Random Reliability Analysis of Gravity Retaining Wall Structural System

Modified subset simulation method for reliability analysis of structural systems

In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from exact (or local) and averaged (or global) response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior.

This paper outlines an improved simulation method for a time-dependent reliability analysis of structural systems subjected to stochastic loads. Strengths of structural elements are assumed to degrade with time proportionally during the life cycle of the structural system, and stochastic load events are modeled as Poisson processes. The structural failure probabilities are estimated through the life cycle simulation, in which the directional simulation method is applied just to sample random load variables to execute each life cycle simulation efficiently. Numerical examples are presented and results are compared with those obtained by the crude Monte Carlo simulation to show the effectiveness of the proposed method. It is shown that the proposed method is effective for the assessment of the time-dependent failure probability of structural systems.

Ordered fuzzy random variables: Definition and the concept of normality

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables.

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

In this paper, several portfolio selection problems with normal mixture distributions including fuzziness are proposed. Until now, many researchers have proposed portfolio models based on the stochastic approach, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, the model including normal mixture distributions with fuzzy numbers has not been proposed yet. Our proposed problems are not well-defined problems due to randomness and fuzziness. Therefore, setting some criterions and introducing chance constraints, main problems are transformed into deterministic programming problems. Finally, we construct a solution method to obtain a global optimal solution of the problem.

Computer simulation and an approximate method were used to study the lifetime behavior of wood floor and roof systems. A simplified beam-spring model was used to model the systems. In this study, two-way action of the sheathing; partially composite action between the sheathing, connectors, and lumber members; the random mechanical properties of the lumber members; the random postyield properties of the partially composite members; and the cumulative damage of wood were included. The approximate method was the first-order reliability method incorporated with the distributions of order statistics. System reliability analysis, including system effects and load duration effects, is presented in this paper. System factors for load and resistance factor design (LRFD) as they are related to component properties, mostly the postyield properties of partially composite members and variability of lumber modulus of rupture (MOR), are determined. The results herein apply only to uniformly loaded systems simply supported at two edges.

Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

A sensitivity analysis estimates the effect of the change in the uncertain variable parameter on the probability of the structural failure. A novel fuzzy random reliability sensitivity measure of the failure probability is proposed to consider the effect of the epistemic and aleatory uncertainties. The uncertainties of the engineering variables are modeled as fuzzy random variables. Fuzzy quantities are treated using the y-cut approach. In fact, the fuzzy variables are transformed into the interval variables using the y-cut approach. Genetic approach considers different possible combinations within the search domain (y-cut) and calculates the parameter sensitivities for each of the combinations.

Reliability analysis of nonlinear structural systems using response surface method

Chatter reliability prediction of turning process system with uncertainties

The present paper focuses on reliability analysis of structural systems under ground motion acceleration taking into account the inherent random nature of the excitation as well as epistemic uncertainties affecting the definition of its spectrum. Specifically, seismic excitation is modelled as a zero-mean stationary Gaussian random process fully characterized by an imprecise power spectral density (PSD) function i.e. with interval parameters. The ranges of such interval parameters are determined by analysing a large set of accelerograms recorded on rigid soil deposits. To discard outliers, the Chauvenet’s Criterion is applied iteratively. The proposed imprecise PSD function may be viewed as representative of the actual accelerograms recorded on rigid soil deposits. Reliability assessment is carried out by incorporating the imprecise PSD function of ground motion acceleration into the formulation of the classical first-passage problem using Vanmarcke’s failure criterion. Due to imprecision of the excitation, the reliability function and the fractile of order p of the selected extreme value response process turn out to have an interval nature. Thus, the aim of reliability analysis is the evaluation of the bounds of such functions which define the range of structural performance. Numerical results show that neglecting imprecision of the PSD may lead to significant overestimation of the safety level.

System and measurement uncertainties play a key role in finding the reliability of complex and safety-critical structural systems such as buildings and bridges. Current mainstream techniques in structural reliability analysis use an iterative first-order reliability method that performs an indirect uncertainty evaluation by finding the most probable failure point. However, such an approach could lead to high computational time due to slower convergence, and in some cases, poor convergence that leads to unreliable results. In order to address the shortcomings, this paper applies a new high-order moment propagation technique (that was initially developed for the measurement uncertainty analysis) to structural reliability analysis problems aiming to obtain results that are simultaneously accurate and computational efficient. The proposed approach was implemented on a three-story elastic frame structure, and the presented results prove that the application of a technique from the field of measurement uncertainly can indeed be applied to complex problems in the structural reliability analysis in order to reduce the trade-off between accuracy and computational efficiency.