Pair-copula based mixture models and their application in clustering

Finite mixtures are often used to perform model based clustering of multivariate data sets. In real life applications, such data may exhibit complex nonlinear form of dependence among the variables. Also, the individual variables (margins) may follow different families of distributions. Most of the existing mixture models are unable to accommodate these two aspects of the data. This paper presents a finite mixture model that involves a pair-copula based construction of a multivariate distribution. Such a model de-couples the margins and the dependence structures. Hence, the margins can be modeled using different families. Again, many possible dependence structures can also be studied using different copulas. The resulting mixture model (called DVMM) is then capable of capturing a broad family of distributions including non-Gaussian models. Here we study DVMM in the context of clustering of multivariate data. We design an expectation maximization procedure for estimating the mixture parameters. We perform extensive experiments on the basis of a number of well-known data sets. A detailed evaluation of the clustering quality obtained by DVMM in comparison to other mixture models is presented. The experimental results show that the performance of DVMM is quite satisfactory.     

Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

A vine is a new graphical model for dependent random variables. Vines generalize the Markov trees often used in modeling multivariate distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence. A general formula for the density of a vine dependent distribution is derived. This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques. Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine. The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions. The so-called canonical vines built on highest degree trees offer the most efficient structure for Gibbs sampling.     

三维园林植被景观构建与虚拟展示

绿地系统具有生态、文化、社会和审美的多重功能,由于植物形态结构复杂多样,城市规划中尚未有系统、定量化的设计。利用虚拟现实、虚拟植物和地理信息系统等新技术,提出了参数化虚拟植被景观规划设计和虚拟展示的概念模型,集成了参数化植物建模方法和植物空间布局方法。结合园林绿地实例,根据参数化植物建模方法,获取绿化植物形态结构参数,建立各种植物造型的三维模型;采用参数化描述植物空间布局的规则,基于Open Scene Graph（OSG）图形渲染引擎,集成Oculus rift虚拟现实设备,实现三维园林植被景观的虚拟构建及展示。以某大学为例,验证了整体方案的有效性。     

基于有向超图的参数代表示模型及其实现

本文提出了一种基于有向超图的参数化图形表示模型．它不仅能够表示图形的尺寸约束和几何约束，而且能够支持图形拓扑结构变化和工程设计约束的表示．在交互绘制图形对象的同时直接建立参数化图形约束模型．由于在图形构造的每一步都保证约束的一致性，因此，不会出现过约束或欠约束的情况．经实践表明，该模型具有实用方便、高效可行的特点，适合于系列化产品的参数化ＣＡＤ系统建模和绘图．     

Construction of parametric model of operator and workstation.

The purpose of development of a parametric model and the construction and formulation of the parametric model are described. To validate the parametric model, the distribution of the difference between the preferred and theoretical seat height settings of a number of office workers was evaluated from the standpoint of the static posture that does not change with time. The results of precise measurements made for an engineering workstation and an operator were also evaluated. Finally, the theoretical seat height settings with dynamic posture were evaluated. The validity of the parametric model was verified under the experimental conditions.     

Spatial multi-taper spectrum estimation for nuclear reactor modelling

Multi-taper univariate and cross-spectral analysis is used to investigate the structure of spatial variation in the temperatures measured across the surface of a nuclear reactor. The construction of the spatial tapers over the approximate circular reactor surface is described, along with derivation and sampling properties of the spectral estimates. It is shown how the analysis can be used to identify regular patterns in the temperature measurements, and the spatial transfer function between the reactor temperatures and fuel characteristics. The results are used to specify a parametric regression model for the temperature measurements.     

基于混合藤Copula和ILHS的概率电压稳定评估算法

为了评估具备复杂相关性的风电、光伏出力对电力系统电压稳定的影响,提出一种基于混合藤Copula和继承拉丁超立方采样(Inherit Latin Hypercube Sampling, ILHS)的概率电压稳定评估(Probabilistic Voltage Stability Evaluation, PVSE)算法。基于模糊C均值聚类对实际电网中风速和光照数据进行场景划分,利用AD距离确定不同场景中的最优藤结构,建立基于混合藤Copula的概率输入模型。基于ILHS在概率输入模型上采样,根据收敛条件逐渐增加样本点直至PVSE收敛,在PVSE过程中不断重复使用之前生成的样本点及计算结果,进而大幅提升概率分析效率。基于IEEE118节点系统对所提算法的有效性进行验证,结果表明,所提算法能准确刻画风光数据的相关性,并大幅提升PVSE的计算精度和速度。     

