基于蒙特卡罗最小二乘的实验数据拟合方法

Monte Carlo method of least squares fitting of experimental data

采用最小二乘法拟合化工实验数据,相关系数接近于1,精度高,但所得的结果与经验关联式大相径庭。蒙特卡罗方法是一种基于概率模型的非确定性数值方法。蒙特卡罗最小二乘拟合方法处理化工实验数据,应用中更为灵活,适用范围更广。在Excel电子表格中,利用工作表中的数据与VBA混合编程很容易完成蒙特卡罗最小二乘数据拟合,VBA实现与Excel电子表格的数据通讯及并行处理实验数据,读取工作表中的实验数据,计算随机点的大致搜索范围,进行最小二乘统计分析,将结果输出到工作表中。蒙特卡罗最小二乘拟合方法采用与最小二乘法相同的精度标准,在符合大数定理的基础上,精度大幅度提高。蒙特卡罗方法在随机搜索点较小时,误差很大,当随机搜索点达到10000时,其精度与最小二乘法相差无几,却得到与经验关联式十分接近的准数关系方程,取得了实践与理论统一的实验效果。

Using the least squares method that fits chemical industry empirical datum,the correlation coefficient approaches in 1,and the precision is high,the results differ with the empirical correlation.Monte Carlo method is a probabilistic model based on non-deterministic numerical methods.Monte Carlo method of least squares fits of experimental data processing chemicals,so the application is more flexible and broader scope.In the Excel spreadsheet,using the worksheet data and VBA programming is easy to complete mixing least-squares data fitting Monte Carlo,VBA and Excel spreadsheets to achieve data communications and parallel processing experimental data,to read the worksheet experimental data and calculate the approximate point random search,the least-squares statistical analysis,and the results output to the worksheet.Monte Carlo method of least squares fits method of least squares using the same precision with the standard,in line with large numbers theorem,which is based on the accuracy improved significantly.Monte Carlo method in the random search point is small,the error, and when the random search points to 10 000,its accuracy is almost the same with the method of least squares.At the same time we can get the empirical correlation that has been very close relationship between the number of quasi-equation sand practice which make unified theory of the experimental results.