Objective Under the action of long-term fatigue loading, the metal structures of the spacecraft, high-speed train, ship, and other large equipment are prone to fatigue crack in the stress concentrated part. Under the repeated action of alternating loading, the structure will be further extended, resulting in failure and fracture, causing major production safety hazards. In the fatigue crack monitoring field, the commonly used technical means are sound emission, ultrasonic guided wave, and strain monitoring. With the development of strain sensors, the strain monitoring method plays an important role in fatigue crack identification and life monitoring. Among them, the fiber Bragg grating (FBG) sensor is characterized by high precision, sensitivity, stability, and portability along with long monitoring range, promoting further development of strain monitoring technology toward higher accuracy, higher sensitivity, higher reliability, and better convenience. In this paper, a real-time continuous crack monitoring method based on the FBG sensor array is proposed for the fatigue crack monitoring of aluminum alloy structures in service.

Methods The research method of this paper is shown in a flow chart (Fig. 1), which is mainly divided into the following four parts: parameter selection, experiment and data processing, prediction and evaluation, and model building. First, fatigue loading test parameters and crack-propagation characteristics are obtained via tensile tests. The strain field distribution characteristics during crack propagation are obtained via extended finite element simulation. Based on the strain field analysis and fatigue loading experiment results of different crack-propagation stages, a reasonable layout of the FBG sensor array is designed. Through fatigue loading and strain monitoring experiments, the relationships among fatigue loading times, wavelength response, and crack length are obtained. Values of peak-peak wavelength are extracted as characteristic values to exclude the interference of temperature and deformation during the stretching process. The three-parameter exponential method is used to fit the a-N (a is the crack length, and N is the loading times) curve of fatigue expansion. Then, based on the experiment, the gradient boosting regression tree (GBRT) algorithm is used to build the prediction model, and the comparison is made using linear regression and support vector regression (SVR) methods. The three models are evaluated based on various indicators, such as explain variance score (EVS), mean absolute error (MAE), mean square error (MSE), R-squared (R²), and five-fold cross-validation. Finally, the best performing method is selected as the final prediction model on the basis of the evaluation results.

Results and Discussions Combined with the finite element simulation, fatigue loading experiment, and machine learning algorithm, this paper presents a method of fatigue crack strain field inversion prediction based on the FBG sensor array. To study the strain field change in the crack-propagation process, the crack extension strain field change is obtained in the cloud via finite element simulation (Fig. 3). Simulation experiment results show that the crack tip is singularity and the strain center will shift with the growing crack tip. Based on the simulation results, a sensor layout method was designed with six FBG sensors equally spaced on both sides of the crack (Fig. 7). The experimental results show that this design can effectively monitor the strain field changes at various stages of crack growth.

After filtering the experimental results of fatigue loading and strain monitoring, peak-peak wavelength values are extracted as the characteristic values. The response curves of loading times, crack length, and wavelength peak-to-peak values can be obtained (Figs. 11--12). The simulation results can be verified via direct analysis of the graph. The direction of crack propagation can be determined by placing sensors in the crack-propagation position.

Based on the strain response data collected in the experiment, the GBRT algorithm was used to invert the strain field in the stable expansion stage. In total, 31000 data with six features were imported into the GBRT model for five-fold cross-validation. The learning rate was 0.1, and the maximum iterations was 150 times. The regression results were consistent with the real value (Fig. 16). To verify the predictive performance of the GBRT method, it is compared with the linear regression and SVR methods. The results of cross-validation show that the SVR and GBRT methods are stable. In the evaluation of EVS, MAE, MSE, and R², the results of the GBRT model were closest to the ideal value best.

Conclusions The study is aimed at the safety monitoring requirements of large equipment in long-term service state and realizes the full-life fatigue crack monitoring of the metal structure parts in its key parts, which is important from the practical application perspective. Based on theoretical analysis, numerical simulation, and strain experiment, using strain field data to invert the crack length is proved to have a reliable theoretical basis and practical feasibility. The proposed FBG sensor array is a good strain monitoring method, which makes the collected local strain show regularity and gradation at different stages of crack growth, and realizes the prediction of crack growth degree and the identification of crack cracking direction. Based on the prediction method of fatigue crack length from experimental data, the GBRT algorithm is compared with linear regression and SVR methods. The results show that the GBRT algorithm performs better in strain field inversion by the evaluation of EVS, MAE, MSE, R², and cross-validation.