On modeling and identification of empirical partially intelligible white noise processes

Abstract

The paper discusses the identification of the empirical, partially intelligible white noise processes generated by deterministic numerical algorithms. The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of autocorrelated white noise processes change as the order of autocorrelation increases. Based on this approach, the original empirical white noise process transformed by the autocorrelation operator can be considered to be random data series (randomlikeness), and at the same time, it has function-like characteristics (functionlikeness), as well. We approach the analysis of the mentioned complementarity by modeling the autocorrelation functions of the empirical white noise processes using tensor product (TP) model transformation.

Performance Improvement of Low-Cost Iterative Learning-Based Fuzzy Control Systems for Tower Crane Systems

“…The main purpose of TP-based model transformation is to map a given Linear Parameter Varying (LPV) or quasi-Linear Parameter Varying (qLPV) state-space model onto a TP model made of Linear Time Invariant (LTI) systems using the Higher Order Singular Value Decomposition. The TP-based model transformation technique was successfully applied recently to tower crane system modeling [92], pendulum cart system modeling [93], [94], black box system modeling [95], induction machine modeling [96], and white noise process modeling [97]. This transformation technique was also used in the TP-based controller design; TP controllers were designed for a big number of processes including more recent ones such as Lotka-Volterra fractional order model [98] and aeroelastic systems [99], but they could be applied to other systems as, for instance, networked control systems [100].…”

Analysis on the Performance of a Second-order and a Third-order RLC Circuit of PRBS Generator

“…Random white noise is the term given to completely random unpredictable noise. It has the property of having components at every frequency [1]. PRBS can also have this property [2].…”

“…MLS contains all possible combinations of a binary sequence [7]. The relationship between the number of generated PRBS signals and the number of shift-register stages shown in (1).…”