Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Three-dimensional pseudo-dynamic reliability analysis of seismic shield tunnel faces combined with sparse polynomial chaos expansion

To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.

Probabilistic back-analysis of rainfall-induced landslides for slope reliability prediction with multi-source information

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters,making the slope reliability assessment closer to the engineering reality.However,multi-source information(including test data,monitored data,field observation and slope survival records)is rarely used in current probabilistic back-analysis.Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved.In this paper,a framework by integrating a modified Bayesian Updating with Subset simulation(mBUS)method with adaptive Conditional Sampling(aCS)algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction.Within this framework,the high-dimensional probabilistic back-analysis problem can be easily tackled,and the multi-source information(e.g.monitored pressure heads and slope survival records)can be fully used in the back-analysis.A real Taoyuan landslide case in Taiwan,China is investigated to illustrate the effectiveness and performance of the established framework.The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations.Furthermore,the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12,2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City,Taiwan,China.

Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

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.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

System Reliability Analysis Method Based on T-S FTA and HE-BN

For high-reliability systems in military,aerospace,and railway fields,the challenges of reliability analysis lie in dealing with unclear failure mechanisms,complex fault relationships,lack of fault data,and uncertainty of fault states.To overcome these problems,this paper proposes a reliability analysismethod based on T-S fault tree analysis(T-S FTA)and Hyper-ellipsoidal Bayesian network(HE-BN).The method describes the connection between the various systemfault events by T-S fuzzy gates and translates them into a Bayesian network(BN)model.Combining the advantages of T-S fault tree modeling with the advantages of Bayesian network computation,a reliability modeling method is proposed that can fully reflect the fault characteristics of complex systems.Experts describe the degree of failure of the event in the form of interval numbers.The knowledge and experience of experts are fused with the D-S evidence theory to obtain the initial failure probability interval of the BN root node.Then,the Hyper-ellipsoidal model(HM)constrains the initial failure probability interval and constructs a HE-BN for the system.A reliability analysismethod is proposed to solve the problem of insufficient failure data and uncertainty in the degree of failure.The failure probability of the system is further calculated and the key components that affect the system’s reliability are identified.The proposedmethod accounts for the uncertainty and incompleteness of the failure data in complex multi-state systems and establishes an easily computable reliability model that fully reflects the characteristics of complex faults and accurately identifies system weaknesses.The feasibility and accuracy of the method are further verified by conducting case studies.

Reliability analysis of carbon fiber rod-reinforced umbilical cable under tension using an improved sampling method

The umbilical cable is a vital component of subsea production systems that provide power,chemical agents,control signals et al.,and its requirement for reliability is exceedingly high.However,as the umbilical cable is a composite structure comprising multiple functional units,the reliability analysis of such cables involves numerous parameters that can impact calculation efficiency.In this paper,the reliability analysis of a new kind of umbilical cable with carbon fiber rod under tension is analyzed.The global dynamic analytical model is first established to determine the maximum tension load,then the local analytical model of umbilical cable including each unit are constructed by finite element method(FEM).Based on the mechanical analytical model,the reliability of umbilical cable under tension load is studied using response surface method(RSM)and Monte Carlo method.During the calculation process,a new tangent plane sampling method to calculate the response surface function(RSF)is proposed in this paper,which could make sampling points faster come close to the RSF curve,and it is proved that the calculation efficiency increases about 33%comparing with traditional method.

Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

Reliability analysis of slope stability by neural network,principal component analysis,and transfer learning techniques

The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-demanding.To assess the slope stability problems with a more desirable computational effort,many machine learning(ML)algorithms have been proposed.However,most ML-based techniques require that the training data must be in the same feature space and have the same distribution,and the model may need to be rebuilt when the spatial distribution changes.This paper presents a new ML-based algorithm,which combines the principal component analysis(PCA)-based neural network(NN)and transfer learning(TL)techniques(i.e.PCAeNNeTL)to conduct the stability analysis of slopes with different spatial distributions.The Monte Carlo coupled with finite element simulation is first conducted for data acquisition considering the spatial variability of cohesive strength or friction angle of soils from eight slopes with the same geometry.The PCA method is incorporated into the neural network algorithm(i.e.PCA-NN)to increase the computational efficiency by reducing the input variables.It is found that the PCA-NN algorithm performs well in improving the prediction of slope stability for a given slope in terms of the computational accuracy and computational effort when compared with the other two algorithms(i.e.NN and decision trees,DT).Furthermore,the PCAeNNeTL algorithm shows great potential in assessing the stability of slope even with fewer training data.

