Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.

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.

A novel method for virtual clearance computation of high-speed train based on model integration and convex hull

The 3D clearance of a high-speed train(HST) is critical to ensure the safety of railway transportation. Many studies have been conducted on the inspection of the clearance profile in railway operation based on the vision system, but few researchers have focused on the computation of the 3D clearance in the design phase of an HST. This paper summarizes the virtual 3D clearance computation of an HST based on model integration and the convex hull method. First, both the aerodynamic and kinetic analysis models of the HST are constructed. The two models are then integrated according to the corresponding relationship map, and an array of transformation matrixes of the HST is created to drive the designed model simulating the physical railway motion. Furthermore, the convex hull method is adopted to compute the 3D envelope of the moving train. Finally, the Hausdorff metric is involved in the measurement of the minimum clearance model and the 3D envelope model. In addition, the color map of the Hausdorff distance is established to verify that the designed shape of the HST meets the national standards. This paper provides an effective method to accurately calculate the 3D clearance for the shape design of an HST, which greatly reduces the development cost by minimizing the physical prototype that must be built.

Material Removal Model Considering Influence of Curvature Radius in Bonnet Polishing Convex Surface

The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.

一种结构不确定分析的改进多维平行六面体模型

多维平行六面体模型是一种能够同时考虑相关变量和独立变量的非概率凸集模型,更适用于工程结构中常见的多源不确定性问题。为更加有效合理地度量结构不确定性,提出一种改进多维平行六面体模型。通过定义区间变量的相关角和边缘区间,给出模型不确定域的显式表达式,进而给出依据实验样本点构建多维平行六面体模型的方法。3个算例分析结果表明,改进多维平行六面体模型能够较好地反映区间变量之间的相关性,是一种比传统多维平行六面体模型更为紧凑合理的模型。

硫酸盐对混凝土侵蚀过程的细观数值分析

硫酸盐侵蚀作为混凝土耐久性损伤的一个重要方面,日益受到人们的普遍关注。根据Fick第二定律和化学反应动力方程,建立了细观层面硫酸盐对混凝土侵蚀过程的数值分析方法。以混凝土随机凸多边形骨料模型为基础,利用Matlab程序对有限元软件进行二次开发,建立了基于扩散-化学反应的硫酸盐对混凝土侵蚀过程的细观数值分析方法,并与试验结果进行了对比。结果表明:硫酸盐侵蚀过程细观数值方法得到的模拟结果与试验结果吻合较好,可以有效模拟硫酸盐对混凝土的侵蚀过程;距混凝土表面一定深度范围内,SO_(4)^(2-)浓度随表面SO_(4)^(2-)浓度的提高而增加;砂浆中SO_(4)^(2-)扩散系数是影响混凝土内SO_(4)^(2-)最大侵蚀深度的主要因素;界面过渡区厚度对硫酸盐环境中混凝土损伤的影响较小。

Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

基于非凸与不可分离正则化算法的电容层析成像图像重建

搅拌器内两相混合是化工生产中常见的现象,电容层析成像(ECT)技术主要对两相分布进行可视化重构,以达到监测的目的。受稀疏贝叶斯学习的启发,提出了一种非凸与不可分离正则化(NNR)算法重建ECT图像。在稀疏先验的基础上引入矩阵低秩特性,采用最大后验估计在潜在空间中提出一个新的优化问题,利用对偶变量将潜在空间的目标函数映射到原始空间进行迭代求解,用来恢复同时稀疏与低秩的矩阵。与凸近似L1范数相比,NNR算法可获得更准确的重建图像,同时比非凸可分离方法更容易收敛到全局最优解。为验证NNR算法的重建效果,通过数值仿真与静态实验的方法分别与其他5种算法进行重建对比。结果表明:NNR算法可以有效减少重建伪影,提升中心物体的重建质量,为搅拌器内两相分布提供了高质量的重建算法。

汽车制动器系统稳定性响应的不确定性和相关性分析

在制动噪声现象中,汽车制动器系统参数不可避免地存在着不确定性和相关性,使得系统响应亦可能同时存在一定的不确定性和相关性,针对该问题开展了制动器系统稳定性响应的不确定性和相关性分析研究。采用多椭球凸模型描述系统参数的不确定性和相关性,以不稳定模态阻尼比表征系统稳定性响应。将多椭球凸模型分别与蒙特卡罗仿真、一阶摄动法和二阶摄动法相结合,提出了三种系统稳定性响应的不确定性分析方法;结合蒙特卡罗仿真和一阶摄动法,分别提出了两种系统不确定响应的相关性分析方法;基于不确定性和相关性分析方法,提出了建立系统响应椭球域的组合方法。通过算例分析验证了方法的有效性。分析结果表明,所提出的方法可有效地求得系统稳定性响应的边界区间、相关系数和椭球域,并且该方法具有较高的计算精度和效率。

