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.

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 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.

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.

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.

Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces

Slope reliability analysis considering inherent spatial variability(ISV)of soil properties is timeconsuming when response surface method(RSM)is used,because of the"curse of dimensionality".This paper proposes an effective method for identification of representative slip surfaces(RSSs)of slopes with spatially varied soils within the framework of limit equilibrium method(LEM),which utilizes an adaptive K-means clustering approach.Then,an improved slope reliability analysis based on the RSSs and RSM considering soil spatial variability,in perspective of computation efficiency,is established.The detailed implementation procedure of the proposed method is well documented,and the ability of the method in identifying RSSs and estimating reliability is investigated via three slope examples.Results show that the proposed method can automatically identify the RSSs of slope with only one evaluation of the conventional deterministic slope stability model.The RSSs are invariant with the statistics of soil properties,which allows parametric studies that are often required in slope reliability analysis to be efficiently achieved with ease.It is also found that the proposed method provides comparable values of factor of safety(FS)and probability of failure(Pf)of slopes with those obtained from direct analysis and lite rature.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

Reliability analysis of earth dams using direct coupling

Numerical methods are helpful for understanding the behaviors of geotechnical installations.However,the computational cost sometimes may become prohibitive when structural reliability analysis is performed,due to repetitive calls to the deterministic solver.In this paper,we show how accurate and efficient reliability analyses of geotechnical installations can be performed by directly coupling geotechnical software with a reliability solver.An earth dam is used as the study object under different operating conditions.The limit equilibrium method of Morgenstern-Price is used to calculate factors of safety and find the critical slip surface.The conmercial software packages Seep/W and Slope/W are coupled with StRAnD structural reliability software.Reliability indices of critical probabilistic surfaces are evaluated by the first-and second-order structural reliability methods(FORM and SORM),as well as by importance sampling Monte Carlo(ISMC)simulation.By means of sensitivity analysis,the effective friction angle(φ′)is found to be the most relevant uncertain geotechnical parameter for dam equilibrium.The correlations between different geotechnical properties are shown to be relevant in terms of equilibrium reliability indices.Finally,it is shown herein that a critical slip surface,identified in terms of the minimum factor of safety(FS),is not the critical surface in terms of the reliability index.

Reliability Analysis of Hydraulic Transmission Oil Supply System of Power-Shift Steering Transmission with GO Methodology

GO methodology is a success-oriented method for system reliability analysis. There are components with multi-fault modes in repairable systems. It is a problem to use the existing GO method to make reliability analysis of such repairable systems. A new GO method for reliability analysis of such repairable systems with multifault modes was presented. Firstly, calculation equations of reliability parameters of operators which were used to describe components with multi-fault modes in reparable systems were derived based on Markov process theory. Then, this new GO method was applied in reliability analysis of a hydraulic transmission oil supply system( HTOSS) of a power-shift steering transmission at low and high speeds. Finally,Compared with fault tree analysis( FTA) and Monte Carlo simulation,the results show that this new GO method is correct and suitable for reliability analysis of repairable system with multi-fault modes.

Reliability Analysis for a Gear-Rack Based on Combination of Simulation and Experiment

In order to analyze the gear-rack reliability under the most serious limit loads which was the new-type transmission mechanism of aircraft slats,the gear-rack static strength under the single tooth meshing was analyzed based on the simulation and experiment. Then,it randomized the load of gear-rack based on the precise finite element analysis( FEA) model,and analyzed the static strength reliability of the gear-rack. Finally,the gear-rack under the most dangerous situation has not been destroyed and it also has a high reliability.

Reliability Analysis on Repairable System with Dual Input Closed-Loop Feedback Link Considering Shutdown Correlation Based on Goal Oriented Methodology

Goal oriented( GO) methodology is a kind of success oriented system reliability analysis method and has been used widely.The repairable system with dual input closed-loop feedback link( DICLFL) considering shutdown correlation didn't make reliability analysis accurately based on existing GO methodology. So, a reliability analysis method used to deal with DICLFL considering shutdown correlation is provided based on GO methodology.Firstly, a new operator, which is used to describe DICLFL considering shutdown correlation,whose number is 1,is created and named as Type 9C operator. And then,the formulas of type 9C operator are derived based on Markov process theory. Finally,the new method presented in this paper is adopted to conduct the reliability analysis of an electro-hydraulic servo speed control system. The analysis result is compared with those of Monte Carlo simulation and fault tree analysis( FTA). The comparison results show that this new reliability analysis method based on GO methodology is feasible and meaningful for reliability analysis of repairable systems with DICLFL considering shutdown correlation.Meantime,it will be useful for more other applications.

