Modeling of nonlinear dynamical systems based on deterministic learning and structural stability基于确定学习和结构稳定理论的非线性动态系统建模

Recently, a deterministic learning (DL) theory was proposed for accurate identification of system dynamics for nonlinear dynamical systems. In this paper, we further investigate the problem of modeling or identification of the partial derivative of dynamics for dynamical systems. Firstly, based on the locally accurate identification of the unknown system dynamics via deterministic learning, the modeling of its partial derivative of dynamics along the periodic or periodic-like trajectory is obtained by using the mathematical concept of directional derivative. Then, with accurately identified system dynamics and the partial derivative of dynamics, a C¹-norm modeling approach is proposed from the perspective of structural stability, which can be used for quantitatively measuring the topological similarities between different dynamical systems. This provides more incentives for further applications in the classification of dynamical systems and patterns, as well as the prediction of bifurcation and chaos. Simulation studies are included to demonstrate the effectiveness of this modeling approach.     

Deterministic Learning and Rapid Dynamical Pattern Recognition

Recognition of temporal/dynamical patterns is among the most difficult pattern recognition tasks. In this paper, based on a recent result on deterministic learning theory, a deterministic framework is proposed for rapid recognition of dynamical patterns. First, it is shown that a time-varying dynamical pattern can be effectively represented in a time-invariant and spatially distributed manner through deterministic learning. Second, a definition for characterizing similarity of dynamical patterns is given based on system dynamics inherently within dynamical patterns. Third, a mechanism for rapid recognition of dynamical patterns is presented, by which a test dynamical pattern is recognized as similar to a training dynamical pattern if state synchronization is achieved according to a kind of internal and dynamical matching on system dynamics. The synchronization errors can be taken as the measure of similarity between the test and training patterns. The significance of the paper is that a completely dynamical approach is proposed, in which the problem of dynamical pattern recognition is turned into the stability and convergence of a recognition error system. Simulation studies are included to demonstrate the effectiveness of the proposed approach     

确定学习与基于数据的建模及控制

确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路.     

Silhouette-based gait recognition via deterministic learning

In this paper, we present a new silhouette-based gait recognition method via deterministic learning theory, which combines spatio-temporal motion characteristics and physical parameters of a human subject by analyzing shape parameters of the subject?s silhouette contour. It has been validated only in sequences with lateral view, recorded in laboratory conditions. The ratio of the silhouette?s height and width (H–W ratio), the width of the outer contour of the binarized silhouette, the silhouette area and the vertical coordinate of centroid of the outer contour are combined as gait features for recognition. They represent the dynamics of gait motion and can more effectively reflect the tiny variance between different gait patterns. The gait recognition approach consists of two phases: a training phase and a test phase. In the training phase, the gait dynamics underlying different individuals? gaits are locally accurately approximated by radial basis function (RBF) networks via deterministic learning theory. The obtained knowledge of approximated gait dynamics is stored in constant RBF networks. In the test phase, a bank of dynamical estimators is constructed for all the training gait patterns. The constant RBF networks obtained from the training phase are embedded in the estimators. By comparing the set of estimators with a test gait pattern, a set of recognition errors are generated, and the average L₁ norms of the errors are taken as the similarity measure between the dynamics of the training gait patterns and the dynamics of the test gait pattern. The test gait pattern similar to one of the training gait patterns can be recognized according to the smallest error principle. Finally, the recognition performance of the proposed algorithm is comparatively illustrated to take into consideration the published gait recognition approaches on the most well-known public gait databases: CASIA, CMU MoBo and TUM GAID.     

轴流压气机旋转失速建模与检测:基于确定学习理论与高阶Moore-Greitzer模型的研究

喘振和旋转失速是轴流压气机研究领域中重要而困难的问题. 本文基于确定学习理论及动态模式识别方法提出一个旋转失速初始扰动 近似准确建模和快速检测的方法. 首先,基于高阶Moore-Greitzer模型（Mansoux模型）,利用确定学习理论提出一个对旋转失速初始扰动的内在系统动态的近似准确建模方法;其次,基于以上近似准确建模,利用 动态模式识别方法提出一个对旋转失速初始扰动的快速检测方法. 基于MIT的Mansoux-C2模型仿真研究验证了 所提方法的有效性. 最后,在北京航空航天大学航空发动机重点实验室的低速轴流压气机试验台上开展了试验研究. 通过对低速轴流压气机试验台参数进行测量,得到基于北航低速轴流压气机试验台的Mansoux模型. 通过对基于北航试验台Mansoux模型进行仿真研究,验证了所提方法的有效性.     

基于确定学习理论和Lempel-Ziv复杂度的非线性系统动态特征提取

对非线性系统产生的非线性非平稳信号进行有效的特征表达是特征提取领域重要且困难的问题.本文基于确定学习理论和Lempel-Ziv复杂度（LZ复杂度）提出一种新的非线性系统动态特征提取方法.新方法将从系统的动力学轨迹中提取特征.通过确定学习理论对产生回归轨迹的非线性动力学系统的未知系统动态进行局部准确建模/辨识,1）使用LZ复杂度对辨识得到的动力学轨迹进行特征表达,并提出时间复杂度和空间复杂度两个指标组成时空LZ复杂度,从时间域和空间域的角度刻画系统动力学轨迹的复杂程度.2）对提出的动态特征提取方法进行敏感度分析,定量评价系统的动态特征指标相对于系统从周期轨迹到混沌轨迹的参数变化敏感程度.3）通过数值仿真和实验分析以验证动态特征提取的有效性.与从系统状态轨迹中提取特征相比,本文提出的动态特征提取方法可以从系统内在动态的角度对原系统进行更好的表达.     

