Application of matrix-based system reliability method in complex slopes

Complex slopes are characterized by large numbers of failure modes,cut sets or link sets,or by statistical dependence between the failure modes.For such slopes,a systematic quantitative method,or matrix-based system reliability method,was described and improved for their reliability analysis.A construction formula of event vector c E was suggested to solve the difficulty of identifying any component E in sample space,and event vector c of system events can be calculated based on it,then the bounds of system failure probability can be obtained with the given probability information.The improved method was illustrated for four copper mine slopes with multiple failure modes,and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB.Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system.Otherwise,the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.

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.

Computer System Reliability Allocation Method and Supporting Tool

This paper presents a computer system reliability allocation method that is based on the theory of statistic and Markovian chain,which can be used to allocate reliability to subsystem, to hybrid system and software modules. A relevant supporting tool built by us is introduced.

Structural Reliability Analysis Method in Fuzzy Environment

In this paper, the fuzzy-set-based structural possibility theory is investigated, and this theory can be used to deal with the subjective uncertainties in the design of engineering structures. Furthermore, a comprehensive model of structural safety assessment, which can merge subjective uncertainties with objective uncertainties, is presented. In this model, the fuzziness of stress-strength inference model, safety margin functions of single or multiple limit-state, structural failure state and the final assessment result are taken into account. This continuous model can be transformed into an equivalent model of probability-based and solved by the present structural reliability analysis method and parallel algorithm. An example is given to show the main idea of the method presented in this paper.

RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

Assessment of buckling-restrained braced frame reliability using an experimental limit-state model and stochastic dynamic analysis

Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.

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

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

Optimization design of piles subjected to horizontal loads based on reliability theory

Based on reliability theory,a general method for the optimization design of piles subjected to horizontal loads is presented.This method takes into consideration various uncertainties caused by pile installation,variability of geotechnical materials from one location to another,and so on.It also deals with behavior and side constraints specified by standard specifications for piles.To more accurately solve the optimization design model,the first order reliability method is employed.The results from the numerical example indicate that the target reliability index has significant influence on design parameters.In addition,the optimization weight increases with the target reliability index.Especially when the target reliability index is relatively large,the target reliability index has significant influence on design weight of piles.

Reliability‑Based Analysis of a Caisson Breakwater with the Application of Bayesian Inference

Caisson breakwaters are mainly constructed in deep waters to protect an area against waves.These breakwaters are con-ventionally designed based on the concept of the safety factor.However,the wave loads and resistance of structures have epistemic or aleatory uncertainties.Furthermore,sliding failure is one of the most important failure modes of caisson breakwaters.In most previous studies,for assessment purposes,uncertainties,such as wave and wave period variation,were ignored.Therefore,in this study,Bayesian reliability analysis is implemented to assess the failure probability of the sliding of Tombak port breakwater in the Persian Gulf.The mean and standard deviations were taken as random variables to consider dismissed uncertainties.For this purpose,the frst-order reliability method(FORM)and the frst principal curvature cor-rection in FORM are used to calculate the reliability index.The performances of these methods are verifed by importance sampling through Monte Carlo simulation(MCS).In addition,the reliability index sensitivities of each random variable are calculated to evaluate the importance of diferent random variables while calculating the caisson sliding.The results show that the reliability index is most sensitive to the coefcients of friction,wave height,and caisson weight(or concrete density).The sensitivity of the failure probability of each of the random variables and their uncertainties are calculated by the derivative method.Finally,the Bayesian regression is implemented to predict the statistical properties of breakwater sliding with non-informative priors,which are compared to Goda’s formulation,used in breakwater design standards.The analysis shows that the model posterior for the sliding of a caisson breakwater has a mean and standard deviation of 0.039 and 0.022,respectively.A normal quantile analysis and residual analysis are also performed to evaluate the correctness of the model responses.

Reliability Assessment of a Fully Laterally Restrained Steel Floor Beam to Eurocode 3

Parametric uncertainties should always be considered when setting design criteria in order to ensure safe and cost effective design of engineered structures. This paper presents the results of the reliability assessment of a fully laterally restrained steel floor I-beam to Eurocode 3 design rules. The failure modes considered are bending, shear and deflection. These were solved to obtain reliability indices using first order reliability method coded in MATLAB environment. Parametric sensitivity analyses were carried out at varying values of the design parameters to show their relative contributions to the safety of the beam. It was seen that reliability indices generally decreased with an increase in load ratio, imposed load, beam span in bending, shear stress and deflection respectively. In addition, increasing the beam span beyond 10 m, load ratio above 1.4 and imposed load beyond 30 kN/m made the beam fail as these parameters gave negative reliability indices. For failure in deflection, reliability index rose with an increase in the radius of gyration and overall depth of the beam section accordingly. Furthermore, the reliability index surged as the thickness of the web increased when taking into account, shear failure. The results of the analysis showed that the steel beam is very safe in shear and at some load ratios and imposed loads for failure in bending and deflection respectively. The average values of reliability indices obtained for load ratios ranging from 1.0 to 1.4 fell from 3.017 to 3.457 for all failure mode studied. These values are within the recommended reliability indices by the Joint Committee on Structural Safety for structure with moderate failure consequences and beams in flexure.

Reliability Sensitivity-based Correlation Coefficient Calculation in Structural Reliability Analysis

The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored,which cannot actually reflect the effects of parameter uncertainties on reliability.To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view,the theory principle of the problem is established based on the results of the reliability sensitivity,and the criterion of correlation among random variables is shown.The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed.Numerical studies have shown the following results：（1） If the sensitivity value of correlation coefficient ρ is less than（at what magnitude 0.000 01）,then the correlation could be ignored,which could simplify the procedure without introducing additional error.（2） However,as the difference between ρs,that is the most sensitive to the reliability,and ρR,that is with the smallest reliability,is less than 0.001,ρs is suggested to model the dependency of random variables.This could ensure the robust quality of system without the loss of safety requirement.（3） In the case of ｜Eabs｜ρ0.001 and also ｜Erel｜ρ0.001,ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis.Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.

