Modelagem matemática determinística do fluxo do tráfego veicular

Nesta dissertação consideramos duas abordagens para o tráfego de veículos: a macroscópica e a microscópica. O tráfego é descrito macroscopicamente por três grandezas físicas interligadas entre si, a saber, a velocidade, a densidade e o fluxo, descrevendo leis de conservação do número de veículos. Há vários modelos para o tráfego macroscópico de veículos. A maioria deles trata o tráfego de veículos como um fluido compressível, traduzindo a lei de conservação de massa para os veículos e requer uma lei de estado para o par velocidade-densidade, estabelecendo uma relação entre eles. Já o modelo descrito pela abordagem microscópica considera os veículos como partículas individuais. Consideramos os modelos da classe "car - following". Estes modelos baseiam-se no princípio de que o (n - 1)-ésimo veículo (denominado de "following-car") acelera em função do estímulo que recebe do n-ésimo veículo. Analisamos a equação de conservação do número de veículos em modelos macroscópicos para fluxo de tráfego. Posteriormente resolvemos esta equação através da linearização do modelo, estudando suas retas características e apresentamos a resolução do problema não linear em domínios limitados utilizando o método das características

A comparison of methods for the coupled analysis of floating structures

The dynamic analysis of a deepwater floating platform and the associated mooring/riser system should ideally be fully coupled to ensure a reliable response prediction. It is generally held that a time domain analysis is the only means of capturing the various coupling and nonlinear effects accurately. However, in recent work it has been found that for an ultra-deepwater floating system (2000m water depth), the highly efficient frequency domain approach can provide highly accurate response predictions. One reason for this is the accuracy of the drag linearization procedure over both first and second order motions, another reason is the minimal geometric nonlinearity displayed by the mooring lines in deepwater. In this paper, the aim is to develop an efficient analysis method for intermediate water depths, where both mooring/vessel coupling and geometric nonlinearity are of importance. It is found that the standard frequency domain approach is not so accurate for this case and two alternative methods are investigated. In the first, an enhanced frequency domain approach is adopted, in which line nonlinearities are linearized in a systematic way. In the second, a hybrid approach is adopted in which the low frequency motion is solved in the time domain while the high frequency motion is solved in the frequency domain; the two analyses are coupled by the fact that (i) the low frequency motion affects the mooring line geometry for the high frequency motion, and (ii) the high frequency motion affects the drag forces which damp the low frequency motion. The accuracy and efficiency of each of the methods are systematically compared. Copyright © 2007 by ASME.

Distributed maximum likelihood for simultaneous self-localization and tracking in sensor networks

We show that the sensor self-localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we implement fully decentralized versions of the Recursive Maximum Likelihood and on-line Expectation-Maximization algorithms to localize the sensor network simultaneously with target tracking. For linear Gaussian models, our algorithms can be implemented exactly using a distributed version of the Kalman filter and a novel message passing algorithm. The latter allows each node to compute the local derivatives of the likelihood or the sufficient statistics needed for Expectation-Maximization. In the non-linear case, a solution based on local linearization in the spirit of the Extended Kalman Filter is proposed. In numerical examples we demonstrate that the developed algorithms are able to learn the localization parameters. © 2012 IEEE.

On high-frequency noise scattering by aerofoils in flow

Abstract A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local 'inner' regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated. © 2013 Cambridge University Press.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.

Stable dynamic walking over rough terrain: Theory and experiment

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated "dynamic walking" biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems. © 2011 Springer-Verlag.

仿射非线性系统的广义逐点最小范数控制

在Freeman的逐点最小范数控制器的基础上,提出了一种新的非线性控制器设计框架-广义逐点最小范数控制器,并证明了其连续性.通过一个引导函数,新的控制器可以和其他的控制器设计策略结合,从而大大提高了控制器设计的灵活性.另外,给出了新方法的两个应用:改善局部线性化控制器稳定域较小的缺陷;及和其它控制器设计方法结合,使之能够简单有效地处理具有输入约束的系统.

基于反馈线性化的无人直升机航向控制

本文着重解决小型无人直升机航向自适应控制问题.通过求非线性函数导数,把原始系统扩展为一个带有伪状态变量的新系统.这种方法不必求解非线性函数的逆,并且降低了计算量.证明了该方法的稳定性.针对实际模型直升机实验平台航向动力学模型,仿真结果表明了该方法的有效性.

