Generate Sample Points Research Articles

A novel algorithm of maximin Latin hypercube design using successive local enumeration

The design of computer experiments (DoCE) is a key technique in the field of metamodel-based design optimization. Space-filling and projective properties are desired features in DoCE. In this article, a novel algorithm of maximin Latin hypercube design (LHD) using successive local enumeration (SLE) is proposed for generating arbitrary m points in n-dimensional space. Testing results compared with lhsdesign function, binary encoded genetic algorithm (BinGA), permutation encoded genetic algorithm (PermGA) and translational propagation algorithm (TPLHD) indicate that SLE is effective to generate sampling points with good space-filling and projective properties. The accuracies of metamodels built with the sampling points produced by lhsdesign function and SLE are compared to illustrate the preferable performance of SLE. Through the comparative study on efficiency with BinGA, PermGA, and TPLHD, as a novel algorithm of LHD sampling techniques, SLE has good space-filling property and acceptable efficiency.

Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems

This paper presents a crashworthiness design optimization method based on a metamodeling technique. The crashworthiness optimization is a highly nonlinear and large scale problem, which is composed various nonlinearities, such as geometry, material and contact and needs a large number expensive evaluations. In order to obtain a robust approximation efficiently, a probability-based least square support vector regression is suggested to construct metamodels by considering structure risk minimization. Further, to save the computational cost, an intelligent sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). In this paper, a cylinder, a full vehicle frontal collision is involved. The results demonstrate that the proposed metamodel-based optimization is efficient and effective in solving crashworthiness, design optimization problems.

GRID-INDEPENDENT METROPOLIS SAMPLING FOR VOLUME VISUALIZATION

We propose a method of sampling regular and irregular-grid volume data for visualization. The method is based on the Metropolis algorithm that is a type of Monte Carlo technique. Our method enables "importance sampling" of local regions of interest in the visualization by generating sample points intensively in regions where a user-specified transfer function takes the peak values. The generated sample-point distribution is independent of the grid structure of the given volume data. Therefore, our method is applicable to irregular grids as well as regular grids. We demonstrate the effectiveness of our method by applying it to regular cubic grids and irregular tetrahedral grids with adaptive cell sizes. We visualize volume data by projecting the generated sample points onto the 2D image plane. We tested our sampling with three rendering models: an X-ray model, a simple illuminant particle model, and an illuminant particle model with light-attenuation effects. The grid-independency and the efficiency in the parallel processing mean that our method is suitable for visualizing large-scale volume data. The former means that the required number of sample points is proportional to the number of 2D pixels, not the number of 3D voxels. The latter means that our method can be easily accelerated on the multiple-CPU and/or GPU platforms. We also show that our method can work with adaptive space partitioning of volume data, which also enables us to treat large-scale/complex volume data easily.

A new algorithm for latent state estimation in non-linear time series models

We consider the problem of optimal state estimation for a wide class of non-linear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering, where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.

DFSS and Robust Optimization Tool for Multibody System with Random Variables

This study presents the DFSS optimization for the dynamic responses of a paper feeding mechanism. The flexible paper is idealized as a series of rigid bars connected by revolute joints and rotational spring dampers. In this mechanism, a paper is fed by a contact and friction mechanism on rollers or guides. The design objective is to minimize the slip amounts between paper and mechanisms and satisfy the 6-sigma constraint for the nip forces of rollers. In order to avoid the difficulty of design sensitivity analysis and overcome the numerical noise, a meta-model based optimization is employed. In this approach, first, the space filling methods and the classical DOE methods are used to generate sampling points. Second, the meta-models are constructed from the Kriging, RBF and RSM methods. Finally, a well-developed numerical optimizer sequentially solves the approximate optimization problem. In the numerical test, the DFSS for the paper feeding mechanism problem, having 8-random design variables, is solved in only 23 analyses.

Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization

For computation-intensive design problems, metamodeling techniques are commonly used to reduce the computational expense during optimization; however, they often have difficulty or even fail to model an unknown system in a large design space, especially when the number of available samples is limited. This article proposes an intuitive methodology to systematically reduce the design space to a relatively small region. This methodology entails three main elements: (1) constructing metamodels using either response surface or kriging models to capture unknown system behavior in the original large space; (2) calculating many inexpensive points from the obtained metamodel, clustering these points using the fuzzy c-means clustering method, and choosing an attractive cluster and its corresponding reduced design space; (3) progressively generating sample points to construct kriging models and identify the design optimum within the reduced design space. The proposed methodology is illustrated using the well-known six-hump camel back problem, a highly nonlinear constrained optimization problem, and a real design problem. Through comparison with other methods, it is found that the proposed methodology can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum in the presence of highly nonlinear constraints. The effect of using either response surface or kriging models in the original design space is also compared and contrasted. Limitations of the proposed methodology are discussed.

Generalized Stochastic Sampling Method for Visualization and Investigation of Implicit Surfaces

Recently we proposed the stochastic sampling method (SSM), which can numerically generate sample points on complicated implicit surfaces quickly and uniformly. In this paper we generalize the method in two aspects: (1) We introduce two kinds of boundary conditions, so that we can sample a finite part of an open surface spreading infinitely. (2) We generalize the stochastic differential equation used in the SSM, so that its solutions can satisfy plural constraint conditions simultaneously. The first generalization enables us to visualize cut views of open surfaces. The second generalization enables us to visualize intersections of static and moving implicit surfaces, which leads to detailed investigation of intersections and other interesting applications such as visualization of contour maps.

Application of the stochastic sampling method to various implicit surfaces

Recently, we proposed the stochastic sampling method (SSM) to numerically generate sample points on implicit surfaces quickly and uniformly. In this paper, we apply the SSM to various complicated implicit surfaces to demonstrate its usefulness. Namely, we demonstrate that the SSM works well for surfaces with much ruggedness and/or many holes, blobbies, and open surfaces. We also show that the SSM enables effective techniques for quick rendering and visualizing outlines of implicit surfaces. Many other new information/hints, which are useful in applying the SSM to complicated surfaces effectively and easily, are also presented.

Monte Carlo techniques for direct lighting calculations

In a distributed ray tracer, the sampling strategy is the crucial part of the direct lighting calculation. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions that are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with a number of sample points that is independent of the number of luminaires.

An improved random walk approach for yield optimization

In this paper, the traditional random walk approach for yield optimization is modified to further improve its efficiency. The orthogonal array of experiment design is employed as an alternative to generating sample points in the circuit parameter space. In addition, the step of the random walk is modified to be adapt. Finally, an example is given to show its high efficiency.