Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields.

Table of Contents

• Contributors
• Chapter 1: Fundamentals of reliability analysis
• Acknowledgments
• 1: Introduction
• 2: Important steps in reliability evaluation
• 3: Elements of set theory
• 4: Quantification of uncertainties in random variables
• 5: Transformation of uncertainty from parameter to the system level
• 6: Fundamentals of reliability analysis
• 7: Performance-based seismic design
• 8: Monte Carlo simulation
• 9: Alternative to simulations
• 10: Computer programs
• 11: Education
• Chapter 2: Modeling wheat yield with data-intelligent algorithms: artificial neural network versus genetic programming and minimax probability machine regression
• Acknowledgments
• 1: Introduction
• 2: Theoretical framework
• 3: Materials and method
• 4: Results
• 5: Discussion: limitations and opportunity for further research
• 6: Conclusion
• Chapter 3: Monthly rainfall forecasting with Markov Chain Monte Carlo simulations integrated with statistical bivariate copulas
• Acknowledgments
• 3.1: Introduction
• 3.2: Theoretical framework
• 3.3: Materials and method
• 3.4: Results
• 3.5: Discussion: limitations and opportunity for further research
• 3.6: Conclusion
• Chapter 4: A model for quantitative fire risk assessment integrating agent-based model with automatic event tree analysis
• 1: Introduction
• 2: Methodology
• 3: Case study
• 4: Results and discussion
• 5: Conclusions
• Chapter 5: Prediction capability of polynomial neural network for uncertain buckling behavior of sandwich plates
• 1: Introduction
• 2: Governing equations
• 3: Polynomial neural network
• 4: Results and discussion
• 5: Conclusion
• Chapter 6: Development of copula-statistical drought prediction model using the Standardized Precipitation-Evapotranspiration Index
• 1: Introduction
• 2: Materials and methods
• 3: Results and discussion
• 4: Further discussion
• 5: Summary
• Chapter 7: An efficient approximation-based robust design optimization framework for large-scale structural systems
• 1: Introduction
• 2: Surrogate-assisted robust design optimization
• 3: Proposed surrogate-assisted robust design optimization framework
• 4: Proposed surrogate models
• 5: Numerical validation
• 6: Summary and conclusions
• Appendix A. Description of the test problems investigated in Section 5.1
• Chapter 8: Probabilistic seasonal rainfall forecasts using semiparametric d-vine copula-based quantile regression
• Acknowledgments
• 1: Introduction
• 2: Data and methodology
• 3: Results
• 4: Discussion
• 5: Conclusions
• Chapter 9: Geostatistics: principles and methods
• 1: Introduction
• 2: Difference between geostatistics and classical statistics methods
• 3: Regionalized variables
• 4: Random variable
• 5: Variogram and semivariogram
• 6: Variogram specifications
• 7: Range
• 8: Sill
• 9: Nugget
• 10: Model fitting to empirical variogram
• 11: Models with sill
• 12: Spherical model
• 13: Exponential model
• 14: Gaussian model
• 15: Models without sill
• 16: Linear model
• 17: Parabolic model
• 18: The DeWijsian model
• 19: Selection of the theoretical variogram models
• 20: Locative continuity analysis of variogram
• 21: Anisotropy in a variogram
• 22: Geometric anisotropy
• 23: Zonal anisotropy
• 24: Geostatistics methods
• 25: Kriging Interpolation method
• 26: Kriging equations
• 27: Kriging types
• 28: Ordinary Kriging
• 29: Simple Kriging
• 30: Lognormal Kriging
• 31: Universal Kriging
• 32: Indicator Kriging
• 33: Disjunctive Kriging
• 34: Co-Kriging
• 35: Kriging parameters
• 36: Weights
• 37: Neighborhood
• 38: Search radius
• 39: Conclusions
• Chapter 10: Adaptive H∞ Kalman filtering for stochastic systems with nonlinear uncertainties
• Acknowledgments
• 1: Introduction
• 2: Problem: H∞ state estimation
• 3: Approach: adaptive H∞ filtering
• 4: Example: maneuvering target tracking in space
• 5: Numerical simulations
• 6: Conclusions
• 7: Appendix
• Chapter 11: R for lifetime data modeling via probability distributions
• 1: Introduction
