基于3-D IFS理论的自然景观模拟

1 引言数学家Mandelbrot在20世纪70年代所提出的分形几何,给出一种描述具有随机形态特征及无穷细节的自然现象的全新的数学工具。此后,以Hutchinson和Barnsley等的工作为基础,人们注意到许多分形集都可以用IFS递归构造出来,并可以用来逼近任意现实对象,可见分形技术是计算机真实感几何造型方面十分活跃且有效的方法和手段。     

3-D motion estimation using a sequence of noisy stereo images:models, estimation, and uniqueness results

A kinematic model-based approach for the estimation of 3-D motion parameters from a sequence of noisy stereo images is discussed. The approach is based on representing the constant acceleration translational motion and constant precession rotational motion in the form of a bilinear state-space model using standard rectilinear states for translation and quaternions for rotation. Closed-form solutions of the state transition equations are obtained to propagate the quaternions. The measurements are noisy perturbations of 3-D feature points represented in an inertial coordinate system. It is assumed that the 3-D feature points are extracted from the stereo images and matched over the frames. Owing to the nonlinearity in the state model, nonlinear filters are designed for the estimation of motion parameters. Simulation results are included. The Cramer-Rao performance bounds for motion parameter estimates are computed. A constructive proof for the uniqueness of motion parameters is given. It is shown that with uniform sampling in time, three noncollinear feature points in five consecutive binocular image pairs contain all the spatial and temporal information. Both nondegenerate and degenerate motions are analyzed. A deterministic algorithm to recover motion parameters from a stereo image sequence is summarized from the constructive proof     

Deterministic balancing and stochastic model reduction

A recent approach to the deterministic model reduction problem is based on the notion of balancing. However, the original development of deterministic balancing did not contain any statistical considerations with which to develop a stochastic model reduction algorithm. Nevertheless, it is shown in this note that there are two stochastic model reduction algorithms in the literature which result in a deterministically balanced model. Their equivalence with deterministic balancing provides a stochastic interpretation to the deterministic algorithm.     

Parameter identification for a traffic flow model

In this paper, a macroscopic model is presented which describes the traffic flow on a freeway by a set of nonlinear, deterministic difference equations. The model is deduced from simple physical and empirical considerations and contains a set of free parameters which have to be estimated using real traffic data. This identification procedure is formulated here as a parameter optimization problem which is solved by nonlinear programming. In addition, the sensitivity of the model with respect to parameter changes and structural changes is investigated. Although stochastic events play a role in traffic dynamics, the results demonstrate that the validated model copes surprisingly well with real traffic behaviour.     

A coupled 1-D atmosphere and 3-D canopy radiative transfer model for canopy reflectance, light environment, and photosynthesis simulation in a heterogeneous landscape

Detailed knowledge of light interactions between the atmosphere and vegetation, and within vegetation are of particular interest for terrestrial carbon cycle studies and optical remote sensing. This study describes a model for 3-D canopy radiative transfer that is directly coupled with an atmospheric radiative transfer model (Forest Light Environmental Simulator, FLiES). The model was developed based on the Monte Carlo ray-tracing method using some existing modeling frameworks. To integrate the canopy radiative transfer model with atmosphere, the same numerical method, sampling technique, and variance reduction technique were employed in both the atmospheric and the canopy modules. Farquhar's leaf photosynthesis model was combined to calculate the canopy level photosynthesis from the light environmental parameters obtained by the radiative transfer calculation. In order to document the quality of the coupled model, we first compared the atmospheric radiative transfer module to well known 1-D atmospheric radiative transfer models, and then evaluated the 3-D canopy radiative transfer module against a series of test cases provided by the RAMI On-line Model Checker (ROMC). We used the model to show the impact of atmospheric properties and 3-D canopy structure on the directionality of downward photosynthetically active radiation (PAR) at the top of canopy, the 3-D distribution of absorbed PAR (APAR), and overall canopy photosynthesis. The results indicate the importance to consider angular geometry of incident light at TOC and 3-D canopy structure.     

