Model Parametric Sensitivity Analysis and Nonlinear Parameter Estimation
| Author | : Malamas Caracotsios |
| Publisher | : |
| Total Pages | : 488 |
| Release | : 1986 |
| Genre | : Parameter estimation |
| ISBN | : |
Model Parametric Sensitivity Analysis And Nonlinear Parameter Estimation
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Online Optimization of Large Scale Systems
| Author | : Martin Grötschel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 789 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662043319 |
In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g. , problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly.
Global Sensitivity Analysis
| Author | : Andrea Saltelli |
| Publisher | : John Wiley & Sons |
| Total Pages | : 304 |
| Release | : 2008-02-28 |
| Genre | : Mathematics |
| ISBN | : 9780470725177 |
Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard. Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications. The book: Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials. Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls. Features numerous exercises and solved problems to help illustrate the applications. Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds. Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.
Nonlinear Sensitivity Analysis of Multi-Parameter Model Systems
| Author | : R. I. Cukier |
| Publisher | : |
| Total Pages | : 118 |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
Large sets of coupled, nonlinear equations arise in a number of disciplines in connection with computer based models of physical, social and economic processes. Solutions for such large systems of equations must be effected by means of digital computers using appropriately designed codes. This paper addresses itself to the critically important problem of how sensitive the solutions are to variations of, or inherent uncertainties in, the parameters of the equation set. We review here, and also present further developments, of our statistical method of sensitivity analysis. The sensitivity analysis presented here is nonlinear and thus permits one to study the effects of large deviations from the nominal parameter values. In addition, since all parameters are varied simultaneously, one can explore regions of parameter space where several parameters deviate simultaneously from their nominal values. Developed her eis a theory of a method of sensitivity analysis, then detail the method of implementation and finally present several examples of its use to date.
Model Calibration and Parameter Estimation
| Author | : Ne-Zheng Sun |
| Publisher | : Springer |
| Total Pages | : 638 |
| Release | : 2015-07-01 |
| Genre | : Mathematics |
| ISBN | : 1493923234 |
This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.
Sensitivity Analysis in Practice
| Author | : Andrea Saltelli |
| Publisher | : John Wiley & Sons |
| Total Pages | : 232 |
| Release | : 2004-07-16 |
| Genre | : Mathematics |
| ISBN | : 047087094X |
Sensitivity analysis should be considered a pre-requisite for statistical model building in any scientific discipline where modelling takes place. For a non-expert, choosing the method of analysis for their model is complex, and depends on a number of factors. This book guides the non-expert through their problem in order to enable them to choose and apply the most appropriate method. It offers a review of the state-of-the-art in sensitivity analysis, and is suitable for a wide range of practitioners. It is focussed on the use of SIMLAB – a widely distributed freely-available sensitivity analysis software package developed by the authors – for solving problems in sensitivity analysis of statistical models. Other key features: Provides an accessible overview of the current most widely used methods for sensitivity analysis. Opens with a detailed worked example to explain the motivation behind the book. Includes a range of examples to help illustrate the concepts discussed. Focuses on implementation of the methods in the software SIMLAB - a freely-available sensitivity analysis software package developed by the authors. Contains a large number of references to sources for further reading. Authored by the leading authorities on sensitivity analysis.
Online Parameter Identification for Optimal Feedback Control of Nonlinear Dynamical Systems
| Author | : Margareta Runge |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2024 |
| Genre | : |
| ISBN | : |
This research aims to enhance current methods for the optimal feedback control of complex nonlinear dynamical systems via online parameter identifications. Accurate knowledge of the system parameters is essential in numerous practical applications to ensure effective control. A considerable number of advanced control algorithms use model-based approaches. However, the model parameters may often be unknown or subject to change over time. This could result in deviations from the feedback control objective, increased expected costs, and even divergence of the controller. The main objective of this thesis is to develop a combined online parameter identification and model-based controller approach that allows continuously estimating the model parameters of a nonlinear system. The available real-time measurements of the system are used to compute an approximation of the searched parameters. This repeated parameter estimation enables the control algorithm to adapt to the changing system dynamics and maintain optimal control accuracy. This study investigates three approaches. First, a coupled algorithm is developed that employs parameter identifications during operation to adapt a linear quadratic regulator using techniques from parametric sensitivity analysis. Additionally, an approach is presented that also examines the information quality in the data used to predict the probability of success of the parameter estimation. An adaptive control algorithm using nonlinear model predictive control (NMPC) and online parameter identification is proposed as a third alternative. All proposed techniques rely on highly efficient numerical methods for solving nonlinear optimization problems (NLP) and the potential to transfer related problems from optimal control into an NLP by discretization. The proposed approaches are extensively evaluated by conducting simulations and comparing them to the existing standard control methods.
Parametric Sensitivity Analysis of Stochastic Reaction Networks
| Author | : Ting Wang |
| Publisher | : |
| Total Pages | : 210 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Reaction networks are systems consisting of several species interacting with each other through a set of predefined reaction channels.Models of real world reaction systems often contain several parameters which play a significant role in determining the system's dynamics. Therefore, parametric sensitivity analysis is an essential tool for the modeling and parameter estimation process. Due to the complex and random nature of the reaction systems, among all approaches for sensitivity analysis, Monte Carlo simulation is the most suitable for the parametric sensitivity analysis because its complexity does not grow dramatically as the problem dimension grows. Most Monte Carlo methods for sensitivity analysis can be classified into three categories, the pathwise derivative (PD), the finite difference (FD) and the Girsanov transformation (GT). Comparisons of these methods for specific examples have been done by many researchers, which showed that when applicable, the PD method and FD method tend to outperform the GT method. However, to the best of our knowledge, no existing literature studies these observations from a theoretical point of view. In this thesis, we provide a theoretical justification for these observations in terms of system size asymptotic analysis. We also examine our result by testing several numerical examples. Other than the analysis for the efficiency of these Monte Carlo estimators, we also provide some sufficient conditions which guarantee the validity of the GT method. Finally, for an ergodic system, there exists a steady state distribution and hence it is reasonable for us to consider the steady state sensitivity estimation problem. We establish an asymptotic correlation result and use this result to justify the ensemble-averaged correlation function method introduced in the literature.
Sensitivity Analysis for Parametric Non-Linear Programming Using Penalty Methods
| Author | : Robert L. Armacost |
| Publisher | : |
| Total Pages | : 44 |
| Release | : 1976 |
| Genre | : Inventory control |
| ISBN | : |
Recently, it has been shown that a class of penalty function algorithms can readily be adapted to generate sensitivity analysis information for a large class of parametric nonlinear programming problems. In particular, estimates of the partial derivatives (with respect to the problem parameters) of the components of a solution vector and the optimal value function have been successfully calculated for a number of nontrivial examples. The approach has been implemented using the well known Sequential Unconstrained Minimization Technique (SUMT) computer program. This paper, a continuation and amplification of a recent paper by Armacost, gives a detailed summary of the significant underlying theoretical results, reviews recent additions to the computer program that include Lagrange multiplier sensitivity calculations, and elaborates on the kind of information that can be generated by further analyzing and interpreting results obtained in applying the techique to a well known inventory model. (Author).