• 2: R installations, help and advantages
• 3: Operators in R
• 4: Programming with user-defined functions
• 5: Loops and if/else statements in R
• 6: Curve plotting in R
• 7: Maximum likelihood estimation
• 8: Lifetime data modeling
• 9: Conclusion
• Chapter 12: Probability-based approach for evaluating groundwater risk assessment in Sina basin, India
• 1: Introduction
• 2: Study area
• 3: Methodology
• 4: Results and discussion
• 5: Conclusions
• Chapter 13: Novel concepts for reliability analysis of dynamic structural systems
• Acknowledgments
• 1: Introduction
• 2: Challenges and trends in risk evaluation
• 3: State-of-the-art in estimating risk of dynamic structural systems
• 4: A novel structural risk estimation procedure for dynamic loadings applied in time domain
• 5: Proposed novel concept for reliability analysis of dynamic structural systems
• 6: Accuracy in generating an IRS
• 7: Reliability estimation
• 8: Numerical examples—verifications and case studies
• 9: Multidisciplinary applications
• 10: Further improvements of Kriging method
• 11: Conclusions
• Chapter 14: Probabilistic neural networks: a brief overview of theory, implementation, and application
• 1: Introduction
• 2: Preliminary concepts: nonparametric estimation methods
• 3: Structure of probabilistic neural networks
• 4: Improving memory performance
• 5: Simple probabilistic neural network example in Python
• 6: Conclusions
• Chapter 15: Design of experiments for uncertainty quantification based on polynomial chaos expansion metamodels
• Chapter points
• 1: Introduction
• 2: Polynomial chaos expansions
• 3: Design of experiments
• 4: Examples
• 5: Summary
• Chapter 16: Stochastic response of primary–secondary coupled systems under uncertain ground excitation using generalized polynomial chaos method
• 1: Introduction
• 2: Details of the generalized polynomial chaos method
• 3: Deterministic model of base-isolated SDOF and base-isolated MDOF structure with secondary system
• 4: Stochastic structural dynamics using gPC method
• 5: Numerical study
• 6: Conclusions
• Chapter 17: Stochastic optimization stochastic diffusion search algorithm
• 1: Introduction
• 2: Stochastic diffusion search
• 3: Search and optimization
• 4: Markov chain model
• 5: Convergence of the stochastic diffusion search
• 6: Time complexity
• 7: Conclusions
• Chapter 18: Resampling methods combined with Rao-Blackwellized Monte Carlo Data Association algorithm
• 1: Introduction
• 2: Rao-Blackwellized Monte Carlo Data Association
• 3: Resampling techniques
• 4: Experiments and simulation results
• 5: Conclusions
• Chapter 19: Back-propagation neural network modeling on the load–settlement response of single piles
• Acknowledgments
• 1: Introduction
• 2: Back-propagation neural network methodologies
• 3: Development of the back-propagation neural network model
• 4: The optimal back-propagation neural network model
• 5: Modeling results
• 6: Parametric relative importance
• 7: Model interpretabilities
• 8: Summary and conclusion
• Appendix A BPNN pile settlement model
• Appendix B weights and bias values for BPNN pile settlement model
• Chapter 20: A Monte Carlo approach applied to sensitivity analysis of criteria impacts on solar PV site selection
• 1: Introduction
• 2: Literature review
• 3: Sensitivity analysis using Monte Carlo simulation
• 4: Conclusion
• Chapter 21: Stochastic analysis basics and application of statistical linearization technique on a controlled system with nonlinear viscous dampers
• 1: Introduction
• 2: Power spectral density
• 3: Input–output relationship
• 4: Monte Carlo simulation
• 5: Fluid viscous dampers
• 6: Conclusion
• Chapter 22: A comparative assessment of ANN and PNN model for low-frequency stochastic free vibration analysis of composite plates
• Acknowledgments
• 1: Introduction
• 2: Governing equations for composite plates
• 3: Artificial neural network
• 4: Polynomial neural network
• 5: Stochastic approach using neural network model
• 6: Results and discussion
• 7: Summary