Dynamic Partial Least Squares Research Articles

An integrated tube robust iterative learning model predictive control strategy based on dynamic partial least squares algorithm for batch processes

AbstractIn this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Orthogonal Multi-Block Dynamic PLS for Quality-Related Process Monitoring

Orthogonal Multi-Block Dynamic PLS for Quality-Related Process Monitoring

Soft analyzer for sulfur content in tail oil of hydrocracking process based on adaptively regularized dynamic polynomial PLS

AbstractHydrocracking process is an essential and widely used means to remove impurities such as sulfur, nitrogen, and oxygen from heavy oil in refineries. The sulfur content in the tail oil of the hydrogenation process is a key quality index that must be strictly monitored and controlled. However, the traditional measurement ways of the sulfur content suffer from either large delays or high investment and maintenance costs. To this end, a predictive model named “adaptively regularized dynamic polynomial partial least squares (ARDPPLS)” is proposed to develop soft analyzer for sulfur content estimation. The ARDPPLS takes complicated characteristics of the hydrogenation process into consideration, including process dynamics, nonlinearities, and transportation delays of materials and energies. Specifically, the dynamics and nonlinearities are modeled by the finite impulse response paradigm and polynomial fitting, respectively, and the delays of explanatory variables are automatically determined using differential evolution. In particular, a Bayesian inference‐based adaptive regularization scheme for the polynomial partial least squares is designed to tackle overfitting that results from high‐order variable augmentation and high‐order polynomials. The performance of the ARDPPLS is evaluated by a real‐world industrial wax oil hydrocracking process, showing the effectiveness of the ARDPPLS.

Analyzing the occurrence of foaming in batch fermentation processes using multiway partial least square approaches

AbstractThis article presents an application of multiway partial least squares (MPLS) methods to develop interpretative correlation models to monitor the foaming occurrence and improve batch fermentation. We choose the exhaust differential pressure as a quality variable to quantify the foaming occurrence and consider three‐dimensional datasets of different batches, process variables, and measurements. We integrate batch‐wise unfolding (BWU) and observation‐wise unfolding (OWU) of plant datasets with standard, dynamic, and kernel PLS methods. We find that dynamic PLS (DPLS) with OWU and time‐lagged quality variables to be the most efficient, accurate, and easy to implement. The BWU approach is useful for analyzing the differences between batches and identifying abnormalities and outliers, while the OWU quantifies the variation within a given batch. With OWU, the DPLS method with one unit of time lag in the quality variable is the most effective, accurate, and easy to implement. With both BWU and OWU, we identify the quantitative effects of process variables on the quality variable and providence guidance to improve fermentation performance.

Iterative learning model predictive control for multivariable nonlinear batch processes based on dynamic fuzzy PLS model

This paper proposes a latent variable nonlinear iterative learning model predictive control method (LV-NILMPC) based on the dynamic fuzzy partial least squares (DFPLS) model to achieve trajectory tracking and process disturbance suppression in multivariable nonlinear batch processes. The dynamic and nonlinear characteristics of the physical system are constructed by integrating the T-S fuzzy model into the regression framework of the dynamic partial least squares (PLS) inner model. The decoupling and dimensionality reduction characteristics of the DFPLS model automatically decompose a multivariable nonlinear system into multiple univariate subsystems operating independently in the latent variable space. Based on the DFPLS model, we design LV-NILMPC controllers corresponding to each latent variable subspace to track the projection of the reference trajectories. Compared with the previous control method, the method proposed in this paper has a faster convergence rate and smaller tracking error. The method is suitable for nonlinear, multivariable and strong coupling batch processes. Finally, the application of two cases shows that the method is effective.

Latent variable point-to-point iterative learning model predictive control via reference trajectory updating

A latent variable point-to-point iterative learning model predictive control algorithm (LV-PTP-ILMPC) that is combined with the reference trajectory updating strategy is proposed in this paper. It is different from the traditional point-to-point iterative learning model predictive control (PTP-ILMPC), which is developed in the original variable space to track a fixed reference trajectory. The proposed algorithm uses a model constructed by dynamic partial least squares (DyPLS) to extract the principal components of multiple input variables in each batch and designs the PTP-ILMPC controller in the latent variable space. Moreover, creating a reference trajectory updated along the batch direction through the desired points. The updating reference trajectory, modified according to the tracking error information, fully utilizes the degrees of freedom of nonspecific tracking points in the latent variable space. The proposed algorithm uses DyPLS to decouple the multiple-input, multiple-output system (MIMO) into a single-input, single-output system, simplifying the multivariable control problem. In addition, the updated reference relaxes the constraints on the system output so that the algorithm has a faster convergence speed and a more comprehensive range of applications. Two studies are proposed to show the effectiveness of the algorithm.

