Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.

Report for Type 2 Bayes-Fuzzy Estimation in No-Data Problem

It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide our mustered service within our cool head and warm heart, where two states of nature are existing upon us. Any system is regarded as the two-dimensional variable error model. On the other hand, we consider that the fuzziness is existing in this system. Though we can usually obtain the fuzzy number from the possibility theory, it is not fuzzy but possibility, because the possibility function is as same as the likelihood function, and we can obtain the possibility measure by the maximal likelihood method (i.e. max product method proposed by Dr. Hideo Tanaka). Therefore, Fuzzy is regarded as the only one case according to Vague, which has both some state of nature in this world and another state of nature in the other world. Here, we can consider that Type 1 Vague Event in other world can be obtained by mapping and translating from Type 1 fuzzy Event in this world. We named this estimation as Type 1 Bayes-Fuzzy Estimation. When the Vague Events were abnormal (ex. under War), we need to consider that another world could exist around other world. In this case, we call it Type 2 Bayes-Fuzzy Estimation. Where Hori et al. constructed the stochastic different equation upon Type 1 Vague Events, along with the general following probabilistic introduction method from the single regression model, multi-regression model, AR model, Markov (decision) process, to the stochastic different equation. Furthermore, we showed that the system theory approach is Possibility Markov Process, and that the making decision approach is Sequential Bayes Estimation, too. After all, Type 1 Bays-Fuzzy estimation is the special case in Bayes estimation, because the pareto solutions can exist in two stochastic different equations upon Type 2 Vague Events, after we ignore one equation each other (note that this is Type 1 case), we can obtain both its system solution and its decision solution. Here, it is noted that Type 2 Vague estimation can be applied to the shallow abnormal decision problem with possibility reserved judgement. However, it is very important problem that we can have no idea for possibility reserved judgement under the deepest abnormal envelopment (ex. under War). Expect for this deepest abnormal decision problem, Bayes estimation can completely cover fuzzy estimation. In this paper, we explain our flowing study and further research object forward to this deepest abnormal decision problem.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique, which modulates data symbols in the delayDoppler(DD) domain, presents a potential solution for supporting reliable information transmission in highmobility vehicular networks. In this paper, we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler. We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP), which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM). The empirical state evolution(SE) analysis is then leveraged to predict the performance of our proposed algorithm. To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM) algorithm. Finally, Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Estimation on principal component of multi-collinearity Gauss-Markov model based on minimum description length

Gauss-Markov model is frequently used in data analysis; the analysis and estimation of its parameters is always a hot issue. Based on the information theory and from the viewpoint of optimal information on description—minimum description length, this paper discusses a case: where there is multi-collinearity in the coefficient matrix, principal component estimation is used to estimate and select the original parameters, so as to reduce its multi-collinearity and improve its credibility. From the viewpoint of minimum description length, this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique,which modulates data symbols in the delay-Doppler(DD)domain,presents a potential solution for supporting reliable information transmission in highmobility vehicular networks.In this paper,we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler.We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP),which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM).The empirical state evolution(SE)analysis is then leveraged to predict the performance of our proposed algorithm.To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM)algorithm.Finally,Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

SEMI-BLIND CHANNEL ESTIMATION OF MULTIPLE-INPUT/MULTIPLE-OUTPUT SYSTEMS BASED ON MARKOV CHAIN MONTE CARLO METHODS

This paper addresses the issues of channel estimation in a Multiple-Input/Multiple-Output (MIMO) system. Markov Chain Monte Carlo (MCMC) method is employed to jointly estimate the Channel State Information (CSI) and the transmitted signals. The deduced algorithms can work well under circumstances of low Signal-to-Noise Ratio (SNR). Simulation results are presented to demonstrate their effectiveness.

H_(∞) state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule

We investigate the problem of H_(∞) state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule,as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously.Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an H_(∞) performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.

基于Gray-Markov的电力设备物流量多目标组合估计

电力设备物流量较多且所涉及到的环节较为复杂,导致物流量多目标组合估计误差增加,所以设计基于Gray-Markov的电力设备物流量多目标组合估计方法。利用数据录入模块、数据分析处理模块搭建数据采集平台,实现电力设备物流量数据采集。改进卷积神经网络,构建深度空洞卷积去噪模型,对采集到的数据实施去噪处理。结合BP神经网络与Gray-Markov实现电力设备物流量多目标组合估计。测试结果表明,该方法的绝对误差平均值最低仅为1 025.21,平均相对误差百分比一直低于1.8%,估计误差比较小,精度较高。

Gauss-Markov估计关于误差分布的稳健性

对于一般线性模型y=Xβ+ε,本文讨论了在广义均方误差准则及均方误差矩阵准则下,未知参数β的可估函数Xβ的Gauss-Markov估计关于误差分布的稳健性,分别给出了误差项ε的最大分布类,使得误差项ε的分布在此范围内变动时,Gauss-Markov估计在相应准则下是最优估计.

