Prediction of subsurface microcrack depth of brittle materials based on co-training SVR

[OBJECTIVES] Brittle materials, characterized by low fracture toughness, are susceptible to subsurface damages such as microcracks during grinding processes. This damage can adversely affect the performance and lifespan of the components. Precise measurement of the depth of subsurface microcracks is crucial for selecting appropriate machining allowance in subsequent processes. While current methods for measuring subsurface microcracks have limitation, machine learning models show significant potential in predicting machining quality of brittle materials. However, these models often require extensive labeled data, which is difficult to obtain in practice, thus limiting their learning capabilities. To address the challenge of limited effective samples for analyzing subsurface microcrack depths in brittle materials ground with fixed abrasives, this study proposes a collaborative training approach for a Support Vector Regression (SVR) model，tailored for small datasets, capable of accurately predicting microcrack depth caused by grinding different brittle materials.

[METHODS] This study employed the SVR model as the foundational learner, with inputs including Mohs hardness, elastic modulus, fracture toughness of the brittle materials, diamond abrasive grain size and grinding pressure. The output was the depth of subsurface microcracks resulting from grinding. Integrating semi-supervised and supervised learning concepts, the study developed both a collaborative training SVR model and a PSO-SVR model. The model’s predictive performances were assessed using mean square error (MSE) and mean absolute percentage error (MAPE). Further, the impact of various labeled training set partitioning strategies on the MSE of the test set was examined using the collaborative training SVR model. The study also compared the predictive performances of the collaborative training SVR model and the PSO-SVR model under separate dataset partitioning strategies. Finally, the study validated the models through grinding and angle polishing experiments to measure subsurface microcrack depths in materials not included in the training set, evaluating the collaborative training SVR model's predictive accuracy against experimental results. 

[RESULTS] When using separate dataset partitioning strategies, the initial MSE values of the two learners in the collaborative SVR model were 5.79 and 0.98, ultimately converging to 1.15 and 0.35, respectively. For mixed dataset partitioning strategy, the initial MSE values were 4.02 and 1.13, converging to 2.0 and 0.70, respectively. When predicting small dataset, the collaborative training SVR model demonstrated a reduction in MSE and MAPE by 9% and 17%, respectively, outperforming the PSO-SVR model. The collaborative model provided more reliable and stable predictions for both individual test samples and entire test sets. The measured subsurface microcrack depths in glass-ceramics and calcium fluoride under different processing conditions were 4.13, 5.03, 5.67, and 5.89 μm, with prediction errors ranging from 1.2% to 13.8%, averaging at 7.7%, which was significantly lower than the test set’s average prediction error of 12.5%.

[CONCLUSION] Dividing the labeled dataset using both separate and mixed partitioning methods can reduce the MSE of the collaborative training SVR model on the test set, with the separate method achieving smaller MSEs and superior outcomes. Compared to the supervised learning PSO-SVR model, the collaborative training SVR model demonstrates smaller MSE and MAPE values, with more stable prediction errors. The close agreement between the experimentally measured subsurface microcrack depths and the model's predictions underscores its robust generalization capability, confirming the model's ability to provide accurate and stable predictions of subsurface microcrack depths in various brittle materials after grinding.