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 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.

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-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.

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.

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-BasedModel for Incomplete Preventive ReplacementMaintenance of Photovoltaic Power Systems

At present,the operation and maintenance of photovoltaic power generation systems mainly comprise regular maintenance,breakdown maintenance,and condition-based maintenance,which is very likely to lead to over-or under-repair of equipment.Therefore,a preventive maintenance and replacement strategy for PV power generation systems based on reliability as a constraint is proposed.First,a hybrid failure function with a decreasing service age factor and an increasing failure rate factor is introduced to describe the deterioration of PV power generation equipment,and the equipment is replaced when its reliability drops to the replacement threshold in the last cycle.Then,based on the reliability as a constraint,the average maintenance cost and availability of the equipment are considered,and the non-periodic incomplete maintenance model of the PV power generation system is established to obtain the optimal number of repairs,each maintenance cycle and the replacement cycle of the PV power generation system components.Next,the inverter of a PV power plant is used as a research object.The model in this paper is compared and analyzed with the equal cycle maintenance model without considering reliability and the maintenance model without considering the equipment replacement threshold,Through model comparison,when the optimal maintenance strategy is(0.80,4),the average maintenance cost of this paper’s model are decreased by 20.3%and 5.54%and the availability is increased by 0.2395% and 0.0337%,respectively,compared with the equal-cycle maintenance model without considering the reliability constraint and the maintenance model without considering the equipment replacement threshold.Therefore,this maintenance model can ensure the high reliability of PV plant operation while increasing the equipment availability to improve the system economy.

Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

The objective of this paper is to evaluate the reliability of a system in its different states (absence of failures, partial failure and total failure) and to propose actions to improve this reliability by an approach based on Monte Carlo simulation. It consists of a probabilistic evaluation based on Markov Chains. In order to achieve this goal, the functionalities of Markov Chains and Monte Carlo simulation steps are deployed. The application is made on a production system. .

Reliability analysis of torpedo loading based on fractional-order optimization model

A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function related to order and background value is established.Taking the average relative error function as the objective function,the optimal value of the two parameters is obtained through the optimization method,and the minimum value of the average relative error is determined.The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2)model.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Mechanical Dispatch Reliability Prediction for Civil Aircraft Considering Operational Parameters

To effectively predict the mechanical dispatch reliability(MDR),the artificial neural networks method combined with aircraft operation health status parameters is proposed,which introduces the real civil aircraft operation data for verification,to improve the modeling precision and computing efficiency.Grey relational analysis can identify the degree of correlation between aircraft system health status(such as the unscheduled maintenance event,unit report event,and services number)and dispatch release and screen out themost closely related systems to determine the set of input parameters required for the prediction model.The artificial neural network using radial basis function(RBF)as a kernel function,has the best applicability in the prediction of multidimensional,small sample problems.Health status parameters of related systems are used as the input to predict the changing trend ofMDR,under the artificial neural network modeling framework.The case study collects real operation data for a certain civil aircraft over the past five years to validate the performance of the model which meets the requirements of the application.The results show that the prediction quadratic error Ep of the model reaches 6.9×10−8.That is to say,in the existing operating environment,the prediction of the number of delay&cancel events per month can be less than once.The accuracy of RBF ANN,BP ANN and GA-BP ANN are compared further,and the results show that RBF ANN has better adaptability to such multidimensional small sample problems.The efforts of this paper provide a highly efficientmethod for theMDR prediction through aircraft system health state parameters,which is a promising model to enhance the prediction and controllability of the dispatch release,providing support for the construction of the civil aircraft operation system.

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.

Research Progress on the Solder Joint Reliability of Electronics Using in Deep Space Exploration

The spacecraft for deep space exploration missions will face extreme environments,including cryogenic temperature,intense radiation,wide-range temperature variations and even the combination of conditions mentioned above.Harsh environments will lead to solder joints degradation or even failure,resulting in damage to onboard electronics.The research activities on high reliability solder joints using in extreme environments can not only reduce the use of onboard protection devices,but effectively improve the overall reliability of spacecraft,which is of great significance to the aviation industry.In this paper,we review the reliability research on SnPb solder alloys,Sn-based lead-free solder alloys and In-based solder alloys in extreme environments,and try to provide some suggestions for the follow-up studies,which focus on solder joint reliability under extreme environments.