Object management in a programming-by-example,parametric, computer-aided-design system

We present the handling of graphical objects in a programming-by-example, CAD system. The object-naming mechanism described here supports the automatic generation of parameter-independent object references in parametric programs. These programs are produced via user interaction during the construction of parametric objects. We use standard programming language control structures and modularity for the parametrisation of variants, repetitive similarities and flexible hierarchical object structure. The object management of parametric entities with varying topology ensures the correctness of their instantiating parametric programs for large domains of parameter values.     

Construction of parametric model of operator and workstation

Abstract

The purpose of development of a parametric model and the construction and formulation of the parametric model are described. To validate the parametric model, the distribution of the difference between the preferred and theoretical seat height settings of a number of office workers was evaluated from the standpoint of the static posture that does not change with time. The results of precise measurements made for an engineering workstation and an operator were also evaluated. Finally, the theoretical seat height settings with dynamic posture were evaluated. The validity of the parametric model was verified under the experimental conditions.     

Analysis of parametric sensitivity and structural optimization of modal control systems with state controllers

The problem of synthesis of parametrically robust modal control systems with inertialess and dynamic state controllers is considered. The dependence of the domain of parametric robustness of the system with the state controller on the mutual position of zeros and poles and the structure of the control plant is studied. It is demonstrated that the analysis of norms of coordinate transformation matrices of a plant and the construction of zones of parametric robustness make it possible to choose the most efficient structure of the modal control system.     

kPCA-Based Parametric Solutions Within the PGD Framework

Parametric solutions make possible fast and reliable real-time simulations which, in turn allow real time optimization, simulation-based control and uncertainty propagation. This opens unprecedented possibilities for robust and efficient design and real-time decision making. The construction of such parametric solutions was addressed in our former works in the context of models whose parameters were easily identified and known in advance. In this work we address more complex scenarios in which the parameters do not appear explicitly in the model—complex microstructures, for instance. In these circumstances the parametric model solution requires combining a technique to find the relevant model parameters and a solution procedure able to cope with high-dimensional models, avoiding the well-known curse of dimensionality. In this work, kPCA (kernel Principal Component Analysis) is used for extracting the hidden model parameters, whereas the PGD (Proper Generalized Decomposition) is used for calculating the resulting parametric solution.     

单锚腿系泊系统参数化设计的研究

对单锚腿系泊系统的构成进行了分析,根据系统中零部件的结构尺寸作了 约束的定义,并据此对系统中零部件作了约束分析,简化了系统参数化设计的复杂性,使得 系统结构的约束分析条理清晰;在约束的定义和分析后,对系统的各零部件进行了关联分析, 确定了建模顺序,在SolidWorks 平台上开发出单锚腿系泊的参数化设计系统。     

基于参数曲面的增材制造保形晶格结构生成方法

晶格结构因其具备特殊的机械性能,已成为增材制造复杂结构设计和制造的重要研究领域之一.针对传统的模型晶格结构生成方法需要通过对参数化建模的晶格结构网格进行裁剪或对其网格进行保形变形实现,且生成效率较低的问题,提出一种基于参数曲面的增材制造保形晶格结构生成方法,实现晶格结构对曲面空间的适应和高效生成.首先,基于一种矩阵方法...     

复合材料磁悬浮列车车体结构数值模拟(Ⅰ)——适应车体设计的参数化有限元模型

为适应高性能复合材料磁悬浮列车车体结构设计和轻量化要求,对由高性能碳纤维材料、铝合金和高性能玻璃材料组合而成的复合材料磁悬浮列车进行参数化设计,使用Siemens NX建立参数化磁悬浮列车几何模型和有限元模型,实现车体结构和连接结构的精确数值模拟,为基于数值模拟技术的磁悬浮列车车体设计打好基础。     

