A multi-model architecture based on deep learning for aircraft load prediction

Monitoring aircraft structural health with changing loads is critical in aviation and aerospace engineering. However, the load equation needs to be calibrated by ground testing which is costly, and inefficient. Here, we report a general deep learning-based aircraft load model for strain prediction and load model calibration through a two-phase process. First, we identified the causality between key flight parameters and strains. The prediction equation was then integrated into the monitoring process to build a more general load model for load coefficients calibration. This model achieves a 97.16% prediction accuracy and 99.49% goodness-of-fit for a prototype system with 2 million collected flight recording data. This model reduces the effort of ground tests and provides more accurate load prediction with adapted aircraft parameters.

The authors proposed a two-phase process for predicting aircraft load with deep learning.They used the flight parameter and strain data of in-service aircraft fleet and got high-accuracy prediction results.The work is interesting and seems suitable for engineering applications.However, the reviewer suggests the publication of this manuscript after the following revisions or illustrations.
Major revision: 1.Personally, the two-phase process may have error accumulation, Why doesn't even basic measurement error accumulate from the results?2.Although traditional load identification has a certain error, it only needs to be calibrated on the ground through the load-strain equation.The proposed two-phase process requires more flight data (including load, strain, flight parameters) for training, which seems difficult to achieve in many application scenarios.Please further elaborate on the applicability and limitations of the methods proposed in the article

Minor revision:
1.There are many citations errors of figures, such as "Figure 2" should be modified as "Figure 3".2.In Figure 3a Table 1, each maneuver type may be divided into multiple codes.How to divide them?Why? 3.At the first line of Page 10, there are division errors for 4 flight points.4.At the same location, there is a concept error.Nz=3 means Nz=3g, but not Nz=3m/s2 Reviewer #2 (Remarks to the Author): In this paper, a novel approach is introduced to predict the aircraft load via using twophase prediction process.The authors propose a multi-model architecture based on deep learning for load prediction, and remarkably demonstrate the effectiveness of the prototype system via high accuracy results compared to collected flight record datasets.The system encompasses various components, including a data preprocessing method, a flight attitude coding rule, a deep learning-based Granger causality test, and interpretability methods, all of which have contributed to uncovering new insights into flight parameters.It is impressive to witness the successful application of such a comprehensive system in aeronautics, which has the potential to impact the conventional research paradigm.Therefore, I suggest publishing the article after implementing a few minor revisions 1.Given the complexity of the overall system, it would be beneficial to include an architecture diagram in the main text to clarify the role of each method in the two-phase process.Although I noticed that such a diagram is provided in the appendix (Fig. 7), I recommend integrating it with Fig. 1 and relocating it to the main text instead of the appendix.2.Several symbols and representations are present in the paper, but some are inadequately defined.The method and related works are elucidated in the appendix; however, symbols used in the main text need to be explained in detail.For instance, in Eq. 3, the meaning of \mathcal{H} remains unclear.It is recommended that the author carefully examines all equation symbols and provides appropriate explanations for each of them.A possible solution would be to include a notation table to explicitly describe the variables.3.The authors should explain why the focus is on investigating causal relationships rather than correlation (Page 6, Result 1), and highlight the specific advantages of the proposed deep learning-based Granger causality method over previous correlation analysis methods.Additionally, it would be helpful to know the overall advantages of the system proposed in this manuscript.I suggest the author provides further explanation or presents additional comparisons between the predictions of the current approach and conventional ones.4.Though the accuracy of the predictions is well presented in Figure 3 and 4. It would be nice to see the direct predictions of time history of forces or loads (compared to the data from the fight test) to show practical application potential of the proposed approach.5.Why design an explanation method NMT during the Phase II calibration process?Is it possible to apply the method for inference in the application, in addition to explaining the calibration rules?6.It would be helpful to provide any relevant experiments that demonstrate the advantages of utilizing a dual objective approach that considers uncertainty (located at the bottom of page 17) in improving model generalization.

Response to Reviewer #1
Dear Reviewer, We are extremely grateful for your review of the manuscript and appreciate your encouragement and valuable suggestions.You have raised a number of important issues.We agree with your comments and have modified our manuscript accordingly.Below we give a point-by-point response to your concerns and suggestions.

Personally, the two-phase process may have error accumulation, why doesn't even basic measurement error accumulate from the results?
Although traditional load identification has a certain error, it only needs to be calibrated on the ground through the load-strain equation.The proposed two-phase process requires more flight data (including load, strain, flight parameters) for training, which seems difficult to achieve in many application scenarios.Please further elaborate on the applicability and limitations of the methods proposed in the article.
Response: We appreciate your thorough advice.In this revision, we have added more discussions about challenges and opportunities for future work (Page 17, Line 9-23).
Compared to directly using strain data, the two-phase process does have the accumulative error, but our method achieves acceptable errors in the aviation industry (less than 5%).Most importantly, our method is mainly to avoid strain gauges that could fail at any time, which is meaningful for the long-term use of an aircraft.
In fact, in our method, "more flight data (including load, strain, flight parameters)" are only required during the model training process; when applying, only flight parameter data is required.However, when using the "load-strain equation" method, strain data is required.As we discussed in Introduction (Page 2, Line 29-41; Page 3, Line 1-14), this method "mainly depends on the strain gauges pasted on the main load-transferred path of each aircraft.But the strain gauges gave the risk of falling off, data drift and missing…and once the strain gauge pasted inside the structure fails, it can hardly be compensated..." Compared with the ineffective and costly strain data, flight parameters, could being collected from flight recording system, are more reliable, readily available, and low-cost.
However, although our method achieves acceptable errors in the aviation industry, it still falls short of the precise strain gauges used in the early stages of an aircraft's life.Currently, our practice is to use sensing strains when the strain gauges are still reliable and to use the prediction method when they fail.To essentially avoid relying on strain gauges that could fail at any time, our future work will focus on improving the adaptability of our two-phase prediction method.At present, we use the fine-turning transfer learning mechanism in our method, which makes the model more robust to new data.Considering new scenarios and aircraft models, our future work will embed few-shot learning and federated learning technologies to make the load model not only applicable to the current fleet but also to other fleets.