Weighted support vector machine for quality estimation in polymerization processes

In this paper, a modified version of the Support Vector Machine (SVM) is proposed as an empirical model for polymerization processes modeling. Usually the exact principle models of polymerization processes are seldom known; therefore, the relations between input and output variables have to be estimated by using an empirical inference model. They can be used in process monitoring, optimization and quality control. The Support Vector Machine is a good tool for modeling polymerization process because it can handle highly nonlinear systems successfully. The proposed method is derived by modifying the risk function of the standard Support Vector Machine by using the concept of Locally Weighted Regression. Based on the smoothness concept, it can handle the correlations among many process variables and nonlinearities more effectively. Case studies show that the proposed method exhibits superior performance as compared with the standard SVR, which is itself superior to the traditional statistical learning machine in the case of high dimensional, sparse and nonlinear data.     

Improved system identification method for Hammerstein-Wiener processes

We propose a new system identification method for Hammerstein-Wiener processes, in which an input static nonlinear block, a linear dynamic block, and an output static nonlinear block are connected in a series. The proposed method can estimate the model parameters in a very simple way without solving the full-dimensional nonlinear optimization problem by activating the process with a specially designed test signal, composed of a relay feedback signal, a binary signal and a multi-step signal. The proposed method analytically identifies the output nonlinear static function and the input nonlinear static function from the relay signal and the multi-step signal, respectively. The linear dynamic subsystem is identified from the relay feedback signal and the binary signal with existing well-established linear system identification methods. We demonstrate with a simple example that the proposed method can be successfully applied to identify the Hammerstein-Wiener-type nonlinear process.     

Adaptive soft sensor for online prediction and process monitoring based on a mixture of Gaussian process models

Linear models can be inappropriate when dealing with nonlinear and multimode processes, leading to a soft sensor with poor performance. Due to time-varying process behaviour it is necessary to derive and implement some kind of adaptation mechanism in order to keep the soft sensor performance at a desired level. Therefore, an adaptation mechanism for a soft sensor based on a mixture of Gaussian process regression models is proposed in this paper. A procedure for input variable selection based on mutual information is also presented. This procedure selects the most important input variables for output variable prediction, thus simplifying model development and adaptation. Apart from online prediction of the difficult-to-measure variable, this soft sensor can be used for adaptive process monitoring. The efficiency of the proposed method is benchmarked with the commonly applied recursive PLS and recursive PCA method on the Tennessee Eastman process and two real industrial examples.     

含时滞测量值下间歇过程的双维状态估计

基于粒子滤波研究了间歇过程的状态估计问题。根据间歇过程双维动态特性,针对关键参数在线检测精度低、离线分析时滞大等问题,分别建立一种双维状态转移模型和时滞测量模型,并利用贝叶斯方法及前/后向平滑,提出一种含时滞测量值下的双维状态估计算法。该算法通过融合先前批次和时滞测量值的信息提高估计精度,并且克服了离线采样周期和时滞时间不确定的问题。在数字仿真和啤酒发酵过程中的仿真应用验证了该算法的有效性。     

Methods for performance monitoring and diagnosis of multivariable model-based control systems

Methods for performance monitoring and diagnosis of multivariable closed loop systems have been proposed aiming at application to model predictive control systems for industrial processes. For performance monitoring, the well-established traditional statistical process control method is empolyed. To meet the underlying premise that the observed variable is univariate and statistically independent, a temporal and spatial decorrelation procedure for process variables has been suggested. For diagnosis of control performance deterioration, a method to estimate the model-error and disturbance signal has been devised. This method enables us to identify the cause of performance deterioration among the controller, process, and disturbance. The proposed methods were evaluated through numerical examples.     

THE ADAPTIVE AUTOREGRESSIVE MODELS FOR THE SYSTEM DYNAMICS AND PREDICTION OF BLAST FURNACE

The blast furnace can be viewed as a time-varying stochastic system. The Adaptive Autoregressive (AAR) models are proposed to characterize such systems. AAR identification is a method of successive parameter estimation by using recursive formulas with variable forgetting factors to closely track time-varying parameters. A simple example is presented to illustrate the parameter tracking capability of the AAR models. Based on the prediction errors, the AAR models of blast furnace are compared with the conventional time series models. Through this comparison, the AAR models prove to be superior to the other time series models, since the latter are suitable only for time-invariant systems. It is concluded that during smooth operation, just the AAR scalar model is required for forecasting as operational guide. When the operation is uneven, the AAR vector model provides the better results. To control the performance of this process the data should be sampled under uneven operating condition, where the AAR vector model is the best among all the models considered and can properly express the dynamic relationship between the input and output variables.     

