基于B样条整体最小二乘的非线性多功能传感器信号重构方法

摘要

提出一种基于B样条整体最小二乘(Total least squares,TLS)的非线性多功能传感器信号重构新方法.该方法利用B样条基函数直接构建描述多功能传感器传递函数反函数的张量积B样条曲面;采用TLS求解超定方程组以获得稳定的控制系数估计.以二输入二输出多功能传感器模型为实验对象,在两种非线性情况下对多功能传感器的输入信号进行了重构,重构相对误差分别为0.162％和1.043％,并与常用重构方法进行了对比分析.理论和实验表明,B样条TLS重构方法对非线性多功能传感器传递函数的反函数具有良好的逼近性能,在信号重构中表现出较好的有效性.%B-spline total least squares (TLS) is proposed for signal reconstruction of the nonlinear multifunctional sensor.In the method,the tensor product B-spline surface for describing the inverse function of the nonlinear multifunctional sensor system transfer function,is directly constructed based on the B-spline basis functions.The total least squares(TLS) algorithm is adopted to solve the overdetermined linear equations.One multifunctional sensor model with two inputs and two outputs is investigated.Input signals are reconstructed under two situations with different nonlinearities.The reconstruction relative errors are 0.162％ and 1.043％,respectively.Reconstruction results using the proposed method and other existing ones are compared and analyzed.Theoretical and experimental results demonstrate that the proposed Bspline TLS approaches well to the inverse function of the nonlinear multifunctional sensor system transfer function,and it can be used for signal reconstruction.