基于改进最小二乘法的分子结构参数拟合与误差分析
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聂佳磊
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江苏海洋大学，江苏连云港， 222005
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摘要：针对传统最小二乘法拟合分子结构参数时鲁棒性弱、易受光谱异常数据干扰、多参数拟合精度低、残差误差累积的问题，本文提出融合自适应权重与迭代残差修正的改进最小二乘算法。该算法根据单次拟合残差动态分配样本权重，削弱噪声与异常数据影响，并通过迭代闭环校正参数，抑制各类误差累积。以有机小分子红外实测光谱数据开展对照实验，结果显示：相比传统算法，本文方法相关系数更高，均方根、平均绝对误差明显降低，在含噪实测数据下仍能精准标定键长、键角、振动频率等分子微观参数。该算法弥补了传统拟合方法在分子解析领域的缺陷，可为量子化学、分子光谱分析、有机分子设计等研究提供高稳定、高精度的数值拟合手段。
关健词：改进最小二乘法；分子结构参数；参数拟合；误差分析；光谱数据；鲁棒拟合 |
Fitting and Error Analysis of Molecular Structure Parameters via Improved Least Squares Method
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Jialei Nie
Jiangsu Ocean University, Lianyungang Jiangsu 222005, China
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Abstract：Traditional least squares suffer from weak robustness, sensitivity to spectral outliers, low multi-parameter fitting precision and accumulated residuals in molecular parameter fitting. This paper proposes an improved least squares algorithm with adaptive weights and iterative residual correction. It dynamically updates sample weights by fitting residuals to weaken noise interference, and adopts closed-loop iteration to curb error accumulation. Comparative experiments on FTIR data of organic small molecules show that the proposed method has higher correlation coefficient and lower root mean square/mean absolute error. It can accurately calibrate bond lengths, bond angles and vibrational frequencies under noisy measurements. The algorithm overcomes the defects of traditional fitting approaches and offers a robust, high-precision fitting tool for quantum chemistry, spectral analysis and molecular design.
Keywords : improved least squares method; molecular structure parameters; parameter fitting; error analysis; spectral data; robust
fitting
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