Abstract: The addition of complex information in the microstructure of the tested object increases the difficulty to establish an effective evaluation curve with minimized errors. To solve this problem, this paper proposes a monotonicity-oriented method of ultrasonic evaluation of α-phase grain size of TC4 titanium alloy. Based on the correlation measure, effective parameters are selected from multiple ultrasonic parameters, and the mapping function is reduced to a single-dimensional parameter and normalized to fit the primary α phase once, constructing a optimization problem of reaching maximized monotonicity where the sample points of feature parameter are successively positive or negative. The problem is solved with the self-adaptive differential evolution (SADE) algorithm to find the most ideal mapping function and fitting function coefficient, finally establishing the monotonicity based on multi-parameter model for ultrasonic evaluation. The experimental results show that the evaluation effect of the established model is more significant than that of the error-oriented evaluation model because it considers the importance of monotonicity. Compared with the single-parameter ultrasonic velocity method, the attenuation coefficient method and the nonlinear coefficient method, the established model contains smaller error, better monotonicity, more stable performance and higher accuracy of evaluation.

Key words: TC4 titanium alloy, grain size, monotonicity, ultrasonic evaluation, self-adaptive differential evolution algorithm