A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Probabilistic Failure Analysis of Composite Beams for Optimum Ply Arrangements under Ballistic Impact

The probabilistic analysis takes into consideration an effect of scatter in elastic and strength properties of composite beam, and velocity of impactor. The damage model is implemented in the FE （finite element） code by a VUMAT （user-defined subroutine）. The inter ply failure is modeled using cohesive surfaces between the plies. Dynamic response is obtained using explicit time domain integration approach. SFEA （stochastic finite element analysis） is used to study the initiation of fiber failure analysis due to ballistic impact. SFEA provided the critical stress input in the limit state which is computationally solved using reliability software. The random variation in these properties is used for determining statistics of stress in the lamina. These are compared to the random strengths in the limit state function and probability failure surface is obtained by using GPRSM （Gaussian process response surface method）. GPRSM is used to predict the Pf （probability of failure） for different ply lay-ups arrangement. The Pf of Chang-Chang initiation of fiber failure for simply supported composite beams with symmetric cross ply lay-ups are （88.9%, 1.47% and 58.1%） greater than the anti-symmetric cross ply, symmetric angle ply and anti-symmetric angle ply, respectively. Sensitivity analysis is also carried out for symmetric cross ply arrangements.

Barton-Bandis criterion-based system reliability analysis of rock slopes

Several potential failure modes generally exist in rock slopes because of the existence of massive structural planes in rock masses. A system reliability analyses method for rock slopes with multiple failure modes based on nonlinear Barton-Bandis failure criterion is proposed. The factors of safety associated with the sliding and overturning failure modes are derived, respectively. The validity of this method is verified through a planar rock slope with an inclined slope top and tension crack. Several sensitivity analyses are adopted to study the influences of structural-plane parameters, geometric parameters, anchoring parameters and fracture morphology on the rock slopes system reliability.

Determination and stability analysis of ultimate open-pit slope under geomechanical uncertainty

In open-pit mines,pit slope as one of the important parameters affects the mine economy and total minable reserve,and it is also affected by different uncertainties which arising from many sources.One of the most critical sources of uncertainty effects on the pit slope design is rock mass geomechanical properties.By comparing the probability of failure resulted from deterministic procedure and probabilistic one,this paper investigated the effects of aforesaid uncertainties on open-pit slope stability in metal mines.In this way,to reduce the effect of variance,it implemented Latin Hypercube Sampling(LHS)technique.Furthermore,a hypothesis test was exerted to compare the effects on two cases in Middle East.Subsequently,the investigation approved high influence of geomechanical uncertainties on overall pit steepness and stability in both iron and copper mines,though on the first case the effects were just over.

Analyzing Effect of Demand Rate on Safety of Systems with Periodic Proof-tests

Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, i.e., design, deployment and phase out. Most safety assessment methods consider only system parameters, such as configuration, hazard rate, coverage, repair rate, etc. along with periodic proof-tests （or inspection）. Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants, chemical plants, etc. In this paper, a basic model of IEC 61508 is used. The basic model is extended to incorporate process demand and behavior of electronic- and/or computer-based system following diagnosis or proof-test. A new safety index, probability of failure on actual demand （PFAD） based on extended model and demand rate is proposed. Periodic proof-test makes the model semi-Markovian, so a piece-wise continuous time Markov chain （CTMC） based method is used to derive mean state probabilities of elementary or aggregated state. Method to determine probability of failure on demand （PFD） （IEC 61508） and PFAD based on these state probabilities are described. In example, safety indices of PFD and PFAD are compared.

Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method

For the system with the fuzzy failure state, the effects of the input random variables and the fuzzy failure state on the fuzzy probability of failure for the structural system are studied, and the moment-independence global sensitivity analysis（GSA） model is proposed to quantitatively measure these effects. According to the fuzzy random theory, the fuzzy failure state is transformed into an equivalent new random variable for the system, and the complementary function of the membership function of the fuzzy failure state is defined as the cumulative distribution function（CDF） of the new random variable. After introducing the new random variable, the equivalent performance function of the original problem is built. The difference between the unconditional fuzzy probability of failure and conditional fuzzy probability of failure is defined as the moment-independent GSA index. In order to solve the proposed GSA index efficiently, the Kriging-based algorithm is developed to estimate the defined moment-independence GSA index. Two engineering examples are employed to verify the feasibility and rationality of the presented GSA model, and the advantages of the developed Kriging method are also illustrated.

