鲁棒PPLS模型及其在过程监控中的应用

概率偏最小二乘(PPLS)模型建立的条件是主元和误差都服从高斯分布,但是高斯分布的期望和方差容易受到离群点的影响,导致模型的鲁棒性较差。针对PPLS模型的不足,提出一种鲁棒概率偏最小二乘(RPPLS)方法,用拖尾更宽的T分布代替高斯分布,通过调整自由度参数,使模型对含离群点数据的拟合效果更好。更进一步,将RPPLS引入过程监控中,提出GT2和GSPE两个监控指标,分别监控过程的受控状态以及模型关系的变化。PPLS和RPPLS在TE过程监控的应用结果表明RPPLS不仅能更准确检测故障的产生,而且能更有效降低故障的漏报率。     

复合PLS模型在近红外光谱分析煤炭中的应用

为了更好地确定偏最小二乘法模型的主成分数,提出一种传统偏最小二乘法和多主成分数偏最小二乘法相结合构建复合偏最小二乘模型的方法。给出了预测时两种样品相似度的计算方式:直接距离法和性质得分距离法。分别采用复合偏最小二乘法和传统偏最小二乘法对煤炭的全硫、灰分、热值和碳含量进行建模预测,比较传统偏最小二乘法和多主成分数偏最小二乘法建模过程中的相关系数和交互验证均方根误差,采用复合偏最小二乘模型对验证集样品预测时,计算了不同相似度计算方式下不同样品间距离算法的预测均方根误差,并同传统偏最小二乘法预测均方根的误差进行比较,结果表明:复合偏最小二乘法建模比传统偏最小二乘法建模有更强的适应性,能够提高预测的准确性。     

Compound PLS Model in Coal Analysis with Near-infrared Spectra

为了更好地确定偏最小二乘法模型的主成分数,提出一种传统偏最小二乘法和多主成分数偏最小二乘法相结合构建复合偏最小二乘模型的方法.给出了预测时两种样品相似度的计算方式:直接距离法和性质得分距离法.分别采用复合偏最小二乘法和传统偏最小二乘法对煤炭的全硫、灰分、热值和碳含量进行建模预测,比较传统偏最小二乘法和多主成分数偏最小二乘法建模过程中的相关系数和交互验证均方根误差,采用复合偏最小二乘模型对验证集样品预测时,计算了不同相似度计算方式下不同样品间距离算法的预测均方根误差,并同传统偏最小二乘法预测均方根的误差进行比较,结果表明:复合偏最小二乘法建模比传统偏最小二乘法建模有更强的适应性,能够提高预测的准确性.     

基于核PLS方法的非线性过程在线监控

针对过程监控数据的非线性特点,提出了一种基于核偏最小二乘（KPLS）的监控方法。KPLS方法是将原始输入数据通过核函数映射到高维特征空间,然后在高维特征空间再进行偏最小二乘（PLS）运算。与线性PLS相比,KPLS方法能充分利用样本空间信息,建立起输入输出变量之间的非线性关系。与其他非线性PLS方法不同,KPLS方法只需要进行线性运算,从而避免非线性优化问题。在对过程进行监控时,首先采用KPLS方法建立模型,得到得分向量,然后计算出T²和SPE统计量及其相应的控制限。Tennessee Eastman(TE)模型上的仿真研究结果表明,所提方法比线性PLS相似文献   

一种基于可预测偏最小二乘法的故障检测方法

将可预测元分析(Fore CA)与偏最小二乘法(PLS)结合用于故障检测,在选取合适的可预测元的基础上,运用偏最小二乘回归,进一步提高模型对系统的预测能力,克服了偏最小二乘回归方法无法反映系统动态时序特性的缺陷,并构造CUSUM统计量和SPE统计量以检测故障是否发生。最后通过TE模型上的仿真实验结果表明:Fore PLS方法能有效检测慢漂移等故障。     

