Zhong Yuru, Jan Kung-Ming, Ju Ki H, Chon Ki H
Department of Biomedical Engineering, State University of New York (SUNY) at Stony Brook, Stony Brook, NY 11794, USA.
IEEE Trans Biomed Eng. 2007 Nov;54(11):1983-92. doi: 10.1109/TBME.2007.895748.
System identification of nonlinear time-varying (TV) systems has been a daunting task, as the number of parameters required for accurate identification is often larger than the number of data points available, and scales with the number of data points. Further, a 3-D graphical representation of TV second-order nonlinear dynamics without resorting to taking slices along one of the four axes has been a significant challenge to date. In this paper, we present a TV principal dynamic mode (TVPDM) method which overcomes these deficiencies. The TVPDM, by design, reduces one dimension, and by projecting PDM coefficients onto a set of basis functions, both nonstationary and nonlinear dynamics can be characterized. Another significant advantage of the TVPDM is its ability to discriminate the signal from noise dynamics, and provided that signal dynamics are orthogonal to each other, it has the capability to separate them. The efficacy of the proposed method is demonstrated with computer simulation examples comprised of various forms of nonstationarity and nonlinearity. The application of the TVPDM to the human heart rate and arterial blood pressure data during different postures is also presented and the results reveal significant nonstationarity even for short-term data recordings. The newly developed method has the potential to be a very useful tool for characterizing nonlinear TV systems, which has been a significant, challenging problem to date.
非线性时变（TV）系统的系统辨识一直是一项艰巨的任务，因为准确辨识所需的参数数量通常大于可用数据点的数量，并且会随着数据点数量的增加而增加。此外，在不沿四个轴之一切片的情况下，对TV二阶非线性动力学进行三维图形表示，迄今为止一直是一项重大挑战。在本文中，我们提出了一种TV主动态模式（TVPDM）方法，该方法克服了这些不足。通过设计，TVPDM减少了一个维度，并且通过将PDM系数投影到一组基函数上，可以表征非平稳和非线性动力学。TVPDM的另一个显著优点是它能够区分信号与噪声动力学，并且只要信号动力学相互正交，它就有能力将它们分离。通过包含各种形式的非平稳性和非线性的计算机仿真示例，证明了所提出方法的有效性。还介绍了TVPDM在不同姿势下人体心率和动脉血压数据中的应用，结果表明即使对于短期数据记录也存在显著的非平稳性。新开发的方法有可能成为表征非线性TV系统的非常有用的工具，而这一直是一个重大的、具有挑战性的问题。
