Generalized Quasi-Orthogonal Functional Networks Applied in Parameter Sensitivity Analysis of Complex Dynamical Systems

Abstract

This paper presents one possible application of generalized quasi-orthogonal functional networks in the sensitivity analysis of complex dynamical systems. First, a new type of first order (k = 1) generalized quasi-orthogonal polynomials of Legendre type via classical quasi-orthogonal polynomials was introduced. The short principle to design generalized quasi-orthogonal polynomials and filters was also shown. A generalized quasi-orthogonal functional network represents an extension of classical orthogonal functional networks and neural networks, which deal with general functional models. A sequence of the first order (k = 1) generalized quasi-orthogonal polynomials was used as a new basis in the proposed generalized quasi-orthogonal functional networks. The proposed method for determining the parameter sensitivity of complex dynamical systems is also given, and an example of a complex industrial system in the form of a tower crane was considered. The results obtained have been compared with different methods for parameter sensitivity analysis.

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

“…The authors of this paper developed several new types of orthogonality in the last ten years. Some of them are almost orthogonality [18], improved orthogonality [26], quasiorthogonality [19], generalised quasiorthogonality [23], and a new type of trigonometric orthogonality [27]. On the other hand, the generalisation of Malmquist-Takenaka polynomials is developed for the modelling purposes of an industrial protector cooling system [20].…”

“…To demonstrate the effectiveness of the proposed method, the experiments were repeated with well-known orthogonal polynomials. We used generalised quasiorthogonal polynomials (order k = 1) of the Legendre type [18], Chebyshev polynomials of the second kind [19], classical Legendre polynomials [13], and Laguerre polynomials [23].…”

“…The newly developed polynomials will be used in the structure of the H-W model as a replacement for the standard functions contained in these models. Unknown systems are identified by the transfer function using the mean square error (MSE) method [18], [23]. In identification systems, we minimise the error value between classical H-W models with our proposed H-W structure with improved almost orthogonal polynomials of Müntz-Legendre type.…”