A PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems

When piecewise affine (PWA) model-based control methods are applied to nonlinear systems, the first question is how to get sub-models and corresponding operating regions. Motivated by the fact that the operating region of each sub-model is an important component of a PWA model and the parameters of a sub-model are strongly coupled with the operating region, a new PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems is initiated. Firstly, construct local data sets from input-output data and get local models by using the least square (LS) method. Secondly, cluster local models according to the feature vectors and identify the parameter vectors of sub-models by weighted least squares (WLS) method. Thirdly, get the initial operating region partition by using a normalized exponential function, which is to partition the operating space completely. Finally, simultaneously determine the optimal parameter vectors of sub-models and the optimal operating region partition underlying the output-error minimization, which is executed by particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the proposed method can improve model accuracy compared with two existing methods.     

Fuzzy min-max neural networks. I. Classification.

A supervised learning neural network classifier that utilizes fuzzy sets as pattern classes is described. Each fuzzy set is an aggregate (union) of fuzzy set hyperboxes. A fuzzy set hyperbox is an n-dimensional box defined by a min point and a max point with a corresponding membership function. The min-max points are determined using the fuzzy min-max learning algorithm, an expansion-contraction process that can learn nonlinear class boundaries in a single pass through the data and provides the ability to incorporate new and refine existing classes without retraining. The use of a fuzzy set approach to pattern classification inherently provides a degree of membership information that is extremely useful in higher-level decision making. The relationship between fuzzy sets and pattern classification is described. The fuzzy min-max classifier neural network implementation is explained, the learning and recall algorithms are outlined, and several examples of operation demonstrate the strong qualities of this new neural network classifier.     

Construction and optimization of CSG representations

Boundary representations (B-reps) and constructive solid geometry (CSG) are widely used representation schemes for solids. While the problem of computing a B-rep from a CSG representation is relatively well understood, the inverse problem of B-rep to CSG conversion has not been addressed in general. The ability to perform B-rep to CSG conversion has important implications for the architecture of solid modelling systems and, in addition, is of considerable theoretical interest.

The paper presents a general approach to B-rep to CSG conversion based on a partition of Euclidean space by surfaces induced from a B-rep, and on the well known fact that closed regular sets and regularized set operations form a Boolean algebra. It is shown that the conversion problem is well defined, and that the solution results in a CSG representation that is unique for a fixed set of halfspaces that serve as a ‘basis’ for the representation. The ‘basis’ set contains halfspaces induced from a B-rep plus additional non-unique separating halfspaces.

An important characteristic of B-rep to CSG conversion is the size of a resulting CSG representation. We consider minimization of CSG representations in some detail and suggest new minimization techniques.

While many important geometric and combinatorial issues remain open, a companion paper shows that the proposed approach to B-rep to CSG conversion and minimization is effective in E², In E³, an experimental system currently converts natural-quadric B-reps in PARASOLID to efficient CSG representations in PADL-2.     

Material interface effects on the topology optimizationof multi-phase structures using a level set method

A level set method is used as a framework to study the effects of including material interface properties in the optimization of multi-phase elastic and thermoelastic structures. In contrast to previous approaches, the material properties do not have a discontinuous change across the interface that is often represented by a sharp geometric boundary between material regions. Instead, finite material interfaces with monotonic and non-monotonic property variations over a physically motivated interface zone are investigated. Numerical results are provided for several 2D problems including compliance and displacement minimization of structures composed of two and three materials. The results highlight the design performance changes attributed to the presence of the continuously graded material interface properties.     

Visual Simulation of Multiple Unmixable Fluids

We present a novel grid-based method for simulating multiple unmixable fluids moving and interacting. Unlike previous methods that can only represent the interface between two fluids （usually between liquid and gas）, this method can handle an arbitrary number of fluids through multiple independent level sets coupled with a constrain condition. To capture the fluid surface more accurately, we extend the particle level set method to a multi-fluid version. It shares the advantages of the particle level set method, and has the ability to track the interfaces of multiple fluids. To handle the dynamic behavior of different fluids existing together, we use a multiphase fluid formulation based on a smooth weight function.     

P-AutoClass: scalable parallel clustering for mining large data sets

Data clustering is an important task in the area of data mining. Clustering is the unsupervised classification of data items into homogeneous groups called clusters. Clustering methods partition a set of data items into clusters, such that items in the same cluster are more similar to each other than items in different clusters according to some defined criteria. Clustering algorithms are computationally intensive, particularly when they are used to analyze large amounts of data. A possible approach to reduce the processing time is based on the implementation of clustering algorithms on scalable parallel computers. This paper describes the design and implementation of P-AutoClass, a parallel version of the AutoClass system based upon the Bayesian model for determining optimal classes in large data sets. The P-AutoClass implementation divides the clustering task among the processors of a multicomputer so that each processor works on its own partition and exchanges intermediate results with the other processors. The system architecture, its implementation, and experimental performance results on different processor numbers and data sets are presented and compared with theoretical performance. In particular, experimental and predicted scalability and efficiency of P-AutoClass versus the sequential AutoClass system are evaluated and compared.     

Finite strain topology optimization based on phase-field regularization

In this paper the topology optimization problem is solved in a finite strain setting using a polyconvex hyperelastic material. Since finite strains is considered the definition of the stiffness is not unique. In the present contribution, the objective of the optimization is minimization of the end-displacement for a given amount of material. The problem is regularized using the phase-field approach which leads to that the optimality criterion is defined by a second order partial differential equation. Both the elastic boundary value problem and the optimality criterion is solved using the finite element method. To approach the optimal state a steepest descent approach is utilized. The interfaces between void and full material are resolved using an adaptive finite element scheme. The paper is closed by numerical examples that clearly illustrates that the presented method is able to find optimal solutions for finite strain topology optimization problems.     

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Level set methods [Osher and Sethian. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the “Dynamic Tubular Grid” or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 1024³     

加移动因子的C-V模型

在变分水平集方法中,C-V模型的优点之一是能够提取以非梯度形式定义的图像边界,然而,在提取该类型边界时,模型仅考虑了图像各区域的均值信息而没有考虑图像的局部信息,因此尽管C-V模型能够得到渐进型边界图像的分割结果,但是存在分割误差。将移动因子引入到C-V模型以解决上述问题。其中移动因子定义为图像局部凸凹性的函数,通过该因子可以调整模型0-水平面的高度,进而使得解平面与目标所在平面更加接近或重合,以达到消除分割误差的目的。文中给出了偏微分形式的模型,并通过实验验证了模型的有效性。