Robust fault detection filter design for a class of time-delay systems via equivalent transformation

This paper is concerned with the robust fault detection filter (RFDF) design for a class of linear timeinvariant systems (LTISs) with output state time delays. Although existing results in literatures study the RFDF for timedelay systems, few is concerned with the output state time-delay systems. The basic idea of our study is to eliminate the time delays of system and transform it to a delay-free system (i.e., a linear time-invariant system without time delays) by the bicausal change of coordinates approach. Then, we design the RFDF for the delay-free LTIS, which is equivalent to the original system with time delays. We first introduce a class of systems with output state time delays, whose fault can be detected by using the RFDF design approach for delay-free systems. Then, since the RFDF design problem can be formulated as a standard H-infinity-model matching problem, it is solved by using H-infinity-optimization LMI techniques. In the last, the adaptive threshold of fault detection is chosen and an illustrative design example is used to demonstrate the validity of the design approach.     

Identification of a class of time-variable linear systems via its output covariance function

The main concern of this paper is to determine the state-space representation of a class of linear time-variable, periodic system, such that when excited by stationary white noise it results in a random process with prescribed covariance function. It is shown that by using a proper transformation on the state covariance matrix of the system it is possible to find a new matrix which has periodicity properties and satisfies a periodic matrix Riceati differential equation; therefore, the time interval of interest, on which the matrix Riceati equation must be solved using previous approaches, will collapse into one period.     

Identification of a class of continuous time-varying linear systems via block pulse functions

Starting from the relations between entries of block pulse operational matrices, block pulse regression equations corresponding to the original differential equation models with time-varying parameters are obtained. Based on simple forms of the regression equations, algorithms developed in discrete-time model identification can be applied directly to estimate the time-varying parameters of the continuous models without much modification. Compared with other identification methods for the same problem, this new method is simple, and can be applied to both batch and recursive estimations of continuous time-varying linear systems from their sampled input and output data by means of digital computers.     

基于非高斯分布和上下文法模型的小波阈值去噪算法

提出了一种新的空间自适应小波阈值去噪算法,该算法是基于非高斯二元分布的贝叶斯统计模型和上下文法模型。非高斯二元分布由两个变元和一个参数组成,能够完全体现小波系数之间相关性,这是广义高斯分布所不能体现的特性。上下文法模型是图像编码技术,用来求取小波系数的方差。试验数据显示该算法不仅在直观视觉上去噪效果明显,而且在信噪比方面也要优于SureShrink、BayesShrink、Wiener2等方法。     

Hierarchical-fuzzy clustering of temporal-patterns and its application for time-series prediction

In a recent paper we presented a new algorithm for hierarchical unsupervised fuzzy clustering (HUFC) and demonstrated its performance for biomedical state identification. In the present paper, a new hybrid algorithm for time series prediction is applying the HUFC algorithm for grouping and modeling related temporal-patterns that are dispersed along a non-stationary signal. Vague and gradual changes in regime are naturally treated by means of fuzzy clustering. An adaptive hierarchical selection of the number of clusters (the number of underlying processes) can overcome the general non-stationary nature of real-life time-series (biomedical, physical, economical, etc.).     

Reducing a class of polygonal path tracking to straight line tracking via nonlinear strip-wise affine transformation

In this paper a piecewise linear homeomorphism is presented that maps a strictly monotone polygonal chain to a straight line. This mapping enables one to reduce the path tracking task for mobile robots to straight line tracking. Due to the simplicity of the transformation, closed form solutions for the direct and inverse mapping are presented. Furthermore, the transformation also defines a feedback equivalence relation between the original and the transformed system equations of the mobile robot. It is shown that the form of the system equations is preserved and that the transformation essentially maps a car-like robot in the original domain, to a car-like robot in the transformed domain. This enables one to use straight line trackers developed solely for this system, for the tracking of arbitrary strictly monotone polygonal curves. Finally, it is shown that the use of this mapping can also simplify the application of existing path tracking controllers since they only need to track straight line paths. In general, one can eliminate from the existing path controllers all parameters that are needed for non-straight paths, thus obtaining respective simplified controllers. For example, it is shown that a fuzzy path controller with 135 rules can be reduced to an equivalent fuzzy straight line tracking controller with 45 rules.     

Identification of non-linear characteristics of a class of block-oriented non-linear systems via Daubechies wavelet-based models

The paper deals with the identification of non-linear characteristics of a class of block-oriented dynamical systems. The systems are driven by random stationary white processes (i.i.d. random input sequences) and disturbed by a zero-mean stationary, white or coloured, random noise. The prior knowledge about non-linear characteristics is non-parametric excluding implementation of standard parametric identification methods. To recover non-linearities, a class of Daubechies wavelet-based models using only input-output measurement data is introduced and their accuracy is investigated in the global MISE error sense. It is shown that the proposed models converge with a growing collection of data to the true non-linear characteristics (or their versions), provided that the complexity of the models is appropriately fitted to the number of measurements. Suitable rules for optimum model size selection, maximizing the convergence speed, are given and the asymptotic rate of convergence of the MISE error for optimum models is established. It is shown that in some circumstances the rate is the best possible that can be achieved in non-parametric inference. We also show that the convergence conditions and the asymptotic rate of convergence are insensitive to the correlation of the noise and are the same for known and unknown input probability density function (assumed to exist). The theory is illustrated by simulation examples.     

