scholarly journals The theory of nonlinear systems as an instrument for solving engineering problems

2018 ◽  
Vol 226 ◽  
pp. 04040
Author(s):  
Olga I. Ohrimenko ◽  
Igor M. Maltsev ◽  
Violetta V. Rokotyanskaya ◽  
Maria L. Vilisova
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Volterra Series ◽  
Dynamic Properties ◽  
Optimization Theory ◽  
Diagnostic System ◽  
Nonlinear Dynamic System ◽  
Weight Functions ◽  
Volterra Operators ◽  
Finite Set

The article outlines theoretical, methodological and practical issues of modern control and optimization theory, as well as the problems of nonlinear systems theory. Theoretical conclusions and results allowed to build mathematical models applicable to the management of objects of different nature with different principles of action, in particular, to the management of complex technical and technological objects that can be considered as nonlinear dynamic systems. The authors find it appropriate to consider nonlinear dynamic integral models as Volterra integro-power series from many functional arguments with multidimensional weight functions and a certain finite set of inputs to the system. The set of multidimensional kernels of integral Volterra operators completely characterizes the nonlinear and dynamic properties, and, consequently, the technical state of the initial system. The application of Volterra series based models allows to take into account the nonlinear and inertial properties of the initial nonlinear dynamic system more fully and accurately, it also makes the model diagnostic of a technical system more universal, raises the reliability of the forecast. The diagnostic procedure in this case is aimed at defining Volterra kernels based on the data of “input-output” experiment and building the diagnostic system of attribute in the space of which the decisive rule of optimal classification is created.

Research and Exploration of Volterra Series on Nonlinear System Identification and Modeling

2010 ◽  
Vol 439-440 ◽  
pp. 584-589 ◽  
Author(s):  
Y. Chen
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Dynamic System ◽  
Nonlinear Dynamic ◽  
System Analysis ◽  
Reproducing Kernel ◽  
Volterra Series ◽  
Kernel Method ◽  
Nonlinear System Identification ◽  
Nonlinear Dynamic System

With the development of analysis and identification way to nonlinear dynamic system, people uses many different method to build up mathematics model to simulate nonlinear dynamic system. This paper introduces some important nonlinear system identification ways and a kind of Volterra series expression type in detail. This kind of way adopts Hilbert reproducing kernel method to build up nonlinear dynamic system model. Hilbert space provides a kind of effective expression type for Fourier series and transfer based on anyorthogonal polynomial. Volterra series function has very strict theory basic, which can be applied into many nonlinear dynamic system analysis and identification filed, and has broad practicality and application prospect.

On interval-data based Type-1 Takagi-Sugeno fuzzy systems for uncertain nonlinear dynamic system identification

2016 ◽  
Vol 64 (6) ◽  
Author(s):  
Salman Zaidi ◽  
Andreas Kroll
Keyword(s):  
Fuzzy System ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic System ◽  
Random Variable ◽  
Interval Data ◽  
Fuzzy Modelling ◽  
Symbolic Data ◽  
Specific Assumption ◽  
Takagi Sugeno

AbstractA novel interval-data based Takagi-Sugeno fuzzy system is proposed to identify uncertain nonlinear dynamic systems by endowing the classical TS fuzzy system with probability theory and symbolic data analysis. Such systems have variability in their outputs, that is they produce varying responses each time when the same stimuli is applied to them under the same condition. Interval data is generated by repeating the identification experiment multiple times and applying the probabilistic techniques to get soft bounds of output. The interval data is then directly used in the TS fuzzy modelling, giving rise to interval antecedent and consequent parameters. This method does not require any specific assumption on the probability distribution of the random variable that models the uncertainty. The developed procedure is demonstrated for a pneumatic drive system.

Using the Kalman Filtering for the Fault Detection and Isolation (FDI) in the Nonlinear Dynamic Processes

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Yahya Chetouani
Keyword(s):  
Fault Detection ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic System ◽  
Chemical Reactor ◽  
Fault Detection And Isolation ◽  
Decision Threshold ◽  
Normal Behaviour ◽  
Batch Mode ◽  
The Moment ◽  
Reactor Operating

This paper presents a Fault Detection and Isolation (FDI) method for stochastic nonlinear dynamic systems. First, the developed fault detection method is based on statistical information generated by the extended Kalman filter (EKF) and is intended to reveal any drift from the normal behaviour of the process. A fault of a chemical origin in a perfectly stirred batch chemical reactor, occurring at an unknown instant, is simulated. The purpose is to detect the presence of this abrupt change, and pinpoint the moment it occurred. It is also shown that the convergence of the EKF is accomplished more or less rapidly according to the nature of the noise generated by the measurement sensors. The state estimate is observed and discussed, as well as the time delay in detection according to the decision threshold. Then, this study shows another method of tackling the problem of the physical origin diagnosis of faults by combining the technique based on the standardized innovations and the technique using the multiple extended Kalman filters for a strongly non-stationary nonlinear dynamic system. The usefulness of this combination is the implementation of all the fault dynamics models if the decision threshold on the standardized innovation exceeds a determined threshold. In the other case, one EKF is enough to estimate all the process state. An algorithm is described and applied to a perfectly stirred chemical reactor operating in a semi-batch mode. The chemical reaction used is an exothermic second order one.

scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

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