基于异构计算的简单行走模型的吸引区域研究

被动行走机器人由于结构简单、能量利用率高而倍受青睐, 但其很容易跌倒, 因此准确把握最终步态与吸引区域成了关键. 由于面对非光滑系统, 大规模数值计算很难避免, 为此本文先提出基于CPU+GPU异构平台的Poincaré映射算法. 该算法可发挥最新平台计算潜力, 比传统CPU上算法快上百倍. 得益于此, 本文针对双足被动行走的最基本模型, 大规模地选取样点进行计算, 不仅清晰地得出吸引区域的形状轮廓和细节特征, 揭示了其内在分形结构, 还得到系统吸引集和吸引区域随倾角k的变化关系, 发现了新的稳定三周期步态和倍周期分岔混沌现象, 并研究了吸引区域.     

三维单向拉伸马蹄的寻找及其在Compass行走模型中的应用

对三维映射,因维数较高,混沌吸引子结构复杂.根据混沌吸引子维数相对较低的特点,在选定不稳定周期轨的附近,对吸引子的局部进行曲面拟合,提出了三维空间中单向拉伸拓扑马蹄的“降维-升维”寻找方法,并实现为MATLAB工具箱.以Compass行走模型为例,详细介绍拓扑马蹄的寻找过程,判定了混沌步态的存在性,刻画了混沌不变集的部分结构.     

周期切换下Chen系统的振荡行为与非光滑分岔分析

研究了不同参数Chen系统之间进行周期切换时的分岔和混沌行为.基于平衡态分析,考虑Chen系统在不同稳态解时通过周期切换连接生成的复合系统的分岔特性,得到系统的不同周期振荡行为.在演化过程中,由于切换导致的非光滑性,复合系统不仅仅表现为两子系统动力特性的简单连接,而且会产生各种分岔,导致诸如混沌等复杂振荡行为.通过Poincaré映射方法,讨论了如何求周期切换系统的不动点和Floquet特征乘子.基于Floquet理论,判定系统的周期解是渐近稳定的.同时得到,随着参数变化,系统既可以由倍周期分岔序列进入混沌,也可以由周期解经过鞍结分岔直接到达混沌.研究结果揭示了周期切换系统的非光滑分岔机理.     

基于开关电感结构的混合升压变换器非线性现象研究

将开关电感结构嵌入到传统Boost变换器中可以显著提高Boost变换器的电压传输比, 同时减少开关器件的电流应力, 降低损耗, 提高效率, 具有广阔的应用前景. 本文首次研究了基于开关电感结构的混合升压变换器的分岔和混沌现象, 导出了连续电流模式下的离散迭代映射模型, 采用分岔图分析了电路参数对系统性能的影响, 发现此变换器不仅发生了倍周期分岔、边界碰撞分岔、切分岔和阵发混沌, 还存在一种特殊的现象: 随着电容C和电感L₂的减小, 电路的运行状态并非严格经历1倍周期、2倍周期和4倍周期, 而是在4倍周期期间发生了分岔轨迹相交的情况, 在相交的一点, 变换器工作于周期3. 最后通过典型的时域波形和相轨图验证了这种特殊现象的存在. 研究结果表明, 当电路参数变化时, 基于开关电感结构的混合升压变换器比传统低维Boost变换器具有更加复杂、多样化的非线性现象. 关键词： 开关电感 混合升压变换器 离散迭代映射 混沌     

