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Accurate characterization of grain features is crucial for understanding and optimizing the comprehensive performance of metallic materials. In this paper, a rapid, non-contact and non-destructive approach is proposed for the quantitative evaluation of grain size statistics of commercial pure titanium (TA1) by coupling laser ultrasonic technology with ridge regression integrated with logarithmic transformation. Six groups of TA1 specimens with diversified grain sizes were prepared via thermal treatment, and their average grain size and corresponding standard deviation were quantitatively measured by electron backscatter diffraction (EBSD) as the benchmark references. The acquired laser ultrasonic signals were denoised by complete ensemble empirical mode decomposition (CEEMD), followed by the extraction of three representative ultrasonic characteristic parameters. Based on the extracted features, two independent ridge regression models were established to respectively predict the average grain size and grain size standard deviation. The results show that the mean absolute error (MAE) and coefficient of determination (R 2 ) for average grain size prediction reach 2.08 μm and 0.9469, while those for grain size standard deviation are 1.18 μm and 0.9266, demonstrating the superior capability of the established models in predicting average grain size and grain size distribution. To intuitively visualize the evaluation results of grain characteristics, the grain distribution maps were further reconstructed through inversion analysis. This study provides a feasible technical route for the rapid assessment of grain size statistics, and offers promising application potential for quality evaluation and process optimization of titanium materials in industrial scenarios.
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Rong et al. (2026) studied this question.
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