Identification of linear systems using polynomial kernels in the frequency domain

In prior work we presented an identification algorithm using polynomials in the time domain. In this article, we extend this algorithm to include polynomials in the frequency domain. A polynomial is used to represent the imaginary part of the Fourier transform of the impulse response. The Hilbert transform relationship is used to compute the real part of the frequency response and hence the complete process model. The polynomial parameters are computed based on the computationally efficient linear least square method. The order of the polynomial is estimated based on residue decrement. Simulated and experimental results show the effectiveness of this method, particularly for short input/output data sequence with high signal to noise ratio. The frequency domain polynomial model complements the time domain methods since it can provide a good estimate of the time to steady state for time domain FIR (finite impulse response) models. Confidence limits in time or frequency domain can be computed using this approach. Noise rejection properties of the algorithm are illustrated using data from both simulated and real processes.     

三角域上生成三角多项式曲面的实用方法

提出一种三角域上带三个形状参数的三角多项式基函数,基于此基函数可以生成一种三角域上的三角多项式曲面。该曲面可以构建边界为椭圆弧、抛物线弧以及圆弧的曲面。在不改变控制网格的情况下,所提出的曲面可以使用形状参数对曲面进行可预测的灵活调整。为了能够高效稳定地计算该三角多项式曲面,提出一种实用的de Casteljau-type算法。此外,还给出了连接两个三角多项式曲面的[G1]连续条件。     

Compression of Human Motion Capture Data Using Motion Pattern Indexing

In this work, a novel scheme is proposed to compress human motion capture data based on hierarchical structure construction and motion pattern indexing. For a given sequence of 3D motion capture data of human body, the 3D markers are first organized into a hierarchy where each node corresponds to a meaningful part of the human body. Then, the motion sequence corresponding to each body part is coded separately. Based on the observation that there is a high degree of spatial and temporal correlation among the 3D marker positions, we strive to identify motion patterns that form a database for each meaningful body part. Thereafter, a sequence of motion capture data can be efficiently represented as a series of motion pattern indices. As a result, higher compression ratio has been achieved when compared with the prior art, especially for long sequences of motion capture data with repetitive motion styles. Another distinction of this work is that it provides means for flexible and intuitive global and local distortion controls.     

Parameter bounds evaluation of Wiener models with noninvertible polynomial nonlinearities

In this paper a three stage procedure is presented for deriving parameters bounds of SISO Wiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear part are bounded by a tight orthotope. Then, given the estimated uncertain nonlinearity and the output measurements collected exciting the system with an input dynamic signal, bounds on the unmeasurable inner signal are computed. Finally, such bounds, together with noisy output measurements, are used for bounding the parameters of the linear block.     

Optimal input design for set-membership identification of Hammerstein models

In this paper the problem of optimal input design for the identification of Hammerstein models is considered under the assumption that the linear dynamic part of the model is a FIR and that lower and upper bounds are available for the additive measurement errors. The parameters of the Hammerstein model can then be estimated via the identification of a linearized augmented Hammerstein model . External approximations of the feasible intervals for the parameters of the original Hammerstein models are then derived (which may correspond to the actual feasible intervals). This paper deals with the design of input sequences minimizing parameter uncertainty for the linearized augmented Hammerstein model . Some new results are also reported about optimal input design for polynomial non-linear blocks, that may be part of Hammerstein models.     

一种基于离散化位姿的月球车运动规划方法

针对障碍环境下具有非完整约束月球车的运动规划问题,提出了一种基于离散化位姿的月球车运动规划方法。该方法首先将月球车的运动轨迹限定于多项式旋线,通过求解多项式旋线参数生成无障碍条件下连接任意位姿状态的运动轨迹。同时,该方法对月球车运动规划问题中的位姿状态空间进行离散化,形成离散化的位姿状态空间。根据离散化位姿状态空间的特点,在离线的条件下生成连接相邻离散位姿的月球车基本的运动轨迹集。最后该方法结合基本运动轨迹集并利用启发式搜索算法最终解决障碍条件下的运动规划问题。基于动力学仿真平台中的实验结果验证了该方法的正确性和有效性。     

非线性系统Wiener模型辨识

本文采用不同幅值的三电平伪随机m序列作为输入信号,辨识了离散非线性系统Wiener模型的线性脉冲响应函数和非线性增益系数.同时讨论了参数估计的统计特性及其区间估计,并附有仿真结果.     

非线性系统Wiener模型辨识

本文采用不同幅值的三电平伪随机m序列作为输入信号,辨识了离散非线性系统Wiener 模型的线性脉冲响应函数和非线性增益系数.同时讨论了参数估计的统计特性及其区间估 计,并附有仿真结果.     

