Samui P., Bui D.T., Chakraborty S., Deo R.C. (eds.) Handbook of Probabilistic Models

New York: Butterworth-Heinemann, 2020. — 561 p.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.Important steps in reliability evaluation
Elements of set theory
Quantification of uncertainties in random variables
Transformation of uncertainty from parameter to the system level
Exact solution
Partial Solutions
Approximate solutions—general function of multiple RVs
Regression analysis
Simple linear regression
Fundamentals of reliability analysis
Limit state equations or functions
Serviceability limit state equation or function
Reliability evaluation methods
Advanced FOSM for statistically independent normal variables (Hasofer–Lind method)
First-order reliability method with two-parameter distributions
Examples
Reliability analysis with correlated variables
Reliability analysis for implicit limit state analysis
Performance-based seismic design
Monte Carlo simulation
Computer programsTheoretical framework
Artificial neural network
Minimax probability machine regression
Genetic programming
Study region
Development of data-intelligent models
Model performance evaluation criteria
Results
Discussion: limitations and opportunity for further researchMarkov Chain Monte Carlo–based statistical copula models
Rainfall data set and study region
Model performance criteria
Results
Discussion: limitations and opportunity for further researchMethodology
Deterministic model
Probabilistic model and data—@RISK
Agent-based model
Rules governing an agent's interactions for the present case
Generating automatic event trees—general rules
Case study
Results and discussion
Property damage due to fire
Varying reliability values of fire safety systems
The effects of different fire growth rate
ConclusionsFurther readingGoverning equations
Polynomial neural network
Results and discussionStandardized Precipitation-Evapotranspiration Index
Copula theory
Vine copula
Joint return periods
Study area and data
Characterization of drought properties
Copula-statistical model development
Selection of copulae
Dependence modeling
Applications on the Standardized Precipitation-Evapotranspiration Index and climate indices
Applications on drought properties and climate mode indices
Applications on drought properties
Further discussionRobust design optimization
Proposed surrogate-assisted robust design optimization framework
Integrating high-dimensional model representation and Polynomial Chaos Expansion (PCE) into Kriging trend
Sparse recovery using Bayesian learning
Sparse recovery using accelerated Bayesian learning
Example : Welded beam design
Example : Multiobjective robust design optimization of a vibrating platform
Problem type : finite element model of a building frame
Summary and conclusions
A Example : Vibrating platformCumulative rainfall index
Copula theorem
Semiparametric d-vine quantile regression
Linear quantile regression
Climate–rainfall relationships
Rainfall quantile forecast
Discussion
ConclusionsDifference between geostatistics and classical statistics methods
Regionalized variables
Variogram and semivariogram
Range
Spherical model
Gaussian model
Selection of the theoretical variogram models
Geometric anisotropy
Kriging equations
Ordinary Kriging
Disjunctive Kriging
NeighborhoodStandard H∞ filter
Conservativeness and optimization
Switched H∞ Kalman filter
Optimal-switched H∞ Kalman filter
Orbital relative motion model
Numerical simulations
Conclusions
AppendixR installations, help and advantages
Operators in R
Data entry in R
Remarks
Loops and if/else statements in R
Curve plotting in R
Maximum likelihood estimation
Maximum likelihood estimate for censored data
The GILD likelihoods and survival estimates
Complete case: maximum flood levels data
Censored case: head and neck cancer dataMethodology
Results and discussionChallenges and trends in risk evaluation
State-of-the-art in estimating risk of dynamic structural systems
A novel structural risk estimation procedure for dynamic loadings applied in time domain
Selection of center point
Factorial design schemes
Reliability estimation using IRS and AFD
Total Number of Deterministic Analyses
Accuracy in generating an IRS
Moving least squares method
Kriging method
Performance levels
Incorporation of uncertainties
Example —verification on AFD—two-Story steel frame
A case study to document the capabilities of the proposed reliability evaluation concept—failure of -Story steel frame lo
Example —implementation of the PBSD concept for - and -Story steel frames
Reliability of electronic packaging—thermomechanical loading
Further improvements of Kriging methodParzen windows
Potential functions
Structure of probabilistic neural networks
Improving memory performance
Feature reduction using principal component analysis
Pattern layer size reduction using clustering
Simple probabilistic neural network example in PythonBasic formulation
Polynomial chaos expansion model accuracy
Monte Carlo sampling
Importance sampling
Analytical problem: Ishigami function
Truss structure
Tensile membrane structureIntroduction to stochastic analysis of structural systems
Forward propagation of uncertainty—an introduction to different approaches
Introduction to multiply supported secondary systems
Details of the generalized polynomial chaos method
Details of orthogonal basis
Convergence of PC expansion
Normal distribution and Hermite polynomial expansion
PC expansion for multidimensional random variable
Intrusive methods—stochastic Galerkin
Discrete projection
Postprocessing of polynomial chaos expansion
Sensitivity analysis—Sobol’ indices
Reliability analysis
Deterministic model of base-isolated SDOF and base-isolated MDOF structure with secondary system
Details of fixed-base primary structure with fixed-base secondary system and base-isolated primary structure with fixed-bas
Fixed-base primary structure with secondary system
Details of laminated rubber bearing base-isolation system
PC expansion of time-independent input uncertainties
PC expansions of time-dependant QoI
Selection of collocation points
Postprocessing of results
Base-isolated SDOF system with random inputs
Stochastic time history response of base-isolated SDOF
Probability measures of QoI
Deterministic response of fixed-base primary structure with fixed-base secondary system and base-isolated primary structure
Stochastic response of fixed-base primary structure with fixed-base secondary system and base-isolated primary structure wi
Stochastic response of the primary structure and secondary system
Probability measures of QoI
Sensitivity analysis
Computing probability of failure from PC expansion
ConclusionsSearch and optimization
Markov chain model
Convergence of the stochastic diffusion search
Time complexity
ConclusionsRao-Blackwellized Monte Carlo Data Association
Resampling techniques
Stratified/systematic resampling method
Residual resampling (remainder resampling)
Residual systematic resampling technique
Dynamic threshold
Fixed threshold
Tracking unknown number of targets in D
Simulation results
ConclusionsBack-propagation neural network methodologies
Development of the back-propagation neural network model
Back-propagation neural network model architecture
Modeling results
Model interpretabilities
Appendix A BPNN pile settlement model
Appendix B weights and bias values for BPNN pile settlement modelCriteria and constraints
Methods in solar site selection
Monte Carlo simulation approachPower spectral density
The autocorrelation function
Ergodicity
Input–output relationship
Example
Monte Carlo simulation
Wind sample generation
Fluid viscous dampers
Statistical linearization techniqueGoverning equations for composite plates
Artificial neural network
Polynomial neural network
Stochastic approach using neural network model
Results and discussion