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.

Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.

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。

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。

基于广义超椭球模型的结构非概率可靠性指标

非概率凸集合模型仅需获知结构不确定性的范围或界限来度量结构可靠性,因而适用于小样本不确定性结构工程问题.针对广义超椭球模型,对其非概率可靠性度量问题进行了研究.首先,提出了基于广义超椭球模型的简单非概率可靠性指标,定义为结构功能函数的均值与离差之比,并讨论了该可靠性指标的不一致性问题.其次,为克服上述不一致性问题,提出了一种比例因子非概率可靠性指标,定义为不确定域向外扩大或向内收缩时,失效面与不确定域接触的最小比例因子.最后,通过3个工程算例分析验证了所提非概率可靠性指标的有效性和可行性.

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。

基于极值响应的某翻转输药机构运动精度非概率可靠性分析

翻转输药机构是弹药自动装填系统的重要组成部分,其运动精度可靠性对于确保发射药输送动作的顺利执行至关重要。现有的机构运动精度可靠性研究主要基于输入参数的概率模型,需要通过大量实验样本数据来确定参数的概率分布函数,这对于很多工程实际问题而言成本极高甚至无法实现。然而,将输入变量考虑成非概率区间模型在一定程度上可以规避上述难点,区间模型不要求输入变量,有详细的样本特征,只需要确定输入变量的不确定幅度或者界限,这相对于确定变量的概率分布较为容易。在此基础上,针对机构运动精度可靠性的评估提出了一种基于输入参数非概率区间模型的新型时变可靠性分析方法。该方法旨在机构完整运动时间区间内搜索输出响应区间域的局部极值时刻,并引入非概率可靠性指标来评估和分析局部极值时刻的瞬时运动精度可靠性,由此将时变可靠性问题转化为瞬时可靠性问题。将该方法应用于某翻转输药机构进行可靠性评估,结果表明所提出的非概率时变可靠性分析方法对机构运动精度可靠性分析具有一定指导意义。

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。

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。

基于扩散概率模型的非均一地震数据插值方法

【目的】能源勘探领域长期面临非均一地震数据插值的难题。由于检波器无法精确放置在理论网格点,现有均一插值技术常导致结果存在偏差和细节失真。【方法】为解决此问题,提出一种基于扩散概率模型的非均一插值新方法。扩散概率模型是一种新兴的生成式深度学习模型,分为扩散和生成两个过程。在扩散过程中,对完整地震数据迭代施加噪声,训练神经网络的去噪能力;在生成过程中,使用神经网络对噪声数据迭代去噪,得到重构数据。利用插值算子计算迭代数据与采集数据的偏差,作为神经网络的额外输入,提高扩散概率模型的非均一插值能力。在数值实验部分,使用二维合成数据集与实际数据集对非均一采样进行了测试,并使用均一插值模型与所提模型进行比较。【结果和结论】结果表明:该方法显著提升了扩散概率模型对非均一采样的处理能力,在合成数据与实际数据测试中,信噪比大约提高了7 dB,有效提高了深度学习方法对非均一插值的精度,为非均一地震数据插值算法提供了新的思路。

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。

Non-Probabilistic Reliability Research on Multi-Variable Hydraulic Turbine Blade Model

Based on the interval mathematics and possibility theory, the variables existing in hydraulic turbine blade are described. Considering the multi-failure mode in turbine blade, multi-variable model is established to meet the actual situation. Thus, non-probabilistic reliability index is presented by comparing with the output range and the given range.

Fatigue reliability based on residual strength model with hybrid uncertain parameters

The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.

Theoretical analysis of non-probabilistic reliability based on interval model

The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,the structural uncertain parameters were described as interval variables.The theoretical analysis model was developed by starting from the 2-D plane and 3-D space.In order to avoid the loss of probable failure points,the 2-D plane and 3-D space were respectively divided into two parts and three parts for further analysis.The study pointed out that the probable failure points only existed among extreme points and root points of the limit state function.Furthermore,the low-dimensional analytical scheme was extended to the high-dimensional case.Using the proposed approach,it is easy to find the most probable failure point and to acquire the reliability index through simple comparison directly.A number of equations used for calculating the extreme points and root points were also evaluated.This result was useful to avoid the loss of probable failure points and meaningful for optimizing searches in the research field.Finally,two kinds of examples were presented and compared with the existing computation.The good agreements show that the proposed theoretical analysis approach in the paper is correct.The efforts were conducted to improve the optimization method,to indicate the search direction and path,and to avoid only searching the local optimal solution which would result in missed probable failure points.

