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Author: Ndumiso Archibald Pete Publisher: ISBN: Category : Dissertations, Academic Languages : en Pages : 168
Book Description
In dynamical systems, the calculation of the unknown parameters which are associated with the differential equations that describe such systems, is confronted by serious challenges. The chosen values are usually based on conjecture and reasonable estimates as per ratio impact expected and interpreted by the experimenter, or field worker in the case of ecological systems. The challenge is to interpret experimental data from mathematical biology, ecology, chemical kinetics and many other dynamical systems, and develop a mathematical model accordingly. In this research project a method of numerical evaluation of unknown parameters of a dynamical system is presented. The proposed method is based on integrating both sides of equations of a dynamical system, and applying regression methods to the over-determined system of linear algebraic equations with constraints. Using the method of least squares and possible constraints, a linear system for determining the unknown parameters can be obtained.
Author: Ndumiso Archibald Pete Publisher: ISBN: Category : Dissertations, Academic Languages : en Pages : 168
Book Description
In dynamical systems, the calculation of the unknown parameters which are associated with the differential equations that describe such systems, is confronted by serious challenges. The chosen values are usually based on conjecture and reasonable estimates as per ratio impact expected and interpreted by the experimenter, or field worker in the case of ecological systems. The challenge is to interpret experimental data from mathematical biology, ecology, chemical kinetics and many other dynamical systems, and develop a mathematical model accordingly. In this research project a method of numerical evaluation of unknown parameters of a dynamical system is presented. The proposed method is based on integrating both sides of equations of a dynamical system, and applying regression methods to the over-determined system of linear algebraic equations with constraints. Using the method of least squares and possible constraints, a linear system for determining the unknown parameters can be obtained.
Author: Rolf Isermann Publisher: Springer Science & Business Media ISBN: 3540788794 Category : Technology & Engineering Languages : en Pages : 705
Book Description
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.
Author: Klaus Schittkowski Publisher: Springer Science & Business Media ISBN: 1441957626 Category : Computers Languages : en Pages : 406
Book Description
Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Author: Seshu Kumar Damarla Publisher: CRC Press ISBN: 0429996896 Category : Mathematics Languages : en Pages : 340
Book Description
The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.
Author: Xuewei Ruan Publisher: ISBN: Category : Languages : en Pages : 85
Book Description
Accurate damage inspection and reliable health monitoring of dynamical systems relies on accurate system identification techniques, where signal procession for accurate extraction of modal parameters from measured dynamical data plays the key role. In theory, if all three variables (i.e., displacement, velocity and acceleration) of each point on a dynamical system are available from measurement, parametric or even nonparametric system identification can be easily and accurately performed. In experiment, however, it is often only one variable is measured because collocating three different sensors at a point is too difficult even if the sensors are small enough not to affect the system's dynamic characteristics. Numerical investigations reveal that velocity is the best choice because the corresponding acceleration and displacement can be estimated by numerical differentiation and integration, and because today's laser vibrometers can provide very accurate measurements of velocities. Real-world dynamical systems often behave nonlinearly especially when they are damaged or aged. Because dynamic characteristics (modal frequencies, damping ratios, mode shapes, etc.) of a nonlinear system change with time, system identification methods for nonlinear systems need to be capable of extracting such time-varying system characteristics and hence time-frequency analysis is essentially needed. Numerical investigation shows that direct time-domain methods based on processing of measured time-domain data can provide accurate identification results only for linear systems. Unfortunately, damping of a linear dynamical system cannot be accurately estimated by direct time-domain methods because its value is too small as compared to the values of stiffness and mass. Because frequency-domain methods are based on the use of frequency response functions from Fourier transform and conventional, linear modal testing techniques, they are also only valid for linear systems. On the other hand, indirect timedomain methods are based on the use of the maximum displacement and velocity states or the timevarying amplitudes and frequencies of responses to perform system identification. A nonparametric system identification method based on the use a spring force function of displacement and a damping force function of velocity or a combined restoring force function of displacement and velocity is developed and shown to work for any nonlinear systems. All these direct time-domain methods, frequency-domain methods, and indirect time-domain methods are presented in this thesis, and advantages and shortcomings of each method are demonstrated and discussed through numerical examples. This thesis concentrates on the nonparametric system identification and presents several numerical techniques for noise filtering. Except numerical examples, experimental vibration data of a beam and a plastic car measured using a PSV-200 scanning laser vibrometer are also used to verify the accuracy of these methods.
Author: Heinz Unbehauen Publisher: ISBN: Category : Computers Languages : en Pages : 402
Book Description
Bringing together important advances in the field of continuous system identification, this book deals with both parametric and nonparametric methods. It pays special attention to the problem of retaining continuous model parameters in the estimation equations, to which all the existing techniques used in estimating discrete models may be applied. It is aimed at both the academic researcher and the control engineer in industry. The techniques covered range from certain simple numerical or graphical methods applicable to some of the frequently encountered model forms, to attractive recursive algorithms for continuous model identification suitable for real time implementation. These include the recent methods based on orthogonal functions such as those of Walsh and Poisson moment functionals. Some techniques based on stable model adaptation principles are also presented and illustrated.
Author: Jan Awrejcewicz Publisher: Springer ISBN: 3319424084 Category : Mathematics Languages : en Pages : 424
Book Description
The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Łódź, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
Author: Yuri Tiumentsev Publisher: Academic Press ISBN: 0128154306 Category : Science Languages : en Pages : 332
Book Description
Neural Network Modeling and Identification of Dynamical Systems presents a new approach on how to obtain the adaptive neural network models for complex systems that are typically found in real-world applications. The book introduces the theoretical knowledge available for the modeled system into the purely empirical black box model, thereby converting the model to the gray box category. This approach significantly reduces the dimension of the resulting model and the required size of the training set. This book offers solutions for identifying controlled dynamical systems, as well as identifying characteristics of such systems, in particular, the aerodynamic characteristics of aircraft. Covers both types of dynamic neural networks (black box and gray box) including their structure, synthesis and training Offers application examples of dynamic neural network technologies, primarily related to aircraft Provides an overview of recent achievements and future needs in this area
Author: Ndumiso Archibald Pete
Author: Ndumiso Archibald Pete
Author: Rolf Isermann
Author: Klaus Schittkowski
Author: Seshu Kumar Damarla
Author: Xuewei Ruan
Author: Heinz Unbehauen
Author: Jan Awrejcewicz
Author: Yuri Tiumentsev
Author: I-Ho Lin
Author: Andreas Sommer