Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.     

Echo state networks based predictive model of vinyl chloride monomer convention velocity optimized by artificial fish swarm algorithm

Conversion rate in the Polyvinylchloride (PVC) polymerizing process has a certain influence on the molecular weight of PVC, porosity, absorption rate of plasticizer, vinyl chloride monomer (VCM) residue and thermal stability. Therefore, a predictive model based on echo state networks (ESN) method optimized by the artificial fish swarm algorithm (AFSA) is proposed to predict the conversion velocity. Firstly, the hot balancing mechanisms of polymerizer and the influenced factors of convention rate of VCM are analyzed in details. Then the auxiliary variables of the predictive model kernel are selected by using the kernel principal component analysis method for reducing the model dimensionality. Thirdly, the structure parameters of the ESN are optimized by the AFSA to realize the nonlinear mapping between input and output variables of the discussed soft-sensor model. The artificial fish swarm behaviors, such as foraging, swarming, chasing, random, are introduced in details. Finally, simulation results show that the proposed model can significantly enhance the predictive accuracy and robustness of the technical index and satisfy the real-time control requirements of PVC polymerizing production process.     

MULTIVARIABLE FUZZY GENERALIZED PREDICTIVE CONTROL

A Takagi-Sugeno (T-S) fuzzy model is used to express non-linear dynamic systems with time-delay in this paper, and an on-line identification algorithm is presented regarding its parameters and structures. A multivariable fuzzy generalized predictive control approach is proposed based on the identified fuzzy model by means of the generalized predictive control principle. The closed-loop stability is analyzed in detail. A simulation study for the multivariable load system of a boiler-turbine unit shows that the approach is superior to convention load control systems.     

D-FNN based soft-sensor modeling and migration reconfiguration of polymerizing process

A soft-sensor modeling method based on dynamic fuzzy neural network (D-FNN) is proposed for forecasting the key technology indicator convention velocity of vinyl chloride monomer (VCM) in the polyvinylchloride (PVC) polymerizing process. Based on the problem complexity and precision demand, D-FNN model can be constructed combining the system prior knowledge. Firstly, kernel principal component analysis (KPCA) method is adopted to select the auxiliary variables of soft-sensing model in order to reduce the model dimensionality. Then a hybrid structure and parameters learning algorithm of D-FNN is proposed to achieve the favorable approximation performance, which includes the rule extraction principles, the classification learning strategy, the precedent parameters arrangements, the rule trimming technology based on error descendent ratio and the consequent parameters decision based on extended Kalman filter (EKF). The proposed soft-sensor model can automatically determine if the fuzzy rules are generated/eliminated or not so as to realize the nonlinear mapping between input and output variables of the discussed soft-sensor model. Model migration method is adopted to realize the on-line adaptive revision and reconfiguration of soft-sensor model. In the end, simulation results show that the proposed model can significantly enhance the predictive accuracy and robustness of the technical-and-economic indexes and satisfy the real-time control requirements of PVC polymerizing production process.     

Dynamic modeling of SOFC based on a T–S fuzzy model

The operating temperature and voltage are the key parameters affecting the performance of Solid Oxide Fuel Cell (SOFC). In this article a Takagi–Sugeno (T–S) fuzzy model is proposed to describe the nonlinear temperature and voltage dynamic properties of the SOFC system. During the process of modeling, a Fuzzy Clustering Means (FCM) method is used to determine the nonlinear antecedent parameters, and the linear consequent parameters are identified by a recursive least squares algorithm. The validity and accuracy of modeling are tested by simulations. The simulation results show that it is feasible to establish the dynamic model of SOFC by using the T–S fuzzy identification method.     

基于模糊建模的冷凝器污脏软测量

提出了一种基于模糊建模的冷凝器污脏软测量方法.该方法选取传热端差作为研究对象,应用模糊建模技术分离出冷凝器污脏对端差的影响.在模糊建模中,采用T-S模型描述变工况传热端差,研究了一种相似度判别法则以确定最优模型结构,并采用实数编码的遗传算法同时优化模型前、后件参数,从而获得了规则简化、精度较高的模糊模型.根据此方法,设计了试验系统,并进行了现场试验.试验结果表明:该方法能有效地在线监测冷凝器污脏,并在冷凝器出现堵管或空气漏入量较大时,取得比热阻法、传热系数法更可靠的测量结果.     

