Handbook of Probabilistic Models

Pijush Samui, Dieu Tien Bui, Subrata Chakraborty, Ravinesh Deo

• Publisher: Butterworth-Heinemann
• Year: 2019
• Print ISBN: 9780128165140
• eBook ISBN: 9780128165461
• Topic: Computer Science
• Subtopic: Data Modelling & Design
• Index: Computer Science

Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences.Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more.- Explains the application of advanced probabilistic models encompassing multidisciplinary research- Applies probabilistic modeling to emerging areas in engineering- Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems

Chapter 1

Fundamentals of reliability analysis

Achintya Haldar Department of Civil and Architectural Engineering and Mechanics, University of Arizona, Tucson, AZ, United States

Abstract

A brief history of the development of uncertainty quantifications, probabilistic models to consider risk-based analysis and design concepts, and their engineering applications are presented in this introductory chapter. The quantification of uncertainties in design variables and approaches used to propagate them from the variable to the system level are presented. The basic concept of risk evaluation in then presented. Because risk is always estimated corresponding to a performance function, how to generate them is discussed. The performance function can be explicit or implicit functions of design variables. Several risk evaluation procedures including simulation for both explicit and implicit performance functions are presented. Risk evaluation for correlated variables is also briefly discussed. The selection of computer programs for risk estimation is discussed. Education of the risk-based design concept can be at best categorized as nonuniform and limited only to graduate education in most cases. It cannot be overlooked any more.

Keywords

Correlated random variables; First-order reliability method; Functions of random variables; Implicit limit state function; Limit state function; Propagation of uncertainty; Reliability analysis; Set theory; Uncertainty analysis

1. Introduction

The presence of uncertainty in every aspect of engineering analysis and design has been under consideration over a long period of time. In fact, a famous mathematician Pierre-Simon Laplace (1749–1827) wrote “… the principal means of ascertaining truth – induction, and analogy – are based on probabilities; so that the entire system of human knowledge is connected with the theory (of probability). …. It leaves no arbitrariness in the choice of opinions and sides to be taken; and by its use can always be determined the most advantageous choice. Thereby it supplements most happily the ignorance and weakness of the human mind.” (Laplace, 1951).

The aforementioned statements by a well-known scholar clearly justify the need for this handbook. More recently, Freudenthal (1956), Ang and Tang (1975), Shinozuka (1983), and Haldar and Mahadevan (2000a) made similar comments justifying the needs for structural safety and reliability analyses. The related areas grew exp...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Contributors
• Chapter 1. Fundamentals of reliability analysis
• Chapter 2. Modeling wheat yield with data-intelligent algorithms: artificial neural network versus genetic programming and minimax probability machine regression
• Chapter 3. Monthly rainfall forecasting with Markov Chain Monte Carlo simulations integrated with statistical bivariate copulas
• Chapter 4. A model for quantitative fire risk assessment integrating agent-based model with automatic event tree analysis
• Chapter 5. Prediction capability of polynomial neural network for uncertain buckling behavior of sandwich plates
• Chapter 6. Development of copula-statistical drought prediction model using the Standardized Precipitation-Evapotranspiration Index
• Chapter 7. An efficient approximation-based robust design optimization framework for large-scale structural systems
• Chapter 8. Probabilistic seasonal rainfall forecasts using semiparametric d-vine copula-based quantile regression
• Chapter 9. Geostatistics: principles and methods
• Chapter 10. Adaptive H∞ Kalman filtering for stochastic systems with nonlinear uncertainties
• Chapter 11. R for lifetime data modeling via probability distributions
• Chapter 12. Probability-based approach for evaluating groundwater risk assessment in Sina basin, India
• Chapter 13. Novel concepts for reliability analysis of dynamic structural systems
• Chapter 14. Probabilistic neural networks: a brief overview of theory, implementation, and application
• Chapter 15. Design of experiments for uncertainty quantification based on polynomial chaos expansion metamodels
• Chapter 16. Stochastic response of primary–secondary coupled systems under uncertain ground excitation using generalized polynomial chaos method
• Chapter 17. Stochastic optimization: stochastic diffusion search algorithm
• Chapter 18. Resampling methods combined with Rao-Blackwellized Monte Carlo Data Association algorithm
• Chapter 19. Back-propagation neural network modeling on the load–settlement response of single piles
• Chapter 20. A Monte Carlo approach applied to sensitivity analysis of criteria impacts on solar PV site selection
• Chapter 21. Stochastic analysis basics and application of statistical linearization technique on a controlled system with nonlinear viscous dampers
• Chapter 22. A comparative assessment of ANN and PNN model for low-frequency stochastic free vibration analysis of composite plates
• Index