Dynamical pattern recognition for univariate time series and its application to an axial compressor

In this paper, a learning and recognition approach is proposed for univariate time series composed of output measurements of general nonlinear dynamical systems. Firstly, a class of dynamical systems in the canonical form is derived to describe the univariate time series by introducing coordinate transformation. An observer-based deterministic learning technique is then adopted to achieve dynamical modeling of the associated transformed systems of the training univariate time series, and the modeling results in the form of radial basis function network (RBFN) models are stored in a pattern library. Subsequently, multiple observer-based dynamical estimators containing the RBFN models in the pattern library are constructed for a test univariate time series, and a recognition decision scheme is proposed by the derived recognition indicator. On this basis, more concise recognition conditions are provided, which is beneficial for verifying the recognition results. Finally, simulation studies on the Rossler system and aero-engine stall warning verify the effectiveness of the proposed approach.     

并行计算在动态模式识别中的实现和应用*

研究一种针对最近提出的动态环境下的机器学习理论——确定学习理论的算法实现,提出一种采用并行计算实现确定学习理论中的动态模式识别的方法。利用并行计算中的OpenMP多核编程环境,采用曙光16核服务器为硬件平台,实现对动态模式识别算法的快速性。同时,以压气机Mansoux模型为应用背景,把确定学习理论的动态模式识别方法应用到压气机旋转失速/喘振的快速检测中,利用多核并行计算实现了从包含多种旋转失速/喘振模式的模式库中快速识别当前模式的方法,为文章中方法提供了一个有效的验证。     

A Network of Neural Oscillators for Fractal Pattern Recognition

Biological neural networks are high dimensional nonlinear systems, which presents complex dynamical phenomena, such as chaos. Thus, the study of coupled dynamical systems is important for understanding functional mechanism of real neural networks and it is also important for modeling more realistic artificial neural networks. In this direction, the study of a ring of phase oscillators has been proved to be useful for pattern recognition. Such an approach has at least three nontrivial advantages over the traditional dynamical neural networks: first, each input pattern can be encoded in a vector instead of a matrix; second, the connection weights can be determined analytically; third, due to its dynamical nature, it has the ability to capture temporal patterns. In the previous studies of this topic, all patterns were encoded as stable periodic solutions of the oscillator network. In this paper, we continue to explore the oscillator ring for pattern recognition. Specifically, we propose algorithms, which use the chaotic dynamics of the closed loops of Stuart–Landau oscillators as artificial neurons, to recognize randomly generated fractal patterns. We manipulate the number of neurons and initial conditions of the oscillator ring to encode fractal patterns. It is worth noting that fractal pattern recognition is a challenging problem due to their discontinuity nature and their complex forms. Computer simulations confirm good performance of the proposed algorithms.     

Rapid dynamical pattern recognition for sampling sequences

In this paper,based on deterministic learning,we propose a method for rapid recognition of dynamical patterns consisting of sampling sequences.First,for the seq...     

复杂性测度在肌电信号模式识别中的应用

针对表面肌电信号(SEMG)的非平稳特性,提出了一种以复杂性测度和支持向量机(SVM)相结合的肌电信号模式识别新方法。肌电信号的复杂度作为一种新的肌电信号特征,算法简单。支持向量机是一种新的机器学习机制。通过对采集的四通道表面肌电信号进行分析,提取其复杂性测度信息构建特征矢量,利用“一对一”分类策略和二叉树构建的多类支持向量机分类器,很好地实现了对前臂的八种动作表面肌电信号的模式分类。实验表明,由支持向量机对肌电信号的复杂度特征进行分类,具有很好的稳定性和准确率,为肌电信号及其它非平稳生理电信号的模式分类提供了一种新思路。     

基于关联度和特征约束的软件设计模式识别方法

在程序理解和软件逆向工程研究中,找到准确和快速地描述软件的设计模式和待识别源代码的方法,对于构建合理的设计模式识别框架和高效的识别算法是至关重要的。运用无向图的邻接表和连通分量的原理,提出类与类之间关联度的概念,由待识别源代码构建一个关联类集合,旨在减小设计模式识别算法的搜索空间;根据设计模式的特征,提出基于关联度和特征约束的设计模式识别算法。对Junit、JHotDraw和JreFactory 3个开源应用程序进行的设计模式识别表明,该算法能够准确高效地完成对源代码设计模式的识别。     

