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.

Sensitivity analysis and probability modelling of the structural response of a single-layer reticulated dome subjected to an external blast loading

The structural response of a single-layer reticulated dome to external explosions is shaped by many variables,and the associated uncertainties imply non-deterministic results.Existing deterministic methods for predicting the consequences of specific explosions do not account for these uncertainties.Therefore,the impact of the uncertainties associated with these input variables on the structures’response needs to be studied and quantified.In this study,a parametric uncertainty analysis was conducted first.Then,local and global sensitivity analyses were carried out to identify the drivers of the structural dynamic response.A probabilistic structural response model was established based on sensitive variables and a reasonable sample size.Furthermore,some deterministic empirical methods for explosion-resistance design,including the plane blast load model of CONWEP,the curved blast load model under the 50%assurance level,and the 20%mass-increased method,were used for evaluating their reliability.The results of the analyses revealed that the structural response of a single-layer reticulated dome to an external blast loading is lognormally distributed.Evidently,the MB0.5 method based on the curved reflector load model yielded results with a relatively stable assurance rate and reliability,but CONWEP did not;thus,the 1.2MB0.5 method can be used for making high-confidence simple predictions.In addition,the results indicated that the structural response is very sensitive to the explosion parameters.Based on these results,it is suggested that for explosion proofing,setting up a defensive barrier is more effective than structural strengthening.

Reliability and sensitivity analysis of wedge stability in the abutments of an arch dam using artificial neural network

In this study,the seismic stability of arch dam abutments is investigated within the framework of the probabilistic method.A large concrete arch dam is considered with six wedges for each abutment.The seismic safety of the dam abutments is studied with quasi-static analysis for different hazard levels.The Londe limit equilibrium method is utilized to calculate the stability of the wedges in the abutments.Since the finite element method is time-consuming,the neural network is used as an alternative for calculating the wedge safety factor.For training the neural network,1000 random samples are generated and the dam response is calculated.The direction of applied acceleration is changed within 5-degree intervals to reveal the critical direction corresponding to the minimum safety factor.The Latin hypercube sampling(LHS)is employed for sample generation,and the safety level is determined with reliability analysis.Three sample numbers of 1000,2000 and 4000 are used to examine the average and standard deviation of the results.The global sensitivity analysis is used to identify the effects of random variables on the abutment stability.It is shown that friction,cohesion and uplift pressure have the most significant effects on the wedge stability variance.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

Reliability Sensitivity Analysis for Location Scale Family

Many products always operate under various complex environment conditions. To describe the dynamic influence of environment factors on their reliability, a method of reliability sensitivity analysis is proposed. In this method, the location parameter is assumed as a function of relevant environment variables while the scale parameter is assumed as an unknown positive constant. Then, the location parameter function is constructed by using the method of radial basis function. Using the varied environment test data, the log-likelihood function is transformed to a generalized linear expression by describing the indicator as Poisson variable. With the generalized linear model, the maximum likelihood estimations of the model coefficients are obtained. With the reliability model, the reliability sensitivity is obtained. An instance analysis shows that the method is feasible to analyze the dynamic variety characters of reliability along with environment factors and is straightforward for engineering application.

Reliability Evaluation and Sensitivity Analysis for Multi-state System Based on Time Degradation Measures

The performance and state of multi-state system depend on its structure and different state combinations of the components. In order to evaluate the reliability of multi-state system effectively,a reliability evaluation and sensitivity analysis method based on the time degradation measures was proposed. The equivalence sets of the multi-state system under different output performances were established. The state combinations were classified according to the performance level. The degradation probability models under different states were established,and the new reliability measures,such as dynamic probability of multi-state system,holding time in each state,dynamic expectation function and integrated expectation function of the performance,were proposed and used to implement the dynamic reliability evaluation and sensitivity analysis. A certain diesel engine fuel feeding system was taken as an application example to illustrate the proposed method. The results show that not only the holding time in the desired state of the components and the system can be predicted,but also the best state component in a certain time period can be obtained.

Improved Reliability Analysis Method Based on the Failure Assessment Diagram

With the uncertainties related to operating conditions,in-service non-destructive testing（NDT） measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram（FAD） approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics（PFM） assessment method is proposed.By integrating 2D kernel density estimation（KDE） technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

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.

Post-buckling Reliability and Sensitivity Analysis of Composite Stiffened Plates Based on Adaptive Kriging Method

Based on the active learning Kriging(ALK)model and the Hashin failure criterion,this paper proposes a new reliability evaluationmodel for composite stiffened panels,and conducts a reliability analysis on the ultimate bearing capacity.In addition,this paper studies the importance ranking of input variables.By comparing the calculation results of the reliability model proposed in this paper with those of the Monte Carlo method,the accuracy and efficiency of the ALK model are verified by case studies.Finally,the effects of longitudinal elastic modulus and fiber-direction tensile strength on post-buckling failure probability are discussed,which provides significant reference and guidance for the optimization and design of composite stiffened plates.