Reliability-Based Optimization:Small Sample Optimization Strategy

The aim of the paper is to present a newly developed approach for reliability-based design optimization. It is based on double loop framework where the outer loop of algorithm covers the optimization part of process of reliability-based optimization and reliability constrains are calculated in inner loop. Innovation of suggested approach is in application of newly developed optimization strategy based on multilevel simulation using an advanced Latin Hypercube Sampling technique. This method is called Aimed multilevel sampling and it is designated for optimization of problems where only limited number of simulations is possible to perform due to enormous com- putational demands.

Repair tolerance assessment for aircraft composite structures using Bayesian updating

Detection and repair of composite damage is crucial to ensure the safety and reliability of aircraft structures.A novel approach to quantitatively evaluate the repair tolerance of composite structures in civil aircraft based on Bayesian updating is presented.The method incorporates historical damage inspection data to determine the prior distribution of damage size,which is then updated with newly collected damage size data using Bayesian theory.Monte Carlo simulation is employed to investigate the probability of failure and estimate maintenance costs,considering various factors such as the frequency and timing of damage events,damage detection,structural strength,gust loads,and maintenance expenses throughout the lifecycle of composite structures.Safety and economic factors are considered to establish a lower threshold for repairs and an upper threshold for maintenance based on the occurrence of accidental impact damage.Verification of the effectiveness and feasibility of a quantitative assessment method for repair tolerance is conducted using damage statistics data from civil aircraft routes utilizing the structural skin panels of composite outer wing.The results demonstrate that the method proposed in conjunction with extensive simulations and full utilization of field damage inspection data can effectively simulate unexpected impact damage situations that may occur during civil aircraft service and evaluate the reliability and economic feasibility of the repair of structure.The research findings hold significant theoretical and practical value for the preparation of documents for continued airworthiness of composite structures,including structural repair manuals and maintenance programs.

Study of risk acceptance criteria for dams

This paper discusses the methods of establishing risk criteria for dams and reviews the application of dam risk criteria for individuals and societies in different countries or districts. Given the conditions in China and considering the public safety and acceptance of dam risk, historical dam break data and current design standards, individual and societal risk criteria for dams are proposed. The tolerable dam risk criteria for individuals should be set to 10-5-10-7 per annum based on project scale, for ex- ample, approximately 1.0xl0 7 per annum, which corresponds to a reliability index of 4.2 based on a 100-year lifespan for a first-class or large project. The societal limit for risk tolerance for dams should be set to approximately 10-3-10-5 per annum, corresponding to the fatality range from 1 to 100 and be horizontally extended to 1000, and F-N curves are proposed. It was also found that the reliability indices of Chinese Standard （GB 50199-2013） and Eurocodel （2002） are different, but they have the same level of safety measured by the annual probability of failure. The research results have significance for establishing dam risk criteria.

A comparison study between 2D and 3D slope stability analyses considering spatial soil variability

In engineering practice,the stability of a slope is often analyzed as a 2D problem assuming a plane-strain condition,which may lead to significant errors.In this paper,a comprehensive study is carried out to compare the results of 2D and 3D slope stability analyses,using the strength reduction method for deterministic analysis and the random field approach for probabilistic analysis,respectively.The results of this comparison study confirm that in the deterministic stability evaluation,the 2D analysis tends to obtain a smaller factor of safety than does its 3D counterpart.In the probabilistic evaluation that considers the spatial variability of soil properties,the 2D analysis tends to yield a larger probability of failure than its 3D counterpart.A significant feature of the 3D probabilistic slope stability analysis is the presence of multiple local failures distributed along the slope longitudinal direction.This paper provides insights regarding the degree of errors in modeling a 3D slope as a 2D problem,which can be regarded as a complement to the previous 3D slope stability analyses.