Ergonomic Reliability Assessment of VDT Systemfor Operation Design Based on Improved BPNN and HCR under Special Circumstances

Ergonomic reliability plays a significant role in the safe operation of devices.With the spread of infectious diseases around the world,in work environments with high loads and high infection rates,medical staff work in a state of high self-protection.The use of visual display terminal(VDT)for medical equipment has undergone fundamental changes,and the traditional medical equipment human-machine interface design needs to be improved.After the completion of design and development,a VDT design enters the experimental testing stage,which has significant limitations for simulating the work of medical staff in the high-load and high-infection environments.The testing cost is high,and subjects face harsh conditions;thus,an ergonomic reliability model that can predict the use of VDT in such special high-infection and high-load circumstances must be established.An ergonomic reliability model based on an improved backpropagation neural network(BPNN)and human cognition reliability(HCR)is proposed for predicting and evaluating operation flows according tomedical equipment VDTs.Firstly,a small data sample can be used to train BPNN to generate a network that can ensure suitable accuracy.To prevent the model from falling into local optimal solutions,the bat algorithm is introduced to improve the BPNN.Compared to a traditional BPNN,the superiority of the improved BPNN is clearly demonstrated.Secondly,the HCR method is used to analyze and highlight changes in the human factor reliability of VDTs for medical equipment in different time processes and operating processes according to BPNN prediction results,to provide a reference for selecting the optimalmethod.Finally,the validity and availability of the proposedmethod are verified through an eye tracker experiment and statistical analysis results.

Assembly-oriented reliability analysis method for the top-connection structure of a nuclear fuel assembly

The nuclear fuel assembly is the core component of a nuclear reactor.In a pressurized water reactor fuel assembly,the top-connection structure connects the top nozzle to the guide thimble.Its performance reliability is essential for the stability of the nuclear fuel assembly.In this study,an assembly-oriented reliability analysis method for top-connection structures is presented by establishing an assembly-oriented top-connection structure parameter modeling method and a nonlinear contact gap and penetration correction method.A reliability model of the top-connection assembly structure,including multiple stochastic design variables,was constructed,and the overall reliability of the top-connection assembly structure was obtained via a Kriging model and Monte Carlo simulation.The acquired experimental data were consistent with real-world failure conditions,which verified the practicability and feasibility of the reliability analysis method proposed in this study.

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.

Active learning accelerated Monte-Carlo simulation based on the modified K-nearest neighbors algorithm and its application to reliability estimations

This paper proposes an active learning accelerated Monte-Carlo simulation method based on the modified K-nearest neighbors algorithm.The core idea of the proposed method is to judge whether or not the output of a random input point can be postulated through a classifier implemented through the modified K-nearest neighbors algorithm.Compared to other active learning methods resorting to experimental designs,the proposed method is characterized by employing Monte-Carlo simulation for sampling inputs and saving a large portion of the actual evaluations of outputs through an accurate classification,which is applicable for most structural reliability estimation problems.Moreover,the validity,efficiency,and accuracy of the proposed method are demonstrated numerically.In addition,the optimal value of K that maximizes the computational efficiency is studied.Finally,the proposed method is applied to the reliability estimation of the carbon fiber reinforced silicon carbide composite specimens subjected to random displacements,which further validates its practicability.

Test re-test reliability of virtual acoustic space identification (VASI) test in young adults with normal hearing

Background:Recent developments in virtual acoustic technology has levered promising applications in the field of auditory sciences,especially in spatial perception.While conventional auditory spatial assessment using loudspeakers,interaural differences and/or questionnaires are limited by the availability and cost of instruments,the use of virtual acoustic space identification(VASI)test has widespread applications in spatial test battery as it overcomes these constraints.Purpose:The lack of test-retest reliability data of VASI test narrows its direct application in auditory spatial assessment,which is explored in the present study.Methods:Data from 75 normal-hearing young adults(mean age:25.11 y±4.65 SD)was collected in three sessions:baseline,within 15 min of baseline(intra-session),and one week after baseline session(inter-session).Test-retest reliability was assessed using the intra-class correlation coefficient(ICC),coefficient of variation(CV),and cluster plots.Results:The results showed excellent reliability for both accuracy and reaction time measures of VASI,with ICC values of 0.93 and 0.87,respectively.The CV values for overall VASI accuracy and reaction time 9.66% and 11.88%,respectively.This was also complemented by the cluster plot analyses,which showed 93.33% and 96.00% of temporal stability in the accuracy and reaction time measures,indicative of high test-retest reliability of VASI test in auditory spatial assessment.Conclusions:The high temporal stability(test-retest reliability)of VASI test validates its application in spatial hearing test battery.