Identification of time-series signals using a dynamic neural network with GA-based training

We propose a dynamic neural network (DNN) that realizes a dynamic property and has a network structure with the properties of inertia, viscosity, and stiffness without time-delayed input elements, and a training algorithm based on a genetic algorithm (GA). In a previous study, we proposed a modified training algorithm for the DNN based on the error back-propagation method. However, in the previous method it was necessary to determine the values of the DNN property parameters by trial and error. In the newly proposed DNN, the GA is designed to train not only the connecting weights but also the property parameters of the DNN. Simulation results show that the DNN trained by the GA obtains good performance for time-series patterns generated from an unknown system, and provides a higher performance than the conventional neural network. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, 0ita, Japan, February 4–6, 2005     

Feedback controlled particle swarm optimization and its application in time-series prediction

Particle swarm optimization (PSO) algorithm is an algorithmic technique for optimization by solving a wide range of optimization problems. This paper presents a new approach of extending PSO to solve optimization problems by using the feedback control mechanism (FCPSO). The proposed FCPSO consists of two major steps. First, by evaluating the fitness value of each particle, a simple particle evolutionary fitness function is designed to control parameters involving acceleration coefficient, refreshing gap, learning probabilities and number of the potential exemplars automatically. By such a simple particle evolutionary fitness function, each particle has its own search parameters in a search environment. Secondly, a local learning method using a competitive penalized method is developed to refine the solution. The FCPSO has been comprehensively evaluated on 18 unimodal, multimodal and composite benchmark functions with or without rotation. Compared with various state-of-the-art algorithms, including traditional PSO algorithms and representative variants of PSO algorithms, the performance of FCPSO is promising. The effects of parameter adaptation, parameter sensitivity and local search method are studied. Lastly, the proposed FCPSO is applied to constructing a radial basis neural network, together with the K-means method for time-series prediction.     

稳定分布噪声下非线性PAR系统辨识新方法

描述了稳定分布的谱表示,提出了共变谱密度的概念,得到一种基于自共变序列与共变谱的稳定分布白噪声与有色噪声的概念及其判断标准,对传统意义上的白噪声进行了广义化,依据多项式自回归（PAR）系统模型,对基于稳定白噪声输入的系统输出非线性稳定有色噪声建立其非线性PAR模型,提出基于最小P范数的EIRLP算法对非线性PAR系统进行辨识。模拟和分析表明,这种算法是一种在高斯和分数低阶 稳定分布噪声条件下具有良好韧性的非线性系统辨识方法,是对传统的二阶统计量基础上的系统辨识方法的改造与推广。     

DENFIS: dynamic evolving neural-fuzzy inference system and itsapplication for time-series prediction

This paper introduces a new type of fuzzy inference systems, denoted as dynamic evolving neural-fuzzy inference system (DENFIS), for adaptive online and offline learning, and their application for dynamic time series prediction. DENFIS evolve through incremental, hybrid (supervised/unsupervised), learning, and accommodate new input data, including new features, new classes, etc., through local element tuning. New fuzzy rules are created and updated during the operation of the system. At each time moment, the output of DENFIS is calculated through a fuzzy inference system based on m-most activated fuzzy rules which are dynamically chosen from a fuzzy rule set. Two approaches are proposed: (1) dynamic creation of a first-order Takagi-Sugeno-type fuzzy rule set for a DENFIS online model; and (2) creation of a first-order Takagi-Sugeno-type fuzzy rule set, or an expanded high-order one, for a DENFIS offline model. A set of fuzzy rules can be inserted into DENFIS before or during its learning process. Fuzzy rules can also be extracted during or after the learning process. An evolving clustering method (ECM), which is employed in both online and offline DENFIS models, is also introduced. It is demonstrated that DENFIS can effectively learn complex temporal sequences in an adaptive way and outperform some well-known, existing models     

Canonical transformation for a class of time-varying multivariable systems

This paper concerns the transformation of time-varying multivariable systems into canonical structures. The study employs differential matrix operators. It leads to a systematic and straightforward technique for developing canonical forms for time-varying multivariable systems that are uniformly observable and «lexicography-fixed’. It shows that canonical forms derived by other authors are special cases of the canonical form of this paper. The derived canonical forms are not unique. However, their structures are controlled by the designer     

Identification and prioritization of differentially expressed genes for time-series gene expression data

Identification of differentially expressed genes (DEGs) in time course studies is very useful for understanding gene function, and can help determine key genes during specific stages of plant development. A few existing methods focus on the detection of DEGs within a single biological group, enabling to study temporal changes in gene expression. To utilize a rapidly increasing amount of single-group time-series expression data, we propose a two-step method that integrates the temporal characteristics of time-series data to obtain a B-spline curve fit. Firstly, a flat gene filter based on the Ljung–Box test is used to filter out flat genes. Then, a B-spline model is used to identify DEGs. For use in biological experiments, these DEGs should be screened, to determine their biological importance. To identify high-confidence promising DEGs for specific biological processes, we propose a novel gene prioritization approach based on the partner evaluation principle. This novel gene prioritization approach utilizes existing co-expression information to rank DEGs that are likely to be involved in a specific biological process/condition. The proposed method is validated on the Arabidopsis thaliana seed germination dataset and on the rice anther development expression dataset.     

