scholarly journals Identification of a Non-Linear System Using Volterra Series Model with Calculated Kernels by Legendre Orthogonal Function

2017 ◽  
Vol 6 (3) ◽  
pp. 185
Author(s):  
Vahid Mossadegh ◽  
Mahmood Ghanbari
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Volterra Series ◽  
Legendre Function ◽  
Model Parameters ◽  
Orthogonal Functions ◽  
Orthogonal Function ◽  
Non Linear ◽  
Non Linear Systems ◽  
Non Linear System

Modeling and identification of non-linear systems have gained lots of attentions especially in industrial processes. Most of the actual systems have non-linear behavior and the first and simplest solution in modeling such systems is to linearize them which in most cases the result of linearization is not satisfactory. In this paper, modeling of non-linear systems is investigated using Volterra series model based on Legendre orthogonal function. Expansion of Volterra series kernels by Legendre orthogonal functions causes a reduction in the number of model parameters; hence, complexity of calculations would be decreased. Besides, if the free parameter is selected properly in these orthogonal functions, error is reduced and convergence speed of parameters is increased which leads to an increase in identification accuracy. In this paper, identification of non-linear system is presented with Volterra series expanded by Legendre function and PSO algorithm is used to calculate the optimum free parameters of Legendre function. Finally, in order to validate the efficacy and accuracy, the proposed algorithm is implemented on a non-linear system i.e. heat exchanger with actual data

Correlation Techniques for the Identification of Non-Linear Systems

1972 ◽  
Vol 5 (8) ◽  
pp. 316-321 ◽  
Author(s):  
R. J. Simpson ◽  
H. M. Power
Keyword(s):  
Linear System ◽  
Frequency Domain ◽  
Recent Work ◽  
Cross Correlation ◽  
Volterra Series ◽  
Kernel Functions ◽  
Non Linear ◽  
Non Linear Systems ◽  
Correlation Techniques ◽  
Non Linear System

The Volterra series expansion of the response of a non-linear system is described, along with its counterpart in the frequency domain. Cross-correlation methods for identifying the kernel functions which occur in this expansion are reviewed, with particular emphasis on techniques for obtaining the linear approximant to a non-linear system. Some recent work which appears to be unrelated to the Volterra approach is also discussed.

Coexistent of Solutions in Non-Linear Systems with Impacts

2014 ◽  
Vol 543-547 ◽  
pp. 1840-1843
Author(s):  
Jin Qian Feng ◽  
Yue Tang Rong ◽  
Jun Li Liu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Shooting Method ◽  
Duffing System ◽  
Coexistence Of Attractors ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System

This paper proposes a corrected shooting method for a general non-linear system with impacts. We define the global Poincaré mapping for period orbits by the discontinuous mapping. It is suitable to construct the strategy of shooting method. As an illustrated example, we investigate the stability of period orbits in a Duffing system with impacts. In Addition, coexistence of attractors and bifurcations for period orbits are considered.

scholarly journals Non-linear system modelling based on constrained Volterra series estimates

2017 ◽  
Vol 11 (15) ◽  
pp. 2623-2629 ◽  
Author(s):  
Przemysław Śliwiński ◽  
Anna Marconato ◽  
Paweł Wachel ◽  
Georgios Birpoutsoukis
Keyword(s):  
Linear System ◽  
Volterra Series ◽  
System Modelling ◽  
Non Linear ◽  
Non Linear System

scholarly journals A Fuzzy MLP Approach for Identification of Nonlinear Systems

2019 ◽  
Vol 65 (1) ◽  
pp. 44-53 ◽  
Author(s):  
A R Marakhimov ◽  
K K Khudaybergenov
Keyword(s):  
Linear Systems ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Fuzzy Model ◽  
Performance Comparison ◽  
Neuro Fuzzy ◽  
Non Linear ◽  
Non Linear Systems ◽  
And Performance ◽  
Non Linear System

In case of decision making problems, identification of non-linear systems is an important issue. Identification of non-linear systems using a multilayer perceptron (MLP) trained with back propagation becomes much complex with an increase in number of input data, number of layers, number of nodes, and number of iterations in computation. In this paper, an attempt has been made to use fuzzy MLP and its learning algorithm for identification of non-linear system. The fuzzy MLP and its training algorithm which allows to accelerate a process of training, which exceeds in comparing with classical MLP is proposed. Results show a sharp reduction in search for optimal parameters of a neuro fuzzy model as compared to the classical MLP. A training performance comparison has been carried out between MLP and the proposed fuzzy-MLP model. The time and space complexities of the algorithms have been analyzed. It is observed, that number of epochs has sharply reduced and performance increased compared with classical MLP.

scholarly journals Method for determining the responses from a non-linear system using the Volterra series

2020 ◽  
Vol 4 (9 (106)) ◽  
pp. 34-44
Author(s):  
Mohammed Kassim Ahmed ◽  
Samah Fakhri Aziz ◽  
Naors Y. Anad Alsaleem ◽  
Konstantyn Sielivanov ◽  
Mykola Moskalets
Keyword(s):  
Linear System ◽  
Volterra Series ◽  
Non Linear ◽  
Non Linear System

scholarly journals Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

2007 ◽  
Vol 11 (1) ◽  
pp. 443-459 ◽  
Author(s):  
J. P. O’Kane ◽  
D. Flynn
Keyword(s):  
Soil Moisture ◽  
Systems Theory ◽  
Linear Systems ◽  
Domain Model ◽  
Model Parameters ◽  
Large Set ◽  
Catchment Scale ◽  
Non Linear ◽  
Moisture Characteristic ◽  
Non Linear Systems

Abstract. Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

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