轮式移动机器人轨迹跟踪的最优控制

深入分析了轮式移动机器人的运动状态,建立了WMR路径偏差系统的非线性数学模型。应用小偏差线性化理论,将该多输入多输出非线性系统简化成一个单输入单输出线性系统。然后基于线性二次型调节器理论进行了系统最优控制器的设计,并针对该理论中加权矩阵Q与R难以确定的问题,从控制效果出发,采用自适应遗传算法对其进行了优化。实现了移动机器人对预定轨迹的满意鲁棒跟踪,同时满足了实时性要求。实验结果证明了该方法的正确性与实用性。

移动机器人数学模型近似线性化及反馈镇定

研究了非线性控制理论中的近似线性化方法在移动机器人控制上的应用问题。针对机器人控制领域中多输入多输出(MIMO)仿射非线性系统,研究了一种基于平衡流形的近似线性化算法,并用此算法解决了一类完整约束正交轮式全方位移动机器人(WMR)的镇定问题。仿真分析表明,此方法不仅能够实现系统的镇定,而且降低了因平衡工作点变动给系统稳定性带来的影响,同时也大大地简化了对非线性系统的综合设计过程,具有良好的控制效果和实用性。

移动机器人数学模型的近似线性化

针对机器人控制领域中一类多输入多输出(MIMO)仿射非线性系统,提出了一种基于平衡流形的近似线性化状态反馈镇定算法,并用此算法解决了一类完整约束轮式移动机器人(WMR)的镇定问题.仿真分析表明,此方法不仅能够实现系统的镇定,而且降低了因平衡工作点变动给系统稳定性带来的影响,同时也大大地简化了对非线性系统的综合设计过程,具有良好的控制效果和实用性.

基于跟随领航者法的多UUV队形控制方法研究

本文主要研究基于跟随领航者法的多 UUV(unmanned underwater vehicle)队形控制。在 UUV 载体坐标系下建立系统的运动学模型,该模型是对笛卡尔坐标系下的运动学模型的改进,避免了极坐标系下奇异点的出现。该模型经过输入输出反馈线性化,获得稳定的队形控制器。同时,为了缩小队形控制律中的控制参数的调整范围,本文提出了辅助算法,在此基础上分析参数的有效范围。将队形控制律在多 UUV 数字仿真平台上验证,证实了改进的运动学模型和控制律的有效性。

一类时滞不确定非线性系统的鲁棒控制器设计

针对一类具有单输入滞后不确定非线性系统 ,采用精确反馈线性化方法和 Lyapunov方法设计出一种使系统终极有界 ( UUB)的无记忆光滑状态反馈鲁棒控制器 .仿真算例表明了本文所采用方法的有效性 .

Pg震相走时的各向异性影响及各向异性结构成像

As the first arrival of seismic phase in deep seismic sounding, Pg is the important data for studying the attributes of the sedimentary layers and the shape of crystalline basement because of its high intensity and reliable detection. Conventionally, the sedimentary cover is expressed as isotropic, linear increasing model in the interpretation of Pg event. Actually, the sedimentary medium should be anisotropic as preferred cracks or fractures and thin layers are common features in the upper crust, so the interpretation of Pg event needs to be taken account of seismic velocity anisotropy. Traveltime calculation is the base of data processing and interpretation. Here, we only study the type of elliptical anisotropy for the poor quality and insufficiency of DSS data. In this thesis, we first investigate the meaning of elliptical anisotropy in the study of crustal structure and attribute, then derive Pg event’s traveltime-offset relationship by assuming a linear increasing velocity model with elliptical anisotropy and present the invert scheme from Pg traveltime-offset dataset to seismic velocity and its anisotropy of shallow crustal structure. We compare the Pg traveltime calculated by our analytic formula with numerical calculating method to test the accuracy. To get the lateral variation of elliptical anisotropy along the profiling, a tomography inversion method with the derived formula is presented, where the profile is divided into rectangles. Anisotropic imaging of crustal structure and attribute is efficient method for crust study. The imaging result can help us interprete the seismic data and discover the attribute of the rock to analyze the interaction between layers. Traveltime calculation is the base of image. Base on the ray tracing equations, the paper present a realization of three dimension of layer model with arbitrary anisotropic type and an example of Pg traveltime calculation in arbitrary anisotropic type is presented. The traveltime calculation method is complex and it only adapts to nonlinear inversion. Perturbation method of travel-time calculation in anisotropy is the linearization approach. It establishes the direct relation between seismic parameters and travetime and it is fit for inversion in anisotropic structural imaging. The thesis presents a P-wave imaging method of layer media for TTI. Southeastern China is an important part of the tectonic framework concerning the continental margin of eastern China and is commonly assumed to comprise the Yangtze block and the Cathaysia block, the two major tectonic units in the region. It’s a typical geological and geophysical zone. In this part, we fit the traveltime of Pg phase by the raytracing numerical method. But the method is not suitable here because the inefficiency of numerical method and the method itself. By the analytic method, we fit the Pg and Sg and get the lateral variation of elliptical anisotropy and then discuss its implication. The northeastern margin of Qinghai-Tibetan plateau is typical because it is the joint area of Eurasian plate and Indian plate and many strong earthquakes have occurred there in recent years．We use the Pg data to get elliptical anisotropic variation and discuss the possible meaning.

