Belief reliability:a scientific exploration of reliability engineering

This paper systematically introduces and reviews a scientific exploration of reliability called the belief reliability.Beginning with the origin of reliability engineering,the problems of present theories for reliability engineering are summarized as a query,a dilemma,and a puzzle.Then,through philosophical reflection,we introduce the theoretical solutions given by belief reliability theory,including scientific principles,basic equations,reliability science experiments,and mathematical measures.The basic methods and technologies of belief reliability,namely,belief reliability analysis,function-oriented belief reliability design,belief reliability evaluation,and several newly developed methods and technologies are sequentially elaborated and overviewed.Based on the above investigations,we summarize the significance of belief reliability theory and make some prospects about future research,aiming to promote the development of reliability science and engineering.

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.

Interrater Reliability Estimation via Maximum Likelihood for Gwet’s Chance Agreement Model

Interrater reliability (IRR) statistics, like Cohen’s kappa, measure agreement between raters beyond what is expected by chance when classifying items into categories. While Cohen’s kappa has been widely used, it has several limitations, prompting development of Gwet’s agreement statistic, an alternative “kappa”statistic which models chance agreement via an “occasional guessing” model. However, we show that Gwet’s formula for estimating the proportion of agreement due to chance is itself biased for intermediate levels of agreement, despite overcoming limitations of Cohen’s kappa at high and low agreement levels. We derive a maximum likelihood estimator for the occasional guessing model that yields an unbiased estimator of the IRR, which we call the maximum likelihood kappa (κML). The key result is that the chance agreement probability under the occasional guessing model is simply equal to the observed rate of disagreement between raters. The κMLstatistic provides a theoretically principled approach to quantifying IRR that addresses limitations of previous κcoefficients. Given the widespread use of IRR measures, having an unbiased estimator is important for reliable inference across domains where rater judgments are analyzed.

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.

Method of non-stationary random vibration reliability of hydro-turbine generator unit

The hydraulic excitation acting on a hydro-turbine generator unit exhibits obvious non-stationary characteristics.In order to account for these characteristics,this study focuses on the non-stationary random vibration reliability of the hydro-turbine generator unit.Firstly,the non-stationary characteristics of the hydraulic excitation are analyzed,and a mathematical ex-pression is constructed using the virtual excitation method.Secondly,a dynamic model of the unit is established to demonstrate the non-stationary random vibration characteristics under hydraulic excitation.Thirdly,an active learning non-stationary vibration reliability analysis method AK-MCS-T-H is proposed combining the Kriging model,the Monte Carlo simulation(MCS)method,and the information entropy learning function H.This method reveals the influence of the non-stationary hydraulic excitation on the random vibration reliability of the hydro-turbine generator unit.Finally,an example is presented to analyze the random vibration reliability.The study shows that the AK-MCS-T-H proposed in this paper can solve the problem of non-stationary random vibration reliability of the Francis hydro-turbine generator unit more effectively.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

A Planning Method for Operational Test of UAV Swarm Based on Mission Reliability

The unmanned aerial vehicle(UAV)swarm plays an increasingly important role in the modern battlefield,and the UAV swarm operational test is a vital means to validate the combat effectiveness of the UAV swarm.Due to the high cost and long duration of operational tests,it is essential to plan the test in advance.To solve the problem of planning UAV swarm operational test,this study considers the multi-stage feature of a UAV swarm mission,composed of launch,flight and combat stages,and proposes a method to find test plans that can maximize mission reliability.Therefore,a multi-stage mission reliability model for a UAV swarm is proposed to ensure successful implementation of the mission.A multi-objective integer optimization method that considers both mission reliability and cost is then formulated to obtain the optimal test plans.This study first constructs a mission reliability model for the UAV swarm in the combat stage.Then,the launch stage and flight stage are integrated to develop a complete PMS(Phased Mission Systems)reliability model.Finally,the Binary Decision Diagrams(BDD)and Multi Objective Quantum Particle Swarm Optimization(MOQPSO)methods are proposed to solve the model.The optimal plans considering both reliability and cost are obtained.The proposed model supports the planning of UAV swarm operational tests and represents a meaningful exploration of UAV swarm test planning.

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.