AUV深度的神经网络辨识和学习控制仿真研究

将自主水下航行器（AUV）的深度控制问题转换为对非线性严格反馈系统的分析,提出了一种结合反步法和确定学习理论的自适应学习控制方法。通过反步法设计了一种输入状态稳定（ISS）神经网络控制器,其中引入小增益定理,避免了控制器设计中存在的奇异值问题,并在满足持续激励（PE）条件下,利用神经网络辨识实现了对系统未知动态的局部准确逼近和部分神经网络权值的收敛,保证了闭环系统的稳定。将从动态模式中学到的知识静态保存,提取动态特征设计学习控制器,仿真结果表明,该控制器避免了执行同样任务时的重复训练,改善了系统控制性能,验证了所提控制方法的有效性。     

Deterministic learning and nonlinear observer design

A “deterministic learning” (DL) theory was recently proposed for identification of nonlinear system dynamics under full‐state measurements. In this paper, for a class of nonlinear systems undergoing periodic or recurrent motions with only output measurements, firstly, it is shown that locally‐accurate identification of nonlinear system dynamics can still be achieved. Specifically, by using a high gain observer and a dynamical radial basis function network (RBFN), when state estimation is achieved by the high gain observer, along the estimated state trajectory, a partial persistence of excitation (PE) condition is satisfied, and locally‐accurate identification of system dynamics is achieved in a local region along the estimated state trajectory. Secondly, by embedding the learned knowledge of system dynamics into a RBFN‐based nonlinear observer, it is shown that correct state estimation can be achieved according to the internal matching of the underlying system dynamics, rather than by using high gain domination. The significance of this paper is that it reveals that the difficult problems in nonlinear observer design can be successfully resolved by incorporating the deterministic learning mechanisms. Simulation studies are included to demonstrate the effectiveness of the approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A neural network approach to characterize pattern parameters in process control charts

Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.     

Hand gesture recognition using Leap Motion via deterministic learning

With the development of multimedia technology, traditional interactive tools, such as mouse and keyboard, cannot satisfy users’ requirements. Touchless interaction has received considerable attention in recent years with benefit of removing barriers of physical contact. Leap Motion is an interactive device which can be used to collect information of dynamic hand gestures, including coordinate, acceleration and direction of fingers. The aim of this study is to develop a new method for hand gesture recognition using jointly calibrated Leap Motion via deterministic learning. Hand gesture features representing hand motion dynamics, including spatial position and direction of fingers, are derived from Leap Motion. Hand motion dynamics underlying motion patterns of different gestures which represent Arabic numbers (0-9) and capital English alphabets (A-Z) are modeled by constant radial basis function (RBF) neural networks. Then, a bank of estimators is constructed by the constant RBF networks. By comparing the set of estimators with a test gesture pattern, a set of recognition errors are generated. The average L₁ norms of the errors are taken as the recognition measure according to the smallest error principle. Finally, experiments are carried out to demonstrate the high recognition performance of the proposed method. By using the 2-fold, 10-fold and leave-one-person-out cross-validation styles, the correct recognition rates for the Arabic numbers are reported to be 94.2%, 95.1% and 90.2%, respectively, for the English alphabets are reported to be 89.2%, 92.9% and 86.4%, respectively.     

Syntactic recognition of ECG signals by attributed finite automata

A syntactic pattern recognition method of electrocardiograms (ECG) is described in which attributed automata are used to execute the analysis of ECG signals. An ECG signal is first encoded into a string of primitives and then attributed automata are used to analyse the string. We have found that we can perform fast and reliable analysis of ECG signals by attributed automata.     

基于动态神经网的非线性鲁棒辨识

研究了一类基于动态神经网络的未知非线性多变量系统的鲁棒辨识问题，用Ｌｙａｐｕｎｏｖ稳定性理论获得了具有保护策略的鲁棒调权律，从理论上证明了被辨识的系统是鲁榛 ，辨识误差按建模误差和未建模动态收敛到一个稳定区域，该策略的特点是不需要离线学习又不需要对象的状态完全可测，仿真结果验证了提出的动态网鲁棒辨识策略的有效性。     

Human behavior clustering for anomaly detection

This paper aims to address the problem of modeling human behavior patterns captured in surveillance videos for the application of online normal behavior recognition and anomaly detection. A novel framework is developed for automatic behavior modeling and online anomaly detection without the need for manual labeling of the training data set. The framework consists of the following key components. 1) A compact and effective behavior representation method is developed based on spatial-temporal interest point detection. 2) The natural grouping of behavior patterns is determined through a novel clustering algorithm, topic hidden Markov model (THMM) built upon the existing hidden Markov model (HMM) and latent Dirichlet allocation (LDA), which overcomes the current limitations in accuracy, robustness, and computational efficiency. The new model is a four-level hierarchical Bayesian model, in which each video is modeled as a Markov chain of behavior patterns where each behavior pattern is a distribution over some segments of the video. Each of these segments in the video can be modeled as a mixture of actions where each action is a distribution over spatial-temporal words. 3) An online anomaly measure is introduced to detect abnormal behavior, whereas normal behavior is recognized by runtime accumulative visual evidence using the likelihood ratio test (LRT) method. Experimental results demonstrate the effectiveness and robustness of our approach using noisy and sparse data sets collected from a real surveillance scenario.     

Chaotic exploration and learning of locomotion behaviors

We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage.