A Least Squares Fitting Method for Uncertain Parameter Estimation in Solidification Model

Abstract

This study proposes an automated method for estimating the uncertain parameters of the solidification model in response to the inefficient and time-consuming problem of manually estimating multiple uncertain parameters of the solidification model. The method establishes an uncertain parameter estimation model based on the relationship between the simulated images equiaxed crystal ratio and the uncertain parameters of the solidification model, fits the parameters of the model by the least squares method, and finally estimates the uncertain parameters in the solidification model using the parameters of the fitted model. In comparison with the traditional method of calculating uncertain parameters manually through empirical formulas, this method reduces the difficulty of tuning parameters and solves the problem of tuning multiple parameters simultaneously in the nonlinear solidification model. The experimental results show that the proposed method can accurately estimate the uncertain parameters of the solidification model, improve the efficiency and accuracy of the solidification model estimation parameters, and play a guiding role in simulating the solidification process of continuously casting billet to control the solidification structure.

Keywords

• equiaxed crystal ratio
• solidification model
• fitted parameters
• parameter estimation model
• least squares