Identification of Multivariable Delay Processes in Presence of Nonzero Initial Conditions and Disturbances

In this paper, a robust identification method is proposed for multiple‐input and multiple‐output (MIMO) continuous‐time processes with multiple time delays. Suitable multiple integrations are constructed and regression equations linear in the aggregate parameters are derived with the use of the test responses and their multiple integrals. The multiple time delays are estimated by solving some algebraic equations without iteration and the other process model parameters are then recovered. Its effectiveness is demonstrated through simulation and real‐time testing.     

Input variable scaling for statistical modeling

Input variable scaling is one of the most important steps in statistical modeling. However, it has not been actively investigated, and autoscaling is mostly used. This paper proposes two input variable scaling methods for improving the accuracy of soft sensors. One method statistically derives the input variable scaling factors; the other one uses spectroscopic data of a material whose content is estimated by the soft sensor. The proposed methods can determine the scales of the input variables based on their importance in output estimation. Thus, it can reduce the negative effects of input variables which are not related to an output variable. The effectiveness of the proposed methods was confirmed through a numerical example and industrial applications to a pharmaceutical and a distillation processes. In the industrial applications, the proposed methods improved the estimation accuracy by up to 63% compared to conventional methods such as autoscaling with input variable selection.     

Fault diagnosis of chemical processes based on partitioning PCA and variable reasoning strategy

Fault detection and identification are challenging tasks in chemical processes, the aimof which is to decide out of control samples and find fault sensors timely and effectively. This paper develops a partitioning principal component analysis (PPCA) method for process monitoring. A variable reasoning strategy is proposed and applied to recognize multiple fault variables. Compared with traditional process monitoring methods, the PPCA strategy not only reflects the local behavior of process variation in each model (each direction of principal components), but also improves the monitoring performance through the combination of local monitoring results. Then, a variable reasoning strategy is introduced to locate fault variables. Unlike the contribution plot, this method locates normal and fault variables effectively, and gives initiatory judgment for ambiguous variables. Finally, the effectiveness of the proposed process monitoring and fault variable identification schemes is verified through a numerical example and TE chemical process.     

A Recursive Nonlinear PLS Algorithm for Adaptive Nonlinear Process Modeling

Partial least squares (PLS) regression has been shown to be a powerful multivariate linear regression method for problems where the data are noisy and highly correlated. However, in many practical situations, the processes being modeled exhibit nonlinear behavior, which cannot be reliably modeled by linear regression methods. Furthermore, the processes often experience time‐varying changes. In this paper, a recursive nonlinear PLS (RNPLS) algorithm is proposed to deal with this problem. First, a nonlinear PLS (NLPLS) model is built by performing PLS regression on the extended input matrix and the output matrix, where the extension of the input matrix includes the outputs of the hidden nodes of an RBF network and a constant column with all elements being one. When new data cannot be described by the old model in the sense that the model performance on a moving window of data is not satisfactory, the recursive algorithm is then used to modify the structure and parameters of the model to adapt process changes. Applications of this RNPLS algorithm to a simulated pH neutralization process and an industrial propylene polymerization process are presented and the results demonstrate that this algorithm adapts the process changes effectively and gives satisfactory prediction results.     

A real-time estimation approach to time-varying time delay and parameters of NARX processes

This paper presents a solution to the joint time-varying time delay and parameter estimation of NARX (nonlinear autoregressive with exogenous inputs) processes, where only pure time delay in input signal is considered. A modified strong tracking filter (MSTF) is proposed, and is adopted as an adaptive estimation algorithm. Three kinds of specific NARX processes are considered. The first is also the simplest, the output signal is the input with time delay plus disturbance; The second one is a simple NARX process plus disturbance; The third NARX process even has unknown time-varying parameters. For each of the NARX processes, we set up a specific estimation model, with these models the proposed MSTF algorithm can be applied to the real-time time delay and parameter estimation of the above three NARX processes. Computer simulation results demonstrate the effectiveness of the proposed approach. Moreover the robustness of the proposed algorithm against some model/process parameter mismatches is also tested via computer simulations.     