Sensitivity Study on Durability Variables of Marine Concrete Structures

In order to study the influence of parameters on durability of marine concrete structures, the parameter＇s sensitivity analysis was studied in this paper. With the Fick＇s 2nd law of diffusion and the deterministic sensitivity analysis method （DSA）, the sensitivity factors of apparent surface chloride content, apparent chloride diffusion coefficient and its time dependent attenuation factor were analyzed. The results of the analysis show that the impact of design variables on concrete durability was different. The values of sensitivity factor of chloride diffusion coefficient and its time dependent attenuation factor were higher than others. Relative less error in chloride diffusion coefficient and its time dependent attenuation coefficient induces a bigger error in concrete durability design and life prediction. According to probability sensitivity analysis （PSA）, the influence of mean value and variance of concrete durability design variables on the durability failure probability was studied. The results of the study provide quantitative measures of the importance of concrete durability design and life prediction variables. It was concluded that the chloride diffusion coefficient and its time dependent attenuation factor have more influence on the reliability of marine concrete structural durability. In durability design and life prediction of marine concrete structures, it was very important to reduce the measure and statistic error of durability design variables.

多维平行六面体模型非概率可靠性灵敏度分析

可靠性灵敏度能够反映基本变量分布参数对可靠度的影响程度,为可靠性分析与优化设计提供指导。提出了一种基于多维平行六面体模型的非概率可靠性灵敏度分析方法。首先,给出基本变量域完全位于安全域时采用非概率可靠性指标,而基本变量域与安全域有交集时采用非概率失效度作为可靠性度量的原因。其次,推导结构线性系统的可靠性灵敏度解析式,并进一步探讨所提方法对结构非线性系统的适应性问题。最后,通过3个工程算例验证文中方法有效可行。

考虑热误差的电主轴建模与可靠性全局灵敏度分析

以数控机床电主轴为研究对象,旨在分析其轴向热伸长量对电主轴可靠性的影响.采用Svenska Kullager-Fabriken(SKF)摩擦力矩模型对轴承生热量进行分析,设定对流换热系数为边界散热条件,建立了热分析有限元耦合模型,求解电主轴的温度以及轴向热伸长分布.将有限元模型与实验结果进行对比,验证了建立的有限元模型的准确性.考虑随机因素的影响,建立电主轴热变形可靠性分析模型,并采用Kriging模型进行可靠性求解.对电主轴热误差可靠性全局灵敏度进行分析,结果表明,转速和冷却水流量对可靠度影响较大,轴向力和径向力对可靠度影响较小.

基于压弯破坏曲面的桥墩可靠性分析

非对称桥梁结构悬臂施工期间会对下部结构产生较大的不平衡弯矩,为分析钢筋混凝土(Reinforced Concrete,RC)墩柱在不平衡弯矩导致的双轴压弯下的可靠性,提出了基于压弯破坏曲面的可靠性分析方法。该方法使用倪克勤公式作为功能函数,并通过钢筋与混凝土本构关系求解倪克勤公式所需要的轴心受压承载力与单向偏压承载力,将RC墩柱的材料特性、几何特性、所受外部荷载作为随机变量,基于可靠指标物理意义,使用罚函数法将可靠指标求解问题转化为无约束最优化问题,利用遗传退火算法求解RC墩柱的可靠指标。采用该方法对文忠路上跨合肥东站改扩建工程主桥46号桥墩进行可靠性分析,结果表明:在悬臂施工至自重不平衡弯矩最大状态下,P1~P3支墩可靠指标分别为5.44、5.05、5.94;对可靠指标影响程度较大的随机变量依次为结构自重、钢筋强度和混凝土抗压强度,而风荷载对可靠指标影响相对较小。

Reliability and reliability sensitivity analysis of structure by combining adaptive linked importance sampling and Kriging reliability method

The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges:small failure probability(typical less than 10-5)and time-demanding mechanical models.This paper proposes an improved active learning surrogate model method,which combines the advantages of the classical Active Kriging–Monte Carlo Simulation(AK-MCS)procedure and the Adaptive Linked Importance Sampling(ALIS)procedure.The proposed procedure can,on the one hand,adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling(IS)density,on the other hand,adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event.Then,the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models.Compared with the classical AK-MCS and Active Kriging–Importance Sampling(AK-IS)procedure,the proposed method neither need to build very large sample pool even when the failure probability is extremely small,nor need to estimate the Most Probable Points(MPPs),thus it is computationally more efficient and more applicable especially for problems with multiple MPPs.The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.

