Ensemble locally weighted partial least squares as a just‐in‐time modeling method

The predictive ability of soft sensors, which estimate values of an objective variable y online, decreases due to process changes in chemical plants. To reduce the decrease of predictive ability, adaptive soft sensors have been developed. We focused on just‐in‐time soft sensors, especially locally weighted partial least squares (LWPLS) regression. Since a set of hyperparameters in an LWPLS model has to be set beforehand and there is only onedataset, a traditional LWPLS model is difficult to accurately predict y‐values in multiple process states. In this study, we propose to combine LWPLS and ensemble learning, and predict y‐values with multiple LWPLS models, whose datasets and sets of hyperparameters are different. The weights of LWPLS models are determined based on Bayes’ theorem, considering their predictive ability. We confirmed that the proposed model has higher predictive accuracy than traditional models through numerical simulation data and two industrial data analyses. © 2015 American Institute of Chemical Engineers AIChE J, 62: 717–725, 2016     

基于时间差分和局部加权偏最小二乘算法的过程自适应软测量建模

工业过程软测量模型常常因为过程的变量漂移、非线性和时变等问题而使得预测性能下降。因此,时间差分已被应用于解决过程变量漂移问题。但是,时间差分框架下的全局模型往往不能很好地描述过程非线性和时变等特性。为此,提出了一种融合时间差分模型和局部加权偏最小二乘算法的自适应软测量建模方法。时间差分模型可以大大减少过程变量漂移的影响,而局部加权偏最小二乘算法作为一种即时学习方法,可以有效解决过程非线性和时变问题。该方法的有效性在数值例子和工业过程实例中得到了有效验证。     

Partial least squares,steepest descent,and conjugate gradient for regularized predictive modeling

In this article, we explore the connection of partial least squares (PLS) to other regularized regression algorithms including the Lasso and ridge regression, and consider a steepest descent alternative to the PLS algorithm. First, the PLS latent variable analysis is emphasized and formulated as a standalone procedure. The PLS connections to the conjugate gradient, Krylov space, and the Cayley–Hamilton theorem for matrix pseudo-inverse are explored based on known results in the literature. Comparison of PLS with the Lasso and ridge regression are given in terms of the different resolutions along the regularization paths, leading to an explanation of why PLS sometimes does not outperform the Lasso and ridge regression. As an attempt to increase resolutions along the regularization paths, a steepest descent PLS is formulated as a regularized regression alternative to PLS and is compared to other regularized algorithms via simulations and an industrial case study.     

基于高阶偏最小二乘的间歇过程建模

间歇过程的产品与现代人的生活息息相关,而建立可靠的模型是保障间歇过程安全运行的基础。针对间歇过程的数据特点,引入一种新的广义线性回归模型--高阶偏最小二乘（higher order partial least squares,HOPLS）。它与传统的间歇过程建模方法具有本质的不同,三维数据（批次×变量×时间）不需要展开成二维矩阵,而是直接被分解成一组正交的Tucker矩阵之和。通过高阶奇异值分解（high order singular value decomposition,HOSVD）,张量变换和高阶正交迭代（higher order orthogonal iteration,HOOI）找到能同时包含自变量和因变量最大信息的潜向量,与此同时得到对应的负载向量。对于新观测值,通过模型就可以实现对因变量的预测。最后利用PenSim2.0,对青霉素发酵过程进行仿真研究,验证了该间歇过程建模方法的有效性。     

Local dynamic partial least squares approaches for the modelling of batch processes

The application of multivariate statistical projection based techniques has been recognized as one approach to contributing to an increased understanding of process behaviour. The key methodologies have included multi‐way principal component analysis (PCA), multi‐way partial least squares (PLS) and batch observation level analysis. Batch processes typically exhibit nonlinear, time variant behaviour and these characteristics challenge the aforementioned techniques. To address these challenges, dynamic PLS has been proposed to capture the process dynamics. Likewise approaches to removing the process nonlinearities have included the removal of the mean trajectory and the application of nonlinear PLS. An alternative approach is described whereby the batch trajectories are sub‐divided into operating regions with a linear/linear dynamic model being fitted to each region. These individual models are spliced together to provide an overall nonlinear global model. Such a structure provides the potential for an alternative approach to batch process performance monitoring. In the paper a number of techniques are considered for developing the local model, including multi‐way PLS and dynamic multi‐way PLS. Utilising the most promising set of results from a simulation study of a batch process, the local model comprising individual linear dynamic PLS models was benchmarked against global nonlinear dynamic PLS using data from an industrial batch fermentation process. In conclusion the results for the local operating region techniques were comparable to the global model in terms of the residual sum of squares but for the global model structure was evident in the residuals. Consequently, the local modelling approach is statistically more robust.     