基于多项式变换的运动估计快速算法

主流的视频编码器普遍采用运动估计与补偿技术来提高压缩比,其中运动估计的计算复杂度高,需要占用大量的计算时间。因此,设计运动估计的快速算法对提高整个视频编码器的性能是至关重要的。此外,视频应用的实时性特点,也要求设计运动估计的快速算法。基于多项式变换的运动估计算法是论文新提出的一种块匹配运动估计算法,既保持了简单而易于硬件实现的特点,同时又极大地提高了计算效率。实验结果表明,基于多项式变换的运动估计算法的执行时间为全搜索算法的9～18%,优于其它快速算法。在噪声环境下,该算法比时间特性最好的WUS(WinnerUpdateSearch)算法以及Spiral算法快2～10倍。     

A polynomial fuzzy neural network for modeling and control

This paper introduces a novel neurofuzzy system based on polynomial fuzzy neural network (PFNN) architecture. A PFNN consists of a set of if-then rules with appropriate membership functions (MFs) whose parameters are optimized via a hybrid genetic algorithm. A polynomial neural network is employed in the defuzzification scheme to improve output performance and to select appropriate rules. A performance criterion for model selection is defined to overcome the overfitting problem in the modeling procedure. For a performance assessment of the PFNN inference system, two well-known problems are employed for a comparison with other methods. The results of these comparisons show that the PFNN inference system out-performs the other methods and exhibits robustness characteristics. This work was presented in part at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

视频标准帧速率上变换的自适应运动补偿方案

提出了一种自适应的运动补偿方案，首先利用预测三步搜索算法进行运动估计，由于此运动估计算法能够很好地利用运动向量的时空相关性．从而能得到更加平滑的运动向量场。其次．为了能够抑制运动向量场中个别奇异向量以及块匹配算法所固有的块效应问题，对向量场进行中值滤波，并采用了一种特殊的向量分配算法。方案的最后一个环节是运动补偿插值，它综合考虑插值帧的局部图像质量以及全局图像质量，利用一种白适应性较强的中值滤波操作来达到一定的综合效果。实验结果证明，此算法与运动补偿时间插值(MCTI)算法相比，插值得到的图像更加平滑，而且，两者的信噪比指标对比也充分说明了本算法的优越性。     

A recurrent fuzzy network for fuzzy temporal sequence processing and gesture recognition.

A fuzzified Takagi-Sugeno-Kang (TSK)-type recurrent fuzzy network (FTRFN) for handling fuzzy temporal information is proposed in this paper. The FTRFN extends our previously proposed network, TRFN, to deal with fuzzy temporal signals represented by Gaussian or triangular fuzzy numbers. In the precondition part of FTRFN, matching degrees between input fuzzy variables and fuzzy antecedent sets is performed by similarity measure. In the TSK-type consequence, a linear combination of fuzzy variables is computed, where two sets of combination coefficients, one for the center and the other for the width of each fuzzy number, are used. Derivation of the linear combination results and final network output is based on left-right fuzzy number operation. There are no rules in FTRFN initially; they are constructed online by concurrent structure and parameter learning, where all free parameters in the precondition/consequence of FTRFN are all tunable. FTRFN can be applied on a variety of domains related to fuzzy temporal information processing. In this paper, it has been applied on one-dimensional and two-dimensional fuzzy temporal sequence prediction and CCD-based temporal gesture recognition. The performance of FTRFN is verified from these examples.     

An analysis of value function learning with piecewise linear control

Reinforcement learning (RL) algorithms attempt to learn optimal control actions by iteratively estimating a long-term measure of system performance, the so-called value function. For example, RL algorithms have been applied to walking robots to examine the connection between robot motion and the brain, which is known as embodied cognition. In this paper, RL algorithms are analysed using an exemplar test problem. A closed form solution for the value function is calculated and this is represented in terms of a set of basis functions and parameters, which is used to investigate parameter convergence. The value function expression is shown to have a polynomial form where the polynomial terms depend on the plant's parameters and the value function's discount factor. It is shown that the temporal difference error introduces a null space for the differenced higher order basis associated with the effects of controller switching (saturated to linear control or terminating an experiment) apart from the time of the switch. This leads to slow convergence in the relevant subspace. It is also shown that badly conditioned learning problems can occur, and this is a function of the value function discount factor and the controller switching points. Finally, a comparison is performed between the residual gradient and TD(0) learning algorithms, and it is shown that the former has a faster rate of convergence for this test problem.     

Reachability and connectivity queries in constraint databases

It is known that standard query languages for constraint databases lack the power to express connectivity properties. Such properties are important in the context of geographical databases, where one naturally wishes to ask queries about connectivity (What are the connected components of a given set?) or reachability (Is there a path from A to B that lies entirely in a given region?). No existing constraint query languages that allow closed-form evaluation can express these properties. In the first part of the paper, we show that, in principle, there is no obstacle to getting closed languages that can express connectivity and reachability queries. In fact, we show that adding any topological property to standard languages like FO+Lin and FO+Poly results in a closed language. In the second part of the paper, we look for tractable closed languages for expressing reachability and connectivity queries. We introduce path logic, which allows one to state properties of paths with respect to given regions. We show that it is closed, has polynomial time data complexity for linear and polynomial constraints, and can express a large number of reachability properties beyond simple connectivity. Query evaluation in the logic involves obtaining a discrete abstraction of a continuous path, and model-checking of temporal formulae on the discrete structure.     