基于局部线性聚类算法的模糊建模

提出了一种新的基于T-S模糊模型的建模方法，首先通过一种局部线性聚类算法，自适应确定模糊规则数目及初始T-S模型的前提和结论参数，建立相应的一阶T-S模糊神经网络．并用梯度下降和递推最小二乘混合算法训练网络参数，从而提高建模精度．最后，通过两个仿真实例验证了本文方法的有效性．     

Neuro-f uzzy system modeling based on automatic f uzzy clustering

A neuro-fuzzy system model based on automatic fuzzy clustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts :1) Automatic fuzzy C-means (AFCM) , which is applied to generate fuzzy rules automatically , and then fix on the size of the neuro-fuzzy network , by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2)Recursive least square estimation ( RLSE) . It is used to update the parameters of Takagi-Sugeno model , which is employed to describe the behavior of the system;3) Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally ,modeling the dynamical equation of the two- link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

深度确定性策略梯度与模糊PID的协同温度控制

针对现有温度控制系统控温时间长、误差大的问题, 本文提出了一种基于深度确定性策略梯度(DDPG)和模糊自整定PID的协同温度控制. 首先, 模糊PID在控制大滞后系统时, 控制器不能立刻对产生的干扰起抑制作用, 且无法保证大滞后系统的稳定性等问题, 本文建立了模糊PID和DDPG算法相结合的温度控制模型, 该模型将模糊PID作为主控制器, DDPG算法作为辅助控制, 利用双控制器模型实现温度协同控制. 接着, 利用遗传算法对模糊PID的隶属函数和模糊规则进行寻优, 获得模型参数最优解. 最后, 在仿真实验中验证所提方法的有效性. 仿真实验结果表明, 本文提出的算法可有效减少噪声干扰, 减小控制系统的响应时间、误差和超调量.     

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

Nonlinear modeling and adaptive fuzzy control of MCFC stack

To improve availability and performance of fuel cells, the operating temperature of molten carbonate fuel cells (MCFC) stack should be controlled within a specified range. However, the most existing models of MCFC are not ready to be applied in synthesis. In this paper, a radial basis function neural networks identification model of MCFC stack is developed based on the input–output sampled data. A novel adaptive fuzzy control procedure for the temperature of MCFC stack is also developed. The parameters of the fuzzy control system are regulated by back-propagation algorithm, and the rule database of the fuzzy system is also adaptively adjusted by the nearest-neighbor-clustering algorithm. Finally using the neural networks model of MCFC stack, the simulation results of the control algorithm are presented. The results show the effectiveness of the proposed modeling and design procedures for MCFC stack based on neural networks identification and the novel adaptive fuzzy control.     

自适应翼肋的建模与分布式协调控制

针对分布式驱动的自适应翼肋进行建模与分布式协调控制研究。基于分析力学的方法建立了自适应翼肋的动力学模型。以这个非线性关联动力学模型为基础,采用Takagi—Sugeno（T—S）模糊逼近理论,建立了自适应翼肋的仿射型T—S模糊关联模型。对仿射型T—S模糊关联模型的物理耦合项进行变换,将系统模型写成空间关联系统的形式,以解耦控制器设计条件。基于并行分配补偿理论,针对系统模型具有耦合项和非零常数项的特点,设计了满足鲁棒性能指标的包含耦合项和偏置项的分布式协调控制器。控制器设计条件具有线性矩阵不等式的形式,并且只包含单个驱动单元的参数,计算量较小。仿真结果表明所设计的自适应翼肋分布式协调控制器,能够在外界扰动作用下使翼肋的形状收敛到期望翼型;翼肋在变形过程中能保持光滑连续的外形。     

基于模糊模型的结构和参数的一体化辨识

基于模糊集合的模糊建模捕述复杂、病态、非线性系统的特性是一种有效方法．文中讨论了从样本数据中通过正交变换和模糊聚类获取模糊规则的方法．利用正交最小二乘对模糊聚类的结果进行变换,采用CGS（Classical Gram—Schmidt）方法确定对建模贡献大的规则,删除对建模贡献小的规则,并对模型中的参数进行估计,能够同时模对糊模型的结构和参数进行辨识．仿真结果表明,提出的方法能够对非线性系统进行模糊建模．     