A novel multiple linear multivariate NIR calibration model‐based strategy for in‐line monitoring of continuous mixing

The capability of near infra‐red (NIR) spectroscopy to predict many different variables, such as concentration and humidity, has been demonstrated in many published works. Several of those articles have been in the subject of real time prediction of continuous operations. However, those demonstrations have been for narrow ranges of the variables, especially for powder concentration, which could present a nonlinear behavior of the NIR absorbance as a function of the entire range of concentration. This work developed a novel strategy to predict the entire range of powder concentration using multiple linear NIR calibration models. The root mean standard error of prediction and relative standard deviation (RSD) parameters were used to establish the number of the multiple linear calibration models; other statistical features were used to establish the correct prediction. It was found that a minimum number of linear partial least squares (PLS) calibration models were necessary to accurately predict the range from 0 to 100% w/w. This technique could also be used with other nonlinear behaviors. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3123–3132, 2014     

Estimation of effluent quality index based on partial least squares stochastic configuration networks

Accurate and reliable measurement of the effluent quality indicators of wastewater treatment plants is the key to successful control and optimization of wastewater treatment plants. Due to the complexity of the operation and the delay of laboratory analysis, it is difficult to achieve real-time control of effluent quality. In order to improve the accuracy and reliability of the estimation, this paper proposes a method of stochastic configuration network based on partial least squares (PLS-SCN). In order to overcome the forecast risk caused by high dimensionality and multicollinearity of the input data, the partial least squares(PLS) is embedded into the stochastic configuration network(SCN) framework replacing the classic ordinary least squares (OLS). The PLS-SCN method extracts the main latent variables that affect the effluent quality from the output of the hidden layer, and enhances the generalization performance through orthogonal projection operations. The simulation results of the effluent quality index of a municipal sewage treatment plant show that the PLS-SCN network has a good input and output relationship, and its performance is better than traditional SCN and PLS, and it can quickly and reliably estimate the sewage quality.     

基于偏最小二乘随机配置网络的污水水质指标估计

准确、可靠地测量污水处理厂的出水水质指标是成功控制和优化污水处理厂的关键。由于现有的离线化验方法存在操作繁复、测量滞后的问题,难以实现水质的实时控制。为了提高估计的准确性和可靠性,提出了一种偏最小二乘的随机配置网络方法 (PLS-SCN)。为了克服输入数据高维度和多重共线性导致的预测风险,将偏最小二乘(PLS)方法嵌入到随机配置网络(SCN)框架中,以代替经典的普通最小二乘(OLS)方法。PLSSCN方法从隐含层输出中提取影响水质指标的主要潜在变量,通过正交投影运算来增强泛化性能。某城市污水处理厂水质指标仿真结果表明,PLS-SCN网络具有良好的输入输出关系,性能优于传统SCN和PLS方法,能够快速、可靠地估计污水水质的质量。     

Adaptive soft sensor modeling framework based on just-in-time learning and kernel partial least squares regression for nonlinear multiphase batch processes

Batch processes are characterized by inherent nonlinearity, multiple phases and time-varying behavior that pose great challenges for accurate state estimation. A multiphase just-in-time (MJIT) learning based kernel partial least squares (KPLS) method is proposed for multiphase batch processes. Gaussian mixture model is estimated to identify different operating phases where various JIT-KPLS frameworks are built. By applying Bayesian inference strategy, the query data is classified into a particular phase with the maximal posterior probability, and thus the corresponding JIT-KPLS framework is chosen for online prediction. To further improve the predictive accuracy of the MJIT-KPLS algorithm, a hybrid similarity measure and an adaptive selection strategy are proposed for selecting local modeling samples. Moreover, maximal similarity replacement rule is proposed to update database. A procedure of input variable selection based on partial mutual information is also presented. The effectiveness of the MJIT-KPLS algorithm is demonstrated through application to industrial fed-batch chlortetracycline fermentation process.     