Application of data-driven modeling approaches to industrial hydroprocessing units

Hydroprocessing units in petroleum refineries comprise of several complex interconnected network of unit operations, and perform the function of removing impurities from the crude, and cracking it to lighter products for subsequent operations. Modeling these units play a pivotal role in predicting future values of important variables, improving the control and optimization of the plant for efficient operation among several other applications. This paper presents the development and implementation of data-based models in estimating product qualities and other key monitoring variables in the hydroprocessing unit of an industrial refinery. Real industrial data from two different units was used and appropriate data-driven modeling strategies were formulated in order to address this problem. In one instance, the usefulness of Dynamic-Partial Least Squares (DPLS) over Partial Least Squares (PLS) in the estimation of important variables of the unit is demonstrated. In the other instance, subspace identification methodology is found to yield a superior model. The methods used in this study can also elegantly handle the missing data problem associated with real data sets, and thus demonstrate the ability, and the importance of using the right data driven technique for specific problems in the context of hydroprocessing refinery.

Adaptive dynamic prediction of effluent quality in wastewater treatment processes using partial least squares embedded with relevance vector machine

Recycling of water resources through wastewater treatment process (WWTP) is widely considered for a viable option for different water demands and sustainable production due to water shortage and pollution. Thus, accurate and real-time prediction of effluent quality is of vital importance to maintain the stable process control of WWTP system. Taking into account the complex biochemical characteristics of WWTP, an adaptive dynamic nonlinear partial least squares (PLS) model has been proposed to improve the prediction performance and stability of effluent quality indexes. First, an adaptive matrix expansion scheme is introduced to exploit the specific dynamic features of different data sets. Then the linear PLS model is conducted and the inner function between each pair of latent variables is rebuilt by relevance vector machine (RVM) with sparse and probabilistic structure, which is robust for the nonlinearity and random noises among process variables. The performance of the proposed adaptive dynamic RVM-based PLS (D-RVM-PLS) model is evaluated through two case studies based on benchmark simulation model No.1 and a real industrial WWTP, respectively. Experimental results show the superiority of the proposed model in prediction accuracy, stability, and execution efficiency. For the modeling accuracy of effluent chemical oxygen demand in real industrial case, adaptive D-RVM-PLS provides the lowest root-mean-square error, which is decreased by approximately 5.01%–49.19% in comparison with linear PLS model, Gaussian process regression-based PLS model, and their dynamic models without adaptive selection procedure.

Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .

Rapid spectral analysis of agro-products using an optimal strategy: dynamic backward interval PLS-competitive adaptive reweighted sampling.

A novel strategy of variable selection approach named dynamic backward interval partial least squares-competitive adaptive reweighted sampling (DBiPLS-CARS) was proposed in this study. Near-infrared data sets of three different agro-products, namely corn, crop processing lamina, and plant leaf samples, were collected to investigate the performance of the proposed method. Weak relevant variables were first removed by DBiPLS and a refined selection of the remaining variables was then conducted by CARS. The Monte Carlo uninformative variable elimination (MCUVE) was used as a classical beforehand uninformative variable elimination method for comparison. Results showed that DBiPLS can select informative variables more continuously than MCUVE. Some synergistic variables which may be omitted by MCUVE can be retained by DBiPLS. By contrast, MCUVE can hardly avoid the disturbance of certain weak relevant variables as a result of its calculation based on the full spectrum regression. Therefore, DBiPLS exhibited the advantage of removing the weak relevant variables before CARS, and simultaneously improved the prediction performance of CARS.

Adaptive PLS inferential soft sensor for continuous online estimation of NOx emission in industrial water-tube boiler

In common industrial application, the use of a linear and static PLS soft sensor for online prediction and monitoring of industrial boiler is often preferred due to its simple and intuitive framework. However, process dynamics and time-variant factors can negatively affect the accuracy and reliability of PLS soft sensor over its long-term application in process industries. In this paper, development of adaptive soft sensor based on dynamic PLS method has been applied to an industrial water-tube boiler for continuous online prediction of Nitric Oxides emission. In the case study, it is found that the adaptive PLS soft sensor which includes lagged measurements of NOx emission in the model input can significantly improve the prediction accuracy and reliability by 72.7% relative to the performance of linear and static PLS soft sensor when tested on online dataset containing gradual and abrupt changes in the process operating conditions.

