Efficient Reliability Method Research Articles

Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables

SummaryIn contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd.

An efficient reliability method combining adaptive importance sampling and Kriging metamodel

In practice, there are many engineering problems characterized by complex implicit performance functions. Accurate reliability assessment for these problems usually requires very time-consuming computation, and sometimes it is unacceptable. In order to reduce the computational load, this paper proposes an efficient reliability method combining adaptive importance sampling and Kriging model based on the active learning mechanism. It inherits the superiorities of Kriging metamodel, adaptive importance sampling and active learning mechanism, and enables only evaluating the interested samples in actual performance function. The proposed method avoids a large number of time-consuming evaluation processes, and the important samples are mainly predicted by a well-constructed Kriging metamodel, thus the calculating efficiency is increased significantly. Several examples are given as validations, and results show that the proposed method has great advantages in the aspect of both efficiency and accuracy.

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.

An efficient reliability method for probabilistic H-infinity robust control of uncertain linear dynamic systems

Achieving balance between robustness and performance is always a fundamental challenge we are faced with in control design of systems in the presence of uncertainties. H∞ robust control theory has been extensively used to deal with the problems of robust stabilization and disturbance attenuation of uncertain systems. However, in traditional H∞ robust control, the most frequently used method for dealing with uncertainties is adopting the assumption of norm-bounded perturbations of arbitrary structure about a nominal plant and the design techniques are based on the deterministic worst-case scenarios that may never occur in a particular control system and thus often led to over-conservative results. In this paper we focus on developing a reliability method for probabilistic H∞ robust control of linear uncertain systems by describing the uncertain parameters as random variables. A new efficient reliability method for robust control of dynamic systems with probabilistic parametric uncertainties is presented systematically. Robust control design is carried out by solving a reliability-based optimization problem where the disturbance attenuation and control cost are minimized under the condition that reliability requirement is satisfied. One of the advantages of the presented reliability method is that it can be used directly for robust control design of parametric uncertain systems. Another advantage of the presented method is that it makes it possible to consider the factors such as system performance, control cost, and reliability simultaneously in an integrated framework and provides an essential basis for the coordination and tradeoffs between these important factors in control design of uncertain systems. Compared to traditional H∞ robust control, the presented method is less-conservative and more reasonable for dealing with probabilistic uncertainties. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. Two numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.

Realistic risk assessment of axially loaded pile–soil system using a hybrid reliability method

The behaviour of an axially loaded pile embedded in a non-homogeneous soil deposit considering the pile–soil nonlinear interaction effect is realistically evaluated, and a new efficient and accurate hybrid reliability method is proposed for estimating the corresponding risk. The complicated problem is first deterministically formulated and then the uncertainties associated with the various design variables are considered explicitly. The hybrid reliability approach intelligently integrates the concepts of the response surface method, the finite difference method, the first-order reliability method, and an iterative linear interpolation scheme. The soil around the pile is represented by a series of springs. The system is expected to represent a realistic and efficient load-transfer mechanism. The soil–pile dual system is then deterministically analysed using the finite difference method. Uncertainties associated with load conditions, material and sectional properties of the pile and non-homogeneous soil properties are then incorporated in to the deterministic formulation resulting in the hybrid reliability approach. The risks corresponding to both service ability and strength limit states are estimated. With the help of an illustrative example, the applicability, accuracy and efficiency of the proposed algorithm in the safety assessment of axially loaded pile–soil systems are demonstrated. The reliability evaluation procedure is verified using the Monte Carlo simulation technique.

Risk Assessment of Axially Loaded Single Piles using RSM-based Reliability Method

An efficient and accurate hybrid reliability method is developed to quantify the risk of an axially loaded pile considering pile-soil interaction behavior and uncertainties in various design variables. It intelligently integrates the concepts of the response surface method, the finite difference method, the first-order reliability method, and the iterative linear interpolation scheme. Uncertainties associated with load conditions, material and section properties of the pile and soil properties are explicitly considered. The algorithm is verified using the Monte Carlo Simulation technique.

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

An approach for the time-dependent reliability analysis of reinforced concrete (RC) columns considering the correlation between the axial load and the bending moment or the uncertainty in the load eccentricity is presented. The approach recursively uses the efficient first-order reliability method for the time-dependent reliability analysis. The proposed approach is more efficient than the ones used in the literature for the reliability analysis of RC columns. The proposed approach is used to carry out sensitivity analyses of the reliability of short RC columns to the time-dependent live load effects and to the correlation between the axial load and the bending moment. Results of the analyses suggest that the reliability of RC columns can be sensitive to the correlation between the axial load and the bending moment due to live load. The differences between the reliability indices obtained by considering the live load modeled as a pulse process and as an extreme variate can be large.Key words: reliability, load, time-dependent, time-independent, uncertainty, correlation, concrete, reinforcement, column.

Assessing uncertainty in subsurface solute transport: efficient first-order reliability methods

Due to the heterogeneity of natural groundwater systems, any quantitative description of aquifer hydraulic properties is subject to uncertainty. Consequently, prediction of groundwater contaminant transport is also subject to uncertainty. Stochastic approaches to transport simulation quantify this uncertainty in terms of random variables and processes. An important practical consideration in the application of such methods is their large computational cost. In recent years the first-order reliability method (FORM) has been introduced as a possible technique for obtaining stochastic results with low computational expense. Specifically, the implementation of FORM known as advanced FORM (AFORM) has been shown to produce reasonably accurate results when applied to simple problems. However, recently published results indicate that the computational burden of AFORM can equal, or even exceed, that of Monte Carlo simulation when applied to groundwater contamination problems with a large number of variables. If FORM is to be a viable alternative, the computational costs of the method must be lowered. In this work we propose two alternative implementations of FORM that have a higher computational efficiency. The primary numerical difficulty that arises in AFORM is locating the linearization point, a procedure that requires the solution of a non-linearly constrained optimization problem. We minimize this difficulty by zoning spatially variable aquifer parameters and by defining a new linearization point that can be found more easily. The new approaches are shown to produce results that are comparable to those obtained with AFORM when applied to a one-dimensional transport problem. Future work will be aimed at generalizing the procedures described herein.

Linearized mechanical model to evaluate reliability of offshore structures

In this paper, an efficient reliability method is proposed for space framed structures. It is based on linearization of the mechanical behaviour. The elastic-plastic behaviour of material is piecewise linearized by a plastic criterion taking into account the interaction of internal forces. The buckling effect is represented by using an equivalent negative strain-hardening, introduced to the material model. In order to identify the negative strain-hardening parameters, a powerful method is given. The proposed model also takes into account the unloading of members and the behaviour at criterion singular points. The structural reliability is estimated by the safety margin concepts. Numerical examples show the high performance of the model, verified by a good precision and a very low computational time.