平衡损失下一般Gauss-Markov模型中回归系数的最优估计（英文）

在平衡损失下,我们研究了一般Gauss-Markov模型中回归系数的最优估计,首先我们得到了线性估计为最佳线性无偏估计的充分必要条件;其次证明了平衡损失下的最佳线性无偏估计在几乎处处意义下是唯一的,并且是普通最小二乘估计和二次损失下最优估计的平衡;最后,我们讨论了最优估计关于损失函数和模型设定的稳健性,并得到了该最优估计在模型误定下具有稳健性的充分必要条件.

复共线Gauss-Markov模型参数估计的最小描述长度方法

Gauss-Markov模型是多元数据分析处理工作中常用的模型,其参数估计与筛选一直是研究的热点。当Gauss-Markov模型的设计矩阵存在复共线性时,常用主成分分析方法来筛选和估计其参数,消去它们之间的复共线性,提高估计准确度。基于最小描述长度原理,提出了一种新的参数筛选估计方法。该方法应用最小描述长度原理选择主成分作为参数,其参数的可靠性较高;从信息的角度看,这种方法的信息损失最小。最后实例说明了该方法的有效性和可靠性。

带约束的一般Gauss-Markov模型下的线性充分性和线性完全性

本文将文[1,2]的结果扩展到了有约束的线性模型。

联邦滤波算法与Gauss-Markov估计的统一性分析

从矩阵论和数理统计理论的角度,阐述了联邦滤波与Gauss-Markov估计的内在联系,论证了联邦全局最优滤波与Gauss-Markov估计的统一性。推导了基于Gauss-Markov估计的联邦滤波信息融合算法,并与最小二乘估计的信息融合算法以及集中卡尔曼滤波算法在舰载组合导航系统中应用进行了对比。仿真结果表明,基于Gauss-Markov估计的联邦滤波信息融合算法与集中式卡尔曼滤波的精度相当,两者的估计精度均高于最小二乘估计,前者具有全局最优性。

Gauss-Markov结构下GM估计关于线性变换的不变性

在文[1]的基础上讨论了Gauss-Markov结构下线性变换对GM估计所产生的偏差,并减弱了文[1]的相关条件,给出了同一可估函数的GM估计具有不变性的充分必要条件.

Low-rank spectral estimation algorithm of learning Markov model

This paper proposes a low-rank spectral estimation algorithm of learning Markov model.First,an approximate projection algorithm for the rank-constrained frequency matrix set is proposed,and thereafter its local Lipschitzian error bound established.Then,we propose a low-rank spectral estimation algorithm for estimating the state transition frequency matrix and the probability matrix of Markov model by applying the approximate projection algorithm to correct the maximum likelihood estimation of the frequency matrix,and prove that there is only a multiplying constant difference in estimation errors between the low-rank spectral estimation and the maximum likelihood estimation under appropriate conditions.Finally,numerical comparisons with the prevailing maximum likelihood estimation,spectral estimation,and rank-constrained maxi-mum likelihood estimation show that the low-rank spectral estimation algorithm is effective.

Augmented input estimation in multiple maneuvering target tracking

This paper presents augmented input estimation(AIE)for multiple maneuvering target tracking.Multi-target tracking(MTT)is based on two main parts,data association and estimation.In data association(DA),the best observations are assigned to the considered tracks.In real conditions,the number of observations is more than targets and also locations of observations are often so scattered that the association between targets and observations cannot be done simply.In this case,for general MTT problems with unknown numbers of targets,we present a Markov chain Monte-Carlo DA(MCMCDA)algorithm that approximates the optimal Bayesian filter with low complexity in computations.After DA,estimation and tracking should be done.Since in general cases,many targets can have maneuvering motions,then AIE is proposed to cover both the non-maneuvering and maneuvering parts of motion and the maneuver detection procedure is eliminated.This model with an input estimation(IE)approach is a special augmentation in the state space model which considers both the state vector and the unknown input vector as a new augmented state vector.Some comparisons based on the Monte-Carlo simulations are also made to evaluate the performances of the proposed method and other older methods in MTT.

Application of Bayesian Approach in the Parameter Estimation of Continuous Lumping Kinetic Model of Hydrocracking Process

Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.

A NEW METHOD OF BISPECTRAL ESTIMATION FOR TRANSIENT SIGNAL

Estimation of model parameter for transient signal is very important in many aspects. This paper presents a new Markov ARMA model Q-slice estimation algorithm for transient signal based on bispectrum. Simulation results show that this new method has some special features, such as higher estimation precision, lower amount of calculation, higher fitting effect even in lower signal-to-noise ratio (SNR) situation.