Nonlinear system identification and model reduction using artificial neural networks

We present a technique for nonlinear system identification and model reduction using artificial neural networks (ANNs). The ANN is used to model plant input–output data, with the states of the model being represented by the outputs of an intermediate hidden layer of the ANN. Model reduction is achieved by applying a singular value decomposition (SVD)-based technique to the weight matrices of the ANN. The sequence of state values is used to convert the model to a form that is useful for state and parameter estimation. Examples of chemical systems (batch and continuous reactors and distillation columns) are presented to demonstrate the performance of the ANN-based system identification and model reduction technique.     

Modification to adaptive model reduction for regulation of distributed parameter systems with fast transients

We focus on output feedback control of distributed processes whose infinite dimensional representation in appropriate Hilbert subspaces can be decomposed to finite dimensional slow and infinite dimensional fast subsystems. The controller synthesis issue is addressed using a refined adaptive proper orthogonal decomposition (APOD) approach to recursively construct accurate low dimensional reduced order models (ROMs) based on which we subsequently construct and couple almost globally valid dynamic observers with robust controllers. The novelty lies in modifying the data ensemble revision approach within APOD to enlarge the ROM region of attraction. The proposed control approach is successfully used to regulate the Kuramoto‐Sivashinsky equation at a desired steady state profile in the absence and presence of uncertainty when the unforced process exhibits nonlinear behavior with fast transients. The original and the modified APOD approaches are compared in different conditions and the advantages of the modified approach are presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4595–4611, 2013     

基于正则化的函数连接神经网络研究及其复杂化工过程建模应用

在化工过程的建模中,由于过程数据的高维度和高非线性,导致计算量大幅提升和建模难度加大。为了解决这一问题,提出了一种基于正则化方法的函数连接神经网络模型(regularization based functional link neural network, RFLNN)。所提出的RFLNN方法里,通过使用正则化的方法对函数连接神经网络的权值进行优化,一方面大幅降低网络计算复杂度和计算量,另一方面极大程度上克服网络局部极值和过拟合的问题,以提高函数连接神经网络的学习速度和精度。为了验证所提出方法的有效性,首先采用UCI数据中Real estate valuation数据对其性能进行测试;随后将所提的方法应用于高密度聚乙烯(high density polyethylene,HDPE)复杂生产过程进行建模。UCI标准数据与工业数据的仿真结果表明,与传统FLNN对比,RFLNN在处理高维复杂化工过程数据时具有收敛速度快、建模精度高等特点。     

Nonlinear dynamic process monitoring based on dynamic kernel PCA

Nonlinear dynamic process monitoring based on dynamic kernel principal component analysis (DKPCA) is proposed. The kernel functions used in kernel PCA (KPCA) are profitable for capturing nonlinear property of processes and the time-lagged data extension is suitable for describing dynamic characteristic of processes. DKPCA enables us to monitor an arbitrary process with severe nonlinearity and (or) dynamics. In this respect, it is a generalized concept of multivariate statistical monitoring approaches. A unified monitoring index combined T² with SPE is also suggested. The proposed monitoring method based on DKPCA is applied to a simulated nonlinear process and a wastewater treatment process. A comparison study of PCA, dynamic PCA, KPCA, and DKPCA is investigated in terms of type I error rate, type II error rate, and detection delay. The monitoring results confirm that the proposed methodology results in the best monitoring performance, i.e., low missing alarms and small detection delay, for all the faults.     

基于主元提取的鲁棒极限学习机研究及其化工建模应用

化工生产过程日益复杂，传统极限学习机(extreme learning machine, ELM)无法有效地对化工过程数据建模。针对该问题，提出一种基于主元提取(principal components extraction, PCE)的鲁棒极限学习机(PCE-RELM)。通过对ELM隐含层进行主元分析，提取数据的主元特征，去除变量间的线性相关性，简化研究问题。可以减小隐含层节点数对模型精度的影响，实现对ELM隐含层节点数的快速随机选取，同时使ELM具有鲁棒性。为验证提出方法的有效性，将PCE-RELM模型应用于精对苯二甲酸(purified terephthalic acid,PTA)生产过程建模。仿真结果显示，相比传统的ELM，PCE-RELM模型具有设计简单、鲁棒性好、精度高等优势，可以对化工过程控制、分析起到指导作用。     

