混凝土斜拉桥施工控制中的优化问题研究

在混凝土斜拉桥施工控制中,结构体系不断变化,求解规模大,影响因素多,使得计算模型复杂。针对该问题,建立多目标、多约束的优化模型,并在目标函数中,增加了决策者的期望值,构造新的评价函数,利用凝聚函数优化方法求解该问题。传统的优化算法通过降维或者构造评价函数,减少目标函数个数,仍在原有约束条件下进行求解,凝聚函数法通过同时对多个目标和多个约束条件进行凝聚,将多目标、多约束问题转化为单目标、单约束优化问题,减小解题规模,该优化方法是对传统计算方法的补充,最后阐述了该方法在实际工程中的应用。     

基于有限元的起重运输设备变幅销轴优化设计

以内点惩罚函数法为基础,建立某取料机变幅销轴约束优化模型,提出求解策略,并通过ANsYS对其进行优化设计,得出了设计变量在迭代过程中的变化历程,并针对优化结果采用有限元接触非线性分析进行校核.销轴系统的数学模型及其有限元优化求解方法,可供相关设计人员参考.     

非概率响应面界限法在桥梁可靠性评估中的应用

桥梁结构中各种不确定性的存在加大了可靠性评估的难度,而且对于复杂桥梁往往难以获取相应的功能函数。本文针对上述问题提出基于非概率可靠性理论的响应面界限法,用于求解非概率可靠性指标,评估在役桥梁的可靠性,建立一套适用于在役桥梁的非概率可靠性评估流程。研究以三跨PC连续刚构桥为例,通过确定区间变量参数,利用Midas软件建立桥梁有限元模型;以中跨的跨中截面为控制截面,获取极限弯矩等参数,利用Matlab软件对获取的数据进行处理,并利用提出的响应面界限法求解非概率可靠性指标η,结果为η=1.157621,表明在役桥梁处于可靠状态。算例分析表明,基于响应面界限法的非概率可靠性评估方法,便于求解非概率可靠度指标,对在役桥梁进行可靠性评估具有较强的优势。     

最大熵法可靠度理论在工程应用中的改进

地震作用下,工程结构响应的随机性无法用确定性方法反映,将最大熵法引入可靠度理论,能在少量的已知条件下求得事件的最小有偏概率分布函数.本文基于最大熵法可靠度理论,提出了既能解决收敛问题,又能保证函数精度的控制方法.分析了样本数量对概率密度函数、超越概率、可靠指标精度的影响,给出了保证工程应用精度的建议样本个数.     

导流隧洞体型系统规划数学模型

本文采用系统工程分析方法研究导流隧洞的体型优化设计,发展了一套隧洞最优设计的非线性规划数学模型,该模型以隧洞造价最小做为设计的目标函数,考虑了几何约束、流动约束、强度约束、受力约束和限裂约束的影响,将隧洞设计归纳为求解复合约束条件下的非线性规划问题.在求解非线性规划问题的过程中,采用了变量变换法和广义拉格朗日乘子法等新方法将复合约束条件下的非线性规划问题转化为无约束非线性规划问题.为了克服受力约束中存在非线性常微分方程组不能解析列出目标函数的梯度方程的限制,采用了一阶差分方法计算目标函数的梯度.为了提高计算效率,采用了DFP变度量算法求解无约束隧洞体型非线性规划问题.采用这一模型,可以同时求出隧洞断面几何参数、衬砌厚度、钢筋配量的最优值.工程实例计算表明采用这一方法可以获得显著的经济效益.这一模型不仅适用于导流隧洞,也适用于其它用途的水工隧洞.     

基于Monte-Carlo法的滑坡稳定可靠性分析

简述了可靠性分析的Monte-Carlo法,结合简化的Bishop法提出了滑坡稳定可靠性分析的状态函数,并通过实例进行了计算分析。证明Monte-Carlo法是求解滑坡稳定可靠性指标和破坏概率的行之有效的方法。     

基于二次正交试验的隧道非概率可靠度方法研究

根据二次回归正交试验设计,研究隧道工程非概率可靠度问题。首先,构建了显式二次响应面功能函数,并对回归待定系数进行显著性检验,判断各不确定变量对响应面函数的影响程度。其次,将二次响应面函数与非概率可靠度分析方法相结合,把可靠度指标的解答转化为基于功能函数梯度信息的最优化问题求解。通过编写基于Rosen梯度投影法的MATLAB程序,获得响应面函数的极值区间,进而求得非概率可靠度指标。最后,应用该方法分析了某隧道工程拱顶围岩稳定可靠度,与概率可靠度结果对比,结果表明基于响应面法的非概率可靠度方法的可行性。     

