论文部分内容阅读
样条函数理论作为数学工具已广泛应用于逼近论、曲线数据拟合、数值分析等方面 .在研究一般多项式最小二乘法建模的基础上 ,针对所建模型易产生欠拟合和过拟合及模型阶数高的问题 ,提出了采用样条最小二乘数据拟合方法来建立数学模型 .基于样条最小二乘数据拟合方法建立的数学模型不仅可以提高模型精度和拟合程度 ,而且模型阶数较低 ,光滑性好 .将该建模方法用于多气体传感器输出信号的建模 ,结果表明 ,方法正确并有效 .
Spline function theory as a mathematical tool has been widely used in approximation theory, curve data fitting, numerical analysis and so on.On the basis of studying the general polynomial least squares method, it is easy to produce under-fitted and over-fitted And the problem of high order of models, a mathematical model based on spline least squares data fitting method is proposed.The mathematical model based on spline least squares data fitting method can not only improve the precision and fitting degree of model, but also The modeling order is low and the smoothness is good. The modeling method is applied to the modeling of multi-gas sensor output signals. The results show that the method is correct and effective.