ABSTRACT

This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of trade-off between model accuracy and complexity.

摘要

本文提出了一种使用特殊设计的正交多项式神经网络对动态系统建模的新方法。这些网络利用以下特性：正交函数构成的基础可用于任意函数的逼近，而它们的正交性可在收敛时间和逼近误差的意义上实现最佳性能。在这方面，考虑了专门为在具有时变行为的复杂动态系统的建模中应用而量身定制的广义拟正交多项式。设计模型的适应性是通过在正交基础内使用可变因子来实现的。所设计的正交神经网络被用于实验室双转子气动系统的建模，作为非线性多输入多输出系统的代表。针对扩展中不同数量的多项式执行详细的比较分析，目的是在模型精度和复杂性之间进行权衡的意义上找到最佳模型。