常微分方程系统中内部激变现象的研究

应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法. 关键词： 广义胞映射 有向图 激变 混沌鞍     

基于时空图像融合与多任务分类网络的步态识别研究

通过研究一种基于多尺度卷积神经网络和人体姿态估计模型相结合的多任务步态识别方法,对神经网络识别结果做出一定的解释说明,同时提高其在面对协变量改变场景下的识别效果。该方法将卷积神经网络提取的步态空间特征和人体姿态估计模型得到人体关节时序特征融合,进行身份的识别。使用步态数据集CASIA-B中的正常行走序列和合成行走序列数据以及TUM-GAID步态数据集进行实验。结果表明,该方法在TUM-GAID步态数据集实验中,三种场景T₁、T₂和T₃下的识别率分别达到95.2%、72.4%和84.5%。在CASIA-B步态数据集实验中,对于正常行走序列以及两种合成行走序列,该方法在识别精度上均有较好的表现,体现该模型有较强的鲁棒性。     

周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析

研究了两种周期脉冲作用下Logistic映射的复杂动力学行为. 随着参数的变化, 该系统产生平衡解、周期解、混沌等现象, 且该系统可经级联倍周期分岔到达混沌. 通过构造Poincaré 映射, 对周期脉冲作用下Logistic映射进行了分岔分析. 最后基于Floquet理论揭示了该系统周期解的分岔机理. 关键词： Logistic映射 脉冲 周期解 分岔机理     

DOG小波映射伸缩和平移的动力学分析

利用对映射的不动点分析和构造相应次数的迭代曲线,分析了由DOG小波窗口函数构造的一维全局光滑迭代映射的动力学特性.随着尺度伸缩和时间平移,映射不动点会发生数量上的增加或减少,产生稳定或不稳定交点、切点或零点.通过数值仿真得到了动力学行为图、参数分岔图和Lyapunov指数谱,研究和讨论了DOG小波映射的倍周期分岔、切分岔、边界危机分岔、周期窗以及不完全Feigenbaum树等非线性物理现象. 关键词： DOG小波映射 伸缩和平移 不动点 迭代曲线     

不连续导电模式DC-DC变换器的倍周期分岔机理研究

根据一般迭代映射的倍周期分岔定理,从数学上论证了电压型不连续导电模式(DCM) Boost和Buck变换器中倍周期分岔现象产生条件,由此揭示了DC-DC变换器中倍周期分岔现象发生的机理,完善了该类变换器倍周期分岔分析的理论和方法. 关键词： 倍周期分岔 迭代映射 Lyapunov 指数 施瓦茨导数     

一类新的边界激变现象:混沌的边界激变

混沌吸引子的激变是一类普遍现象.借助于广义胞映射图论(generalized cell mapping digraph)方法发现了嵌入在分形吸引域边界内的混沌鞍,这个混沌鞍由于碰撞混沌吸引子导致混沌吸引子完全突然消失,是一类新的边界激变现象,称为混沌的边界激变.可以证明混沌的边界激变是由于混沌吸引子与分形吸引域边界上的混沌鞍相碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混沌吸引子连同它的吸引域突然消失,同时这个混沌鞍也突然增大 关键词： 广义胞映射 有向图 激变 混沌鞍     

A method for extracting human gait series from accelerometer signals based on the ensemble empirical mode decomposition

In this paper,the ensemble empirical mode decomposition(EEMD) is applied to analyse accelerometer signals collected during normal human walking.First,the self-adaptive feature of EEMD is utilised to decompose the accelerometer signals,thus sifting out several intrinsic mode functions(IMFs) at disparate scales.Then,gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity.Compared with the method based on the empirical mode decomposition(EMD),the EEMD-based method has the following advantages:it remarkably improves the detection rate of peak values hidden in the original accelerometer signal,even when the signal is severely contaminated by the intermittent noises;this method effectively prevents the phenomenon of mode mixing found in the process of EMD.And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method.Meanwhile,the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions.The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.     

