基于全局优化的多组元熔体互扩散分析方法

Based on global optimization method for inter-diffusion analysis of multicomponent melts

不同于传统的确定多元互扩散系数的"扩散路径法"和"平方根扩散系数法"等方法,本文基于遗传算法和模拟退火算法的全局搜索功能,将这些智能算法与Levenberg-Marquardt算法进行有机结合从而提出一种既具有全局搜索能力又能够保证最优解精度的算法.通过扩散实验的成分谱构建目标函数,利用本算法对目标函数进行优化得到最优解,从而获得多组元体系的互扩散系数.为了说明本算法能够方便、可靠地处理多组元熔体的互扩散过程,本文分别对正常扩散情形,上坡扩散情形,理想扩散情形(不存在随机误差),大噪声比情形(随机误差范围为1个原子百分比)的扩散偶进行了分析,结果表明本算法都能适用于这些情形并给出很好的分析结果.此外,相对于"扩散路径法"等传统方法,本算法还具有精度高,通用性强等优点.

Different from the traditional methods to determine the inter-diffusion coefficients, such as the ＂diffusion path＂ method and ＂square root diffusion coefficient＂ method, this paper proposed a new algorithm, which was based on the genetic algorithm and simulated annealing algorithm of global search feature, to calculate inter-diffusion coefficients for multicomponent systems. Due to this algorithm combines those intelligent algorithm with the LevenbergMarquardt algorithm, it has both the capability of global search and ensures optimum accuracy. Using this algorithm to optimize the objective function, which is constructed from the diffusion profiles, we can obtain the inter-diffusion coefficients from the optimal solution. In order to test whether the algorithm are easy and reliable for handling the diffusion process of multicomponent melts, this paper analyzes the diffusion couple with normal diffusion situation, uphill diffusion situation, ideal diffusion situation（do not exist random errors） and large noise ratio situation（with random error in the range of 1 at.%）, respectively. The results show that the algorithm can be well applied in those situations and gives very good results. Since the solving process of obtaining the inter-diffusion coefficients by the algorithm is only based on a single diffusion profiles, it can significantly reduce the workload. At the same time, because the calculated process does not need to smooth the measured experimental data and determine the gradient or integral from the measured experimental data, this method improves the precision of measurement of the inter-diffusion coefficients. In addition, this method also has high versatility. This paper shows the calculated process in a three-component melt system, and theoretically, this algorithm can be easily extended into four-component melt system and above to determine the inter-diffusion coefficients. Therefore, compared with the traditional methods, for instance, the ＂diffusion path＂ method and ＂square root diffusion coefficient＂ method, the method proposed in this paper not only has high precision and versatility, but also obviously reduces the workload of measurement experiments.