Damage tolerance design can ensure the structural safety of civil aircraft throughout its life cycle, which requires accurate analysis of crack extension life and crack extension length. This paper proposes an XGBoost-based crack extension life and crack extension length prediction method for civil aircraft structures. The method uses machine learning algorithms to train the structural state prediction model. The advantage of this method is that it can quickly determine the crack life and crack length without relying on the processing technology and engineering diagnosis experience of a large amount of collected data, which provides a more flexible method to determine the crack extension life and crack extension length under various influencing factors. By comparing a variety of machine learning algorithms, XGBoost model obtained the highest test scores, the experimental results show that the method achieves accurate prediction of crack extension life and critical crack length, which can be used for rapid engineering evaluation.
Damage tolerance design is a modern fatigue fracture control method developed and progressively
applied since the 1970s to ensure the structural safety of structures throughout their life cycle. The
theory assumes that each structural material has internal defects in the course of processing or using, so
the rate of expansion of these defects and the remaining strength of the structure needs to be determined
using various damage theories (such as fracture mechanics) and a given external load [
XGBoost, which is short for eXtreme Gradient Boosting, is an algorithmic toolkit based on the
Boosting framework and is very powerful in parallel computation efficiency, missing value handling,
and prediction performance [
The current theories based on data-driven deep learning and machine learning, as the latest research
results in pattern recognition, have achieved fruitful results in big data processing in various fields with
powerful modeling and characterization capabilities. Therefore, using XGBoost-based crack extension
prediction can get rid of the reliance on the traditional analysis method of mechanism-based fracture
mechanics, complete the adaptive extraction of structural states and the construction of complex models,
and finally realize end-to-end modeling to complete the prediction of complex indicators [
As a part of the aircraft, the fuselage skin is an important part of the whole aircraft structure. In this paper, crack expansion prediction is performed for the fuselage and wing skin structure, which is usually considered as the central crack of an infinite plate, and the simplified model is shown below.
This section covers the modeling and prediction of crack extension life/critical crack length based on XGBoost, and also includes the modeling process, data preprocessing, parameter optimization, model training, model testing results and comparison of other algorithms. 3.1.
The overall XGBoost prediction model can be divided into several parts: data reading and preprocessing, parameter optimization for cross-validation, model training, model testing, and result output. The flow is shown in Figure 2.
The original data was saved in csv format, and after removing the samples containing missing values and samples with too high lifetimes, the final 900 data sets were left. The total data set was partitioned 8:2, in which 80% of the training set (720 samples) was used for training the xgboost model and 20% of the test set (180 samples) was used for performance testing.
In modeling and training with xgboost, where the boosting round as an important parameter can be searched using the cross-validation function that comes with the model. In this paper, we use Random Search to find the optimal boosting round, with the upper limit of 500 cycles, Early stopping and automatic termination after 5 times of no change in the optimization index, tolerance of 0.01, crossvalidation of 10fold, and optimization index of MSE. The final best The final best value of boosting round is 143. 3.3.
The XGBoost model is trained using the training dataset, where the boosting round is 143. the rest
of the model parameters are listed in the following table [
lambda
eta grow_policy alpha objective
1.0 0.3 depthwise
1.0 reg:squared error
The model performance was tested using the full test set data, and the test set prediction scores are shown in the figure. After 143boosting rounds of training, the performance metrics of the model are shown in the following table.
The predicted model weights are analyzed. As shown in figure 5, the weights vary widely among the different attributes, which is of greater significance for analyzing the key influencing factors and optimizing the model inputs, and the relatively high-weighted attribute such as width may provide more information about the overall structural state of the aircraft.
This study also applies other machine learning methods for modeling, including generalized linear
regression models, decision tree, and support vector machine, to model the prediction of crack
expansion number and critical crack length as well. The prediction models were all trained using the
same 80% dataset (720 samples) and tested using 20% dataset (180 samples). One of the decision tree
models, max_depth, was kept consistent with the XGBoost parameters above. The corresponding
evaluation indexes are given for the performance of XGBoost and the other three prediction models in
the test set. The prediction result scores for the number of crack expansion cycles are shown in Table
3, and the prediction result scores for the critical crack length are shown in Table 4 [
The XGBoost model has the best test score regardless of the number of crack expansion cycles or the length of critical cracks, and the model accuracy can meet engineering applications. Among the other tested models, the decision tree model has the closest score to Xgboost, which is also consistent with the performance consistency of the same tree model on the same data set.
In this paper, the Xgboost-based model achieves the prediction of the extended life and critical crack length of the center penetration crack of a flat plate. The model can be applied to the rapid assessment of damage tolerance in engineering. However, the model data is obtained based on fracture mechanics software simulations, which will have some deviation when applied to real aircraft structures, and can be combined with crack extension test data for further migration learning.
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