Modeling and Bayesian parameter estimation for semibatch pH‐shift reactive crystallization of l‐glutamic acid

A mathematical model for semibatch pH‐shift reactive crystallization of l ‐glutamic acid is developed that takes into account the effects of protonation and deprotonation in the species balance of glutamic acid, crystal size distribution, polymorphic crystallization, and nonideal solution properties. The crystallization mechanisms of  α‐ and β‐forms of glutamic acid are addressed by considering primary and secondary nucleation, size‐dependent growth rate, and mixing effects on nucleation. The kinetic parameters are estimated by Bayesian inference from batch experimental data collected from literature. Probability distributions of the estimated parameters in addition to their point estimates are obtained by Markov Chain Monte Carlo simulation. The first‐principles model is observed in good agreement with the experimental data and can be further used for model predictions in robust control strategies. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2828–2838, 2014     

A Time‐Symmetric Self‐Normalization Approach for Inference of Time Series

Self‐normalization has been celebrated as an alternative approach for inference of time series because of its ability to avoid direct estimation of the nuisance asymptotic variance. However, when being applied to quantities other than the mean, the conventional self‐normalizer typically exhibits certain degrees of asymmetry, an undesirable feature especially for time‐reversible processes. This paper considers a new self‐normalizer for time series, which (i) provides a time‐symmetric generalization to the conventional self‐normalizer, (ii) is able to automatically reduce to the conventional self‐normalizer in the mean case where the latter is already time‐symmetric to yield a unified inference procedure, and (iii) possibly leads to narrower confidence intervals when compared with the conventional self‐normalizer. For the proposed time‐symmetric self‐normalizer, we establish the asymptotic theory for its induced inference procedure and examine its finite sample performance through numerical experiments.     

A novel Bayesian inference soft sensor for real‐time statistic learning modeling for industrial polypropylene melt index prediction

A novel real‐time soft sensor based on a sparse Bayesian probabilistic inference framework is proposed for the prediction of melt index in industrial polypropylene process. The Bayesian framework consists of a relevance vector machine for predicting melt index and a particle filtering algorithm for soft sensor optimization. An online correcting strategy is also developed for improving the performance of real‐time melt index prediction. The method takes advantages of the probabilistic inference and using prior statistical knowledge of polymerization process. Developed soft sensors are validated with ten public databases from UCI machine learning repository and real data from industrial polypropylene process. Experimental results indicate the effectiveness of proposed method and show the improvement in both prediction precision and generalization capability compared with the reported models in literatures. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45384.     

A quality relevant non‐Gaussian latent subspace projection method for chemical process monitoring and fault detection

Partial least‐squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement‐variable and quality‐variable spaces that have the maximum covariances. Therefore, PLS method relies on the second‐order statistics of covariance only but does not takes into account the higher‐order statistics that may involve certain key features of non‐Gaussian processes. Moreover, the derivations of control limits for T² and squared prediction error (SPE) indices in PLS‐based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non‐Gaussian and mutually independent by means of maximizing the high‐order statistics such as negentropy instead of the second‐order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non‐Gaussian relationships between process measurement and quality variables, a novel projection‐based monitoring method termed as quality relevant non‐Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement‐variable and quality‐variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I² and SPE statistics are developed for quality relevant fault detection of non‐Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS‐based monitoring method. © 2013 American Institute of Chemical Engineers AIChE J 60: 485–499, 2014     

In‐line near‐infrared spectroscopy: A tool to monitor the preparation of polymer‐clay nanocomposites in extruders

In‐line diffuse reflectance and on‐line transmission near‐infrared spectroscopy (NIR) measurements are performed at the same location of the barrel of a twin screw extruder during the preparation of a polypropylene/clay nanocomposite. Their performance is evaluated by means of a 7‐parameter chemometric model using off‐line rheological and structural (FTIR) data obtained from samples prepared under different screw speed, compatibilizer content and clay loading, as well as a process‐related thermomechanical index. Despite the higher variability of the diffuse reflectance signal, the two models present analogous high quality indices. The aptness of the reflectance measurements is thus validated, which has direct practical advantages, as this probe can be fixed in any typical melt pressure transducer port. The probe is then used for the real‐time in‐line monitoring of the production of the same nanocomposite but now using different throughputs, and the chemometric‐based predictions are compared with experimental off‐line characterization data. The nonlinear effect of throughput is correctly anticipated. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013