复杂高阶对象的预测PID控制

针对复杂高阶对象提出了一种基于数值最优模型降阶方法,并基于这种降阶模型设计了预测PID控制器,将此控制器应用于原始模型能够得到很好地控制效果。数值最优模型降阶算法使高阶对象能近似为一阶加时滞对象或二阶加时滞对象,通过模型阶跃响应和Bode图对比,降阶模型曲线很好地逼近原始模型曲线。预测PID对大时滞对象有着很好地控制效果,模型降阶使得预测PID很好地控制复杂高阶对象,且其结构简单,可调参数少的特点。     

基于递推参数辨识的齿轮箱故障在线检测

为实现齿轮箱故障的在线检测,提出基于递推AR模型参数辨识的齿轮箱振动信号在线辨识方法。对实验室的齿轮箱进行不同工况下振动信号的检测,利用最优辅助变量法确定其自回归模型的阶次和模型参数的初值,以自回归模型系数作为状态变量,采用Kalman滤波器技术进行在线递推参数辨识。实验结果表明,该方法中参数变化量的2-范数会发生突变,能检测出齿轮磨损和轴承外圈剥落的故障。     

一种高阶无迹卡尔曼滤波方法

现有的研究中,高阶无迹变换（Unscented transform,UT）还不存在具体的解析解,因此,无法利用高阶无迹变换获得具备更高精度的高阶无迹卡尔曼滤波器（Unscented Kalman filter,UKF）.为了解决这一问题,本文在五阶容积变换（Cubature transform,CT）的基础上,通过引入一个自由参数κ,得到高阶无迹变换的解析解,从而获得了高阶无迹卡尔曼滤波器（Unscented Kalman filter,UKF）.同时验证了现有的五阶容积变换和五阶无迹变换分别是本文所提出的高阶无迹变换在κ=2和κ=6-n时的两个特例.进而分析和讨论了高阶无迹卡尔曼滤波器在系统不同维数条件下κ值的最优选取,并讨论了其稳定性.纯方位跟踪模型和弹道目标再入模型仿真验证了本文方法的正确性,且与现有方法相比具有更高的精度.     

快速非递推最小二乘AR建模算法

本文将推导一种基于对AR参数求向前向后预测误差最小二乘解的非递推建模算法(NLS)。它的精度和Marple算法、LUD算法相当,但其建模速度却快于它们。对于p阶AR模型,其建模计算量约为1/6p~3+Np。     

输入函数的参数偏离时最优简化模型的一类误差估计

当大系统的输入函数的初始参数发生偏离时,其最优简化模型的近似模型可以利用输入函数的渐近展开得到。本文提出高阶模型和其最优简化模型的近似模型之间近似程度的一种估计。     

自回归滑动平均建模中观测噪声方差估计的新方法

目前的自回归滑动平均(ARMA)建模方法由于只利用了观测数据的高阶自协方差构建Yule-Walker方程,而没有利用观测数据的低阶自协方差信息,导致观测噪声方差的估计精度不高,并且在自回归(AR)阶次p小于或等于滑动平均(MA)阶次q时无法估计出观测噪声方差.为此,本文提出了一种单独估计观测噪声方差的新方法,即先将ARMA模型近似为一高阶AR模型,再构建从观测数据1阶自协方差开始的Yule-Walker方程.由于充分利用了观测数据的统计信息,有利于提高观测噪声方差的估计精度,为后续的AR和MA参数估计精度的提高奠定了基础,也解决了p小于或等于q时观测噪声方差无法估计的问题,仿真和实验结果验证了该方法的有效性.     

