On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Time series prediction of reservoir bank landslide failure probability considering the spatial variability of soil properties

Historically,landslides have been the primary type of geological disaster worldwide.Generally,the stability of reservoir banks is primarily affected by rainfall and reservoir water level fluctuations.Moreover,the stability of reservoir banks changes with the long-term dynamics of external disastercausing factors.Thus,assessing the time-varying reliability of reservoir landslides remains a challenge.In this paper,a machine learning(ML)based approach is proposed to analyze the long-term reliability of reservoir bank landslides in spatially variable soils through time series prediction.This study systematically investigated the prediction performances of three ML algorithms,i.e.multilayer perceptron(MLP),convolutional neural network(CNN),and long short-term memory(LSTM).Additionally,the effects of the data quantity and data ratio on the predictive power of deep learning models are considered.The results show that all three ML models can accurately depict the changes in the time-varying failure probability of reservoir landslides.The CNN model outperforms both the MLP and LSTM models in predicting the failure probability.Furthermore,selecting the right data ratio can improve the prediction accuracy of the failure probability obtained by ML models.

AN IMPROVED FOSM METHOD FOR CALCULATING FAILURE PROBABILITY OF WELDED PIPES WITH FLAWS

The R F first order second moment method will produce more error for calculating the reliability of welded engineering pipe structures when the failure function is seriously nonlinear and the random variables don′t serve as normal distribution. In order to increase the computing accuracy of reliability, an improved FOSM method is used for calculating the failure probability of welded pipes with flaws in this paper. Because of solving the problems of the linear expansion of failure function at the failure point and constructing equivalent normal variables, the new algorithm can greatly improve the calculating accuracy of probability of the welded pipes with cracks. The examples show that this method is simple, efficient and accurate for reliability safety assessment of the welded pipes with cracks. It can save more time than the Monte Carlo method does, so that the improved FOSM method is recommended for engineering reliability safety assessment of the welded pipes with flaws.

Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines.Open stoping is the most widely practiced underground excavation method in these mines,and creates large stopes which are subjected to stress-induced failure.The probability of failure(POF)depends on many factors,of which the geometry of an open stope is especially important.In this study,a methodology is proposed to assess the effect of stope geometrical parameters on the POF,using numerical modelling.Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines.A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D,to generate model realizations containing stopes with different geometrical features.The probability of failure(POF)for different categories of stope geometry,is calculated by considering two modes of failure;relaxation-related gravity driven(tensile)failure and rock mass brittle failure.The individual and interactive effects of stope geometrical parameters on the POF,are analyzed using a general multi-level factorial design.Finally,mathematical optimization techniques are employed to estimate the most stable stope conditions,by determining the optimal ranges for each stope’s geometrical parameter.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

Reliable Failure Restoration with Bayesian Congestion Aware for Software Defined Networks

SoftwareDefined Networks(SDN)introduced better network management by decoupling control and data plane.However,communication reliability is the desired property in computer networks.The frequency of communication link failure degrades network performance,and service disruptions are likely to occur.Emerging network applications,such as delaysensitive applications,suffer packet loss with higher Round Trip Time(RTT).Several failure recovery schemes have been proposed to address link failure recovery issues in SDN.However,these schemes have various weaknesses,which may not always guarantee service availability.Communication paths differ in their roles;some paths are critical because of the higher frequency usage.Other paths frequently share links between primary and backup.Rerouting the affected flows after failure occurrences without investigating the path roles can lead to post-recovery congestion with packet loss and system throughput.Therefore,there is a lack of studies to incorporate path criticality and residual path capacity to reroute the affected flows in case of link failure.This paper proposed Reliable Failure Restoration with Congestion Aware for SDN to select the reliable backup path that decreases packet loss and RTT,increasing network throughput while minimizing post-recovery congestion.The affected flows are redirected through a path with minimal risk of failure,while Bayesian probability is used to predict post-recovery congestion.Both the former and latter path with a minimal score is chosen.The simulation results improved throughput by(45%),reduced packet losses(87%),and lowered RTT(89%)compared to benchmarking works.

Methodology for estimating probability of dynamical system's failure for concrete gravity dam

Methodology for the reliability analysis of hydraulic gravity dam is the key technology in current hydropower construction.Reliability analysis for the dynamical dam safety should be divided into two phases:failure mode identification and the calculation of the failure probability.Both of them are studied based on the mathematical statistics and structure reliability theory considering two kinds of uncertainty characters(earthquake variability and material randomness).Firstly,failure mode identification method is established based on the dynamical limit state system and verified through example of Koyna Dam so that the statistical law of progressive failure process in dam body are revealed; Secondly,for the calculation of the failure probability,mathematical model and formula are established according to the characteristics of gravity dam,which include three levels,that is element failure,path failure and system failure.A case study is presented to show the practical application of theoretical method and results of these methods.

