基于 OLS 法及改进 LM 法的 ICP-AES非线性标准曲线拟合方法研究

针对电感耦合等离子体原子发射光谱法( ICP-AES)分析过程中出现的元素浓度-光强关系的非线性标准曲线,提出基于正交最小二乘法(OLS)及改进 LM(Levenberg-Marquardt)算法的标准曲线拟合方法,以实现元素浓度的准确分析。 采用二次多项式、三次多项式、Limbek 表达式、Lwin 表达式作为标准曲线的非线性模型,以适用不同数据的分布特点。 依据各表达式在拟合过程中的损失函数特性,对二次、三次多项式利用 OLS 法计算其最优拟合参数,对 Limbek、Lwin 表达式利用改进 LM 法得到其最优拟合参数,实现标准曲线的拟合。 针对 Sb、Cd、Sn、Mo、Ni、Ba 元素的一系列不同浓度标准样品的光强实测数据,进行上述方法的标准曲线拟合实验。 实验结果表明,各元素的浓度-光强数据均可拟合得到决定系数在 0. 999 以上的非线性标准曲线,且标准曲线对于已知数据点的拟合浓度的相对误差均在±5%。

Research on nonlinear standard curve fitting method of ICP-AES basedon OLS algorithm and improved LM algorithm

Aiming at the non-linear standard curve of the relationship between concentration and light intensity in the ICP-AES analysisprocess, a standard curve fitting method based on the OLS algorithm and the improved LM algorithm is proposed to realize the accurateanalysis of element concentration. Quadratic polynomial, cubic polynomial, limbek expression and Lwin expression are used as thenonlinear model of the standard curve to suit the distribution characteristics of different data. According to the loss functioncharacteristics of each expression in the fitting process, the OLS algorithm is used to calculate the optimal fitting parameters of quadraticand cubic polynomials, and the improved LM algorithm is used to obtain the optimal fitting parameters of limbek and Lwin expressions,so as to realize the fitting of standard curve. The light intensity measured data of a series of standard samples with different concentrationsof Sb, Cd, Sn, Mo Ni and Ba elements are used to carry out the standard curve fitting experiment of the above method. The experimentalresults show that the concentration-light intensity data of each element can be fitted to obtain a nonlinear standard curve with a R2above0. 999, and the relative error of the fitted concentration of the standard curve to the known data points is within ±5%.