scholarly journals Identification of Nonlinear Systems: Volterra Series Simplification

10.14311/976 ◽  
2007 ◽  
Vol 47 (4-5) ◽  
Author(s):  
A. Novák
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Transfer Function ◽  
Linear System ◽  
Impulse Response ◽  
Volterra Series ◽  
Series Representation ◽  
Multimedia Systems ◽  
Audio Amplifier ◽  
Enormous Number

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown. 

scholarly journals Steady state response of a nonlinear system

1980 ◽  
Vol 3 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear System ◽  
Linear Model ◽  
Series Solution ◽  
Steady State Response ◽  
State Response ◽  
Equivalent Linear Model

This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.

scholarly journals Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

2021 ◽  
Author(s):  
Yun-Peng Zhu ◽  
Z. Q. Lang ◽  
Yu-Zhu Guo
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Model ◽  
System Analysis ◽  
Volterra Series ◽  
Engineering Practice ◽  
Small Range ◽  
Stable Regime ◽  
Analysis And Design ◽  
Wide Range

AbstractIn engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.

scholarly journals Reduced-Orderl2−l∞Filter Design for a Class of Discrete-Time Nonlinear Systems with Multiple Sensor Faults

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wenbai Li ◽  
Huxiong Li
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear System ◽  
Discrete Time ◽  
Sensor Faults ◽  
Reduced Order ◽  
Fuzzy Linear System ◽  
Multiple Sensor ◽  
Error System ◽  
Takagi Sugeno

The reduced-order filtering problem for a class of discrete-time smooth nonlinear systems subject to multiple sensor faults is studied. It is well known that a smooth complex nonlinear system can be approximated by a Takagi-Sugeno fuzzy linear system with finite number of subsystems. In this work, firstly, the discrete-time smooth nonlinear system is transferred into a Takagi-Sugeno fuzzy linear system with finite number of subsystems. Secondly, a filter with the reduced order of the original system is proposed to be designed. Different from the traditional assumption in which the measurement of the output is ideal, the measurement of the output is subject to sensor faults which are described via Bernoulli processes. By using the augmentation technique, a stochastic Takagi-Sugeno filtering error system is obtained. For the stochastic filtering error system, the exponential stability and the energy-to-peak performance are investigated. Sufficient conditions which can guarantee the exponential stability and thel2−l∞performance are obtained. Then, with the proposed conditions, the design procedure of the filter for the nonlinear system is proposed. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.

scholarly journals Power spectral density analysis for nonlinear systems based on Volterra series

2021 ◽  
Author(s):  
Penghui Wu ◽  
Yan Zhao ◽  
Xianghong Xu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Random Vibration ◽  
Volterra Series ◽  
Harmonic Excitation ◽  
Random Load ◽  
Vibration Prediction ◽  
Power Spectral

AbstractA consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Exact Stationary Response Solution for Second Order Nonlinear Systems Under Parametric and External White Noise Excitations: Part II

1988 ◽  
Vol 55 (3) ◽  
pp. 702-705 ◽  
Author(s):  
Y. K. Lin ◽  
Guoqiang Cai
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Probability Distribution ◽  
White Noise ◽  
Probability Density ◽  
Detailed Balance ◽  
Stationary Probability ◽  
Probability Flow ◽  
Parametric And External Excitations ◽  
White Noises

A systematic procedure is developed to obtain the stationary probability density for the response of a nonlinear system under parametric and external excitations of Gaussian white noises. The procedure is devised by separating the circulatory portion of the probability flow from the noncirculatory flow, thus obtaining two sets of equations that must be satisfied by the probability potential. It is shown that these equations are identical to two of the conditions established previously under the assumption of detailed balance; therefore, one remaining condition for detailed balance is superfluous. Three examples are given for illustration, one of which is capable of exhibiting limit cycle and bifurcation behaviors, while another is selected to show that two different systems under two differents sets of excitations may result in the same probability distribution for their responses.

scholarly journals Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Qinming Liu ◽  
Ming Dong
Keyword(s):  
Monte Carlo ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Markov Model ◽  
Sequential Monte Carlo ◽  
Health Management ◽  
Health State ◽  
Health States ◽  
Complex Nonlinear System ◽  
Complex Nonlinear Systems

Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM) with sequential Monte Carlo (SMC) methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.

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