A novel parametric fuzzy CMAC network and its applications

This paper shows fundamentals and applications of the novel parametric fuzzy cerebellar model articulation controller (P-FCMAC) network. It resembles a neural structure that derived from the Albus CMAC algorithm and Takagi–Sugeno–Kang parametric fuzzy inference systems. The Gaussian basis function is used to model the hypercube structure and the linear parametric equation of the network input variance is used to model the TSK-type output. A self-constructing learning algorithm, which consists of the self-clustering method (SCM) and the backpropagation algorithm, is proposed. The proposed the SCM scheme is a fast, one-pass algorithm for a dynamic estimation of the number of hypercube cells in an input data space. The clustering technique does not require prior knowledge of things such as the number of clusters present in a data set. The backpropagation algorithm is used to tune the adjustable parameters. Illustrative examples were conducted to show the performance and applicability of the proposed model.     

Parametric human body shape modeling framework for human-centered product design

The objective of this study is the development of a novel parametric human body shape modeling framework for integration into various product design applications. Our modeling framework is comprised of three phases of database construction, statistical analysis, and model generation. During the database construction phase, a 3D whole body scan data of 250 subjects are obtained, and their data structures are processed so as to be suitable for statistical analysis. Using those preprocessed scan data, the characteristics of the human body shape variation and their correlations with several items of body sizes are investigated in the statistical analysis phase. The correlations obtained from such analysis allow us to develop an interactive modeling interface, which takes the body sizes as inputs and returns a corresponding body shape model as an output. Using this interface, we develop a parametric human body shape modeling system and generate body shape models based on the input body sizes. In our experiment, our modeler produced reasonable results having not only a high level of accuracy but also fine visual fidelity. Compared to other parametric human modeling approaches, our method contributes to the related field by introducing a novel method for correlating body shape and body sizes and by establishing an improved parameter optimization technique for the model generation process.     

A framework for robust parametric set membership identification

This paper proposes a new framework for studying robust parametric set membership identification. The authors derive some new results on the fundamental limitations of algorithms in this framework, given a particular model structure. The new idea is to quantify uncertainty only with respect to the (finite dimensional) parametric part of the model and not the (fixed size) unmodeled dynamics. Thus, the measure of uncertainty is different from the measures used in previous robust identification work where system norms are used to quantify uncertainty. As an example, the results are used to assess the fidelity of a certain approximate robust parametric set membership identification algorithm     

Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains

A tensor-based method is proposed for the solution of partial differential equations defined on uncertain parameterized domains. It provides an accurate solution which is explicit with respect to parameters defining the shape of the domain, thus allowing efficient a posteriori probabilistic or parametric analyses. In the proposed method, a fictitious domain approach is first adopted for the reformulation of the parametric problem on a fixed domain, yielding a weak formulation in a tensor product space (product of space functions and parametric functions). The paper is limited to the case of Neumann conditions on uncertain parts of the boundary. The Proper Generalized Decomposition method is then introduced for the construction of a tensor product approximation (separated representation) of the solution. It can be seen as an a priori model reduction technique which automatically captures reduced bases of space functions and parametric functions which are optimal for the representation of the solution. This tensor-based method is made computationally tractable by introducing separated representations of variational forms, resulting from separated representations of the parameterized indicator function of the uncertain domain. For this purpose, a method is proposed for the construction of a constrained tensor product approximation which preserves positivity and therefore ensures well-posedness of problems associated with approximate indicator functions. Moreover, a regularization of the geometry is introduced to speed up the convergence of these tensor product approximations.     

Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.     

Computing parameter ranges in constructive geometric constraint solving: Implementation and correctness proof

In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation. One of the main issues when generating the solution instance for the actual set of parameters is that the user does not know in general which is the set of parameter values for which the parametric solution is feasible. Similarly, in constraint-based dynamic geometry, knowing the set of critical points where construction feasibility changes would allow to avoid unexpected and unwanted behaviors.We consider parametric models in the Euclidean space with one internal degree of freedom. In this scenario, in general, the set of values of the variant parameter for which the parametric model is realizable and defines a valid shape is a set of intervals on the real line.In this work we report on our experiments implementing the van der Meiden Approach to compute the set of parameter values that bound intervals for which the parametric object is realizable. The implementation is developed on top of a constructive, ruler-and-compass geometric constraint solver. We formalize the underlying concepts and prove that our implementation is correct, that is, the approach exactly computes all the feasible interval bounds.