Download or read book Parameter Estimation in Nonlinear Continuous time Dynamic Models with Modelling Errors and Process Disturbances written by M. Saeed Varziri and published by . This book was released on 2008 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model-based control and process optimization technologies are becoming more commonly used by chemical engineers. These algorithms rely on fundamental or empirical models that are frequently described by systems of differential equations with unknown parameters. It is, therefore, very important for modellers of chemical engineering processes to have access to reliable and efficient tools for parameter estimation in dynamic models. The purpose of this thesis is to develop an efficient and easy-to-use parameter estimation algorithm that can address difficulties that frequently arise when estimating parameters in nonlinear continuous-time dynamic models of industrial processes. The proposed algorithm has desirable numerical stability properties that stem from using piece-wise polynomial discretization schemes to transform the model differential equations into a set of algebraic equations. Consequently, parameters can be estimated by solving a nonlinear programming problem without requiring repeated numerical integration of the differential equations. Possible modelling discrepancies and process disturbances are accounted for in the proposed algorithm, and estimates of the process disturbance intensities can be obtained along with estimates of model parameters and states. Theoretical approximate confidence interval expressions for the parameters are developed. Through a practical two-phase nylon reactor example, as well as several simulation studies using stirred tank reactors, it is shown that the proposed parameter estimation algorithm can address difficulties such as: different types of measured responses with different levels of measurement noise, measurements taken at irregularly-spaced sampling times, unknown initial conditions for some state variables, unmeasured state variables, and unknown disturbances that enter the process and influence its future behaviour.
Download or read book Modelling and Parameter Estimation of Dynamic Systems written by J.R. Raol and published by IET. This book was released on 2004-08-13 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed examination of the estimation techniques and modeling problems. The theory is furnished with several illustrations and computer programs to promote better understanding of system modeling and parameter estimation.
Download or read book Parameter Estimation Techniques for Nonlinear Dynamic Models with Limited Data Process Disturbances and Modeling Errors written by Hadiseh Karimi and published by . This book was released on 2013 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis appropriate statistical methods to overcome two types of problems that occur during parameter estimation in chemical engineering systems are studied. The first problem is having too many parameters to estimate from limited available data, assuming that the model structure is correct, while the second problem involves estimating unmeasured disturbances, assuming that enough data are available for parameter estimation. In the first part of this thesis, a model is developed to predict rates of undesirable reactions during the finishing stage of nylon 66 production. This model has too many parameters to estimate (56 unknown parameters) and not having enough data to reliably estimating all of the parameters. Statistical techniques are used to determine that 43 of 56 parameters should be estimated. The proposed model matches the data well. In the second part of this thesis, techniques are proposed for estimating parameters in Stochastic Differential Equations (SDEs). SDEs are fundamental dynamic models that take into account process disturbances and model mismatch. Three new approximate maximum likelihood methods are developed for estimating parameters in SDE models. First, an Approximate Expectation Maximization (AEM) algorithm is developed for estimating model parameters and process disturbance intensities when measurement noise variance is known. Then, a Fully-Laplace Approximation Expectation Maximization (FLAEM) algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities and measurement noise variances in nonlinear SDEs. Finally, a Laplace Approximation Maximum Likelihood Estimation (LAMLE) algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear SDEs. The effectiveness of the proposed algorithms is compared with a maximum-likelihood based method. For the CSTR examples studied, the proposed algorithms provide more accurate estimates for the parameters. Additionally, it is shown that the performance of LAMLE is superior to the performance of FLAEM. SDE models and associated parameter estimates obtained using the proposed techniques will help engineers who implement on-line state estimation and process monitoring schemes.
Download or read book Identification of Dynamic Systems written by Rolf Isermann and published by Springer Science & Business Media. This book was released on 2010-11-22 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Measurement Data Modeling and Parameter Estimation written by Zhengming Wang and published by CRC Press. This book was released on 2011-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics. Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference: Introduces the basic concepts of measurements and errors Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data Covers Kalman filtering with colored noises and its applications Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors’ research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.
Download or read book Optimal Estimation of Dynamic Systems written by John L. Crassidis and published by CRC Press. This book was released on 2004-04-27 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation. Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals receiv
Download or read book Continuous time Block oriented Nonlinear Modeling with Complex Input Noise Structure written by Dongmei Zhai and published by . This book was released on 2005 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous-time closed-form algorithms to sinusoidal input changes are proposed and presented for single-input, single-output (SISO) Hammerstein and Wiener systems with the first-order, second-order, and second-order plus lead dynamics. By simulation on theoretical Hammerstein and Wiener systems, the predicted responses agree exactly with the true process values. They depend on only the most recent input change. The algorithms to SISO Hammerstein and Wiener systems can be conveniently extended to the multiple-input, multiple-output (MIMO) systems as shown by the two-input, two-output examples and demonstrated by the simulated seven-input, five-output continuous stirred tank reactor (CSTR). The predictions and the simulated theoretical responses agree exactly and the predicted multiple CSTR outputs are close to the true process outputs. The proposed algorithms can predict the responses closer to the true values when comparing with the piece-wise step input approximation of the sinusoidal input changes on a simulated MIMO CSTR. In addition, as the noisy process input could be decomposed as summation of sinusoidal signals imposed on a step input change; the proposed algorithms can be employed to predict outputs for the noisy process inputs once the decomposition is done and the predicted noisy process outputs are shown to be close to the true ones, and are much better than the predictions based on the perfect filtering of the input signals. The estimating equations based on the moment method are proposed for the Wiener dynamic process with stochastically correlated process input disturbances or noises and they work well for the parameter estimation. No one has ever proposed such method before. This approach has led to stable and robust estimators that have reasonable estimation errors and there is no need to measure the input disturbances or noises, or to calculate the time derivative of the observed output variable. Only the original process output observations over time are needed. The original model can be shifted to an approximate model under some conditions. This approximation is acceptable based on some analysis and derivation. The estimating equation methodology was shown to work well for the approximate model, while other existing methods do not work at all.
