Data Of Nonlinear Systems Research Articles

Knowledge Discovery from Dynamic Data on a Nonlinear System

A method is presented for performing knowledge discovery on the dynamic data of a nonlinear system. In the proposed approach, a synchronized phasor measurement technique is used to acquire the dynamic data of the nonlinear system and a hyper-rectangular type neural network (HRTNN) is then applied to extract crisp and fuzzy rules with which to estimate the system stability. The effectiveness of the proposed methodology is verified using the dynamic data of a typical real-world nonlinear system, namely an AEP-14 bus, and the extracted rules are relating to the knowledge discovery of the stability levels for the nonlinear system. The discovered relationships among the dynamic data (i.e., the operating state), the extracted rules, and the system stability are confirmed by means of a two-stage confirmatory factor analysis.

Set membership inversion and robust control from data of nonlinear systems

SUMMARYA set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley & Sons, Ltd.

Physics constrained nonlinear regression models for time series

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data.

A simple approach to direct LPV filter design from data for nonlinear systems

A simple approach to the design of Linear Parameter Varying (LPV) filters for nonlinear systems is proposed. The approach relies on individuating several working conditions of the system. For each of these conditions, an almost optimal Linear Time Invariant (LTI) filter is directly identified from data. The designed LTI filters are then suitably combined to give an LPV filter. The identification of a nonlinear model and the design of a nonlinear filter are thus avoided. The direct filter design approach is applied to a problem involving real data, regarding the estimation of vehicles yaw rate.

Eliciting transparent fuzzy model using differential evolution

In this paper a new technique for eliciting a fuzzy inference system (FIS) from data for nonlinear systems is proposed. The strategy is conducted in two phases: in the first one, subtractive clustering is applied in order to extract a set of fuzzy rules, in the second phase, the generated fuzzy rule base is refined and redundant rules are removed on the basis of an interpretability measure. Finally the centers and widths of the Membership Functions (MFs) are tuned by means differential evolution. Case studies are presented to illustrate the efficiency and accuracy of the proposed approach. The results obtained are compared and contrasted with those obtained from a conventionally neuro-fuzzy technique and the superiority of the proposed approach is highlighted.

Open-loop frequency response method for nonlinear servomechanisms

This paper develops a useful graphical representation similar to the common Nyquist diagrams for the measured or calculated open-loop frequency response data of nonlinear systems.1,2,3,4 This representation indicates the frequency response characteristics and other phenomena such as limit cycles5 and response hysteresis, or jump phenomenon,6 of closed-loop systems. Likewise, this open-loop representation is convenient for the synthesis of linear filters, which can be inserted in the error amplifier to improve the closed-loop response of such nonlinear systems. In fact, the closed-loop frequency response of the nonlinear system with a linear filter in the error or forward section of the loop can be determined if both the transfer function of the linear filter and the open-loop frequency response of the nonlinear servo without the filter are known. Many who have measured the response of servo systems assumed to be linear have realized that the assumption of linearity is not always satisfactory. For very small input signals, backlash and coulomb friction cause nonlinear distortion, as does saturation when the input signal is large.7 It is hoped that the method used in this paper will help the servo engineer improve the response of nonlinear systems.