Nonlinear multiscale modelling for fault detection and identification

In order to detect abnormal events at different scales, a number of multiscale multivariate statistical process control (MSPC) approaches which combine a multivariate linear projection model with multiresolution analysis have been suggested. In this paper, a new nonlinear multiscale-MSPC method is proposed to address multivariate process performance monitoring and in particular fault diagnostics in nonlinear processes. A kernel principal component analysis (KPCA) model, which not only captures nonlinear relationships between variables but also reduces the dimensionality of the data, is built with the reconstructed data obtained by performing wavelet transform and inverse wavelet transform sequentially on measured data. A guideline is given for both off-line and on-line implementations of the approach. Two monitoring statistics used in multiscale KPCA-based process monitoring are used for fault detection. Furthermore, variable contributions to monitoring statistics are also derived by calculating the derivative of the monitoring statistics with respect to the variables. An intensive simulation study on a continuous stirred tank reactor process and a comparison of the proposed approach with several existing methods in terms of false alarm rate, missed alarm rate and detection delay, demonstrate that the proposed method for detecting and identifying faults outperforms current approaches.     

基于D-FNN的聚合过程转化速率软测量建模及重构

引言以氯乙烯单体(VCM)为原料,采用悬浮法聚合工艺生产聚氯乙烯(PVC)树脂是一种典型的间歇式化工生产过程。VCM的转化率对PVC树脂产品质量有很大影响,不同转化率时对PVC     

基于IJB-PCA-ICA算法的故障检测

针对现代工业过程数据的高维性和分布复杂性等问题,提出了一种基于IJB-PCA-ICA（improved Jarque-Bera-principal component analysis-independent component analysis）的故障检测方法。首先采用改进的Jarque-Bera检测方法（J-B test）对原始数据划分高斯与非高斯核心部分,并对其中的高斯性与非高斯性均不明显的变量划分半高斯部分。将半高斯部分通过高斯分布置信概率加权与高斯核心部分和非高斯核心部分分别建立高斯子空间和分高斯子空间,然后对高斯子空间进行相关性划分后采用PCA方法得到高斯子空间的统计量;对非高斯子空间进行主元投影划分后采用ICA方法得到非高斯子空间的统计量,接着通过贝叶斯推断得到的联合统计量进行故障检测。最后通过Tenessee Eastman（TE）仿真实验,有效验证了所提出方法的有效性。     

基于潜变量自回归算法的化工过程动态监测方法

从建立潜变量自回归（AR）模型的角度出发，提出了一种基于潜变量自回归（LVAR）算法的化工过程动态建模与监测方法，旨在提取动态潜变量的同时给出各潜变量的AR模型。LVAR算法在最小化潜变量的AR模型残差的约束下，通过同时搜寻投影变换向量与AR系数向量，实现了对动态潜变量的特征提取及其AR模型的建立。此外，LVAR算法通过先提取动态潜变量后提取静态成分信息的方式，有效地区分了采样数据中的自相关性与交叉相关性。在对比实验中，通过比较分析LVAR方法与其他三种典型的动态过程监测方法在经典化工过程对象上的故障监测结果，验证了LVAR方法在动态过程监测上的优越性与可靠性。     

基于Gath-Geva算法和核极限学习机的多阶段间歇过程软测量

间歇过程具有较强的非线性,多阶段、慢时变及批次间存在变化,采用单一预测模型不能反映间歇过程的多阶段特性及阶段间过渡特性。提出一种基于Gath-Geva聚类和核极限学习机（kernel extreme learning machine,KELM）的多模型软测量方法。首先采用主成分分析（principal component analysis,PCA）对输入做特征提取,然后利用Gath-Geva算法对间歇过程进行多阶段工况划分,根据生产工况特性划分为不同的操作阶段后,分别建立局部KELM模型。对任一待预测样本,分别计算其对应各局部模型的预测值,最后采用贝叶斯集成,将其隶属于各局部模型的模糊隶属度作为权重和预测值融合得到最终预测值。以青霉素发酵数据进行实验测试,结果表明所提多模型算法相较于单一模型,具有更高的预测精度。     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

基于MPCA-MDPLS的间歇过程的故障诊断

针对间歇过程的故障诊断问题,提出了一种新的混合模型方法——MPCA-MDPLS.这种方法包括两个模型：多向主元分析(MPCA)模型和多向判别部分最小二乘(MDPLS)模型.这两个模型的建模数据不仅包括正常工况的数据,而且还包含了各种已知故障数据.因此,MPCA模型具有检测未知故障的能力.给出了MDPLS模型故障诊断限,对经MPCA模型检测不是未知故障的故障做进一步诊断.如果故障是未知的,可以采取其他的方法来分析新的故障,并按不同类别存入到数据库中.当多次出现这种故障之后（一般≥5次）,把新的故障数据加入到建模数据中,并重新建立MPCA-MDPLS模型.通过对实际工业链霉素发酵过程数据的分析,表明了提出的算法是可行的、有效的,并具有识别未知新故障的能力.     

