Low-discrepancy sampling for structural reliability sensitivity analysis

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

During the service of the missile suspension structure, the unexpected fatigue failure is emerged because of the dimension dispersibility resulting from machining deviation and design tolerance. In order to get the main factor of failure, based on the moment method of structural reliability assessment and PCL (Patran Command Language) redevelopment technology of finite element parameter analysis, an effective method is proposed to perform the missile suspension structure fatigue life reliability and parameter sensitivity analysis. Using proposed method, the result of reliability and parameter sensitivity analysis can be got readily with only 81 samples of finite element analysis. Compared with Monte-Carlo, proposed method in this paper is more effective with deducing the number of samples, especially fit for some structural reliability and parameter sensitivity analysis under implicit limit state equation.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

Efficient sampling methods for global reliability sensitivity analysis

The limit state function (LSF) is implicit to many structure reliability analysis problems, which may make some classical reliability method complicated to be applied. One of the surrogate methods-support vector classification (SVC) was applied in the structural reliability analysis herein which has not been applied to structure reliability analysis until recent years. Then the advanced first order second moment method (AFOSM) can be applied. The expressions of structure system reliability sensitivity to basic variable were deduced. The flow of how to call the SVC program was presented. An example was shown to compare the SVC based method with some other classical reliability analysis methods. The results are accurately accepted and the advantages of SVC are analyzed.

The paper describes a quantitative model for risk-based integrity maintenance planning for offshore pipelines. The model calculates the risk level as the product of failure consequences and failure probabilities. Failure consequences considered include financial aspects relating to repair, interruption and restoration; safety aspects related to platform and vessel occupants; and environmental aspects associated with spills. Distinction is made between small leaks, large leaks and ruptures, and the major failure causes (namely, corrosion and mechanical damage) are considered. The model quantifies the benefits associated with different maintenance alternatives by calculating their impact on the probability of failure and risk level. A formal decision analysis approach is then used to evaluate the costs and benefits associated with each alternative, and identify the best overall maintenance strategy. This model differs from previous work in risk-based planning in that it:utilizes structural pipe failure models and reliability analysis techniques to calculate failure probabilities;quantifies the impact of maintenance on risk; andutilizes a methodology based on decision theory to identify optimal choices. It is applicable to various aspects of maintenance planning for offshore pipelines such as the selection of inspection tools, inspection intervals and defect repair criteria; and the optimization of damage prevention activities including mechanical protection, cover monitoring and public awareness programs. The paper will include the results of simulations dealing with maintenance optimization for corrosion and mechanical damage. These results demonstrate that risk-based planning is a powerful tool for minimizing risk by maintaining high reliability at the lowest possible cost. The most significant aspect of this work is that it provides a novel approach to managing pipeline integrity in a cost-effective manner. Introduction The goal of an effective pipeline integrity maintenance program is to ensure that the limited resources available are utilized most effectively in reducing the risks posed by pipeline failures to life, the environment and financial assets. The uncertainties associated with making such an assessment has led to a recognition of risk analysis as a sound basis for making decisions on integrity maintenance. Risk, in this context, is defined as the probability of line failure multiplied by a measure of the associated adverse consequences. The risks associated with a pipeline system and its individual segments, and the potential risk reductions resulting from different maintenance activities can be used as a basis for evaluating different alternatives and developing an optimal maintenance plan. This paper describes a comprehensive methodology for risk-based integrity maintenance optimization of offshore natural gas, crude oil and petroleum product pipelines. The methodology has been developed and implemented in a software package called PIRAMID?, (Pipeline Risk Analysis for Maintenance and Inspection Decisions) under a joint industry program sponsored by a number of transmission companies and government agencies (see Acknowledgements). The types of decisions addressed by the methodology include the choice of inspection methods (e.g., cover depth survey, in-line inspection) and inspection intervals, as well as the choice of maintenance actions (e.g., corrosion inhibition, hydro-test, coating reconditioning and replacement).

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

Structural Reliability Analysis (SRA) is a useful tool in structural engineering. Uncertainty in input parameters and model uncertainties in the analysis predictions are explicitly modelled by random variables. With this methodology, the uncertainties involved are handled in a consistent and transparent way. Compared to a deterministic analysis, SRA provides improved insight in how the various uncertainties involved influence the results. The main results from SRA is the calculated probability of structural failure, but other useful results such as uncertainty importance factors and design points being the most likely combination of all variables at failure represent helpful information. The present paper illustrates some the features using SRA for two different types of application. The first application is the use of SRA as a tool for code calibration and the second shows the application of SRA to a problem where common practice is likely to be rather conservative and therefore leading to unacceptable results, but where the degree of conservatism is not known. Two examples are chosen to illustrate code calibration; i.e. hull girder ultimate limit state (ULS) for tankers and ULS for mooring design in the ULS for floating offshore vessels. Code calibration involves both SRA and design analysis following the code. It is shown how the design analysis can be modified in order to better reflect a chosen target reliability level across a selected set of test cases representative for what the code should cover. Fatigue of subsea wellhead systems is selected as an example of a special case when application of existing rules may lead to unsatisfactory results which are likely to be rather conservative. It is shown how results can be presented in terms of the accumulated probability of fatigue failure as a function of time. This may be a more suitable basis for decision making than a calculated fatigue life from a standard analysis. It is also illustrated how importance factors from the SRA can be used as guidance on how to prioritize effort in order to improve prediction of the fatigue damage. The present paper is not intended to be detailed in all input and analysis methodology, but draw the attention towards the possibilities and benefits of applying SRA in structural engineering, where the examples are used to illustrate this potential.

Variance-based reliability sensitivity with dependent inputs using failure samples

A new bivariate dimension reduction method for efficient structural reliability analysis

A mixture distribution with fractional moments for efficient seismic reliability analysis of nonlinear structures

Sensitivity and Hessian matrix analysis of structural reliability for uniformly modulated random seismic response

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.

PurposeBecause of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).Design/methodology/approachIn DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.FindingsThe computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.Originality/valueThis paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

Some transmission structures exhibit important geometric and material nonlinearities that should be considered in their analysis and design. Unless simplifying assumptions are made, reliability analysis of these structures is complex and can be very computer-time intensive. This paper describes an approximate method to conduct reliability analysis of nonlinear transmission structures. It is shown that for most transmission structures, the design point is close to the 50-year return period loads. Using this result, approximate g-functions for nonlinear problems are obtained with minimum computational effort. It is also shown that when the material strengths are highly correlated, g-functions that include interaction of axial load and bending moments may be reduced to g-functions with no interaction. These simplifying results are implemented in a microcomputer program, RELIAB, which can handle complex transmission structures such as large latticed structures, tension-only structures, or structures that exhibit nonlinearities. RELIAB's accuracy is ascertained by comparing results with another computer program, TRANSREL, which accounts for the residual strength of latticed towers following progressive failure of one or more components.