Convex Set Theory for Reliability Assessment of Steel Beam with Bounded Uncertainty

Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on the robustness of system to uncertainty. The non-probabilistic reliability model,the infinite norm model,and the probabilistic model were used to assess the reliability of a steel beam,respectively. The results show that the resistance is allowed to couple with the action effect in the non-probabilistic reliability model. Additionally,the non-probabilistic reliability model becomes the same accurate as probabilistic model with the increase of the bounded uncertain information. The model is decided by the available data and information.

水平集高斯过程的非星凸形扩展目标跟踪算法

针对复杂环境下的非星凸形不规则形状扩展目标跟踪问题,该文提出基于能量泛函的水平集高斯过程扩展目标跟踪算法。首先,利用水平集随机超曲面模型(Level-Set RHM)通过多边形方法对形状内部进行建模。然后,用高斯过程(GP)学习Level-Set建模输入与输出的非线性映射关系,以求得边界函数最大值,并进一步推导Level-Set与GP相融合的非线性量测方程。在最优非线性滤波的框架下,最终推导得到水平集高斯过程(Level-Set GP)算法,并利用面积差作为不规则形状扩展目标形状估计的评价指标。仿真实验表明了所提算法对非星凸形不规则形状扩展目标形状估计的有效性。

船舶推进轴系振动的不确定性分析

[目的]针对传统的船舶推进轴系确定性振动分析存在安全性与可靠性不足的问题,开展轴系在不确定性激励下的振动响应分析。[方法]采用基于非概率凸模型过程的非随机振动分析方法,以区间上下界的形式描述不确定性激励和振动响应,降低对大量激励样本数据的依赖。与相关文献的计算结果对比,验证所编求解二自由度系统响应边界程序的正确性,并基于在此,探究轴系的不确定振动问题。[结果]当轴系受到螺旋桨[-30 N,30 N]的横向激励力激励时,在轴承处产生了量级约为10-6m的位移响应,表明轴系受到某一区间的激励,则必会产生某一区间的响应。[结论]将基于非概率凸模型过程的非随机振动分析方法应用于船舶推进轴系不确定性振动分析领域,可求得轴系受到不确定性激励时的振动位移响应边界,并可在激励样本较少的情况下为提高轴系系统动态响应预测的稳健性提供有益参考。

基于碳流理论考虑用户侧碳排放配额的最优潮流

由于双碳目标下碳排放配额将成为一个有限的公共资源,聚焦用户侧展开减碳调度研究。考虑到区域间发展及资源状况存在差异,采用基于比例共享原则的碳流理论来计量用户侧的碳排放。通过解决用户侧碳排放配额约束的潮流方向问题,建立了基于碳流理论、考虑用户侧碳排放配额约束的混合整数非线性最优潮流模型,并采用一种基于潮流计算更新的粒子群算法进行求解。经算例测试,在用户侧考虑碳排放配额约束不仅能够满足各类用户的用电碳排放需求,还能在调度中兼顾电力部门减排责任的公平原则。所提算法在小规模算例中相较于精确求解在计算速度上具有显著优势,在大规模算例中相较于非线性规划求解器在收敛性能上具有显著优势。与传统粒子群算法相比,解决了收敛难度大、参数整定困难的问题。

基于非凸惩罚融合套索模型的电机轴承复合故障诊断

针对非凸全变分去噪(non-convex total variation denoising,NCTVD)在提取电机轴承复合微弱故障时存在稀疏性能欠佳和无法准确识别故障的问题,该研究提出一种基于非凸惩罚融合套索模型(non-convex fused lasso model,NCFLM)的复合故障诊断方法。基于反正切惩罚因子的NCTVD模型引入广义极小极大凹函数(generalized minimax concave,GMC),将其拓展成融合套索模型的形式并得到NCFLM,利用前向后向算法(forward-backward algorithm,FBA)对该模型进行求解,再引入遍历方法寻找相关峭度最大时正则化参数的最优取值并将求解结果与其他非凸惩罚模型进行对比。最后,利用采集到的电机轴承复合故障信号进行NCFLM处理,提取复合故障特征,试验结果表明,NCFLM的原子压缩数目、收敛速度、重构准确度、稀疏度、L0范数逼近程度分别比原始arctan-NCTVD模型提高了9.2%、6.6%、10%、46.2%和15%,可实现电机轴承复合故障的准确诊断。