多项式解耦方法在多项式NARX模型中的应用
Applying Polynomial Decoupling Methods to the Polynomial NARX Model
摘要：
系统辨识使用动态系统的输入和输出的测量来重建该系统的数学模型。这些可以是机械的、电的、生理的等等。由于我们周围的大多数系统都表现出某种形式的非线性行为，非线性系统辨识技术是帮助我们更好地了解周围环境并有可能提高其性能的工具。通常用于表示非线性系统的一个模型是多项式NARX模型，这是一种方程误差模型，其中输出是过去输入和输出的多项式函数。也就是说，多项式NARX模型的一个主要缺点是参数的数量随着多项式阶数的增加而迅速增加。此外，多项式NARX模型是一个黑箱模型，因此很难解释。本文讨论了多项式NARX模型的一种解耦算法，即用一个变换矩阵代替多元多项式，然后用一组一元多项式代替多元多项式。这大大减少了模型参数的数量，并且还对黑盒NARX模型施加了结构。由于这种识别技术需要非凸优化，因此初始化是要考虑的重要因素。在本文中的解耦算法开发结合几种不同的初始化技术。所得到的算法被应用到两个非线性基准问题：从银盒的测量数据和模拟数据从Bouc-Wen摩擦模型，并在模拟和预测不同的验证信号的性能进行评估。
英文摘要：
System identification uses measurements of a dynamic system's input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinear behavior, nonlinear system identification techniques are the tools that will help us gain a better understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial function of the past inputs and outputs. That said, a major disadvantage with the polynomial NARX model is that the number of parameters increases rapidly with increasing polynomial order. Furthermore, the polynomial NARX model is a black-box model, and is therefore difficult to interpret. This paper discusses a decoupling algorithm for the polynomial NARX model that substitutes the multivariate polynomial with a transformation matrix followed by a bank of univariate polynomials. This decreases the number of model parameters significantly and also imposes structure on the black-box NARX model. Since a non-convex optimization is required for this identification technique, initialization is an important factor to consider. In this paper the decoupling algorithm is developed in conjunction with several different initialization techniques. The resulting algorithms are applied to two nonlinear benchmark problems: measurement data from the Silver-Box and simulation data from the Bouc-Wen friction model, and the performance is evaluated for different validation signals in both simulation and prediction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