广义预测鲁棒自适应控制

本文指出自校正控制中广泛采用的CARMA模型会导致控制系统对确定性扰动和非平稳随机扰动缺乏鲁棒性;在CARMA模型中引入相应于上述扰动的不可控模态,给出了一种广义的CARMA模型;基于内模原理,提出一种新的广义预测鲁棒自适应控制器;并从理论上揭示其鲁棒性机理;给出了数字仿真。理论分析和数字仿真结果表明:这种广义预测自适应控制器对各类扰动和对象参数变化具有很强的鲁棒性。     

Animation of stochastic motion of 3-D cloth objects

This paper presents a physically-based aerodynamic force model for the realistic animation of a three-dimensional cloth object, such as a skirt. The model is based on the theory of low speed aerodynamics with some modifications to model the unsteady movement of a 3-D cloth object in air flow. The consideration of the solid object in the vicinity of the cloth, the porosity of the cloth and the collision detection of the cloth with other objects and with itself are also included. To achieve more realistic animation, a stochastic wind model has been proposed to model the free stream air flow. Realistic animation results of a skirt moving in air flow have been obtained by applying these models.     

Asymptotical stability of 2-D linear discrete stochastic systems

The main goal of the present paper is to find computable stability criteria for two-dimensional stochastic systems based on Kronecker product and nonnegative matrices theory. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini–Marchesini?s second model into stochastic matrices. The elements of these stochastic matrices are second-order, weakly stationary white-noise sequences. Second, a necessary and sufficient condition for 2-D stochastic systems is presented, this is the first time that has been proposed. Third, computable mean-square asymptotic stability criteria are derived via Kronecker product and the nonnegative matrix theory. The criteria are only sufficient conditions. Finally, illustrative examples are provided.     

三维体可视化若干问题研究

首先对可视化技术特别是三维可视化算法进行了分析和对比，并根据体数据的建模方法对算法进行了归类，并指出了目前三维可视化技术存在的问题，继而从基于小波的分辨率模型的体绘制算法和基于Cluster模型的并行体绘制算法这两个方面具体探讨了对三维体可视化算法进一步研究的思路，首次提出了参数化的光照模型和图像质量评价的数学模型等概念。     

The self-trapping attractor neural network. I. Analysis of a simple 1-D model

Attractor neural networks (ANNs) based on the Ising model are naturally fully connected and are homogeneous in structure. These features permit a deep understanding of the underlying mechanism, but limit the applicability of these models to the brain. A more biologically realistic model can be derived from an equally simple physical model by utilizing recurrent self-trapping inputs to supplement very sparse intranetwork interactions. This paper reports the analysis of a one-dimensional (1-D) ANN coupled to a second system that computes overlaps with a single stored memory. Results show that: 1) the 1-D self-trapping model is equivalent to an isolated ANN with both full connectivity of one strength and nearest neighbor synapses of an independent strength; 2) the dynamics of ANN and self-trapping updates are independent; 3) there is a critical synaptic noise level below which memory retrieval occurs; 4) the 1-D self-trapping model converges to a fully connected Hopfield model for zero strength nearest neighbor synapses, and has a greater magnitude memory overlap for nonzero strength nearest neighbor synapses; and (5) the mechanism of self-trapping is an iterative map on the mean overlap as a function of the reentrant input.     

A Galerkin Method for the Simulation of the Transient 2-D/2-D and 3-D/3-D Linear Boltzmann Equation

Many production steps used in the manufacturing of integrated circuits involve the deposition of material from the gas phase onto wafers. Models for these processes should account for gaseous transport in a range of flow regimes, from continuum flow to free molecular or Knudsen flow, and for chemical reactions at the wafer surface. We develop a kinetic transport and reaction model whose mathematical representation is a system of transient linear Boltzmann equations. In addition to time, a deterministic numerical solution of this system of kinetic equations requires the discretization of both position and velocity spaces, each two-dimensional for 2-D/2-D or each three-dimensional for 3-D/3-D simulations. Discretizing the velocity space by a spectral Galerkin method approximates each Boltzmann equation by a system of transient linear hyperbolic conservation laws. The classical choice of basis functions based on Hermite polynomials leads to dense coefficient matrices in this system. We use a collocation basis instead that directly yields diagonal coefficient matrices, allowing for more convenient simulations in higher dimensions. The systems of conservation laws are solved using the discontinuous Galerkin finite element method. First, we simulate chemical vapor deposition in both two and three dimensions in typical micron scale features as application example. Second, stability and convergence of the numerical method are demonstrated numerically in two and three dimensions. Third, we present parallel performance results which indicate that the implementation of the method possesses very good scalability on a distributed-memory cluster with a high-performance Myrinet interconnect.     