双洞公路隧道中夹岩柱可靠度研究

目的为了探究双洞隧道开挖后中夹岩柱的变形规律及破坏特征,改进岩柱稳定性定量评估方法。方法以某市公路双洞隧道为例,建立了非侵入式随机有限元-蒙特卡罗分析框架,提出基于中夹岩柱中部轴线变形的应变失稳准则。通过改变岩土体的物理力学参数变异系数、岩柱宽度以及隧道埋深研究双洞隧道开挖后中夹岩柱的失效概率,并分析其变化规律,进而采用系统稳定性分析法对影响岩柱的参数进行敏感性分析。结果在该工程背景下的中夹岩柱失效概率为0.2204,需定期进行稳定性监测。比较各影响因素归一化敏感度因子,岩柱失效概率对各因素敏感性由高到低依次为弹性模量变异系数、岩柱宽度、黏聚力变异系数、内摩擦角变异系数与隧道埋深,后续设计相似岩体参数分布的双洞隧道时,应关注弹性模量变异系数对岩柱稳定性的影响。结论非侵入式随机有限元-蒙特卡罗分析框架能够对中夹岩柱可靠度进行计算,实现结构的稳定性定量评估,为双洞隧道设计及稳定性控制提供一定的理论依据。

Reliability and variance-based sensitivity analysis of arch dams during construction and reservoir impoundment

The static performance of arch dams during construction and reservoir impoundment is assessed taking into account the effects of uncertainties presented in the model properties as well as the loading conditions.Dez arch dam is chosen as the case study;it is modeled along with its rock foundation using the finite element method considering the stage construction.Since previous studies concentrated on simplified models and approaches,comprehensive study of the arch dam model along with efficient and state-of-the-art uncertainty methods are incorporated in this investigation.The reliability method is performed to assess the safety level and the sensitivity analyses for identifying critical input factors and their interaction effects on the response of the dam.Global sensitivity analysis based on improved Latin hypercube sampling is employed in this study to indicate the influence of each random variable and their interaction on variance of the responses.Four levels of model advancement are considered for the dam foundation system:1)Monolithic dam without any joint founded on the homogeneous rock foundation,2)monolithic dam founded on the inhomogeneous foundation including soft rock layers,3)jointed dam including the peripheral and contraction joints founded on the homogeneous foundation,and 4)jointed dam founded on the inhomogeneous foundation.For each model,proper performance indices are defined through limit-state functions.In this manner,the effects of input parameters in each performance level of the dam are investigated.The outcome of this study is defining the importance of input factors in each stage and model based on the variance of the dam response.Moreover,the results of sampling are computed in order to assess the safety level of the dam in miscellaneous loading and modeling conditions.

Resonance System Reliability and Sensitivity Analysis Method for Axially FGM Pipes Conveying Fluid with Adaptive Kriging Model

This paper aims to solve the resonance failure probability and develop an effective method to estimate the effects of variables and failure modes on failure probability of axially functionally graded material(FGM)pipe conveying fluid.Correspondingly,the natural frequency of axially FGM pipes conveying fluid is calculated using the differential quadrature method(DQM).A variable sensitivity analysis(VSA)is introduced to measure the effect of each random variable,and a mode sensitivity analysis(MSA)is introduced to acquire the importance ranking of failure modes.Then,an active learning Kriging(ALK)method is established to calculate the resonance failure probability and sensitivity indices,which greatly improves the application of resonance reliability analysis for pipelines in engineering practice.Based on the resonance reliability analysis method,the effects of fluid velocity,volume fraction and fluid density of axially FGM pipe conveying fluid on resonance reliability are analyzed.The results demonstrate that the proposed method has great performance in the anti-resonance analysis of pipes conveying fluid.

考虑动态腐蚀的输流管道时变共振可靠性及灵敏度分析

考虑输流管道受到环境动态腐蚀,壁厚变化引发输流管道固有频率变化,从而可能导致共振。因此,考虑时间变化以及输流管道结构参数、流体参数和外部激励频率的不确定性,采用Galerkin法求解输流管道固有频率,建立时变防共振功能函数,引入基于自适应Kriging模型的时变可靠性算法对时变失效概率进行高效求解,并与MCS法和SL-ALK法对比验证了方法的准确性,采用变量灵敏度指标评估各随机变量对时变失效概率的影响,分析了流体密度和流速对于时变共振失效概率的影响规律。

基于疲劳失效的行星齿轮减速器时变可靠性分析

随着科技革新与社会发展,对行星齿轮减速器的可靠性要求越来越高。行星齿轮减速器运行过程中存在疲劳因素,会导致可靠度发生变化。针对这一问题,首先,根据应力-强度干涉理论,构建行星齿轮减速器在疲劳失效(主要是齿面接触疲劳失效和齿根弯曲疲劳失效)下的时变可靠性模型;其次,结合单调性定理,将时变可靠性模型简化,利用Matlab编程,求解了行星齿轮减速器的可靠度;对时变可靠性模型的各变量进行了灵敏度分析;最后,以PM90精密行星齿轮减速器为例,分别得到基于疲劳失效下的可靠度和各变量的灵敏度,阐述了在接触疲劳失效和弯曲疲劳失效下的可靠性时变规律,为行星齿轮减速器的时变可靠性分析奠定了基础。