对称混沌系统的非线性动力学行为及控制

基于线性反馈控制思想，提出了一种对称动力学系统及其控制混沌的方法，给出了预期各周期轨道反馈系数的选择原则，适当选择反馈系数，即可得到不同的周期轨道.将此方法应用 到Logistic映射中，取得了良好的控制效果. 关键词： 反馈控制 周期转道 对称系统     

基于小波变换的人体步态序列提取

将小波变换用于处理人体行走时产生的加速度信号.利用离散小波变换的多尺度、多分辨率特性对原始加速度信号进行尺度分解,在对小波基以及分解尺度进行合理选取后准确地从加速度信号中提取出隐藏的步态节律.与利用阈值法直接对原始加速度信号提取峰值的算法比较后发现：利用小波分解得到与步态节律相关的特征尺度后再进行峰值检测能显著地提高信号峰值的检出率;即使当原始信号存在较严重的噪声干扰时,该方法也能保证所提取出的步态序列的准确性.这对于步态序列的后续分析具有至关重要的意义.研究表明,离散小波变换是一种有效的提取步态节律的方 关键词： 小波变换 步态序列 峰值检测 特征尺度     

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.     

Acoustically-observable properties of adult gait

An approach has been developed for extracting human gait parameters from micro Doppler sonar grams. Key parameters include average speed of walking, torso velocity, walk cycle time, and peak leg velocity. The approach is a modification of a technique previously used in radar data analysis. It has been adapted because of differences between sonar and radar micro Doppler grams. The approach has been applied to an acoustic data set of 16 female and 60 male walkers. Statistics have been tabulated that illustrate the similarities and dissimilarities between female and male gait. Males tend to walk with larger walk cycle times and peak leg velocities than females.     

Automated quantitative gait analysis in animal models of movement disorders

Background  

Accurate and reproducible behavioral tests in animal models are of major importance in the development and evaluation of new therapies for central nervous system disease. In this study we investigated for the first time gait parameters of rat models for Parkinson's disease (PD), Huntington's disease (HD) and stroke using the Catwalk method, a novel automated gait analysis test. Static and dynamic gait parameters were measured in all animal models, and these data were compared to readouts of established behavioral tests, such as the cylinder test in the PD and stroke rats and the rotarod tests for the HD group.     

Decrease in Hurst exponent of human gait with aging and neurodegenerative diseases

In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.     

一种基于激光辐照热效应的薄膜参数反演方法

本文研究并建立了一种基于激光辐照热效应的薄膜参数反演方法.首先给出激光辐照薄膜产生温升问题的热传导理论模型,并利用拉普拉斯变换得到了膜层和基底温度场的解析解;然后以膜层和基底的导热系数为反演参数,基于非线性共轭梯度算法给出反演基本原理及流程,并推导得到了反演过程中灵敏度系数的解析表达式;以aluminum,silver,copper和gold四种金属薄膜为例,通过与有限元法的计算结果对比验证了温度场解析解的正确性;最后结合四种金属薄膜进行了参数反演,通过考察分析不同随机噪声等条件下的参数反演结果,验证了本文方法在薄膜参数反演精度与反演效率等方面的有效性.反演结果显示:本文方法具有较高的反演精度和效率,在迭代截止误差为10~(-7)时只需用少于20次迭代就能收敛;在测量数据中加入的随机噪声越小,反演的迭代收敛次数就越少,即使是在迭代初值与反演结果相差较大时,用包含5%随机噪声的测量数据反演也能快速收敛.本文提出的薄膜参数反演方法不仅适用于反演导热系数,也可扩展用于反演膜层反射系数或吸收率等参数,具有一定的适用性.本文方法对于激光加工或激光损伤过程中的参数反演及优化具有一定的指导意义.     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.     

Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method

Normal incidence of a plane electromagnetic wave on a periodical structure can be simulated by the finite-difference time-domain method using a single unit cell with periodical boundary conditions imposed on its borders. For the oblique wave incidence, the boundary conditions would contain time delays and thus are difficult to implement in the time-domain method. We propose a method of oblique incidence simulation, based on an iterative algorithm. The accuracy of this method is demonstrated by comparing it with the layer Korringa-Kohn-Rostoker frequency-domain method for calculation of transmission spectra of a monolayered photonic crystal.