基于多元统计方法的过程单元缓变故障识别

在实际化工生产过程中存在一些缓变故障,在发生的初期过程偏离正常工况的程度较少,且受生产数据噪声的影响,不易被传统过程监测方法及时发现。本文针对缓变故障的特点,提出了一种基于偏最小二乘法-主元分析法（PLS-PCA）的过程监测方法。首先利用偏最小二乘法（PLS）回归提取出各变量之间的关系,通过获取变量实测值与回归预测值之间的误差,以放大装置运行状态与预设状态之间的偏差,在此基础上建立基于主元分析法（PCA）的过程监测模型,实现了对缓变故障的早期识别。该过程监测模型被应用在某制氢装置预转化反应器上,结果表明该方法对缓变故障具有较好的早期识别效果,能够比工程师提前13h,比基于传统PCA的过程监测模型提前8h。     

基于支持向量数据描述的非高斯过程故障重构与诊断

提出一种基于支持向量描述（SVDD）的统计过程监控与故障重构及诊断算法,避免了PCA、PLS等传统统计过程监控方法假设过程数据服从高斯分布的不足。鲁棒故障重构算法通过迭代保证重构后的数据对应的SVDD监控统计量最小化。诊断算法根据故障集中的不同故障重构后监控统计量是否恢复正常,确定实际发生的过程故障。CSTR过程的仿真研究表明了所提出方法的有效性。     

基于LSNPE算法的化工过程故障检测

复杂化工过程通常具有多个操作模态,而且采集的数据不服从单一的高斯或非高斯分布。针对化工过程的多模态和复杂数据分布问题,将局部标准化（local standardized,LS）策略应用于邻域保持嵌入（neighborhood preserving embedding,NPE）算法,提出了一种新的基于局部标准化邻域保持嵌入（local standardized neighborhood preserving embedding,LSNPE）算法的故障检测方法。首先,使用LSNPE算法提取高维数据的低维子流形,进行维数约减,同时保持邻域结构不变。其次,通过特征空间中样本的局部离群因子（local outlier factor,LOF）构造监控统计量并确定其控制限。相较于监控多模态化工过程的多模型策略,提出的LSNPE方法不需要过程先验知识的支持,只需建立一个全局的监控模型。最后,通过数值仿真及Tennessee Eastman（TE）过程仿真研究验证了本文提出方法的有效性。     

应用加权LSSVM算法的PVC气提塔温度建模

研究基于最小二乘支持向量机(LSSVM)建立了PVC汽提塔的预测模型。为了提高LSSVM的鲁棒性,过滤离群点,将加权最小二乘支持向量机(WLSSVM)应用到PVC汽提过程的温度建模中,对汽提塔温度进行建模和仿真实验。对比仿真实验结果表明:WLSSVM建模具有更高的建模精度和更优秀的性能。     

基于三维荧光的污水处理过程中COD的检测

采用三维荧光光谱分析方法研究了某污水处理厂处理过程中的初沉池、二沉池和终沉池出水的化学耗氧量（COD）的检测方法,并对采用主成分回归（PCA）、偏最小二乘（PLS）、平行因子法（PARAFAC）及多维偏最小二乘等方法所建立校正模型的性能进行了比较,结果表明：对于工业污水COD值的检测,常规PLS要好于平行因子法及多维偏最小二乘法等三维建模方法.     

Fault detection and diagnosis in a non-Gaussian process with modified kernel independent component regression

Quality-related fault detection and diagnosis are crucial in the data-driven process monitoring field. Most existing methods are based on principal component analysis (PCA) or partial least squares (PLS), which will miss high-order statistical information when the industrial process does not satisfy a Gaussian distribution. Meanwhile, the traditional contribution plot is difficult to directly apply to nonlinear processes in some cases due to its limitation of convergence. As such, a modified kernel independent component regression (MKICR) model, which considers high-order statistical information, is proposed for quality-related fault detection and faulty variable identification. First, the relationship between the independent components and quality variables is established by kernel independent component regression, and the correlation matrix is obtained. Then, the kernel independent components can be suitably divided into quality-related and quality-unrelated parts. Finally, an analysis of the contribution of each variable to the statistics based on Lagrange's mean value theorem is presented. In addition, a numerical case and the Tennessee Eastman process (TEP) demonstrate the efficacy and superiority of the proposed method.     

