Modified subset simulation method for reliability analysis of structural systems

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.

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

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.

Reliability analysis of nonlinear structural systems using response surface method

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.

According to present deficiency of gravity retaining wall design method and considering the fuzzy uncertainties of the parameters of stochastic variables, first-order second-moment method (FOSM) is adopted to set up fuzzy random reliability analyzing model. By using decomposing theorem and by introducing cut set, fuzzy numbers were convened into a series of interval numbers and fuzzy random reliability computing technology was received. The major instability modes of gravity retaining walls are overturning and sliding. Two structural performance functions against overturning and sliding of gravity retaining walls were established and the fuzzy random variables were confirmed. Two kinds of invalid modes are calculated separately by the use of fuzzy random reliability computation method, which two fuzzy random reliability indexes and corresponding failure probabilities are obtained. Comparing the result of computation method with that of related literature, it is shows that obvious differences are between them. It is pointed out that structural performance function Z of the gravity retaining wall is assumed as normal distribution in related literature, which contributing to errors in the probability density function f(Z) in this treatment. The calculated results of fuzzy random reliability by adopting cut set way are conformed to reality better.

Assessing small failure probabilities by combined subset simulation and Support Vector Machines

In the practical engineering, to solve the small failure probabilities with correlated high-dimensional variables, the subset simulation (SS) is combined together with the Monte Carlo and importance sampling (IS) method. The samples from the probability density functions (PDF) of the importance sampling are used to construct the intermediate failure events, by which the small failure probabilities are turned into a Markov chain (MC), which is a continuous product made of a series large failure probability or conditional failure probability (CFP) which is easily answered, on which the structural reliability can be efficiently simulated by directly obtaining the samples with correlated ones. Finally, the 3 planet carriers of 3 grade planetary reducers in shield tunneling machine(STM) are as examples to check the algorithm above, the results show that the SS of the IS with correlated variables can highly simulate failure probability.

A method is presented for the evaluation of the seismic reliability function of realistic structural systems. The method is based on a preliminary simulation involving three-dimensional nonlinear time history analysis of the soil-interface-building system. The design procedure is performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of system reliability problem with correlated demands and capacities. The Structural behavior is evaluated by means of the methodology of Performance-Based Seismic Design (PBSD). This study has taken into account the stochastic nature of the spatial ground motion in Tbilisi region. The method is demonstrated with an application to a 3D RC Buildings subjected to seismic excitation for the specified hazard at the site. The developed method and obtained results can be used in seismic risk study for new buildings of examined type under design, as well as for existing RC buildings of old generation for future seismic activity.

In engineering practice, structural system with dynamic output performance has gained more and more attention. Reliability analysis of these dynamic systems based on the real performance function is normally time-consuming, which is hard to accept in engineering. An SVR-NARX (Support vector machine regression-Nonlinear autoregressive with exogenous input) model is, therefore, established in this paper to replace the real performance function for reliability analysis. To further improve the efficiency for dynamic systems with small failure probability, importance sampling is combined with SVR-NARX model. Two nonlinear examples in this paper show that the established SVR-NARX model can accurately describe the dynamic behavior of the systems, and the proposed method is efficient and accurate for the reliability analysis of dynamic systems.

In recent years, there often exist multiple priors from experienced experts or historical experiments with the rapid development of system structure in engineering fields. Bayesian Melding Method is commonly used for integrating multiple priors, which is based on the deterministic system structure. However, if the system model cannot be described by an explicit expression, the traditional Bayesian Melding Method is not feasible for system reliability analysis anymore. In order to describe the structure relationship clearly, Bayesian Network is applied in this paper to construct the complex system structure model and the system reliability is calculated by node probability tables rather than explicit expressions. Combining the advantages of the Bayesian Melding Method and Bayesian Network, a multi-prior integration and updating algorithm is developed for the system reliability analysis of complex system structures. Finally, a satellite attitude control system is used to demonstrate the proposed method. The system is established by the Bayesian Network and the comparison between natural prior and updated prior is discussed at length.

Chatter reliability prediction of turning process system with uncertainties

Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation

Heliostats represent the most important maintenance cost in the solar power tower plant. The aim of this work is to provide a failure probability analysis for heliostat design in order to minimize this maintenance cost. Based on mechanics of material study and wind aerodynamic analysis, a performance function, with five random variables, has been developed wherein the random variables are: wind speed, inside and outside pedestal diameters, pedestal yield stress and mirror mass. Four main methods have been proposed: first order reliability method, second order reliability method, Monte Carlo (MC) method and subset simulation (SS) method. The variation of failure probability with the variation of pedestal wall thickness and wind speed, for different outside diameters and heliostat azimuth and elevation angles, has been simulated. The results show that SS is more efficient and accurate for small failure probabilities; however, MC is more accurate for high failure probabilities.