基于改进Kalman滤波算法的多模型融合建模方法

针对聚合物生产过程重要质量控制指标或状态变量的软测量问题,提出了一种基于改进Kalman滤波算法的多模型融合建模方法。将混合核函数主元分析(K₂PCA)与人工神经网络(ANN)相结合,建立一种基于K₂PCA-ANN的数据驱动模型;利用改进Kalman滤波算法实现K₂PCA-ANN模型与机理模型融合,构建一种并联结构的混合模型;协调二次滤波(线性滑动平滑)和方差更新对混合模型进行优化处理,使混合模型的估计性能尽可能地达到最优,使混合模型的预测稳定性得到有效改善。将该多模型融合建模方法应用于氯乙烯聚合过程聚合速率软测量中,应用研究结果表明:与单一的机理模型或K₂PCA-ANN数据驱动模型的预测性能相比,该建模方法建立的聚合速率模型具有更佳的预测性能。该建模方法的运用为进一步开展聚合物生产过程优化与控制等研究提供基础条件。     

Improved kernel PCA-based monitoring approach for nonlinear processes

Conventional kernel principal component analysis (KPCA) may not function well for nonlinear processes, since the Gaussian assumption of the method may be violated through nonlinear and kernel transformation of the original process data. To overcome this deficiency, a statistical local approach is incorporated into KPCA. Through this method, a new score variable which was called improved residual in the statistical local approach is constructed. The new variable approximately follows Gaussian distribution, in spite of which distribution the original data follows. Two new statistics are constructed for process monitoring, with their corresponding confidence limits determined by a χ² distribution. Besides of the improvement made on KPCA, the new joint local approach-KPCA method also shows superiority on detection sensitivity, especially for small faults slow changes of the process. The new method is exemplified using a numerical study and also tested in the complicated Tennessee Eastman (TE) benchmark process.     

基于主元分析-概率神经网络的制冷系统故障诊断

制冷系统由于内部物质形态的多样性以及系统参数间的高度耦合而较为复杂,也增加了出现故障后的检测及诊断难度。针对制冷系统常见的7种故障,包括局部故障与系统故障,运用主元分析法提取故障样本主要特征,对样本进行降维处理后,基于概率神经网络进行故障诊断。主元分析法可将原始的62个参数分解为相互独立的主元,根据累计贡献率选取一定量的主元,并将其样本输入概率神经网络进行故障诊断,结果表明结合主元分析后的概率神经网络在一定范围内对spread值不敏感,不仅诊断正确率有所提高,而且缩短了诊断耗时。可见,主元分析法的使用可有效优化概率神经网络的诊断性能。     

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes☆

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in-cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal com-ponent analysis. In this approach, mutual information estimation and Bayesian information criterion (BIC) are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation (BP) network is applied whose input is multivar-iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis (LKPCA) model for incipient fault prognosis. The new method has been exemplified in a sim-ple nonlinear process and the complicated Tennessee Eastman (TE) benchmark process. The results indicate that the new method has superiority in the fault prognosis sensitivity over other traditional fault prognosis methods. ? 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

基于特征线法的一阶双曲型分布参数模型辨识及其在烟气脱硫过程中的应用

引言在现代控制工程领域中,许多工业对象实际上是非线性分布参数系统。由于这类对象的复杂性,原始模型常常进行集中线性化处理后分析和设计控制系统,然而系统本质的分布特性以及非线性引起的模型失配将造成控制的失败。这种情况促使在先进控制中越来越多地直接采用非线性分布参数机理     

Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM

In this paper, some drawbacks of original kernel independent component analysis (KICA) and support vector machine (SVM) algorithms are analyzed for the purpose of multivariate statistical process monitoring (MSPM). When the measured variables follow non-Gaussian distribution, KICA provides more meaningful knowledge by extracting higher-order statistics compared with PCA and kernel principal component analysis (KPCA). However, in real industrial processes, process variables are complex and are not absolutely Gaussian or non-Gaussian distributed. Any single technique is not sufficient to extract the hidden information. Hence, both KICA (non-Gaussion part) and KPCA (Gaussion part) are used for fault detection in this paper, which combine the advantages of KPCA and KICA to develop a nonlinear dynamic approach to detect fault online compared to other nonlinear approaches. Because SVM is available for classifying faults, it is used to diagnose fault in this paper.For above mentioned kernel methods, the calculation of eigenvectors and support vectors will be time consuming when the sample number becomes large. Hence, some dissimilar data are analyzed in the input and feature space.The proposed approach is applied to the fault detection and diagnosis in the Tennessee Eastman process. Application of the proposed approach indicates that proposed method effectively captures the nonlinear dynamics in the process variables.