Hybrid response surface method for system reliability analysis of pilereinforced slopes

To consider the complex soil-structure interaction in a pile-slope system,it is necessary to analyze the performance of pile-slope systems based on a three-dimensional(3D)numerical model.Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability.In this paper,an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes,where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure,respectively.The versatility of the suggested method is illustrated in detail with an example.For the example examined in this paper,it is found that the pile failure can significantly contribute to system failure,and the reinforcement ratio can effectively reduce the probability of pile failure.There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio.The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope.There exists an optimal location and an optimal length for the stabilizing piles.

Analysis of the Effect of Temperature and Relative Humidity on the Reliability of a Photovoltaic Module

Photovoltaic energy occupies a significant place in the renewable energy market, with photovoltaic (PV) modules playing a vital role in converting solar energy into electricity. However, their effectiveness is likely to be affected by variations in environmental conditions, including temperature and relative humidity. The study examines the impact of these major climatic factors on the reliability of PV modules, aiming to provide crucial information for optimizing and managing these systems under varying conditions. Inspired by Weibull’s law to model the lifespan of components, we proposed a mathematical model integrating a correction factor linked to temperature and relative humidity. Using this approach, simulations in Matlab Simulink reveal that increasing temperature and relative humidity have an adverse impact on the reliability and lifespan of PV modules, with a more pronounced impact on temperature. The results highlight the importance of considering these environmental parameters in the management and optimization of photovoltaic systems to ensure their long-term efficiency.

Analysis of English Testing Based on Reliability Theory in Language Testing-Taking the English Midterm Test for the First Grade of a Middle School in Hangzhou as an Example

Based on the reliability theory in language testing,this study analyzes the midterm English test of a first grade class in Hangzhou using SPSS software.We will analyze the overall structure and reliability of the test paper,and use cloze as a representative of objective questions to calculate their difficulty and discrimination,in order to explore the quality of the questions and the mastery of the knowledge learned by students.The purpose of this analysis and research is to improve the quality of exam questions and help teachers get useful information from exam results,thereby improving teaching quality.

Detailed seismic risk analysis of electrical substation equipment using a reliability based approach

This paper proposes a risk analysis framework for substation structures based on reliability methods.Even though several risk assessment approaches have been developed for buildings,detailed risk analysis procedures for infrastructure components have been lacking in prior studies.The proposed framework is showcased by its application to a system of interconnected structures at a power substation in Tehran.Finite element models of structures are developed and validated in accordance with previous experiments.The uncertainties in the material,mass,and geometric properties of structures are described by random variables that are input to the finite element model.An artificial ground motion model is employed to comprehensively consider uncertainty in ground motion.Monte Carlo sampling is subsequently conducted on the library of probabilistic models.The analysis resulted in the loss distribution in the life cycle of structures.Additionally,the loss associated with six earthquake scenarios having specific magnitudes and return periods is computed.The application provides insight into the most vulnerable equipment in the considered system.Furthermore,introduced risk measures can guide stakeholders to make risk-based decisions to optimize design or prioritize a retrofit of infrastructure components under conditions of uncertainty.

A practical framework for performance-based reliability analysis of subway stations based on a faultestructure combined system

It is necessary to pay particular attention to the uncertainties that exist in an engineering problem to reduce the risk of seismic damage of infrastructures against natural hazards.Moreover,certain structural performance levels should be satisfied during strong earthquakes.However,these performance levels have been only well described for aboveground structures.This study investigates the main uncertainties involved in the performance-based seismic analysis of a multi-story subway station.More than 100 pulse-like and no pulse-like ground motions have been selected.In this regard,an effective framework is presented,based on a set of nonlinear static and dynamic analyses performed by OpenSees code.The probabilistic seismic demand models for computing the free-field shear strain of soil and racking ratio of structure are proposed.These models result in less variability compared with existing relations,and make it possible to evaluate a wider range of uncertainties through reliability analysis in Rtx software using the Monte Carlo sampling method.This work is performed for three different structural performance levels(denoted as PL1ePL3).It is demonstrated that the error terms related to the magnitude and location of earthquake excitations and also the corresponding attenuation relationships have been the most important parameters.Therefore,using a faultestructure model would be inevitable for the reliability analysis of subway stations.It is found that the higher performance level(i.e.PL3)has more sensitivity to random variables than the others.In this condition,the pulse-like ground motions have a major contribution to the vulnerability of subway stations.

