Mathematical Models for Structural Reliability Analysis

Stochastic Process Models (F. Casciati and M. Di Paola)IntroductionThe Orthogonal-Increment ModelThe Correlation-Stationary Model Time-Invariant Linear Systems Models of Common UseThe Evolutionary Model Time-Invariant Linear SystemsMarkov Processes A Model of Common Use Ito Stochastic Differential Equation Some Examples Approximation of Mechanical Processes: Physical versus Ito EquationsThe Random Pulse Train Model The Delta-Correlated Model Fokker Planck and Moment Equations for Parametric Delta Correlated Input Quasi-Linear Systems Simulation of Delta Correlated Processes and Response Simulation of Normal White Noise Input and Response Orthogonal-Increment Model for Delta Correlated ProcessesMultidegree-of-Freedom Systems Under Parametric Delta Correlated Input Moment Equation Approach for MDOF Systems Simulation of Multivariate Delta Correlated Processes and ResponseConclusions and ReferencesAppendix Characterization of Random Variables Joint Characterization of Random Variables Operation on Stochastic Processes Kronecker Algebra: Some FundamentalsDimension Reduction and Discretization in Stochastic Problems by Regression Method (O. Ditlevsen)IntroductionLinear RegressionNormal DistributionNon-Gaussian Distributions and Linear RegressionMarginally Transformed Gaussian Processes and FieldsDiscretized Fields Defined by Linear Regression on a Finite Set of Field ValuesDiscretization Defined by Linear Regression on a Finite Set of Linear FunctionalsPoisson Load Field ExampleStochastic Finite Element Methods and Reliability CalculationsClassical versus Statistical-Stochastic Interpolation Formulated on the Basis of the Principle of Maximum LikelihoodComputational Practicability of the Statistical-Stochastic Interpolation MethodField Modeling on the Basis of Measured Noisy DataDiscretization Defined by L