Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.

Effect of 2D spatial variability on slope reliability: A simplified FORM analysis

To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.

A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

Reliability-based concurrent subspace optimization method

To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

Structural Reliability Assessment by a Modified Spectral Stochastic Meshless Local Petrov-Galerkin Method

This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.

基于FORM的齿轮传动多学科优化设计

通常多学科设计优化是一种确定性设计方法,未考虑不确定性因素的影响。为降低多学科设计优化过程中不确定性因素对系统性能的影响,将一次可靠性方法与协同优化方法相结合,应用到多学科设计优化中。建立基于一次可靠性方法的协同优化的数学模型,并阐述其求解流程,该方法可用于多学科设计优化领域的可靠性设计问题。分别运用协同优化方法和基于一次可靠性方法的协同优化实现了减速器齿轮传动的多学科优化设计,在这两种方法的系统级优化中,引入松弛变量,将一致性等式约束转化为不等式约束,使算法易于收敛。优化结果表明基于一次可靠性方法的协同优化方法求得的最优解使得约束条件满足了可靠性要求,提高了系统的可靠性,具有实际工程意义。

RSM-FORM 的改进与环肋圆柱壳结构的可靠性计算(英文)

文章在用有限元法对结构进行强度计算和分析的基础上,应用RSM确定了环肋圆柱壳结构强度失效的功能函数;在对相关可靠度理论进行研究的基础上,将RSM与FORM相结合,对FORM进行了改进,解决了当量正态化和参数独立化问题,保留了功能函数的二次项,使计算精度满足实际工程的需要;最后用RSM-FORM对环肋圆柱壳结构强度的可靠性进行了计算分析,计算结果表明,RSM-FORM具有较好的计算精度。

中国南海神狐海域水合物储层井壁稳定可靠度分析

天然气水合物具有巨大的潜在经济和环境价值,其开发利用对国家能源安全和实现国家碳达峰碳中和的“双碳目标”具有战略意义。我国天然气水合物资源主要分布于南海海域,海洋环境的复杂性和隐蔽性使工程测量数据具有较大不确定性,影响钻井安全。目前未见有水合物储层井壁稳定可靠度研究。为定量评估在我国南海神狐海域水合物储层钻井风险,基于水合物储层钻井井壁稳定解析理论和南海神狐海域具体地质条件,结合可靠度分析方法中的改进一次二阶矩法和响应面法,研究南海神狐海域水合物储层钻井井壁失稳概率分布特征,分析该海域井壁失稳概率及安全钻井液压力窗口对主要参数均值和不确定性的敏感性,结果表明:(1)若测量数据足够精确,在我国南海神狐海域水合物储层进行钻井活动的安全性较高,安全钻井液压力窗口也较大。测量数据的不确定性增大将使井壁失稳概率显著升高,缩窄安全钻井液压力窗口。(2)较低的钻井液温度对降低井壁失稳概率略有帮助,且能明显地扩大安全钻井液压力窗口。(3)5个主要参数的均值和不确定性对井壁失稳概率的影响次序相同,均为初始地应力>初始内摩擦角>弹性模量比>初始黏聚力>初始弹性模量。实际工程中对初始地应力数据精确测量,能够显著提高水合物储层钻井井壁稳定性。

基于变密度法深孔钻床主轴箱可靠性拓扑优化

以TBT-ML500深孔钻床主轴箱为研究对象,考虑随机因素的影响,通过基于变密度法的可靠性拓扑优化设计方法,进行了考虑可靠性和稳定性要求的结构轻量化设计。在传统拓扑优化的基础上增加概率约束,建立了应力和位移约束下的可靠性拓扑优化模型;以可靠性指标为约束条件,使用一阶可靠性法和Roenblatt逆变换将可靠性拓扑优化问题解耦为可靠性分析和确定性拓扑优化,最后进行变密度拓扑优化。算例分析结果表明:此方法在实现轻量化的同时更好地满足了实际应用中的安全要求,同时为深孔钻床其他基础件的可靠性拓扑优化提供了参考。

基于序关系法-熵权法的矿井通风网络可靠性评价方法研究

矿井通风网络可靠性评价在确保矿井生产安全与稳定方面具有重要意义。为了准确反映通风网络的可靠性,结合序关系法和熵权法构建了矿井通风网络可靠性评价体系。为了建立指标体系的层次结构,引用了鱼骨图法,将矿井通风网络可靠性确定为总体指标,并细化为通风方式、生产布局、风网结构、设备水平、能耗效率和成本造价等分支指标。在评价通风网络可靠性的总体指标方面,融合了稳定性、完备性、合理性和经济性等因素。这些因素综合考虑了通风网络在长期运行中的稳定性、信息传递的完备性、设计与实际应用的合理性,以及经济效益的实现。本文研究建立了序关系法-熵权法模型,采用了国内某矿的实测数据来验证评价模型的可行性。通过该方法,能够评估和分析矿井通风网络的可靠性。这种方法为矿井通风网络可靠性评价提供了一种有效的方法和工具,可以帮助决策者全面评估矿井通风网络的可靠性,并制定更科学合理的决策,以确保矿井通风网络的安全与稳定。

可靠性分析的FORM和SORM组合法

为了提高极限状态函数具有多极值点时失效概率计算的精度,文章提出了FORM和SORM组合法。该方法根据需要,分别选择FORM或SORM在极值点处进行线性或二次展开计算失效概率,并将二次展开的极限状态函数近似用线性极限状态函数替代,以方便地完成FORM和SORM的组合,实现原极限状态函数失效概率的近似计算。算例表明,文中的方法可以提高失效概率计算的精度。

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.

可靠性分析的FORM和SORM组合法

为了提高极限状态函数具有多极值点时失效概率计算的精度,文章提出了FORM和SORM组合法。该方法根据需要,分别选择FORM或SORM在极值点处进行线性或二次展开计算失效概率,并将二次展开的极限状态函数近似用线性极限状态函数替代,以方便地完成FORM和SORM的组合,实现原极限状态函数失效概率的近似计算。算例表明,文中的方法可以提高失效概率计算的精度。

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.

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.

基于FORM法的小型舵机可靠性优化设计方法

针对传统小型舵机可靠性分析方法存在局限的问题,建立了基于FORM法小型舵机的可靠度评估模型.通过空气动力学仿真计算确定影响舵机可靠性的敏感部位,建立参数化失效模型,确认舵机舵轴与舵面的关键参数,采用FORM法对小型舵机进行可靠性分析,得到可靠度R=0.970671;为满足设计要求对小型舵机结构进行优化设计,对比优化前的结构,舵轴所受的最大应力由462.5 MPa降低为146.8 MPa,舵轴对力的抵抗能力得到了显著提升.小型舵机可靠度由0.970671提高到0.999955,满足关键产品的设计要求,实现了小型舵机的优化设计.

Higher Order Solitary Wave Solutions of the Standard KdV Equations

Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

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 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.