基于近似动态规划的微粒群系统参数优化研究

从系统最优控制的角度对微粒群参数的动态优化问题进行探讨. 针对离散动态规划的``维数灾"问题, 将群体启发式随机搜索机制引入动态规划的最优策略求解, 提出了一种群体智能近似动态规划模式; 基于该模式给出简化的确定型微粒群反馈控制系统参数优化的近似计算方法, 并扩展应用于具有随机变量的微粒群系统; 仿真计算得到了微粒群加速因子的近似最优动态规律, 并将所得策略与一种时变加速因子(Time-varying acceleration coefficients, TVAC)策略进行了函数优化性能的比较与分析, 初步实验结果表明该近似动态规划模式可有效地用于微粒群系统参数的动态优化设置.     

在3D-Mesh网络中的两种路由研究

在研究并行计算机系统容错时,路由算法是一个极为重要的研究课题。主要研究的是自适应路由算法和确定性路由算法在3D-Mesh网络上的性能。在每个结点具有独立的出错概率的模型下,提出的方法使得能够严格地推导出路由算法的成功概率,从而能够对算法进行分析和比较。研究结果表明,自适应路由算法具有明显的优势。一方面,自适应路由算法基于局部信息而变得高效;另一方面,自适应路由算法对于结点出错和网络规模具有更好的健壮性,而使其具有更高的成功概率。     

On the global nonlinear stochastic dynamical behavior of a class of exothermic CSTRs

The problem of assessing the short and long time effects of stochastic fluctuations on the global-nonlinear dynamics of a class of closed-loop continuous exothermic reactors with temperature control and mono or bistable isothermal dynamics is addressed. The consideration of the problem within a Fokker–Planck (FP) stochastic framework yields: (i) the characterization of the global-nonlinear stochastic dynamics, and (ii) the connection between the deterministic and stochastic modeling approaches. The evolution of the state probability density function (PDF) is explained as the result of a complex interplay between deterministic dynamical features, initial PDF shape, and noise intensity. The correspondence between stationary PDF mono (or bi) modality and deterministic mono (or bi) stability is established, and the stochastic settling time is put in perspective with the deterministic, noise-diffusion, and escape times. The conditions for the occurrence of a retarded response, with respect to deterministic and noise-diffusion times, are identified. The proposed approach: (i) is illustrated with representative case class example, and (ii) constitutes an inductive step towards the development of a general-purpose stochastic modeling approach in chemical process systems engineering.     

Robust M-ary detection filters and smoothers for continuous-time jump Markov systems

In this paper, we consider a dynamic M-ary detection problem when Markov chains are observed through a Wiener process. These systems are fully specified by a candidate set of parameters, whose elements are, a rate matrix for the Markov chain and a parameter for the observation model. Further, we suppose these parameter sets can switch according to the state of an unobserved Markov chain and thereby produce an observation process generated by time varying (jump stochastic) parameter sets. Given such an observation process and a specified collection of models, we estimate the probabilities of each model parameter set explaining the observation. By defining a new augmented state process, then applying the method of reference probability, we compute matrix-valued dynamics, whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process. These matrix-valued dynamics satisfy a stochastic integral equation with a Wiener process integrator. Using the gauge transformation techniques introduced by Clark and a pointwise matrix product, we compute robust matrix-valued dynamics for the joint probabilities on the augmented state space. In these new dynamics, the observation Wiener process appears as a parameter matrix in a linear ordinary differential equation, rather than an integrator in a stochastic integral equation. It is shown that these robust dynamics, when discretised, enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path. In contrast, no such upper bounds can be computed for Taylor expansion approximations, such as the Euler-Maryauana and Milstein schemes. Finally, by exploiting a duality between causal and anticausal robust detector dynamics, we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations. A computer simulation demonstrating performance is included.     

A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities

3-D analysis in GIS is still one of the most challenging topics for research. With the goal being to model possible movement within the built environment, this paper, therefore, proposes a new approach to handling connectivity relationships among 3-D objects in urban environments in order to implement spatial access analyses in 3-D space. To achieve this goal, this paper introduces a 3-D network data model called the geometric network model (GNM), which has been developed by transforming the combinatorial data model (CDM), representing a connectivity relationship among 3-D objects using a dual graph. For the transformation, this paper presents (1) an O(n ²) algorithm for computing a straight medial axis transformation (MAT), (2) the processes for transforming phenomena from 3-D CDM to 3-D GNM, and (3) spatial access algorithms for the 3-D geometric network based upon the Dijkstra algorithm. Using the reconstructed geometric network generated from the transformations, spatial queries based upon the complex connectivity relationships between 3-D urban entities are implemented using Dijkstra algorithm. Finally, the paper presents the results of an experimental implementation of a 3-D network data model (GNM) using GIS data of an area in downtown Columbus, Ohio.     