基于Matlab的AR模型参数估计

AR(自回归)模型是时域信号分析中的一种常见模型。基于Matlab用时间序列的最小二乘估计和FPE、AIC准则对AR(n)模型进行参数估计的传统方法为利用多次复杂的矩阵转换求解。在传统理论的基础上,笔者利用Matlab自有函数对AR(n)模型进行参数估计,确定出AR(n)模型的最优阶次,极大简化了原有程序,分析简单易懂,增强了参数估计结果的可操作性。     

基于模型降阶的最优分数阶PID控制器设计

由于一些受控对象较为复杂或者模型系统阶次较高,使得控制器的设计变得非常困难,这会造成控制系统的鲁棒性和动态特性下降;文章在H2范数模型降阶的基础上提出一种新的降阶模型结构,它可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统,并以降阶后模型的幅频、相频和对象增益变化的鲁棒特性为约束条件进行最优分数阶PID控制器的设计;仿真实验证明,与原有闭环控制系统相比,基于模型降阶的最优分数阶PID控制器控制下的闭环系统具有更好的动态性能,并且鲁棒性较强。     

基于高阶统计量的心音信号分析

对高阶统计量方法应用于心音信号分析进行了研究。建立了心音信号的AR双谱模型,获得了心音的双谱幅度图,并采用模型参数作为特征参量对心音信号进行了二类模式识别。实验结果表明,高阶统计量在心音信号分析和处理中具有较大的应用潜力。     

高阶模型最优简化的积分平方误差法的若干性质

大系统的模型最优简化的积分平方误差法,至今仅仅对输入函数为脉冲、幂函数和正弦函数时有效。本文首先指出,指数函数等一类函数输入时的高阶模型也能用积分平方误差法进行最优简化。其次证明,和原系统有相同输出意义的等价系统具有叠加性,从而把高阶模型的最优简化工作推广到相当广泛的范围。 正弦函数输入时高阶模型的最优简化模型是与角频率有关的。本文最后给出,当角频率有偏离时,其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。     

An “impossibility” theorem on a class of high-order discrete-time nonlinear control systems

A high-order discrete-time nonlinear system with unknown parameters and Gaussian noise is studied in this paper, and it is shown that under a simple algebraic condition concerning the nonlinearity of the system, there does not exist any feedback controller that globally stabilizes the uncertain system. This impossibility result attempts to understand the capability and limitation of feedback mechanism of a high-order discrete-time nonlinear system and continues a series of previous research on similar first-order systems. This result shows that for the high-order discrete-time nonlinear system studied here, a polynomial corresponding to the first-order principle part of the system determines the limit of the feedback mechanism.     

AN ENHANCED DETERMINISTIC FUZZY TIME SERIES FORECASTING MODEL

The study of fuzzy time series has attracted great interest and is expected to expand rapidly. Various forecasting models including high-order models have been proposed to improve forecasting accuracy or reducing computational cost. However, there exist two important issues, namely, rule redundancy and high-order redundancy that have not yet been investigated. This article proposes a novel forecasting model to tackle such issues. It overcomes the major hurdle of determining the k-order in high-order models and is enhanced to allow the handling of multi-factor forecasting problems by removing the overhead of deriving all fuzzy logic relationships beforehand. Two novel performance evaluation metrics are also formally derived for comparing performances of related forecasting models. Experimental results demonstrate that the proposed forecasting model outperforms the existing models in efficiency.     

利用1~2阶分数阶微分掩模的边缘检测

现有的分数阶微分边缘检测算子大都是基于0~1阶分数阶微分而构造,鲜有文献讨论基于1~2阶分数阶微分的边缘检测算子。为此,分析了1~2阶分数阶微分对信号的作用,基于1~2阶分数阶微分构造了一种新的边缘检测掩模算子。实验结果表明,该算子不仅优于常用整数阶微分算子,而且比现有的一些0~1阶分数阶微分算子具有更好的边缘检测效果。     

Identifiability of the AR parameters of an ARMA process usingcumulants

The problem of estimating the autoregressive (AR)-order and the AR parameters of a causal, stable, single input single output (SISO) autoregressive moving average (ARMA) (p,q) model, excited by an unobservable i.i.d. process, is addressed. The observed output is corrupted by additive colored Gaussian noise, whose power spectral density is unknown. The ARMA model may be mixed-phase, and have inherent all-pass factors and repeated poles. It is shown that consistent AR parameter estimates can be obtained via the normal equations based on (p+1) 1-D slices of the mth-order ( m>2) cumulant. It is shown via a counterexample that consistent AR estimates cannot, in general, be obtained from a subset of these p+1 slices. Necessary and sufficient conditions for the existence of a full-rank slice are also derived     

