残差分析自动选择多项式拟合最佳阶数的方法

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中图分类号：TP391.9 文献标志码：B

A residual analysis approach to automatic selection of optimal polynomial order in curve fitting

WANG Yang

（SiFotonics Technologies Co.，Ltd.，NanJing21180O，China）

Abstract： To address the challnge of selecting the appropriate polynomial order in curve fitting，a method for automatically determining the optimal polynomial fiting order within the LabVIEW environment is proposed. A variable-order cyclic fiting framework is constructed. By comprehensively evaluating multiple quantitative metrics，such as the goodness-of-fit，root mean square errr（RMSE） and its rate of change，and combining qualitative analysis of the residual distribution，an optimal trade-off between model complexity and fiting accuracy is achieved. The results show that for a given set of nonlinear data，the method can automatically and accurately identify the optimal fiting order as 4.The comprehensive goodness-of-fit reaches 0.998 874，with a root mean square error of 0.004 002 45，which is significantly better than lower-order models and shows no overfiting typical of higher orders.

Key words： LabVIEW； polynomial; optimal order; goodness-of-fit； root mean square error（RMSE）;residual analysis

0 引言

LabVIEW作为一款强大的图形化编程语言，被广泛应用于数据采集、仪器控制和信号处理。（剩余3639字）