Numerical method of slope failure probability based on Bishop model

Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

Life-cycle failure probability analysis of deteriorated RC bridges under multiple hazards of earthquakes and strong winds

Engineering structures may be exposed to one or more extreme hazards during their life-cycles.Current structural design specifications usually treat multiple hazards separately in designing structures and there is a limited probabilistic basis on extreme load combinations.Additionally,the performance of engineering structures will be deteriorated by the aggressive environments during their service periods,such as chloride attack,concrete carbonation,and wind-induced fatigue.This study presents a probabilistic methodology to assess the time-dependent failure probability of RC bridges with chloride-induced corrosion under the multiple hazards of earthquakes and strong winds.The loss of cross-section area of reinforcements and the reduction in strength of reinforcing steel and concrete cover induced by the chloride attack are considered.Moreover,the Poisson model is employed to obtain the occurrence probabilities of the individual and concurrent earthquake and strong wind events.The convolution integral is used to determine the joint probability distribution of combined load effects under simultaneous earthquakes and strong winds.Numerical results indicate that the structural failure probability under multiple hazards increases significantly during the bridge′s life-cycle due to the chloride corrosion effect.The contribution of each hazard event on the total structural failure probability varies with time.Thus,neglecting the combined influences of multiple hazards and chloride-induced corrosion may bring erroneous predictions in failure probability estimates of RC bridges.

Failure probability analysis of coal crushing induced by uncertainty of influential parameters under condition of in-situ reservoir

The uncertainties of some key influence factors on coal crushing,such as rock strength,pore pressure and magnitude and orientation of three principal stresses,can lead to the uncertainty of coal crushing and make it very difficult to predict coal crushing under the condition of in-situ reservoir.To account for the uncertainty involved in coal crushing,a deterministic prediction model of coal crushing under the condition of in-situ reservoir was established based on Hoek-Brown criterion.Through this model,key influence factors on coal crushing were selected as random variables and the corresponding probability density functions were determined by combining experiment data and Latin Hypercube method.Then,to analyze the uncertainty of coal crushing,the firstorder second-moment method and the presented model were combined to address the failure probability involved in coal crushing analysis.Using the presented method,the failure probabilities of coal crushing were analyzed for WS5-5 well in Ningwu basin,China,and the relations between failure probability and the influence factors were furthermore discussed.The results show that the failure probabilities of WS5-5 CBM well vary from 0.6 to 1.0; moreover,for the coal seam section at depth of 784.3-785 m,the failure probabilities are equal to 1,which fit well with experiment results; the failure probability of coal crushing presents nonlinear growth relationships with the increase of principal stress difference and the decrease of uniaxial compressive strength.

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.

GENERAL FAILURE PROBABILITY SIMULATION AND APPLICATION FOR MULTI-MODE

A general failure probability simulation and deviation evaluation methods were presented for fuzzy safety state and fuzzy failure state. And the corresponding number integral method was simultaneously established. As the distribution of state variable and the membership of the state variable to the fuzzy safety set were normal, the general failure probability of the single failure mode had precise analytic solution, which was used to verify the precision of the presented methods. The results show that the evaluation of the simulation method convergences to the analytic solution with the number increase of the sampling. The above methods for the single failure mode was extended to the multi-mode by the expansion and probability principles. The presented methods were applied to the engineering problem. For the number of significant mode is not too many, the high precision solution can be given by the presented number simulation and number integral methods, which is illustrated by the engineering examples. In addition, the application scope of the methods was discussed.

Genetic Algorithm Optimization Model for Determining the Probability of Failure on Demand of the Safety Instrumented System