Dynamic Selection and Estimation of the Digital Predistorter Parameters for Power Amplifier Linearization

This paper presents a new technique that dynamically estimates and updates the coefficients of a digital predistorter (DPD) for power amplifier (PA) linearization. The proposed technique is dynamic in the sense of estimating, at every iteration of the coefficient’s update, only the minimum necessary parameters according to a criterion based on the residual estimation error. At the first step, the original basis functions defining the DPD in the forward path are orthonormalized for DPD adaptation in the feedback path by means of a precalculated principal component analysis (PCA) transformation. The robustness and reliability of the precalculated PCA transformation (i.e., PCA transformation matrix obtained off line and only once) is tested and verified. Then, at the second step, a properly modified partial least squares (PLS) method, named dynamic partial least squares (DPLS), is applied to obtain the minimum and most relevant transformed components required for updating the coefficients of the DPD linearizer. The combination of the PCA transformation with the DPLS extraction of components is equivalent to a canonical correlation analysis (CCA) updating solution, which is optimum in the sense of generating components with maximum correlation (instead of maximum covariance as in the case of the DPLS extraction alone). The proposed dynamic extraction technique is evaluated and compared in terms of computational cost and performance with the commonly used QR decomposition approach for solving the least squares (LS) problem. Experimental results show that the proposed method (i.e., combining PCA with DPLS) drastically reduces the amount of DPD coefficients to be estimated while maintaining the same linearization performance.

Computing meaningful models of continuous data

Parameters controlling continuous chemical processes as well as all instruments found in such processes generate a huge amount of data. Calculating models to predict critical quality attributes (in y) from process data (in X) can be fastidious. Partial-Least-Squares (PLS) regression is now widely present in the industry for process analysis and modelling purposes. However, this methodology requires static data while the majority of chemical processes operate continuously. Some dynamic PLS variants have been developed, but they cannot associate specific critical process parameters with meaningful process dynamics. This work presents a novel Dynamic-PLS variant developed to resolve these issues. Using one real dataset and artificial cases, the performances of this novel methodology is compared to standard regression methodologies. It is demonstrated that the proposed methodology calculates the most robust models in validation. With the real dataset, it is also demonstrated that the predictive model calculated from the proposed methodology can easily be interpreted, leading to better process understanding.

Regression on dynamic PLS structures for supervised learning of dynamic data

Partial least squares (PLS) regression is widely used to capture the latent relationship between inputs and outputs in static system modeling. Several dynamic PLS algorithms have been proposed to capture the characteristics of dynamic data. However, none of these algorithms provides an explicit expression for the dynamic inner and outer models. In this paper, a dynamic inner PLS algorithm is proposed for dynamic data modeling. The proposed algorithm provides an explicit dynamic inner model that is ensured in deriving the outer model. Several examples are presented to demonstrate the effectiveness of the proposed algorithm.

Dynamic mutual information similarity based transient process identification and fault detection

Industrial process status can be modified according to continuous operations, which are required by different production specifications. Commonly, in a multimode process, attention was always paid to stable modes, while transitions were neglected. In a transition process, the process may be externally time varying or nonstationary so that the identification and the modelling are intractable to implement using traditional statistical methods. In this article, a transition identification and process monitoring method is proposed to handle the above problems based on a novel dynamic mutual information similarity (DMIS) analysis. Firstly, a multimode process is represented by a series of overlapping moving windows to consider the local information. In order to extract the corresponding dynamic information, each of these windows is modelled using the dynamic partial least squares (DPLS) method. Then, the mutual information algorithm is introduced to calculate the similarity between different latent variables. The hierarchical clustering method is employed to transfer the similarity information into a visualized dendrogram where the whole process, including a transition, is divided into several segments. The statistical characteristics in each segment are relatively stable and can be characterized by conventional multivariate statistical process control methods. Online identification and fault detection are then carried out for the multimode process through a series of DPLS models, established in the offline steps. The feasibility and effectiveness of the proposed method are validated by the Tennessee Eastman (TE) benchmark and a real process. The results of the proposed methods have shown superior performance compared to previous works.

