Dempsey Erika J, Westwick David T
Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4 Canada.
IEEE Trans Biomed Eng. 2004 Feb;51(2):237-45. doi: 10.1109/TBME.2003.820384.
This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses a separable least squares Levenberg-Marquardt optimization to identify Hammerstein cascades whose nonlinearities are modeled by either cubic splines or polynomials. These algorithms are compared in simulation, where the effects of variations in the input spectrum and distribution, and those of the measurement noise are examined. The two algorithms are used to fit Hammerstein models to stretch reflex electromyogram (EMG) data recorded from a spinal cord injured patient. The model with the cubic spline nonlinearity provides more accurate predictions of the reflex EMG than the polynomial based model, even in novel data.
本文考虑使用三次样条函数而非多项式来表示块结构模型中的静态非线性。它介绍了一种针对哈默斯坦结构的系统辨识算法，该结构为一个静态非线性环节后接一个线性滤波器，其中三次样条函数表示静态非线性，线性动态特性则使用有限脉冲响应滤波器进行建模。该算法采用可分离最小二乘列文伯格 - 马夸特优化方法来辨识哈默斯坦级联，其非线性部分由三次样条函数或多项式建模。在仿真中对这些算法进行了比较，研究了输入频谱和分布变化以及测量噪声的影响。这两种算法被用于将哈默斯坦模型拟合到从一名脊髓损伤患者记录的拉伸反射肌电图（EMG）数据上。即使在新数据中，具有三次样条函数非线性的模型对反射EMG的预测也比基于多项式的模型更准确。