Concurrent PLS-based process monitoring with incomplete input and quality measurements

The process monitoring based on concurrent partial least square (CPLS) performs well on the monitoring of input and quality variables through five monitoring statistics. However, in practice, the case of missing variable is very common and the incomplete measurements will make it difficult to implement this monitoring method. Considering the presence of missing measurements occurring in both input and quality variables, this paper analyzes the influence of missing measurements on monitoring performance based on the assumption that input and quality variables satisfy multivariate Gaussian distribution under normal operation. The proposed method estimates the conditional distributions of missing variables, scores and residuals given the observable variables, and denotes monitoring statistics with these conditional distributions. Then, the probabilistic uncertain ranges of monitoring statistics are derived by calculating the general quadratic formulations of Gaussian-distributed missing variables. To determine the process operation in the presence of missing variables, the proposed method employs these uncertain ranges as monitoring statistics. Simulation examples illustrate feasibility of this proposed method and demonstrate its effectiveness.     

Improved Kernel PLS-based Fault Detection Approach for Nonlinear Chemical Processes

In this paper, an improved nonlinear process fault detection method is proposed based on modified ker-nel partial least squares （KPLS）. By integrating the statistical local approach （SLA） into the KPLS framework, two new statistics are established to monitor changes in the underlying model. The new modeling strategy can avoid the Gaussian distribution assumption of KPLS. Besides, advantage of the proposed method is that the kernel latent variables can be obtained directly through the eigen value decomposition instead of the iterative calculation, which can improve the computing speed. The new method is applied to fault detection in the simulation benchmark of the Tennessee Eastman process. The simulation results show superiority on detection sensitivity and accuracy in com-parison to KPLS monitoring.     

Robust modeling of mixture probabilistic principal component analysis and process monitoring application

In this article, a robust modeling strategy for mixture probabilistic principal component analysis (PPCA) is proposed. Different from the traditional Gaussian distribution driven model such as PPCA, the multivariate student t‐distribution is adopted for probabilistic modeling to reduce the negative effect of outliers, which is very common in the process industry. Furthermore, for handling the missing data problem, a partially updating algorithm is developed for parameter learning in the robust mixture PPCA model. Therefore, the new robust model can simultaneously deal with outliers and missing data. For process monitoring, a Bayesian soft decision fusion strategy is developed which is combined with the robust local monitoring models under different operating conditions. Two case studies demonstrate that the new robust model shows enhanced modeling and monitoring performance in both outlier and missing data cases, compared to the mixture probabilistic principal analysis model. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2143–2157, 2014     

Three-way data analysis with time lagged window for on-line batch process monitoring

In this paper, on-line batch process monitoring is developed on the basis of the three-way data structure and the time-lagged window of process dynamic behavior. Two methods, DPARAFAC (dynamic parallel factor analysis) and DTri-PLS (dynamic trilinear partial least squares), are used here depending on the process variables only or on the process variables and quality indices, respectively. Although multivariate analysis using such PARAFAC (parallel factor analysis) and Tri-PLS (trilinear partial least squares) models has been reported elsewhere, they are not suited for practicing on-line batch monitoring owing to the constraints of their data structures. A simple modification of the data structure provides a framework wherein the moving window based model can be incorporated in the existing three-way data structure to enhance the detectability of the on-line batch monitoring. By a sequence of time window of each batch, the proposed methodology is geared toward giving meaningful results that can be easily connected to the current measurements without the extra computation for the estimation of unmeasured process variables. The proposed method is supported by using two sets of benchmark fault detection problems. Comparisons with the existing two-way and three-way multiway statistical process control methods are also included.     

Robust probabilistic principal component analysis for process modeling subject to scaled mixture Gaussian noise

Conventionally, for probabilistic principal component analysis (PPCA) based regression models, noise with a Gaussian distribution is assumed for both input and output observations. This assumption makes the model to be vulnerable to large random errors, known as outliers. In this article, unlike the conventional noise assumption, a mixture noise model with a contaminated Gaussian distribution is adopted for probabilistic modeling to diminish the adverse effect of outliers, which usually occur due to irregular process disturbances, instrumentation failures or transmission problems. This is done by downweighing the effect of the noise component which accounts for contamination on output prediction. Outliers are common in process industries; therefore, handling this issue is of practical importance. In comparison with conventional PPCA based regression model, prediction performance of the developed robust probabilistic regression model is improved in presence of data contamination. To evaluate the model performance two case studies were carried out. A simulated set of data with specific characteristics to highlight the presence of outliers was used to demonstrate the robustness of the developed model. The advantages of this robust model are further illustrated via a set of real industrial process data.     

Mixture robust L1 probabilistic principal component regression and soft sensor application

In this paper, the multivariate Laplace distribution (also called L1 distribution) is adopted to construct a robust probabilistic principal component regression model (MRPPCR-L1) under multiple operating modes. In the practical industrial chemistry process, outliers exist due to incorrect recording, disturbances, and process noises and might result in modelling distortion. To address this problem, Laplace distribution, instead of the Gaussian distribution in traditional methods, is introduced to reduce the negative influence of outliers. Moreover, probabilistic principal component regression is employed for dealing with the mixture modelling problem owing to its probabilistic property to determine the operating modes. The formulation of this approach is derived with the expectation maximum algorithm and the soft sensing model is also developed for prediction. Compared to the conventional method, a numerical example and the Tennessee Eastman process are used to demonstrate the robust modelling performance of the proposed method.     

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。     

基于约翰逊转换的鲁棒化工过程监控方法

化工厂中一个小故障可能导致大事故,从而造成生命财产损失和环境破坏。为了防止小故障演变成大事故,化学工业需要有效的过程监控来及时检测故障和诊断故障原因。传统化工过程监控方法主元分析法(Principal Component Analysis, PCA)假设数据服从高斯分布,实践中有时并不满足该条件。此外,其使用方差、协方差捕捉数据非线性变化时,鲁棒性较差。本工作提出一种改进的主元分析法—基于约翰逊转换的鲁棒过程监控方法。首先引入约翰逊正态转换(Johnson Transformation)使过程数据服从高斯分布;其次使用鲁棒性强的斯皮尔曼相关系数(Spearman Correlation Coefficient)矩阵代替传统主元分析法的协方差矩阵提取特征向量,构造特征空间;最后将过程数据投影到特征空间,使用T2和SPE统计量实施过程监控。将此方法应用于TE过程故障案例,并与PCA和核主元分析法(Kernel Principal Component Analysis, KPCA)对比,验证了此方法的有效性。     

双线性约束过程的鲁棒自适应数据校正方法

采用污染正态分布模型进行数据校正,相对于传统的最小二乘方法具有较好的鲁棒性,然而参数估计结果的精确度依赖于误差发生概率和方差比值两个先验模型参数的选取,这在实际生产中难以获得,采用固定的方差比也不符合实际,因而其应用受到了限制。本文针对污染正态分布模型的不足,提出了一种鲁棒自适应误差分布模型,该模型具有与标准正态分布模型相似的分布密度函数,不同之处在于采用鲁棒自适应可变权重因子调节误差方差,通过放大显著误差方差,减小其对参数估计的影响。将该模型用于双线性约束数据校正问题,并采用Lagrange乘子法得到鲁棒自适应最小二乘分析解,同时还对鲁棒自适应数据校正中的测量数据相关性问题进行了研究。仿真结果证实了该方法的有效性。