Sensitivity of Sample for Simulation-Based Reliability Analysis Methods

In structural reliability analysis,simulation methods are widely used.The statistical characteristics of failure probability estimate of these methods have been well investigated.In this study,the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample,called‘contribution indexes’,are proposed to measure the contribution of sample.The contribution indexes in four widely simulation methods,i.e.,Monte Carlo simulation(MCS),importance sampling(IS),line sampling(LS)and subset simulation(SS)are derived and analyzed.The proposed contribution indexes of sample can provide valuable information understanding the methods deeply,and enlighten potential improvement of methods.It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples,which are the main factors to the efficiency of the methods.Moreover,numerical examples are used to validate these findings.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

Kriging-based reliability analysis of the long-term stability of a deep driftconstructed in the Callovo-Oxfordian claystone

Callovo-Oxfordian(COx)claystone has been considered as a potential host rock for geological radioactive waste disposal in France(Cigéo project).During the exploitation phase(100 years),the stability of drifts(e.g.galleries/alveoli)within the disposal is assured by the liner,which includes two layers:concrete arch segment and compressible material.The latter exhibits a significant deformation capacity(about 50%)under low stress(<3 MPa).Although the response of these underground structures can be governed by complex thermo-hydro-mechanical coupling,the creep behavior of COx claystone has been considered as the main factor controlling the increase of stress state in the concrete liner and hence the long-term stability of drifts.Therefore,by focusing only on the purely mechanical behavior,this study aims at investigating the uncertainty effect of the COx claystone time-dependent properties on the stability of an alveolus of Cigéo during the exploitation period.To describe the creep behavior of COx claystone,we use Lemaitre’s viscoplastic model with three parameters whose uncertainties are identified from laboratory creep tests.For the reliability analysis,an extension of a well-known Kriging metamodeling technique is proposed to assess the exceedance probability of acceptable stress in the concrete liner of the alveolus.The open-source code Code_Aster is chosen for the direct numerical evaluations of the performance function.The Kriging-based reliability analysis elucidates the effect of the uncertainty of COx claystone on the long-term stability of the concrete liner.Moreover,the role of the compressible material layer between the concrete liner and the host rock is also highlighted.

Reliability Analysis of Heterogeneous Sensor-Cloud Systems against Targeted Attacks

Based on the wide application of cloud computing and wireless sensor networks in various fields,the Sensor-Cloud System(SCS)plays an indispensable role between the physical world and the network world.However,due to the close connection and interdependence between the physical resource network and computing resource network,there are security problems such as cascading failures between systems in the SCS.In this paper,we propose a model with two interdependent networks to represent a sensor-cloud system.Besides,based on the percolation theory,we have carried out a formulaic theoretical analysis of the whole process of cascading failure.When the system’s subnetwork presents a steady state where there is no further collapse,we can obtain the largest remaining connected subgroup components and the penetration threshold.Theoretically,this result is the critical maximum that the coupled SCS can withstand.To verify the correctness of the theoretical results,we further carried out actual simulation experiments.The results show that a scale-free network priority attack’s percolation threshold is always less than that of ER network which is priority attacked.Similarly,when the scale-free network is attacked first,adding the power law exponentλcan be more intuitive and more effective to improve the network’s reliability.

Reliability Analysis of Slope Stability Considering Temporal Variations of Rock Mass Properties

Temporal variation of rock mass properties,especially the strength degradation due to drying-wetting cycles as well as the acidic wetting fluid(rainfall or reservoir water)is crucial to stability of reservoir rock slopes.Based on a series of drying-wetting cycling and experiments considering the influences of pH values,the degradation degree models of the reduced cohesion𝑐𝑐′,friction angle𝜑𝜑′are developed.2D stability analysis of the slope is subsequently carried out to calculate the factor of safety(Fs)via limit equilibrium method(LEM)and a predictive model of Fs is built using multivariate adaptive regression splines(MARS),revealing the effect of the drying-wetting cycles and pH value.The reliability analysis by Monte Carlo simulation is performed to rationally consider the uncertainty and the temporal variation of the shear strength parameters of rock mass.Results indicate that the MARS-based model can estimate the Fs accurately.The Fs and the reliability indexβdecrease with increase of drying-wetting cycles,and the temporal variation of rock mass properties has significant influence on the slope reliability.Overlooking the temporal variation of rock properties may overestimate the Fs and reliability indexβin the longer term.