Download or read book Model Based Parameter Estimation written by Hans Georg Bock and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable efficient methods of applied mathematics and computer-based modeling can be to enhancing the quality of interdisciplinary research. The use of scientific computing to model, simulate, and optimize complex processes has become a standard methodology in many scientific fields, as well as in industry. Demonstrating that the use of state-of-the-art optimization techniques in a number of research areas has much potential for improvement, this book provides advanced numerical methods and the very latest results for the applications under consideration.
Download or read book Parameter Estimation in Nonlinear Dynamic Systems written by W. J. H. Stortelder and published by . This book was released on 1998 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Systems Models written by Josif A. Boguslavskiy and published by Springer. This book was released on 2015-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.
Download or read book Smoothing Filtering and Prediction written by Garry Einicke and published by BoD – Books on Demand. This book was released on 2012-02-24 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the classical smoothing, filtering and prediction techniques together with some more recently developed embellishments for improving performance within applications. It aims to present the subject in an accessible way, so that it can serve as a practical guide for undergraduates and newcomers to the field. The material is organised as a ten-lecture course. The foundations are laid in Chapters 1 and 2, which explain minimum-mean-square-error solution construction and asymptotic behaviour. Chapters 3 and 4 introduce continuous-time and discrete-time minimum-variance filtering. Generalisations for missing data, deterministic inputs, correlated noises, direct feedthrough terms, output estimation and equalisation are described. Chapter 5 simplifies the minimum-variance filtering results for steady-state problems. Observability, Riccati equation solution convergence, asymptotic stability and Wiener filter equivalence are discussed. Chapters 6 and 7 cover the subject of continuous-time and discrete-time smoothing. The main fixed-lag, fixed-point and fixed-interval smoother results are derived. It is shown that the minimum-variance fixed-interval smoother attains the best performance. Chapter 8 attends to parameter estimation. As the above-mentioned approaches all rely on knowledge of the underlying model parameters, maximum-likelihood techniques within expectation-maximisation algorithms for joint state and parameter estimation are described. Chapter 9 is concerned with robust techniques that accommodate uncertainties within problem specifications. An extra term within Riccati equations enables designers to trade-off average error and peak error performance. Chapter 10 rounds off the course by applying the afore-mentioned linear techniques to nonlinear estimation problems. It is demonstrated that step-wise linearisations can be used within predictors, filters and smoothers, albeit by forsaking optimal performance guarantees.
Download or read book Nonlinear Parameter Estimation written by Yonathan Bard and published by . This book was released on 1974 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problem formulation; Estimators and their properties; Methods of estimation; Computation of estimates; Interpretation of the estimates; Dynamic models; Some special problems; Design of experiments.
Download or read book World Congress on Neural Networks San Diego written by and published by Psychology Press. This book was released on 1994 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Canadian Journal of Chemical Engineering written by and published by . This book was released on 2008-08 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parameter Estimation and Adaptive Control for Nonlinear Servo Systems written by Shubo Wang and published by Elsevier. This book was released on 2024-02-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter Estimation and Adaptive Control for Nonlinear Servo Systems presents the latest advances in observer-based control design, focusing on adaptive control for nonlinear systems such as adaptive neural network control, adaptive parameter estimation, and system identification. This book offers an array of new real-world applications in the field. Written by eminent scientists in the field of control theory, this book covers the latest advances in observer-based control design. It provides fundamentals, algorithms, and it discusses key applications in the fields of power systems, robotics and mechatronics, flight and automotive systems. Presents a clear and concise introduction to the latest advances in parameter estimation and adaptive control with several concise applications for servo systems Covers a wide range of applications usually not found in similar books, such as power systems, robotics, mechatronics, aeronautics, and industrial systems Contains worked examples which make it ideal for advanced courses as well as for researchers starting to work in the field, particularly suitable for engineers wishing to enter the field quickly and efficiently
Download or read book Process Dynamics and Control written by Dale E. Seborg and published by John Wiley & Sons. This book was released on 2016-09-13 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new 4th edition of Seborg’s Process Dynamics Control provides full topical coverage for process control courses in the chemical engineering curriculum, emphasizing how process control and its related fields of process modeling and optimization are essential to the development of high-value products. A principal objective of this new edition is to describe modern techniques for control processes, with an emphasis on complex systems necessary to the development, design, and operation of modern processing plants. Control process instructors can cover the basic material while also having the flexibility to include advanced topics.
Download or read book World Congress on Neural Networks written by Paul Werbos and published by Routledge. This book was released on 2021-09-10 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: Centered around 20 major topic areas of both theoretical and practical importance, the World Congress on Neural Networks provides its registrants -- from a diverse background encompassing industry, academia, and government -- with the latest research and applications in the neural network field.
