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.

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.

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.

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.