Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometric Reliability Index Generalized Reliability Index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis Introduction to Process Descriptions.

https://chodor-projekt.net/wp-content/uploads/BiNSK/Literatura/Dilevsen,Madsen,%20Structural%20Reliability%20Methods%20(2007).pdf

Structural Reliability Methods

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

The problem of deriving approximations for multinormal integrals is examined using results of asymptotic analysis. The boundary of the integration domain given by g(x¯)=0 is simplified by replacing g(x¯) by its Taylor expansion at the points on the boundary with minimal distance to the origin. Two approximations which are obtained by using a linear or quadratic Taylor expansion are compared. It is shown that, applying a quadratic Taylor expansion, an asymptotic approximation for multinormal integrals can be obtained, whereas using linear approximations large relative errors may occur.

Asymptotic approximations for multinormal integrals

A comprehensive framework is set forth for the analysis of structural reliability under incomplete probability information. Under stipulated requirements of consistency, invariance, operability, and simplicity, a method is developed to incorporate in the reliability analysis incomplete probability information on random variables, including moments, bounds, marginal distributions, and partial joint distributions. The method is consistent with the philosophy of Ditlevsen’s generalized reliability index and complements existing second-moment and full-distribution structural reliability theories.

Structural reliability under incomplete probability information

Many engineering applications are characterized by implicit response functions that are expensive to evaluate and sometimes nonlinear in their behavior, making reliability analysis difficult. This paper develops an efficient reliability analysis method that accurately characterizes the limit state throughout the random variable space. The method begins with a Gaussian process model built from a very small number of samples, and then adaptively chooses where to generate subsequent samples to ensure that the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex and nonlinear limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e., in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally efficient even for expensive response functions. This new method is applied to a collection of example problems including one that analyzes the reliability of a microelectromechanical system device that current available methods have difficulty solving either accurately or efficiently.

Bernd Flessler

Papers

Structural reliability under combined random load sequences