Aircraft structural health monitoring is crucial for preventing damage and accidents. Fatigue failure, often caused by alternating loads during flight, is a major concern. Current load identification methods rely on on-board flight parameters and a load model (F = f(X)), but this model requires costly and time-consuming ground testing for calibration. Classical methods used strain gauges, but these are unreliable and prone to failure. This paper proposes a two-phase deep learning approach to create a more general and accurate aircraft load model without relying heavily on ground tests. Phase I predicts strains from flight parameters, while Phase II calibrates the strain-load equation. This combines the advantages of classical methods (strain-load equation) and practical methods (flight parameter-load model) to address the limitations of each. The complexities involved in integrating the strain prediction method into the load monitoring process are addressed by considering factors such as complex response relations between flight parameters and strains, noise, and the impact of flight attitude on strain prediction.

Existing research on aircraft load prediction primarily focuses on either using strain gauges (classical method) which are prone to errors and failures, or relying on a single aircraft’s load model for an entire fleet (practical method) resulting in lower accuracy due to subtle structural differences. While these methods have limitations, previous studies have demonstrated the existence of relationships between flight parameters, strains and loads, laying the groundwork for the development of a data-driven model to predict load without relying heavily on strain gauges or extensive ground testing. However, these classical methods and practical methods have limitations that this paper seeks to overcome using deep learning based techniques.

The proposed methodology consists of a two-phase process. **Phase I: Strain Prediction** This phase utilizes a deep learning-based multi-model architecture to predict strains from flight parameters. The process involves: 1. **Data Preprocessing:** Flight parameters undergo several steps including filtering, outlier detection using angle-based outlier detection, multicollinearity analysis and principal component analysis to remove redundant features, feature extraction in frequency domain and creation of additional features through fusion of different frequency domains. This improved the prediction accuracy by about 13%. 2. **Deep Learning-based Granger Causality:** A deep learning-based Granger causality test is used to identify causal relationships between flight parameters and strains, improving the reliability of the model. 3. **Flight Attitude Coding:** A hybrid strategy combining maneuver code and PITS (Point-in-the-Sky) rules divides the dataset into 36 subsets based on different flight attitudes. This accounts for variations in the relationship between flight parameters and strains under diverse flight conditions. 4. **Multi-model Architecture:** A multi-model architecture, using MLP, RR, and LightGBM, is employed to address the different data distributions resulting from different flight attitudes. Each model is optimized with feedback mechanisms, model uncertainty evaluation, neural architecture search, and a tailored parameter update strategy. This is shown to be superior to using a single model across all flight conditions. **Phase II: Coefficient Calibration** This phase calibrates the strain-load equation, improving the generality of the model: 1. **Strain Pair Construction:** A prediction-based method is proposed to efficiently construct strain pairs between the reference aircraft (with ground-tested load data) and other aircraft, without directly comparing millions of data points. 2. **Clustering-based Coefficient Calibration:** An iterative process using distribution-based and density-based clustering methods refines the strain coefficient (SF) between aircraft, optimizing the goodness-of-fit of the load model. Clustering improves the overall R-squared value while maintaining high local values. **Model Interpretation:** Two techniques are used: 1. **Key Feature-based Interpretation:** SHAP values are employed to identify the most influential flight parameters for strain prediction by each model. 2. **Alternative Model-based Interpretation:** A Nonredundant Multiple Tree (NMT) is developed to interpret the coefficient calibration process. This creates an easily understandable set of if-else rules based on key flight parameters for classification of interception values. The entire process is illustrated in Figure 1.

The research yielded several key findings: 1. **Deep Learning-based Granger Causality:** A deep learning-based Granger causality test confirmed the existence of causal relationships between flight parameters and strains. This allows for the prediction of strains using flight parameters, eliminating the need for direct strain gauge measurements. 2. **Data Corruption and Feature Engineering:** The most significant data corruption issues were spikes, steps, and composite corruptions. Correcting this corruption and extending features to include products of flight parameters improved prediction accuracy by approximately 13%. 3. **Flight Attitude Impact:** The relationship between flight parameters and strains varies significantly with flight attitudes (e.g., takeoff, landing, turning). The study's hybrid coding strategy based on maneuver and PITS, dividing the dataset into 36 subsets, improved prediction accuracy substantially. 4. **Multi-Model Superiority:** The multi-model architecture with MLP, RR, and LightGBM outperformed individual models in prediction accuracy, especially in scenarios with limited data points per subset. It also improved generalization to new data. 5. **Coefficient Calibration:** The clustering-based coefficient calibration method improved the overall model accuracy and reduced the cost associated with ground testing, demonstrating a 99.49% goodness-of-fit. 6. **Model Interpretability:** The SHAP and Nonredundant Multiple Tree (NMT) methods provided interpretable results. SHAP identified key flight parameters influencing strain prediction, and NMT explained the coefficient calibration steps. This interpretability increases the trust and adoption of the model in the aviation engineering workflow.

The findings demonstrate the effectiveness of the proposed two-phase deep learning method for aircraft load prediction. The model's high accuracy and generalization capabilities significantly reduce the reliance on costly and unreliable strain gauges and expensive ground tests. The model's interpretability is particularly valuable in the aviation industry, enhancing trust and facilitating model validation by engineers. The hybrid strategy for handling different flight attitudes is crucial for real-world applications, highlighting the complexity of the data and the need for tailored models. By identifying key flight parameters, the study provides insights into the relationships between flight conditions and aircraft loads, potentially informing future design and maintenance practices.

This research presents a novel two-phase deep learning approach for aircraft load prediction. The method achieves high accuracy while significantly reducing the need for expensive ground tests. The multi-model architecture and data preprocessing techniques address real-world challenges in flight data. Future research could focus on data augmentation, federated learning, and exploration of other deep learning models to further improve performance and adaptability.

The study's generalizability might be limited by the specific aircraft models used in the dataset. The dataset is specific to a certain type of aircraft and therefore might not be immediately transferable to different types of aircraft, highlighting the need for further testing and model calibration across a broader range of aircraft types. While the model addresses many data challenges, the accuracy of the prediction is still dependent on the quality of the flight data, and advanced data cleaning techniques could further enhance model performance.