基于混合自回归潜周期模型的网络结构分析

格兰杰因果关系是推导网络结构最强有力的工具,特别是对于时间序列数据而言,它有非常精确的时间空间和频率空间的表示形式,所以它的应用越来越广泛。但是实际问题中的很多数据表现出明显的周期特点,且实际测量到的数据通常会受到历史记录的影响,对于这种类型的数据,可以用混合自回归潜周期模型来进行处理。将传统格兰杰因果关系模型应用到包含调和振子的混合自回归潜周期模型,对模型中的参数进行了估计,在此基础上,利用格兰杰因果关系的思想推导出网络的结构。     

A generalized least absolute deviation method for parameter estimation of autoregressive signals

This paper proposes a generalized least absolute deviation (GLAD) method for parameter estimation of autoregressive (AR) signals under non-Gaussian noise environments. The proposed GLAD method can improve the accuracy of the estimation of the conventional least absolute deviation (LAD) method by minimizing a new cost function with parameter variables and noise error variables. Compared with second- and high-order statistical methods, the proposed GLAD method can obtain robustly an optimal AR parameter estimation without requiring the measurement noise to be Gaussian. Moreover, the proposed GLAD method can be implemented by a cooperative neural network (NN) which is shown to converge globally to the optimal AR parameter estimation within a finite time. Simulation results show that the proposed GLAD method can obtain more accurate estimates than several well-known estimation methods in the presence of different noise distributions.     

ARMA model parameter estimation based on the equivalent MA approach

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low- and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results.     

复杂脉内调制雷达信号的识别方法

提出一种识别包括相位编码、频率编码,以及脉内混合调制等复杂雷达信号的方法。该方法结合AR模型功率谱估计分析方法和小波变换模极大值方法,将复杂混合调制信号转化成相位编码信号,然后基于高次方频谱分析的方法提取信号的频率特征,首次实现了对6种复杂雷达信号的分类。实验表明,在信噪比为0 dB时,大多数信号的识别率可以达到93%以上。     

基于高阶累积量和DNN模型的井下信号识别方法

针对矿井复杂异构的无线环境,提出一种基于高阶累积量和DNN模型的井下信号识别方法,实现了井下BPSK,QPSK,8PSK,2FSK,4FSK,8FSK,32QAM,64QAM,OFDM等数字信号的自动调制识别。分析得到9种数字信号的高阶累积量理论值,并通过傅里叶变换提高信号辨识度;分析井下小尺度衰落信道对高阶累积量的影响,推导出经过井下衰落信道后信号的高阶累积量计算表达式,根据高阶累积量理论值构造特征参数并训练DNN模型,实现信号识别。仿真分析结果表明,该方法在矿井Nakagami-m衰落信道下有出色的调制识别性能,信噪比为-5 dB时平均正确识别率为89.2%以上,信噪比为5 dB以上时平均正确识别率为100%。该方法为在特殊复杂环境下的信号识别检测提供了新思路。     

基于故障传播的模块化BP神经网络电路故障诊断

大规模的数模混合电路所含故障模式众多,电路故障状态复杂,且易发生传播,因而电路故障诊断难度较大。针对大规模电路发生故障时存在故障传播的问题,提出一种基于故障传播的模块化BP神经网络（MBPFP）故障诊断方法。首先,在电路模块划分的基础上分析子电路间的故障传播,并将故障源和故障传播源"模块化";然后,通过子电路的异常检测模型进行一级定位,缩小故障原因集合,确定故障模块;最后,利用目标模块的BP神经网络模型进行二级定位,实现故障诊断并识别故障模式。与传统BP神经网络等方法进行比较的实验结果表明,MBPFP故障诊断方法具有较高的故障覆盖率,在定位准确率方面提高了至少8个百分点,其性能优于传统BP神经网络等方法。