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 Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms

It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.

An improved interval model updating method via adaptive Kriging models

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

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.

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.

A Bayesian Updating Method for Non-Probabilistic Reliability Assessment of Structures with Performance Test Data

For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.

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.

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.

A Numerical Convex Lens for the State-Discretized Modeling and Simulation of Megawatt Power Electronics Systems as Generalized Hybrid Systems

Modeling and simulation have emerged as an indispensable approach to create numerical experiment platforms and study engineering systems.However,the increasingly complicated systems that engineers face today dramatically challenge state-of-the-art modeling and simulation approaches.Such complicated systems,which are composed of not only continuous states but also discrete events,and which contain complex dynamics across multiple timescales,are defined as generalized hybrid systems(GHSs)in this paper.As a representative GHS,megawatt power electronics(MPE)systems have been largely integrated into the modern power grid,but MPE simulation remains a bottleneck due to its unacceptable time cost and poor convergence.To address this challenge,this paper proposes the numerical convex lens approach to achieve state-discretized modeling and simulation of GHSs.This approach transforms conventional time-discretized passive simulations designed for pure-continuous systems into state-discretized selective simulations designed for GHSs.When this approach was applied to a largescale MPE-based renewable energy system,a 1000-fold increase in simulation speed was achieved,in comparison with existing software.Furthermore,the proposed approach uniquely enables the switching transient simulation of a largescale megawatt system with high accuracy,compared with experimental results,and with no convergence concerns.The numerical convex lens approach leads to the highly efficient simulation of intricate GHSs across multiple timescales,and thus significantly extends engineers’capability to study systems with numerical experiments.

Review: Recent Developments in the Non-Probabilistic Finite Element Analysis

Generally, the finite element analysis of a structure is completed under deterministic inputs.However,uncertainties corresponding to geometrical dimensions,material properties, boundary conditions cannot be neglected in engineering applications. The probabilistic methods are the most popular techniques to handle these uncertain parameters but subjective results could be obtained if insufficient information is unavailable. Non-probabilistic methods can be alternatively employed,which has led to the procedures for nonprobabilistic finite element analysis. Each non-probabilistic finite element analysis method consists of two individual parts,including the core algorithm and pre-processing procedure. In this context,three types of algorithms and two typical pre-processing procedures as well as their effectiveness are described in detail,based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.

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.

Secure planar convex hull protocol for large-scaled point sets in semi-honest model

Efficiency and scalability are still the bottleneck for secure multi-party computation geometry （SMCG）. In this work a secure planar convex hull （SPCH） protocol for large-scaled point sets in semi-honest model has been proposed efficiently to solve the above problems. Firstly, a novel priva- cy-preserving point-inclusion （PPPI） protocol is designed based on the classic homomorphic encryp- tion and secure cross product protocol, and it is demonstrated that the complexity of PPPI protocol is independent of the vertex size of the input convex hull. And then on the basis of the novel PPPI pro- tocol, an effective SPCH protocol is presented. Analysis shows that this SPCH protocol has a good performance for large-scaled point sets compared with previous solutions. Moreover, analysis finds that the complexity of our SPCH protocol relies on the size of the points on the outermost layer of the input point sets only.

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。

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。

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。

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。

一种6-DOF小行星着陆轨迹序列凸优化方法

针对6自由度的小行星动力着陆多约束轨迹优化问题,提出了一种基于序列凸优化的小行星着陆轨迹优化算法。首先采用多面体引力场模型计算小行星的引力场,其可用于描述任意形状的小行星引力场,且比质点群法和球谐函数展开法等方法计算精度更高。为了在凸约束下解决小行星着陆过程燃料消耗最优问题,通过对探测器动力学模型及其约束进行线性化和离散化,将原来的非凸连续时间优化问题转化为凸化的子问题,即二阶锥规划问题(SOCP);然后引入了虚拟控制项和信赖域,以增强算法的鲁棒性。通过在形状不规则小行星上的着陆模拟,验证了所提出算法的有效性,仿真结果满足各项约束条件,可实现高精度着陆和燃料消耗最优的目标。

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。