System Reliability Analysis of Offshore Strctures and Component Safety Rank Assessment

Offshore structures will encounter serious environmental load, so it is important to study the structural system reliability and to evaluate the structural component safety rank. In this paper, the bracnch-and-bound method is adopted to search the main failure path, and the Ditlevsen bound method is used to calculate the system failure probability. The structure is then assessed by the fuzzy comprehensive assessment method, which evaluates the structural component safety rank. The ultimate equation of the tubular cross- section is analyzed on the basis of ultimate stregnth analysis. The influence of effect coefficients on the structural system failure probability is investigated, and basic results are obtained. A general program for spatial frame structures by means of the above method is developed, and verified by the numerical examples.

Reliability and sensitivity analyses of HPT blade-tip radial running clearance using multiply response surface model

To reasonably design the blade-tip radial running clearance(BTRRC) of high pressure turbine and improve the performance and reliability of gas turbine, the multi-object multi-discipline reliability sensitivity analysis of BTRRC was accomplished from a probabilistic prospective by considering nonlinear material attributes and dynamic loads. Firstly, multiply response surface model(MRSM) was proposed and the mathematical model of this method was established based on quadratic function. Secondly, the BTRRC was decomposed into three sub-components(turbine disk, blade and casing), and then the single response surface functions(SRSFs) of three structures were built in line with the basic idea of MRSM. Thirdly, the response surface function(MRSM) of BTRRC was reshaped by coordinating SRSFs. From the analysis, it is acquired to probabilistic distribution characteristics of input-output variables, failure probabilities of blade-tip clearance under different static blade-tip clearances δ and major factors impacting BTRRC. Considering the reliability and efficiency of gas turbine, δ=1.87 mm is an optimally acceptable option for rational BTRRC. Through the comparison of three analysis methods(Monte Carlo method, traditional response surface method and MRSM), the results show that MRSM has higher accuracy and higher efficiency in reliability sensitivity analysis of BTRRC. These strengths are likely to become more prominent with the increasing times of simulations. The present study offers an effective and promising approach for reliability sensitivity analysis and optimal design of complex dynamic assembly relationship.

IEC 62059 Standards' Application in Reliability Prediction and Verification of Smart Meters

This article introduces the current situation of the smart then describes the relationship of meter reliability characteristics meter＇s reliability and the failure mechanisms at first, and combined with its Bathtub Curve. It also introduces both the feasible failure tree model for meter lifecycle prediction based on actual experiences and meter reliability prediction methodology by SN 29500 norms based on this model. This article also brings forward that it is necessary that the ＂Learning Factor＂ shall be adopted in meter reliability prediction for new materials, new process, and customized parts by referring to GJB/Z299C. Thereafter, this article also tries to apply IEC 62059 and JB/T 50070 to introduce the feasible method for the lifecycle prediction result verification by accelerated lifecycle test. Furthermore, the article also explores ways to increase the firmware reliability in smart meter.

PROBABILISTIC METHODOLOGY OF LOW CYCLE FATIGUE ANALYSIS

The cyclic stress-strain responses (CSSR), Neuber's rule (NR) and cyclic strain-life relation (CSLR) are treated as probabilistic curves in local stress and strain method of low cycle fatigue analysis. The randomness of loading and the theory of fatigue damage accumulation (TOFDA) are considered. The probabilistic analysis of local stress, local strain and fatigue life are constructed based on the first-order Taylor's series expansions. Through this method proposed fatigue reliability analysis can be accomplished.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

Quantitative Human Reliability Analysis for Crew During Shipping Operation

A simplified bi-variable human error probability calculation method is developed by incorporating two common performance condition( CPC) factors, which are modified from factors employed in cognitive reliability and error analysis method(CREAM) to take into account the characteristics of shipping operations. After the influencing factors are identified, Markov method is used to calculate the values of human reliability. The proposed method does not rely on the involvement of experts in the field of human factor nor depend on historical accidents or human error statistics. It is applied to the case of the crew on board of an ocean going dry bulk carrier. The caculated results agree with the actual case, which verifies the validity of the model.

THE RANDOM VARIATIONAL PRINCIPLE IN FINITE DEFORMATION OF ELASTICITY AND FINITE ELEMENT METHOD

In the present paper, we hare mtroduced the random materials. loads. geometricalshapes, force and displacement boundary condition directly. into the functionalvariational formula, by. use of a small parameter perturbation method, a unifiedrandom variational principle in finite defomation of elastieity and nonlinear randomfinite element method are esiablished, and used.for reliability, analysis of structures.Numerical examples showed that the methods have the advontages of simple andconvenient program implementation and are effective for the probabilistic problems inmechanics.

Reliability Measure of a Relay Parallel System under Dependence Conditions

In a relay system of dependent components, the failure to close reliability measure is given as a Girsanov transform of the failure to open reliability measure.

Probabilistic analysis of ultimate seismic bearing capacity of strip foundations

This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method(FORM) is employed to calculate the reliability index. The response surface methodology(RSM) is used to assess the Hasofer e Lind reliability index and then it is optimized using a genetic algorithm(GA). The random variables used are the soil shear strength parameters and the seismic coefficients(khand kv). Two assumptions(normal and non-normal distribution) are used for the random variables. The assumption of uncorrelated variables was found to be conservative in comparison to that of negatively correlated soil shear strength parameters. The assumption of non-normal distribution for the random variables can induce a negative effect on the reliability index of the practical range of the seismic bearing capacity.