On a Java computer algebra system, its performance and applications

This paper considers Java as an implementation language for a starting part of a computer algebra library. It describes a design of basic arithmetic and multivariate polynomial interfaces and classes which are then employed in advanced parallel and distributed Groebner base algorithms and applications. The library is type-safe due to its design with Java’s generic type parameters and thread-safe using Java’s concurrent programming facilities. We report on the performance of the polynomial arithmetic and on applications built upon the core library.     

Automatic synthesis of uncertain models for linear circuit simulation: A polynomial chaos theory approach

A generalized and automated process for the evaluation of system uncertainty using computer simulation is presented. Wiener–Askey polynomial chaos and generalized polynomial chaos expansions along with Galerkin projections, are used to project a resistive companion system representation onto a stochastic space. Modifications to the resistive companion modeling method that allow for individual models to be produced independently from one another are presented. The results of the polynomial chaos system simulation are compared to Monte Carlo simulation results from PSPICE and C++. The comparison of the simulation results from the various methods demonstrates that polynomial chaos circuit simulation is accurate and advantageous. The algorithms and processes presented in this paper are the basis for the creation of a computer-aided design (CAD) simulator for linear networks containing uncertain parameters.     

A polynomial kernel neural network classifier based on random sampling and information gain

In this paper, we propose a polynomial kernel neural network classifier (PKNNC) based on the random sampling and information gain. Random sampling is used here to generate datasets for the construction of polynomial neurons located in the neural networks, while information gain is used to evaluate the importance of the input variables (viz. dataset features) of each neuron. Both random sampling and information gain stem from the concepts of well-known random forest models. Some traditional neural networks have certain limitations, such as slow convergence speed, easily falling to local optima and difficulty describing the polynomial relation between the input and output. In this regard, a general PKNNC is proposed, and it consists of three parts: the premise, conclusion, and aggregation. The method of designing the PKNNC is summarized as follows. In the premise section, random sampling and information gain are used to obtain multiple subdatasets that are passed to the aggregation part, and the conclusion part uses three types of polynomials. In the aggregation part, the least squares method (LSM) is used to estimate the parameters of polynomials. Furthermore, the particle swarm optimization (PSO) algorithm is exploited here to optimize the PKNNC. The overall optimization of the PKNNC combines structure optimization and parameter optimization. The PKNNC takes advantage of three types of polynomial kernel functions, random sampling techniques and information gain algorithms, which have a good ability to describe the higher-order nonlinear relationships between input and output variables and have high generalization and fast convergence capabilities. To evaluate the effectiveness of the PKNNC, numerical experiments are carried out on two types of data: machine learning data and face data. A comparative study illustrates that the proposed PKNNC leads to better performance than several conventional models.

     

Probabilistic free vibration analysis of beams subjected to axial loads

A stochastic finite-element-based algorithm for the probabilistic free vibration analysis of beams subjected to axial forces is proposed in this paper through combination of the advantages of the response surface method, finite element method and Monte Carlo simulation. Uncertainties in the structural parameters can be taken into account in this algorithm. Three response surface models are proposed. Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms.A separate set of finite element data is generated to verify the models. The results show that the Model II is the most promising one in view of its accuracy and efficiency. Probabilistic free vibration analysis of a simply supported beam is performed to investigate the effects of various parameters on the statistical moments of the frequency response of beams. It is found that the geometric properties of beams have significant effects on the variation of frequency response.     

结合H.263与SLCCA的新的极低比特率小波视频编码

小波对于静止图像编码取得了巨大成功,但对于视频编码只有少数较为成功的尝试,提出一种针对极低比特率应用的新的结合H.263与SLCCA的混合小波视频编码算法,在提出的算法中,首先,用基于H.263的微调运动估计减少时间冗余,用无遗漏覆盖块运动补偿保证运动补偿误差帧的连续性;第2,对运动补偿误差帧进行小波变换得到全局能量压缩;第3,用SLCCA组织和表示小波变换后的数据;最后,运动向量的水平和垂直分量分别用自适应算法编码,算法在A级测试序列Akiyo和B级测试序列Foreman（QCIF）上测试取得了良好效果。     

Shape-From-Silhouette Across Time Part II: Applications to Human Modeling and Markerless Motion Tracking

In Part I of this paper we developed the theory and algorithms for performing Shape-From-Silhouette (SFS) across time. In this second part, we show how our temporal SFS algorithms can be used in the applications of human modeling and markerless motion tracking. First we build a system to acquire human kinematic models consisting of precise shape (constructed using the temporal SFS algorithm for rigid objects), joint locations, and body part segmentation (estimated using the temporal SFS algorithm for articulated objects). Once the kinematic models have been built, we show how they can be used to track the motion of the person in new video sequences. This marker-less tracking algorithm is based on the Visual Hull alignment algorithm used in both temporal SFS algorithms and utilizes both geometric (silhouette) and photometric (color) information.Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.