基于多边凸集模型的电动汽车悬置系统分析

工程实际中,电动汽车悬置系统参数存在着一定的不确定性和相关性.首先,引入基于主成分分析的多边凸集模型,有效处理了系统不确定参数同时存在相关性和独立性的复杂情形;然后,结合蒙特卡洛法提出了一种悬置系统固有特性的不确定性分析方法,并给出了方法的具体分析步骤;最后,将方法应用于某电动乘用汽车的悬置系统分析,以验证方法的有效性.数值分析结果表明:相较于未考虑参数相关性的区间方法,所提出方法求得的系统固有特性响应范围更加合理;与基于多维平行六面体模型的分析方法对比,所提出方法能更有效地处理系统不确定参数样本分布边界不规则的情形;对于所研究模型,其右、前悬置点的刚度参数相关性对系统固有特性有较大的影响,在设计研究过程中应予以重视.

基于双深度输入凸神经网络多模型的中间点过热度预测控制

新能源大量并网,超临界火电机组参与调峰容易造成中间点过热度较大波动,从而导致过热蒸汽超温等问题。为较好控制中间点过热度达到稳定,提出了一种基于双深度输入凸神经网络多模型(muti-DDICNN model)的中间点过热度预测方法,分别训练了不同预测步长下子模型,构建了中间点过热度状态预测网络(SPNN)和误差预测网络(EPNN)。利用此预测网络凸性质,设计了一种基于双深度输入凸神经网络多模型预测控制器(DDICNN-MPC),将控制问题转化为凸优化问题,求取控制矩阵对目标函数的雅可比矩阵,采用梯度下降法计算控制矩阵最优解。仿真结果表明,DDICNN-MPC能快速平稳地跟踪中间点过热度设定值,且稳态误差较小,具有较好的调节能力。

基于非凸log模型的脑电时-频-空特征选择方法

针对运动想象脑电时-频-空特征选择问题,提出了基于非凸log模型的稀疏特征选择方法(LOG方法)。首先,对原始脑电信号进行时-频分解,得到多个时-频段;其次,针对每个时-频段使用共空域模式(CSP)提取特征,得到时-频-空特征集合;最后,通过提出的基于log函数的非凸稀疏优化模型进行特征选择和分类,该模型可有效缓解L1范数正则化的有偏估计。为验证本方法的有效性,用3个公开的运动想象脑电数据集进行实验,相比现有的凸稀疏优化模型,非凸log模型取得了82.5%的平均分类准确率。实验结果表明,LOG方法不仅分类准确率高,且模型具有较好的稳定性和鲁棒性。

基于模型的非凸聚类算法

由于数据可能分布在非规则的流形上,其中潜在的簇往往呈现非凸的形状和结构,针对这类数据的聚类问题被统称为非凸聚类。现有的主流非凸聚类方法包括基于原始空间的方法和基于空间变换的方法,均忽略了非凸数据模式的显式描述。提出一种描述性模型用于非凸聚类。首先,基于核密度方法定义了一种具有混合形式的特征加权核密度模型,其无需事先假定任何概率分布模型且不限制簇的形状,这是传统基于模型的聚类方法无法实现的。其次,基于提出的模型推导了聚类目标函数,并基于期望最大化算法提出一种求解密度函数局部区域密度极大值的优化算法,那些上升到密度函数相同密度极大值的样本点被划分为同一个簇。最后,定义了一种基于模型的非凸聚类算法。算法不需人为定义簇的数量,并且能够为每个簇分配一个显式的概率密度函数,有助于更稳健和更准确地表征集群。除此之外,算法不仅在优化过程中进行自适应带宽选择,而且在优化过程中赋予了样本空间特征权重,实现了嵌入式特征选择。

考虑不确定性的楼宇综合能源系统日前调度

综合能源系统能够实现多种形式能源的互补利用,随着分布式电源装机容量的急剧攀升,其间歇性和随机性也给系统的运行效率和运行安全带来了巨大挑战。为了应对源荷双侧不确定性对楼宇综合能源系统经济调度的影响,首先,分别考虑综合能源各子系统的运行特性,对电网、天然气网及各耦合设备进行建模。其次,基于温度、热辐射和热负荷之间的定量关系,构建楼宇用户的热室模型。继而,以最小化综合能源系统运行成本为优化目标,建立基于机会约束规划的楼宇综合能源系统日前优化调度模型,并通过凸松弛技术将非线性调度模型转化为易于求解的混合整数二阶锥规划问题。最后,在Python环境中进行仿真分析,利用CPLEX求解器求解。结果表明:所提模型及求解方法能够有效描述和处理系统的不确定性风险,促进新能源消纳,提升系统运行经济性。