基于自组织神经网络的非线性系统建模

针对基于T-S模糊模型的非线性系统建模问题,提出了一种基于自组织神经网络的新方法.在T-S模糊模型的建模中,目前常用的模糊C均值聚类算法存在迭代次数多,计算耗时的缺点.首先,利用竞争学习算法对输入空间进行聚类,基于此结果,借助于模糊C均值聚类算法进一步优化聚类结果,提取T-S模糊模型的规则前件隶属函数参数.然后,采用最小二乘法求得T-S模糊模型的规则后件参数,从而建立起非线性系统的T-S模糊模型.最后,仿真结果表明,该方法可以为模糊建模提供好的模型结构,并且有较高的计算效率和精度.     

模糊灰色认知网络的建模方法及应用

针对具有不确定性非线性系统的机理模型难以建立的问题,提出了基于模糊灰色认知网络（Fuzzy grey cognitive networks,FGCN）的非线性系统建模方法.该方法将模糊认知网络和灰色系统理论相结合,把模糊认知网络的节点状态值和权值扩展为灰色区间,引入灰度来评判可靠性.采用一种带终端约束的非线性Hebbian学习算法（Nonlinear hebbian learning,NHL）辨识FGCN的模型参数,引入了与FGCN模型中节点的系统实际测量值对应的灰数值,在更新机制中增加了包含系统测量值与预测值之差的修正项,对权值进行有监督的修正.利用水箱控制系统进行的仿真实验结果表明,本文提出的建模方法能解决对数据存在不确定性或缺失的复杂系统建模的难题,所建的模型能做出接近人类智能的控制决策,所采用的权值学习方法具有收敛速度快、学习结果精准等优点,并克服了传统非线性Hebbian算法对初始值依赖性强的缺点,对不确定性系统的建模具有广泛适用性.     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。     

Designing neurofuzzy system based on ICART algorithm and its application for modeling jet fuel endpoint of hydrocracking process

In this paper, a neuro-fuzzy system based on improved CART algorithm (ICART) is presented, in which the ICART algorithm is used to design neuro-fuzzy system. It is worth noting that ICART algorithm partitions the input space into tree structure adaptively, which avoids the curse of dimensionality (number of rules goes up exponentially with number of input variables). Moreover, it adopts density function to construct the local model for every node in order to overcome the discontinuous boundaries existed in CART algorithm. In addition, a supervised scheme is used to adjust parameters to minimize the network output error and construct more accurate fuzzy model on the basis of the ICART algorithm. Finally, to illustrate the validity of the proposed method, a simulation research and a practical application are done. The results show that the proposed method can provide optimal model structure and parameters for fuzzy modeling, possesses high learning efficiency, and is smoother than CART algorithm. It can be successfully applied to modeling jet fuel endpoint of hydrocracking processing.     

模糊自整定PID温度控制系统的建模与仿真

针对炒茶机的加热控制系统跟踪设定的温度值滞后、自动调节加热装置实时性差的问题,设计一种模糊自整定比例积分微分(PID)参数控制器。采用PID控制和模糊控制算法相结合的方法,实现模糊控制对PID参数的调整。利用Matlab在Simulink中建立模型,并对该控制器进行仿真分析。结果表明,模糊PID自整定控制器的超调量 ≈1%,稳态误差es=0。该方法可提高温度控制系统的性能。     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

发酵过程的多模型融合建模算法

提出了利用多模型融合技术进行发酵过程建模的新方法， 该方法能够将在线参数和离线参数同时用于建模中． 首先给出了多模型融合建模算法框架， 并描述了基于自适应模糊神经网络和模糊推理技术两个参与融合的子模型的建立方法. 采用三个非线性函数分别运用GMDH-PTSV算法、傅里叶神经网络和多模型融合建模算法进行建模精度比较. 最后给出了多模型融合建模算法在青霉素发酵过程中应用的结果．