Quality-Related and Process-Related Fault Monitoring With Online Monitoring Dynamic Concurrent PLS

The partial least squares (PLS) method has been widely used in quality-related industrial process monitoring because of its ability to extract quality-related information. Generally, online quality monitoring data cannot be obtained in real time, and in this case, updating the online monitoring model is a serious challenge. In this paper, an online monitoring dynamic PLS (OMD-PLS) model that uses the relation between time-delay process data and time-delay quality data is proposed. To accurately monitor the quality-related and process-related fault data, we also propose an online monitoring dynamic concurrent PLS (OMDC-PLS) model based on OMD-PLS, which has the ability to detect slight deviations. Furthermore, an alarm-parameter alarm method based on the OMDC-PLS model is proposed and effectively reduces the false alarm rate. Finally, numerical simulations and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed methods.

A Modified Dynamic PLS for Quality Related Monitoring of Fractionation Processes

The fractionation process is a typical dynamic process, and practitioners highly pay attention to the quality-related abnormal in the real refining processes. In this paper, a modified dynamic PLS (MDPLS) modeling method and the corresponding process monitoring strategy are proposed. The main contributions of the proposed method are in the following. First, a clear dynamic relation is captured between process data and quality indices. Moreover, the process and quality space are comprehensively divided into dynamic quality-related subspace, static quality-unrelated subspace as well as the residual space for improving the performance of monitoring. Finally, the effectiveness of the proposed algorithm is demonstrated with the data from a real fractionation process.

DPLS-MSOM Modeling for Visual Industrial Fault Diagnosis and Monitoring Based on Variation Data from Normal to Anomalous

Process variables obtain significant dynamic variation characteristics from the moment faults are introduced through a continuous period of time. Therefore, these data possess not only strong corresponding fault information but also robust dynamic characteristics that can be effectively used for fault diagnosis. Accordingly, the dynamic partial least squares (DPLS) and self-organizing map (SOM) combination methodology is utilized for visual fault diagnosis and monitoring. Different types of fault data (from normal to anomalous) are collected and trained by DPLS in the form of a dynamic data matrix to reveal the most discriminated orientations for the different statuses. A multilayer SOM is then trained to model the relationship with different status data under such orientations to the regular positions on a two-dimensional map. The trained map can be used for deciding the real operating state of the online observations. Excellent experimental results on the Tennessee Eastman chemical process have demonstr...

A novel dynamic non-Gaussian approach for quality-related fault diagnosis with application to the hot strip mill process

This paper addresses the dynamic non-Gaussian, quality-related fault diagnosis problem for process industries, which is driven by the fact that the quality indices of the industrial products, such as the thickness and flatness in the hot strip mill process (HSMP), are increasingly emphasized. Traditionally, partial least squares (PLS)-based methods are extensively used for quality-related fault diagnosis, however, they are preferred for the static processes. In this paper, a new dynamic PLS model is developed to deal with the quality-related fault diagnosis issue for dynamic processes. In addition, to handle the non-Gaussian property of the dynamic variables, an independent component analysis (ICA) model is successfully combined with the dynamic PLS model. Finally, the proposed method is firstly examined using the Tennessee Eastman process, where it is shown that the new methods perform better than the existing methods. Then they are applied to a real HSMP, where the effectiveness is further convinced from real industrial data.

Quality-related process monitoring for dynamic non-Gaussian batch process with multi-phase using a new data-driven method

In this paper, a quality-related monitoring scheme of batch process using multi-phase dynamic non-Gaussian model is presented. Product quality of a batch process is difficult to be effectively guaranteed because of its frequent start-stop operation, variable operating conditions, strong dynamic and non-Gaussian character of process data. A direct dynamic PLS (DDPLS), in which weighted time-lagged matrix is used to extract dynamic components, is introduced to the dynamic problem. Meanwhile, independent component analysis (ICA) is proposed to deal with non-Gaussianity of dynamic components in DDPLS. Considering most batch processes are multi-phase in nature, in order to well describe the characteristics of every phase and set up sub-models, GMM algorithm is adopted for phase division and fuzzy membership method for transition identification. TE benchmark is used to verify the validity and superiority of our new method over traditional PLS, DPLS. Then the new method is applied to a real hot strip mill production plant.