Deterministic and stochastic model based run-to-run control for batch processes with measurement delays of uncertain duration

A novel run-to-run control algorithm integrating deterministic and stochastic model based control is developed for batch processes with measurement delays of uncertain duration. This control algorithm is referred to as deterministic and stochastic model based control (DSMBC). The deterministic component responds quickly to deterministic changes while the stochastic component minimizes the effects arising from measurement delays of uncertain duration. The deterministic component uses a linear process model with parameters that are updated online. The stochastic component uses an error probability density function (PDF) to characterize the effects due to measurement delays and this error PDF is determined from deviations between the set-point and the available process output. To integrate the two control algorithms, the control input is determined by minimizing the weighted sum of the predicted error from the deterministic model and the information entropy of the error probability density distribution. Using a simulated setting where the rate of chemical vapor deposition is controlled, the performance of the proposed DSMBC is shown to be superior to that of EWMA.     

A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs

This paper presents a new stochastic asset pricing model in a context of bounded rationality, where beliefs about future prices are formed via an expectations updating rule characterized by a stochastic multiplicative random variable, working as an agent-based time dependent weight of the conditional expectation of the fundamental. The agent’s belief about future prices depends on his confidence in the forecasts made by other agents, measured by the distribution type of agents and by a confidence parameter. The resulting stochastic dynamical system is firstly analyzed in a deterministic setting, deriving conditions for uniqueness and stability of steady states and proving that, for high values of the confidence parameter, no complicated dynamics can be exhibited, hence the new component has a stabilizing effect on the qualitative dynamics. Differently, for small values of the confidence parameter, we prove the existence of a stability region in the parameters plane where the only possible dynamics is convergence to a steady state, while complexity is exhibited outside such region. Starting from the results obtained in the deterministic case, the model is then explored by reintroducing randomness. More specifically, we analyze the stability region in three directions: first of all, a robust estimate of the stability region’s measure is provided; second, a long run equilibrium relation between the parameters of the system is obtained; third, the persistence properties of the series describing the bifurcation curves is performed. We finally underline some economic implications.     

二维随机FM-II系统的状态估计

This paper is concerned with state estimation of two-dimensional (2-D) discrete stochastic systems. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini-Marchesini's second model into stochastic matrices. Each element of these stochastic matrices is second-order weakly stationary white noise sequences. Secondly, a linear and unbiased full-order state estimation problem for 2-D discrete linear stochastic model is formulated. Two estimation problems considered are the designs for the mean-square bounded estimation error and for the mean-square stochastic version of the suboptimal H∞ estimator, respectively. Our results can be seen as extensions of the 2-D linear deterministic case. Finally, illustrative examples are provided.     

Constructing a 3-D mesh model for electrical cardiac activity simulation.

The 3-D ventricle model in this study was reconstructed from a series of MRI torso cross-section data. We used a 3-D voxel array to represent the ventricle. As in cardiac simulations proposed by previous studies, the activation sequence and body surface ECG were simulated in this model. But to reduce the amount of elements in the model, so that the amount of parameters in the model can be handled numerically, we propose another approach to simulate cardiac activity. A mesh model was constructed on the closed surface formed by epicardiac and endocardiac surfaces of the ventricle. We propose a method to simulate the activation sequence on the epicardiac and endocardiac surfaces of the mesh model. As with the uniform double layer theorem, body surface ECG can be estimated in terms of epicardiac and endocardiac surface current source. Consequently, we can also generate ECG waveforms corresponding to this mesh simulation. Both the depolarization sequence and ECG simulated by the mesh model resemble those generated by the 3-D voxel model. However, the mesh model greatly simplified the process of ECG simulation. Both the simulation of depolarization and ECG estimation were expressed in terms of clear and simple mathematical representations. Consequently, we can analytically investigate the effects of the mesh model's parameters on the cardiac activation sequence and ECG. It could be a useful tool to numerically study the relation of ECG waveforms and electrical activity of the heart.