Fault diagnosis and fault-tolerant control for non-Gaussian nonlinear stochastic systems via entropy optimisation

ABSTRACT

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for non-linear stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithms, the minimum entropy FD is adopted to minimise the residual entropy and control the shape of the probability density function (PDF) of the residual signal. The observation error system can be proved to be locally and ultimately bounded in the mean square sense. Since entropy can be used to characteriSe the uncertainty of the tracking error for non-Gaussian stochastic systems, the FTC controller is obtained by minimising the performance function with regard to the entropy of the tracking error in this paper. The PDF of the output tracking error is approximated by the B-spline model. An illustrative example is utilised to demonstrate the effectiveness of the FD and FTC algorithm, and satisfactory results have been obtained.     

Neural network based auto association and time-series prediction for biosignal processing in brain-computer interfaces

Neural networks (NNs) can be deployed in many different ways in signal processing applications. This paper illustrates how neural networks are employed in a prediction based preprocessing framework, referred to as neural-time-series-prediction-preprocessing (NTSPP), in an electroencephalogram (EEG)-based brain-computer interface (BCI). NTSPP has been shown to increase feature separability by mapping the original EEG signals via time-series-prediction to a higher dimensional space. Preliminary results of a similar novel framework are also presented where, instead of using predictive NNs, auto-associative NNs are employed and features are extracted from the output of auto-associative NNs trained to specialize on EEG signals for particular brain states. The results show that this preprocessing framework referred to as auto-associative NN preprocessing (ANNP) also has the potential to improve the performance of BCIs. Both the NTSPP and ANNP are compared with and deployed in conjunction with the well know common spatial patterns (CSP) to produce a BCI system which significantly outperforms either approach operating independently and has the potential to produce good performances even with a lower number of EEG channels compared to a multichannel BCI. Multichannel BCIs normally perform better that 2-3 channel BCIs however reducing the number of EEG channels required can positively impact on the time needed to mount electrodes and minimize the obtrusiveness of the electrode montage for the user. It is also shown that NTSPP can improve the potential for employing existing BCI methods with minimal subject-specific parameter tuning to deploy the BCI autonomously. Results are presented with six different classification approaches including various statistical classifiers such as Linear Discriminant Analysis (LDA), Support Vector Machines (SVM) and a Bayes classifier.     

Modeling and prediction with a class of time delay dynamic neural networks

In this paper, we propose a time delay dynamic neural network (TDDNN) to track and predict a chaotic time series systems. The application of artificial neural networks to dynamical systems has been constrained by the non-dynamical nature of popular network architectures. Many of the drawbacks caused by the algebraic structures can be overcome with TDDNNs. TDDNNs have time delay elements in their states. This approach provides the natural properties of physical systems. The minimization of a quadratic performance index is considered for trajectory tracking applications. Gradient computations are presented based on adjoint sensitivity analysis. The computational complexity is significantly less than direct method, but it requires a backward integration capability. We used Levenberg–Marquardt parameter updating method.     

Identification of potential land cover changes on a continental scale using NDVI time-series from SPOT VEGETATION

The identification of land cover changes on a continental scale is a laborious and time-consuming process. A new methodology is proposed based exclusively on SPOT VGT data, illustrated for the African Continent using GLC2000 as reference to select 26 distinct land cover types (classes). For each class, the normalized difference vegetation index (NDVI) time-series are extracted from SPOT VGT images and a hierarchical aggregation is done using two different methods: one that preserves the initial signatures throughout the hierarchical process, and another that recalculates the signatures for each aggregation level. The average classification agreement was above 89% using 26 classes. Reducing the number of classes improves classification agreement. In order to study the influence of temporal variability in the classification results, the methodology was applied on data from 1999, 2001, 2008, and 2010. With 26 classes, the best average classification agreement obtained was 94.5% with annual data, against 74.1% with interannual data.     

一类特殊的列混合变换的研究

提出了一类特殊列混合变换的概念,并对其枝数和计数问题进行了深入的研究和分析。研究了该类列混合变换的枝数分布状况,给出固定多项式c（x）的重量与其枝数之间的精确关系,解决了该类列混合变换的计数问题。最后针对有关分组密码编码环节的设计问题进行了讨论,从而为分组密码的设计与分析提供重要的依据和支持。     

Stabilization of a class of switched systems via designingswitching laws

In this paper, one state transformation is used to construct switching laws for a class of switched systems totally composed of unstable subsystems. Some sufficient conditions for determining the switching law, such that the system is asymptotically stable, are derived