Multimodal process monitoring based on transition-constrained Gaussian mixture model

Reliable process monitoring is important for ensuring process safety and product quality. A production process is generally characterized by multiple operation modes, and monitoring these multimodal processes is challenging. Most multimodal monitoring methods rely on the assumption that the modes are independent of each other, which may not be appropriate for practical application. This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring. This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data. This process enables the identified modes to reflect the stability of actual working conditions, improve mode identification accuracy, and enhance monitoring reliability in cases of mode overlap. Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach in multimodal process monitoring with mode overlap.     

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H₂ optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.     

Nonlinear dimension reduction based neural modeling for distributed parameter processes

Many chemical processes are nonlinear distributed parameter systems with unknown uncertainties. For this class of infinite-dimensional systems, the low-order model identification from process data is very important in practice. The dimension reduction with a principal component analysis (PCA) is only a linear approximation for nonlinear problem. In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes. First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain. Then, a neural system can be easily identified to model this low-dimensional temporal data. Finally, the spatio-temporal dynamics can be reproduced using the nonlinear time/space reconstruction. The simulations on a typical nonlinear transport-reaction process show that the proposed approach can achieve a better performance than the linear PCA based modeling approach.     

Fault identification for process monitoring using kernel principal component analysis

In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T²and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.     

Two-degree-of-freedom output feedback controllers for discrete-time nonlinear systems

A discrete-time, model-based output feedback control structure for nonlinear processes is developed in the present work. The structure makes use of a closed-loop observer, while at the same time it guarantees that the overall feedback controller possesses integral action. An algebraic transformation is applied on the observer states to insure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The resulting control algorithm is a two-degree-of-freedom control law, in the sense that the output and the set point are processed in different ways. The control structure is shown not only to have the same properties as the standard model-state feedback structure, but also that it emerges from a model algorithmic control framework. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to evaluate the closed-loop performance of the proposed method.     

利用状态空间模型和不敏卡尔曼滤波的分批补料发酵过程在线估计(英文)

On-line estimation of unmeasurable biological variables is important in fermentation processes, directly influencing the optimal control performance of the fermentation system as well as the quality and yield of the targeted product. In this study, a novel strategy for state estimation of fed-batch fermentation process is proposed. By combining a simple and reliable mechanistic dynamic model with the sample-based regressive measurement model, a state space model is developed. An improved algorithm, swarm energy conservation particle swarm optimization (SECPSO), is presented for the parameter identification in the mechanistic model, and the support vector machines (SVM) method is adopted to establish the nonlinear measurement model. The unscented Kalman filter (UKF) is designed for the state space model to reduce the disturbances of the noises in the fermentation process. The proposed on-line estimation method is demonstrated by the simulation experiments of a penicillin fed-batch fermentation process.     

Adaptive Generic Model Control of Multivariable Processes: Application to Semi-Batch Reactors with Different Relative Degrees

In this study, a multivariable Generic Model Control (GMC) approach is proposed based on input-output linear-in-parameters time series data-driven models. Adaptation of the model parameters is carried out at every sampling instant. For higher relative degree systems, two different definitions are used for output derivatives, yielding two versions of adaptive GMC for multivariable processes. The performance of the proposed control algorithms is illustrated by application to multivariable semi-batch reactors without and with coolant dynamics for control of temperature and one of the reactant concentrations. The study indicated that the adaptive GMC (AGMC) algorithms for higher relative degree multiple-input and multiple-output (MIMO) systems with a different relative degree have exhibited performance comparable to or better than the phenomenological model-based GMC with respect to both set point tracking and smooth input profiles, and also that the predictive version of AGMC (AGMC-II) has exhibited slightly lower integral square error (ISE) values compared to AGMC-I in case of multivariable semi-batch reactor with coolant dynamics.     

Distributed lyapunov‐based model predictive control with neighbor‐to‐neighbor communication

This work considers distributed predictive control of large‐scale nonlinear systems with neighbor‐to‐neighbor communication. It fulfills the gap between the existing centralized Lyapunov‐based model predictive control (LMPC) and the cooperative distributed LMPC and provides a balanced solution in terms of implementation complexity and achievable performance. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. For each subsystem, an LMPC is designed based on the subsystem model and the LMPC only communicates with its neighbors. At a sampling time, a subsystem LMPC optimizes its future control input trajectory assuming that the states of its upstream neighbors remain the same as (or close to) their predicted state trajectories obtained at the previous sampling time. Both noniterative and iterative implementation algorithms are considered. The performance of the proposed designs is illustrated via a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J 60: 4124–4133, 2014     

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time-scale multiplicity

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.