基于Spreadsheet法的盾构衬砌截面可靠度分析

采用Spreadsheet法这一可靠度计算方法计算盾构衬砌截面可靠度,该方法可避免相关变量的独立变换以及极限状态方程对基本变量求偏导这两个问题。承载能力极限状态下,建立衬砌截面的正截面偏心受压破坏和斜截面受剪破坏失效模式下的功能函数,采用Spreadsheet法计算相应的可靠度指标,并计算这两种失效模式串联导致衬砌截面破坏的失效概率。正常使用极限状态下,建立截面开裂、纵缝张开和直径收敛失效模式下的功能函数,采用Spreadsheet法计算相应的可靠度指标。同时,采用Monte Carlo法计算不同失效模式下部分截面的可靠度指标,并与Spreadsheet法的相应计算结果进行比较。结果表明,Spreadsheet法与Monte Carlo法计算的可靠度指标误差最大不超过4%,但是Spreadsheet法节省了大量的计算时间。因此,采用本文建立的承载能力极限状态和正常使用极限状态功能函数,并采用Spreadsheet法求解可靠度指标,提供了一种分析盾构隧道衬砌截面可靠度快速、准确、便捷的方法。     

工程设计中的概率极限状态设计方法

在工程设计中，采取以概率论基础的极限状态设计法，以可靠指标度量结构构件的可靠度，采用以分项系数的设计表达式进行设计，是概率极限状态设计方法区另于一般根据限状态设计方法区另于一般根限状态设计方法的重点。概率极限状态设计法为电子计算机技术在工程界的应用和普及提供了一种光明的前景。本文试从一个工程设计的实例中来解释如何应用这种设计方法。     

边坡稳定有限元可靠度分析的有限步长迭代法

边坡稳定一阶可靠度分析的常用方法是验算点法,该方法在求解可靠指标时需要进行迭代计算。但是,对于边坡稳定的有限元可靠度分析,其功能函数形式常为高度非线性的,采用常规的验算点法可能会出现迭代计算不收敛、无法计算可靠指标的问题。将结构可靠度分析中的有限步长迭代法引入边坡稳定的有限元可靠分析,探讨有限步长迭代法中初始步长及步长调整系数的取值方法。在边坡的可靠指标计算方面,采用以基于滑面应力分析的弹塑性随机有限元理论为基础的方法。其中功能函数的形式是以考虑滑面方向的Mohr-Coulomb屈服准则来建立的;导数的求解采用的是基于增量切线刚度法及Aitken加速算法的偏微分法;边坡整体可靠指标取的是所有可能滑面的可靠指标的最小值。算例分析表明,将有限步长迭代法用于边坡稳定的有限元可靠度分析是可行的,该方法可保证在功能函数为高度非线性时可靠指标的迭代计算也能收敛,而且收敛速度较快,从而大大提高有限元可靠分析的计算速度。     

Investigation of reliability method formulations in DAKOTA/UQ

Reliability methods are probabilistic algorithms for quantifying the effect of simulation input uncertainties on response metrics of interest. In particular, they compute approximate response function distribution statistics (probability, reliability and response levels) based on specified input random variable probability distributions. In this paper, a number of algorithmic variations are explored for both the forward reliability analysis of computing probabilities for specified response levels (the reliability index approach (RIA)) and the inverse reliability analysis of computing response levels for specified probabilities (the performance measure approach (PMA)). These variations include limit state linearizations, probability integrations, warm starting and optimization algorithm selections. The resulting RIA/PMA reliability algorithms for uncertainty quantification are then employed within bi-level and sequential reliability-based design optimization approaches. Relative performance of these uncertainty quantification and reliability-based design optimization algorithms are presented for a number of computational experiments performed using the DAKOTA/UQ software.     

Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and non-probabilistic uncertainties

It is meaningful to account for various uncertainties in the optimization design of the adhesive bonded steel-concrete composite beam. Based on the definition of the mixed reliability index for structural safety evaluation with probabilistic and non-probabilistic uncertainties, the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem. The performance measure approach is employed to improve the convergence and the stability in solving the inner-loop. Moreover, the double-loop optimization problem is transformed into a series of approximate deterministic problems by incorporating the sequential approximate programming and the iteration scheme, which greatly reduces the burdensome computation workloads in seeking the optimal design. The validity of the proposed formulation as well as the efficiency of the presented numerical techniques is demonstrated by a mathematical example. Finally, reliability-based optimization designs of a single span adhesive bonded steel-concrete composite beam with different loading cases are achieved through integrating the present systematic method, the finite element analysis and the optimization package.     

Fatigue performance assessment and service life prediction of high-speed ship structures based on probabilistic lifetime sea loads

This article focuses on estimating probabilistic lifetime sea loads for high-speed ship structures with the aim of assessing fatigue performance and predicting service life from available data. Performance assessment and service life prediction for naval ship structures are extremely important issues. In particular, understanding the effect of sea loading on naval high-speed vessels is still a challenge. Potential lifetime load effects including low frequency wave-induced and high frequency slam-induced whipping loadings are investigated in this article by using a probabilistic approach. Clearly, integration of probabilistic sea loads into structural reliability assessment and service life prediction will provide a more reliable estimation of the long-term structural performance. Accordingly, this article presents an approach for fatigue reliability evaluation of ship structures based on the estimated lifetime sea loads. Loading information associated with sea states, ship speeds and relative wave headings is obtained from a joint high-speed sealift ship monohull structural seakeeping trials, while the S–N curves are established based on the British Standards.     