A more accurate determination for the Probability of Failure on Demand(PFD)of the Safety Instrumented System(SIS)contributes to more SIS realiability,thereby ensuring more safety and lower cost.IEC 61508 and ISA TR.84.02 provide the PFD detemination formulas.However,these formulas suffer from an uncertaity issue due to the inclusion of uncertainty sources,which,including high redundant systems architectures,cannot be assessed,have perfect proof test assumption,and are neglegted in partial stroke testing(PST)of impact on the system PFD.On the other hand,determining the values of PFD variables to achieve the target risk reduction involves daunting efforts and consumes time.This paper proposes a new approach for system PFD determination and PFD variables optimization that contributes to reduce the uncertainty problem.A higher redundant system can be assessed by generalizing the PFD formula into KooN architecture without neglecting the diagnostic coverage factor(DC)and common cause failures(CCF).In order to simulate the proof test effectiveness,the Proof Test Coverage(PTC)factor has been incorporated into the formula.Additionally,the system PFD value has been improved by incorporating PST for the final control element into the formula.The new developed formula is modelled using the Genetic Algorithm(GA)artificial technique.The GA model saves time and effort to examine system PFD and estimate near optimal values for PFD variables.The proposed model has been applicated on SIS design for crude oil test separator using MATLAB.The comparison between the proposed model and PFD formulas provided by IEC 61508 and ISA TR.84.02 showed that the proposed GA model can assess any system structure and simulate industrial reality.Furthermore,the cost and associated implementation testing activities are reduced.

Bayesian Estimation and Hierarchical Bayesian Estimation of Zero-failure Data

The zero_failure data research is a new field in the recent years, but it is required urgently in practical projects, so the work has more theory and practical values. In this paper, for zero_failure data (t i,n i) at moment t i , if the prior distribution of the failure probability p i=p{T【t i} is quasi_exponential distribution, the author gives the p i Bayesian estimation and hierarchical Bayesian estimation and the reliability under zero_failure date condition is also obtained.

Towards multiple hazard resilient bridges:a methodology for modeling frequent and infrequent time-varying loads Part I,Comprehensive reliability and partial failure probabilities

The current AASHTO load and resistance factor design （LRFD） guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads （also referred to as multiple hazard or MH loads） can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions： （1） formulate the failure probabilities; （2） normalize various load distributions; and （3） establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.

Processing for Zero-Failure Data of the Products

In this paper, an estimation method for reliability parameter in the case of zero-failuare data-synthetic estimation method is given. For zero-failure data of double-parameter exponential distribution, a hierarchical Bayesian estimation of the failure probability is presented. After failure information is introduced, hierarchical Bayesian estimation and synthetic estimation of the failure probability, as well as synthetic estimation of reliability are given. Calculation and analysis are performed regarding practical problems in case that life distribution of an engine obeys double-parameter exponential distribution.

Load-redistribution strategy based on time-varying load against cascading failure of complex network

Cascading failure can cause great damage to complex networks, so it is of great significance to improve the network robustness against cascading failure. Many previous existing works on load-redistribution strategies require global information, which is not suitable for large scale networks, and some strategies based on local information assume that the load of a node is always its initial load before the network is attacked, and the load of the failure node is redistributed to its neighbors according to their initial load or initial residual capacity. This paper proposes a new load-redistribution strategy based on local information considering an ever-changing load. It redistributes the loads of the failure node to its nearest neighbors according to their current residual capacity, which makes full use of the residual capacity of the network. Experiments are conducted on two typical networks and two real networks, and the experimental results show that the new load-redistribution strategy can reduce the size of cascading failure efficiently.

Strength Reliability Analysis of Stiffened Cylindrical Shells Considering Failure Correlation

The stiffened cylindrical shell is commonly used for the pressure hull of submersibles and the legs of offshore platforms. There are various failure modes because of uncertainty with the structural size and material properties, uncertainty of the calculation model and machining errors. Correlations among failure modes must be considered with the structural reliability of stiffened cylindrical shells. However, the traditional method cannot consider the correlations effectively. The aim of this study is to present a method of reliability analysis for stiffened cylindrical shells which considers the correlations among failure modes. Firstly, the joint failure probability calculation formula of two related failure modes is derived through use of the 2D joint probability density function. Secondly, the full probability formula of the tandem structural system is given with consideration to the correlations among failure modes. At last, the accuracy of the system reliability calculation is verified through use of the Monte Carlo simulation. Result of the analysis shows the failure probability of stiffened cylindrical shells can be gained through adding the failure probability of each mode.

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 ANALYSIS FOR A REPAIRABLE PARALLEL SYSTEM WITH TIME-VARYING FAILURE RATES

To solve a real problem:how to calculate the reliability of a system with time-varying failure rates in industry systems,this paper studies a model for the load-sharing parallel system with time-varying failure rates,and obtains calculating formulas of reliability and availability of the system by solving differential equations.In this paper,the failure rates are expressed in polynomial configuration.The constant,linear and Weibull failure rate are in their special form.The polynomial failure rates provide flexibility in modeling the practical time-varying failure rates.