System Reliability Analysis for Truss Structures Based on Automatic Updated Model

Multiple failure modes tend to be identified in the reliability analysis of a redundant truss structure.This identification process involves updating the model for identifying the next potential failure members.Herein we intend to update the finite element model automatically in the identification process of failure modes and further perform the system reliability analysis efficiently.This study presents a framework that is implemented through the joint simulation of MATLAB and APDL and consists of three parts:reliability index of a single member,identification of dominant failure modes,and system-level reliability analysis for system reliability analysis of truss structures.Firstly,RSM(response surface method)combines with a constrained optimization model to calculate the reliability indices ofmembers.Then theβ-unzipping method is adopted to identify the dominant failuremodes,and the system function in MATLAB,as well as the EKILL command in APDL,is used to facilitate the automatic update of the finite element model and realize load-redistribution.Besides,the differential equivalence recursion algorithmis performed to approximate the reliability indices of failuremodes efficiently and accurately.Eventually,the PNET(probabilistic network evaluation technique)is used to calculate the joint failure probability as well as the system reliability index.Two illustrative examples demonstrate the accuracy and efficiency of the proposed system reliability analysis framework through comparison with corresponding references.

Reliability Analysis of Satellite Turntable System under Multiple Operation Modes Based on Multi-Valued Decision Diagrams

As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions to be completed are different,consecutive and non-over-lapping,from which the turntable system can be considered to be a phased-mission system(PMS).Reliability analysis for PMS has been widely studied.However,the system mode cycle characteristic has not been taken into account before.In this paper,reliability analysis method of the satellite turntable system is proposed considering its multiple operation modes and mode cycle characteristic.Firstly,the multi-valued decision diagrams(MDD)manipulation rules between two adjacent mission cycles are proposed.On this basis,MDD models for the turntable system in different states are established and the reliability is calculated using the continuous time Markov chains(CTMC)method.Finally,the comparative study is carried out to show the effectiveness of our proposed method.

Reliability Analysis of Correlated Competitive and Dependent Components Considering Random Isolation Times

In the Internet of Things(IoT)system,relay communication is widely used to solve the problem of energy loss in long-distance transmission and improve transmission efficiency.In Body Sensor Network(BSN)systems,biosensors communicate with receiving devices through relay nodes to improve their limited energy efficiency.When the relay node fails,the biosensor can communicate directly with the receiving device by releasing more transmitting power.However,if the remaining battery power of the biosensor is insufficient to enable it to communicate directly with the receiving device,the biosensor will be isolated by the system.Therefore,a new combinatorial analysis method is proposed to analyze the influence of random isolation time(RIT)on system reliability,and the competition relationship between biosensor isolation and propagation failure is considered.This approach inherits the advantages of common combinatorial algorithms and provides a new approach to effectively address the impact of RIT on system reliability in IoT systems,which are affected by competing failures.Finally,the method is applied to the BSN system,and the effect of RIT on the system reliability is analyzed in detail.

AWK-TIS:An Improved AK-IS Based on Whale Optimization Algorithm and Truncated Importance Sampling for Reliability Analysis

In this work,an improved active kriging method based on the AK-IS and truncated importance sampling(TIS)method is proposed to efficiently evaluate structural reliability.The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature.The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly,and the whale optimization algorithm(WOA)is employed to acquire the optimal Krigingmodel and themost probable point(MPP).To verify the performance of theAWK-TISmethod for structural reliability,four numerical cases which are utilized as benchmarks in literature and one real engineering problem about a jet van manipulate mechanism are tested.The results indicate the accuracy and efficiency of the proposed method.

Reliability analysis for vertical integration of protection,measurement,merge unit,and intelligent terminal device

The reliability analysis of vertically integrated protection devices is crucial for designing International Electrotechnical Commission(IEC)61850-based substations.This paper presents the hardware architecture of a four-inone vertically integrated device and the information transmission path of each function based on the functional information transmission chain of protection devices,measurement and control devices,merging units,and intelligent terminals.Additionally,a reliability analysis model of the protection device and its protection system is constructed using the fault tree analysis method while considering the characteristics of each module of the vertically integrated device.The stability probability of the protection system in each state is analyzed by combining the state-transfer equations of line and busbar protection with a Markov chain.Finally,the failure rate and availability of the protection device and its protection system are calculated under different ambient temperatures using a 110 kV intelligent substation as an example.The sensitivity of each device module is analyzed.