overfitting. Additionally, to facilitate efficient information flow and alleviate the gradient vanishing problem in deep networks, the TCN layer incorporates a 1\(\times\)1 convolutional residual connection mechanism, ensuring smooth feature propagation between the input and output. Building on the deep features extracted by the TCN layer, the BiLSTM layer further models the time-series data. Compared to traditional LSTM, BiLSTM captures bidirectional dependencies in the time series, providing a more comprehensive understanding of the dynamic characteristics of fault data.