B. Gaspar

Adaptive surrogate model with active refinement combining Kriging and a trust region method

The reliability analysis of engineering structural systems with limit state functions defined implicitly by time-consuming numerical models (e.g. finite element analysis structural models) requires the use of efficient solution strategies in order to keep the required computational costs at acceptable levels. In this paper, an adaptive Kriging surrogate model with active refinement is proposed to solve component reliability assessment problems (i.e. involving one single design point) with nonlinear and time-consuming implicit limit state functions with a moderate number of input basic random variables. The proposed model, in the first stage, uses an adaptive Kriging-based trust region method to search for the design point in the standard Gaussian space and predict an initial failure probability based on the first-order reliability method as well as sensitivity factors for the input basic random variables. This initial prediction is then verified or improved efficiently in a second stage using Monte Carlo simulation with importance sampling based on a Kriging surrogate model defined iteratively around the design point using an active refinement algorithm. A convergence criterion that detects the stabilization of the failure probability prediction during the active refinement process is also proposed and implemented. The usefulness of the proposed adaptive Kriging surrogate model in terms of accuracy and efficiency for reliability assessment of engineering structural systems is shown in the paper with two relevant numerical examples, involving a highly nonlinear analytical limit state function in two-dimensions and an advanced nonlinear finite element analysis structural model in a larger dimensional space.

System Reliability Analysis by Monte Carlo Based Method and Finite Element Structural Models

In principle, the reliability of complex structural systems can be accurately predicted by Monte Carlo simulation. This method has several attractive features for structural system reliability, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. However, the computational cost involved in the simulation may be prohibitive for highly reliable structural systems. In this paper a new Monte Carlo based method recently proposed for system reliability estimation that aims at reducing the computational cost is applied. It has been shown that the method provides good estimates for the system failure probability with reduced computational cost. In a numerical example the usefulness and efficiency of the method to estimate the reliability of a system represented by a nonlinear finite element structural model is presented. To reduce the computational cost involved in the nonlinear finite element analysis the method is combined with a response surface model. [DOI: 10.1115/1.4025871]

Reliability analysis of plate elements under uniaxial compression using an adaptive response surface approach

This paper presents a reliability analysis of plate elements under uniaxial compression using an adaptive response surface approach. The limit state considered is the buckling collapse failure of the plate elements computed through nonlinear finite element analysis. A response surface model based on second-order polynomials is combined with the first-order reliability method in order to compute reliability estimates at moderate computational time. An adaptive interpolation scheme combined with a Latin hypercube sampling technique is used to define the response surface model iteratively in the region of the basic random variables space that most contributes to the failure probability. Plate elements typical of the deck structure of double hull tankers with random thickness, material properties and amplitude of weld-induced initial distortions are used as case study. The uniaxial compressive load is defined considering extreme values in a reference time period of one year of operation of the ship. The effect of considering constrained or restrained boundary conditions along the longitudinal plate edges as well as corroded plate elements on the reliability analysis results is determined. Sensitivity analyses are performed to identify the relative contribution and importance of each basic random variable to the estimated reliability indices.

Efficient System Reliability Analysis by Finite Element Structural Models

In principle, the reliability of complex structural systems can be accurately predicted through Monte Carlo simulation. This method has several attractive features for structural system reliability, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. However, the computational cost involved in the simulation may be prohibitive for highly reliable structural systems. In this study a new Monte Carlo based method recently proposed for system reliability estimation that aims at reducing the computational cost is applied. It has been shown that the method provides good estimates for the system failure probability with reduced computational cost. By a numerical example the usefulness and efficiency of the method to estimate the reliability of a system represented by a nonlinear finite element structural model is demonstrated. To reduce the computational cost involved in the nonlinear finite element analysis the method is combined with a response surface model.Copyright