A review of extreme condition effects on solder joint reliability:Understanding failure mechanisms

Solder joint,crucial component in electronic systems,face significant challenges when exposed to extreme conditions during applications.The solder joint reliability involving microstructure and mechanical properties will be affected by extreme conditions.Understanding the behaviour of solder joints under extreme conditions is vital to determine the durability and reliability of solder joint.This review paper aims to comprehensively explore the underlying failure mechanism affecting solder joint reliability under extreme conditions.This study covers an in-depth analysis of effect extreme temperature,mechanical stress,and radiation conditions towards solder joint.Impact of each condition to the microstructure including solder matrix and intermetallic compound layer,and mechanical properties such as fatigue,shear strength,creep,and hardness was thoroughly discussed.The failure mechanisms were illustrated in graphical diagrams to ensure clarity and understanding.Furthermore,the paper highlighted mitigation strategies that enhancing solder joint reliability under challenging operating conditions.The findings offer valuable guidance for researchers,engineers,and practitioners involved in electronics,engineering,and related fields,fostering advancements in solder joint reliability and performance.

On the relationship between imprint and reliability in Hf_(0.5)Zr_(0.5)O_(2) based ferroelectric random access memory

The detrimental effect of imprint,which can cause misreading problem,has hindered the application of ferroelectric HfO_(2).In this work,we present results of a comprehensive reliability evaluation of Hf_(0.5)Zr_(0.5)O_(2)-based ferroelectric random access memory.The influence of imprint on the retention and endurance is demonstrated.Furthermore,a solution in circuity is pro-posed to effectively solve the misreading problem caused by imprint.

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.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

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.

Reliability Assessment of a New General Matching Composed Network

The reliability of a network is an important indicator for maintaining communication and ensuring its stable operation. Therefore, the assessment of reliability in underlying interconnection networks has become an increasingly important research issue. However, at present, the reliability assessment of many interconnected networks is not yet accurate,which inevitably weakens their fault tolerance and diagnostic capabilities. To improve network reliability,researchers have proposed various methods and strategies for precise assessment. This paper introduces a novel family of interconnection networks called general matching composed networks(gMCNs), which is based on the common characteristics of network topology structure. After analyzing the topological properties of gMCNs, we establish a relationship between super connectivity and conditional diagnosability of gMCNs. Furthermore, we assess the reliability of g MCNs, and determine the conditional diagnosability of many interconnection networks.

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.

Introduction to the Special Issue on Computer-Aided Uncertainty Modeling and Reliability Evaluation for Complex Engineering Structures

1 Summary With the advancement of science and technology,complex engineering structures are widely used in extreme environments[1].In equipment service,many uncertainty factors significantly affect safety and reliability[2–5].Therefore,ensuring high reliability of structures has become an important research direction in engineering design.At the same time,the importance of equipment health management of complex engineering structures is becoming increasingly prominent[6–8].Computer-aided uncertainty modeling and reliability assessment have become key tools,and finite element simulation and algorithmic innovation play a key role in the reliability analysis of complex equipment[9,10].These techniques can accurately simulate stress and damage accumulation under various operating environments,providing engineers with important decision support and optimization solutions.

Interobserver and intraobserver reliability of skull base angles measured on magnetic resonance images

BACKGROUND Determination of platybasia and basilar kyphosis are significant parts of routine cranial magnetic resonance(MR)interpretations.These situations may explain a patient’s symptoms or may be associated with other anomalies.AIM To indicate the interobserver and intraobserver reliability of the skull base angles(SBA)(Koenigsberg standard)and modified SBA(mSBA)measurement techniques.METHODS In total,391 patients who had undergone cranial MR imaging were re-assessed regarding the SBA measurements.The SBA and mSBA techniques were used on MR images.Two reviewers independently measured the same angles twice within a 15-day interval,using different monitors.Intraclass correlation coefficient(ICC)was calculated to reveal the intraobserver and interobserver agreements.RESULTS There was an excellent agreement between reviewers regarding both angle measurements(ICC was 0.998 for SBA and mSBA).Excellent agreement levels were also observed for intraobserver measurements.ICC was 0.998 for SBA and 0.999 for mSBA for reviewer 1.ICC was 0.997 for SBA and 0.999 for mSBA according to the measurement results of reviewer 2.Higher SBA and mSBA values were observed for females compared to males.There was no correlation between SBA and age for SBA.However,a negative and low-level correlation was observed between mSBA values and age for both reviewers.CONCLUSION SBA and mSBA measurements indicated excellent agreement regarding interobserver and intraobserver differences.The study results showed that SBA angles were reliable measurement techniques to be used on MR images.