## 1 Introduction
### Related Work
The ability of these methods to automatically extract local features has made them highly effective in extracting fatigue damage features, especially when combined with LSTM for long-term dependency modeling. [PERSON] [14] combined CNN and LSTM, using initial fatigue residual stiffness as input parameters, to construct a neural network modelthat learns characteristics directly from raw stiffness data, enabling subsequent predictions of residual stiffness. Besides LSTM-based architecture, the subsequent DL models also show potential for time series forecasting. For instance, the Temporal Convolutional Network (TCN), proposed in 2018, can extract information from historical data relevant to the prediction moment and avoid the problems of vanishing and exploding gradients. It is more efficient and more effective at learning long-term dependencies when performing time series predictions [15]. [PERSON] [16] proposed a RUL prediction model based on feature extraction methods and an improved TCN, which achieved a better prediction performance than other mainstream models did. Furthermore, the Encoder-Decoder Attention Mechanism [17] and Transformer [18] provide alternatives to LSTM. The attention mechanism enables the model to concentrate on the most relevant sections of the sequence when making predictions. Owing to their impressive prediction accuracy, transformer models have significantly outperformed expectations across many tasks. One of the key advantages of deep learning in industrial applications is its ability to process vast amounts of heterogeneous data, including real-time sensor measurements, vibration signals, acoustic emissions, and thermal imaging data, while maintaining higher accuracy and adaptability. For instance, in the wind energy sector, deep learning-based predictive maintenance systems leverage multi-source sensor data to detect early-stage damage in wind turbine blades, enabling condition-based maintenance and reducing unplanned downtime [19]. When dealing with small-scale univariate data, these models share common issues: first, the complexity of the model structures often leads to inefficient use of computational resources on small datasets, and limited data size increases the risk of overfitting. Additionally, the computational complexity of models such as the transformer increases quadratically with input size, making them computationally expensive and less advantageous for small datasets. To address these issues, this study adopts the N-BEATS model. N-BEATS not only demonstrates excellent performance on large-scale time series datasets but also has a simple and efficient architecture that is suited for small-scale univariate data. First, N-BEATS, through forward and backward residual connections, enables cross-learning across multiple time series, which allows it to extract shared features across sequences while capturing the unique patterns of each sequence [20]. This characteristic is particularly crucial in this study's stiffness prediction task under five different loading conditions, helping to better identify the commonalities and specificities of each dataset. Additionally, N-BEATS exhibits high flexibility when dealing with univariate data, providing accurate and efficient prediction results with minimal computational overhead, significantly enhancing the model's applicability in this study.