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-Variant Reliability Analysis of FPSO Hull Girder Considering Corrosion Based on Statistics

FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at dock like other kinds of ships, the reliability of FPSO hull girder during the whole service should be focused. Based on latest corrosion database and rational corrosion model, the ultimate strength of one FPSO is calculated under the conditions of slight, moderate and severe corrosion. The results not only provide the reliabihty under different corrosion conditions, but also do well for further inspection and maintenance research. The results provide necessary foundation for deciding inspection intervals and maintenance measure, which has practical sense to improve the general safety level of ocean engineering.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstem-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine （SVM） was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c andfon reliability index of slopes was taken into discussion and the changing trend was observed.

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.

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.

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.

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.

Time-variant reliability analysis of a continuous system with strength deterioration based on subset simulation

To conduct a reliability analysis for mechanical components, it is necessary to consider the combined influence of strength deterioration and dynamic loads. An efficient method based on subset simulation is proposed in this paper to analyze time-variant reliability by considering the strength deterioration of mechanical components in a continuous system. A gamma process is used to describe the deterioration of system strength. A model for timevariant reliability considering strength deterioration is constructed for a continuous system. A representative example and tubular cantilever structure are assessed to demonstrate the efficiency and accuracy of the proposed method. The reliability probability examples were analyzed using a first-order reliability method and benchmark results for the proposed method were derived using direct Monte Carlo simulation (MCS). The results of the proposed method and MCS are consistent, indicating that the proposed method is an effective reliability analysis method for evaluating small failure probabilities in a continuous system subjected to strength deterioration and dynamic loads.

Load Profile Analysis for Mitigating Load-Shedding in Central Africa: Case of Kinshasa

Load shedding is a major problem in Central Africa, with negative consequences for both society and the economy. However, load profile analysis can help to alleviate this problem by providing valuable information about consumer demand. This information can be used by power utilities to forecast and reduce power cuts effectively. In this study, the direct method was used to create load profiles for residential feeders in Kinshasa. The results showed that load shedding on weekends results in significant financial losses and changes in people’s behavior. In November 2022 alone, load shedding was responsible for $ 23,4 08,984 and $ 2 80,9 07,808 for all year in losses. The study also found that the SAIDI index for the southern direction of the Kinshasa distribution network was 122.49 hours per feeder, on average. This means that each feeder experienced an average of 5 days of load shedding in November 2022. The SAIFI index was 20 interruptions per feeder, on average, and the CAIDI index was 6 hours, on average, before power was restored. This study also proposes ten strategies for the reduction of load shedding in the Kinshasa and central Africa power distribution network and for the improvement of its reliability, namely: Improved load forecasting, Improvement of the grid infrastructure, Scheduling of load shedding, Demand management programs, Energy efficiency initiatives, Distributed Generation, Automation and Monitoring of the Grid, Education and engagement of the consumer, Policy and regulatory assistance, and Updated load profile analysis.

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.

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.

Developing Reliable Digital Healthcare Service Using Semi-Quantitative Functional Resonance Analysis

Since entering the era of Industry 4.0,the concept of Healthcare 4.0 has also been put forward and explored by researchers.How to use Information Technology(IT)to better serve people’s healthcare is one of the most featured emerging directions in the academic circle.An important field of Healthcare 4.0 research is the reliability engineering of healthcare service.Because healthcare systems often affect the health and even life of their users,developers must be very cautious in the design,development,and operation of these healthcare systems and services.The problems to be solved include the reliability of business process,system functions,and personal healthcare data.The Functional Resonance Analysis Method(FRAM)has been applied in reliability engineering for safety-critical systems in available studies,using both qualitative and quantitative approaches.However,the method has not been applied in the field of digital healthcare services development.Therefore,to narrow the gap,we present in this paper a semi-quantitative functional resonance analysis method to develop reliable healthcare services for diabetics.Moreover,this paper has tried to improve the reliability design of the service-oriented architecture(SOA)of traditional insulin pump therapy by system thinking.

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.

Complex Modal Analysis for the Time-Variant Dynamical Problem of Rotating Pipe Conveying Fluid

A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.

Reliability analysis of piles constructed on slopes under laterally loading

Response surface method is used to study the reliability analysis of laterally loaded piles in sloping ground. A development load-displacement （p-y） curve for laterally loaded pile response in sloping ground is used to model the pile-soil system, both the pile head displacement and the maximum bending moment of the piles are used as the performance criteria in this study. The reliability analysis method of the laterally loaded pile in sloping ground under the pile head displacement and the maximum bending moment failure modes is proposed, which is in good agreement with the Monte Carlo method. The influences on the probability index of failure by a number of parameters are discussed. It is shown that the variability of pile head displacement increases with the increase in the coefficients of variation of ultimate bearing capacity factor （Npu）, secant elastic modulus at 50%（E50） and level load （H）. A negative correlation between Npu and non-dimensional factor （λ） leads to less spread out probability density function （PDF） of the pile head displacement;in contrast, a positive correlation between Npu andλgives a great variation in the PDF of pile head displacement. As for bearing capacity factor on ground surface （Npo） and λ, both negative and positive correlations between them give a great variation in the PDF of pile head displacement, and a negative correlation will obviously increase the variability of the response.

Reliability Analysis of a Mixed Redundant Model in C 3I System

Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.

GENERAL RELIABILITY ANALYSIS FOR TWO DIMENSIONAL SLOPES

The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.