The possibilistic reliability theory: theoretical aspects and applications

The need to treat uncertainties in the design or assessment of structures today induces a lot of concerns in order to ensure the best security levels. This paper presents an original alternative to the probabilistic reliability theory, keeping the same features regarding some theoretical concepts (design points, reliability indexes) but highlighting easy implementations. The probabilistic or classical reliability theory is built on the principles of probability theory which introduces the probabilistic measure for evaluating confidence levels; the theory introduced in this paper is based on the possibility theory which uses a new confidence measure: the measure of possibility. While the probabilistic approach requires optimization of a multivariate function, the possibilistic approach reduces the study to the optimization of a variable function. Care is taken in explaining how to implement such a technique and for estimating distributions of possibility. Comparisons between the possibilistic and the probabilistic reliability theories are also given. Finally a section is dedicated to a concrete application: the reliability assessment of welded joints damaged by fatigue. This example provides a full application of the possibilistic reliability theory, from uncertainty modeling and possibility distribution estimation to failure possibility determinations.     

On the reliability-based design of structures including passive energy dissipation systems

This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.     

一种新的边坡稳定性因素敏感性分析方法——可靠度分析方法

传统的边坡稳定性因素敏感性分析方法基于确定性计算,仅能得到边坡稳定性对各变量的敏感性大小,无法获得边坡稳定性对不同滑面位置上的同一岩土参数的敏感性。在可靠度分析基础上提出一种新的边坡稳定性因素敏感性分析方法——可靠度分析方法,该方法采用随机场模型来描述边坡滑面上岩土参数的空间变异性,通过验算点法优化求解实现,分析结果可得到边坡的最小可靠指标、概率临界滑面、参数敏感性因子在临界滑面上的分布曲线。研究结果表明,敏感性因子分布曲线随边坡尺度和岩土参数波动范围的相对大小变化而变化,根据边坡可靠度指标在临界滑面上的不同位置上的敏感性因子,可对边坡加固位置提出设计改进,将有限的加固措施加于敏感性因子较高的位置,能够更有效地提高边坡的稳定性,较之传统的边坡稳定性因素敏感性分析方法具有明显的优越性。     

路面预防性养护措施的选择——寿命周期成本分析

目前,广大道路管理者已接受了路面预防性养护(PPM)的理念,但在措施选择方面还很少从经济的角度进行考虑。探讨了寿命周期成本分析在PPM措施选择方面的应用。通过比较分析某高速公路的五种备选PPM措施的寿命周期成本,验证了该方法的可靠性及实用价值。     

The basic properties of some typical systems’ reliability in interval form

A proper mathematical representation of uncertainties is indispensable for reliability analysis of a practical engineering structural system. A general uncertainty analysis approach is probability bounds analysis (PBA), which propagates constraints on a distribution function through mathematical operations. The uncertainty about a probability distribution is represented by the set of cumulative distribution functions lying entirely within a pair of bounding distribution functions, which is called a P-box. Interval analysis as a special case of PBA is useful when there is no or less probabilistic information. It is common sense that great efforts must be paid to get enough probabilistic information used for probabilistic analysis of large and complex engineering structural systems. Even if there is no or less probabilistic information; the interval of possible values of probability of an event can be easily specified, such as the interval value of each element’s reliability of an engineering structural system.

This paper aims to introduce the concept of system reliability and its relationship to the reliability of its individual elements in an interval form. In terms of extension principle, interval arithmetic and possibility degree formula (PDF) for ranking interval numbers, basic properties of system reliability in interval form are investigated. The conclusion is that relationships between point reliability (point reliability used to describe a precise value of probability reliability is distinct with interval reliability) of some typical systems, such as series system, parallel system, series–parallel system, parallel–series system and r/n(G) system, etc., and point reliability of their individual elements are maintained in their interval forms. This is called quasi-consistency in this paper. A simple review of order relations of interval numbers, which will play an important role in interval reliability analysis, is given. The proposed quasi-consistency establishes the foundations for interval reliability analysis of a complex engineering structural system.     

Reliability-based strength limit state for steel railway bridges

Railway bridges require special attention to provide safe and economical service. To assess the reliability of a structure, all critical parameters need to be specified. Load and resistance are random in nature; hence, the probabilistic approach is the best method for accurate evaluation of the performance of a bridge. In this study, identification of critical parameters was conducted on a typical through-plate girder, riveted, open deck railway bridge. This type of structure is a weakest link system. In such a system, the failure of one component can lead to failure of the entire structural system. This research involved identification of the basic load and resistance parameters and the development of analytical procedures for modelling the structural behaviour. The finite element method (FEM) was used to investigate the structural performance characteristics of the evaluated bridge. A three-dimensional structural model was developed to determine stress distribution in the members and connections. Based on the results of FEM analysis, the reliability indices were calculated for critical components.