基于量子蒙特卡罗的地震波反演方法

The primary approaches for people to understand the inner properties of the earth and the distribution of the mineral resources are mainly coming from surface geology survey and geophysical/geochemical data inversion and interpretation. The purpose of seismic inversion is to extract information of the subsurface stratum geometrical structures and the distribution of material properties from seismic wave which is used for resource prospecting, exploitation and the study for inner structure of the earth and its dynamic process. Although the study of seismic parameter inversion has achieved a lot since 1950s, some problems are still persisting when applying in real data due to their nonlinearity and ill-posedness. Most inversion methods we use to invert geophysical parameters are based on iterative inversion which depends largely on the initial model and constraint conditions. It would be difficult to obtain a believable result when taking into consideration different factors such as environmental and equipment noise that exist in seismic wave excitation, propagation and acquisition. The seismic inversion based on real data is a typical nonlinear problem, which means most of their objective functions are multi-minimum. It makes them formidable to be solved using commonly used methods such as general-linearization and quasi-linearization inversion because of local convergence. Global nonlinear search methods which do not rely heavily on the initial model seem more promising, but the amount of computation required for real data process is unacceptable. In order to solve those problems mentioned above, this paper addresses a kind of global nonlinear inversion method which brings Quantum Monte Carlo (QMC) method into geophysical inverse problems. QMC has been used as an effective numerical method to study quantum many-body system which is often governed by Schrödinger equation. This method can be categorized into zero temperature method and finite temperature method. This paper is subdivided into four parts. In the first one, we briefly review the theory of QMC method and find out the connections with geophysical nonlinear inversion, and then give the flow chart of the algorithm. In the second part, we apply four QMC inverse methods in 1D wave equation impedance inversion and generally compare their results with convergence rate and accuracy. The feasibility, stability, and anti-noise capacity of the algorithms are also discussed within this chapter. Numerical results demonstrate that it is possible to solve geophysical nonlinear inversion and other nonlinear optimization problems by means of QMC method. They are also showing that Green’s function Monte Carlo (GFMC) and diffusion Monte Carlo (DMC) are more applicable than Path Integral Monte Carlo (PIMC) and Variational Monte Carlo (VMC) in real data. The third part provides the parallel version of serial QMC algorithms which are applied in a 2D acoustic velocity inversion and real seismic data processing and further discusses these algorithms’ globality and anti-noise capacity. The inverted results show the robustness of these algorithms which make them feasible to be used in 2D inversion and real data processing. The parallel inversion algorithms in this chapter are also applicable in other optimization. Finally, some useful conclusions are obtained in the last section. The analysis and comparison of the results indicate that it is successful to bring QMC into geophysical inversion. QMC is a kind of nonlinear inversion method which guarantees stability, efficiency and anti-noise. The most appealing property is that it does not rely heavily on the initial model and can be suited to nonlinear and multi-minimum geophysical inverse problems. This method can also be used in other filed regarding nonlinear optimization.