基于改进颜色线模型的水下图像增强算法

为解决水下设备采集图像存在的雾化和颜色失真等退化问题,提出一种基于改进颜色线模型的水下图像增强方法。首先,提出一种基于改进四叉树细分的水下背景光估计方法,消除水下因素的干扰,得到更加准确的背景光估计值。其次,建立基于颜色线规律的局部透射率优化模型,并设计一种新的Gauss-Seidel型交替线性极小化(Gauss-Seidel Type Inertial Proximal Alternating Linearized Minimization Algorithm,GiPALM)非凸优化方法求解透射率,在提高模型收敛速度的同时得到更加准确的透射率估计值。最后,在背景光和透射率估计得到恢复图像的基础上,进一步采用线性拉伸校正图像的颜色信息,得到符合人眼感官视觉的水下增强图片。实验结果表明,本文方法在主观评价、客观评价、颜色准确度和应用测试等方面均优于其他先进算法,展现了出色的性能,有效提高了水下图像的清晰度和可视性。

基于Python-ABAQUS的三维细观凹凸骨料建模及骨料不同形状影响分析

为了探究混凝土内部细观尺度下的损伤机理,利用Python语言对ABAQUS进行二次开发,建立了包含界面过渡区的三维细观凹凸型骨料混凝土模型,并提出了一种可直接用于判断凹凸型骨料空间干涉的方法。随后,对该模型进行准静态下的数值模拟,以验证其可靠性。最后,进行了不同骨料形状下的单轴压缩数值模拟分析。研究结果表明,采用本方法可以实现60%以上的骨料体积比的高密实投放。在不同形状的骨料下,混凝土的抗压强度方面影响不大;然而,在导致混凝土裂缝扩展与体积破坏方面,不同形状的骨料产生较大影响。随着骨料表面凹凸性和不规则程度的增加,混凝土受压时的损伤破坏程度逐步加深。这些发现有助于更深入地理解混凝土内部损伤机理,并为混凝土结构设计提供了有益的参考。

工程结构椭球凸集模型可靠度的二次型计算方法研究

工程结构概率可靠度在理论上已经建立了完整的计算体系,但在实际工程应用中却停留在近似或半经验阶段。对于既有工程结构的可靠度评估,由于测试数据有限,采用椭球凸集模型可靠度进行评估有很高的工程价值和广泛的应用前景。椭球凸集模型可靠度有很多种不同的定义,但无论何种定义,如果完全脱离概率可靠度与失效概率的基本假定,则很难与现在基于概率可靠度评估方法的主流实现有效的衔接。从多维正态联合概率密度出发,推导了斜椭球方程及其标准化方法,同时结合极限状态方程,给出了椭球凸集模型可靠度与概率可靠度之间的数学关系。算例表明,得出的特殊简化情况下的椭球凸集模型可靠度计算方法和几何解释,可进一步推动该类可靠度在工程中的应用。

某内河航道整治工程凸角裁弯方案研究

结合实际工程案例,为确定转向角度大的两条航道交汇处的碍航凸角裁弯方案,在根据规范进行尺度论证的基础上,结合数学模型,对各方案的水沙条件变化情况进行预测分析。裁弯后,河段整体冲淤趋势未发生明显改变,裁弯附近河段随着挖深及疏浚面积的增大,回淤量随之增加,但总体回淤强度不大;横流明显减小,弯曲航道航行条件得到改善,船舶转弯半径更大,航行视路更开阔,有利于船舶操纵与航行安全。裁弯工程已按本文所荐及优化方案实施完成,可供类似工程借鉴和参考。

部分线性空间自回归模型的惩罚最小二乘方法

部分线性空间自回归模型因具有参数空间自回归模型的解释能力和非参数空间自回归模型的灵活性而成为一类备受关注的半参数空间自回归模型。主要研究部分线性空间自回归模型的变量选择问题,基于轮廓拟最大似然方法和一类非凸罚函数,提出了一类惩罚最小二乘方法同时选择该模型的参数部分中重要解释变量和估计相应的非零回归系数。在适当的正则条件下,推导了回归系数的惩罚估计的收敛速度,并证明了所提出的变量选择方法具有Oracle性质。模拟研究和实际数据分析均表明所提出的变量选择方法具有满意的有限样本性质。