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.     

Communication delays and data losses in distributed adaptive high‐gain EKF

In this work, we consider distributed adaptive high‐gain extended Kalman filtering for nonlinear systems subject to data losses and delays in communications. Specifically, we consider a class of nonlinear systems that consist of several subsystems interacting with each other via their states. A local adaptive high‐gain extended Kalman filter is designed for each subsystem and the distributed estimators communicate to exchange the information. Each subsystem estimator takes the advantage of a predictor accounting for the delays and data losses simultaneously. The predictor of each subsystem is used to generate state predictions of interacting subsystems for interaction compensation. To get a reliable prediction, the predictors are designed based on a prediction‐update algorithm. The convergence of the proposed distributed state estimation is ensured under sufficient conditions handling communication delays and data losses. Finally, a chemical process example is used to evaluate the applicability and effectiveness of the proposed design. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4321–4333, 2016     

Distributed state estimation from infrequent and delayed measurements in large-scale processes

Effective control and monitoring of a process usually require frequent and delay-free measurements of important process output variables. However, these measurements are often either not available or available infrequently with significant time delays. This article presents a method that allows for improving the performance of distributed state estimators implemented on large-scale manufacturing processes. The method uses a sample state augmentation approach that permits using delayed measurements in distributed state estimation. The method can be used with any state estimator, including unscented Kalman filters, extended Kalman filters, and moving horizon state estimators. The method optimally handles the tradeoff between computational time and estimation accuracy in distributed state estimation implemented using a computer with parallel processors. Its implementation and performance are shown using a few simulated examples.     

AN OPTIMAL EXTENDED KALMAN FILTER DESIGNED BY GENETIC ALGORITHMS

A Geno-Kalman filter is utilized for state estimation of a bench-scale batch reactor that handles an exothermic reaction between H₂O₂ and Na₂S₂O₃. This reaction system includes three different states including the concentration of reactants as well as the temperature of the reactor. All of the states are measured during the process. The proposed procedure is to run an optimal extended Kalman filter by which the Kalman design parameters, Q and R, are obtained by genetic algorithms. The extended Kalman filter is initially designed by trial and error and used as a baseline in this study. Then an optimal white-bound extended Kalman filter design is obtained through an optimization on the baseline estimator, using genetic algorithms. The results show a significant improvement in the performance of the estimator. Moreover, a color-bound extended Kalman filter was also designed to allow a dynamic linear trend for the change in nonzero elements of the process noise covariance matrix.     

Recursive state estimation techniques for nonlinear differential algebraic systems

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. While state and parameter estimation of ODE systems has been studied extensively, differential algebraic equation (DAE) systems have received much less attention. However, most realistic chemical engineering processes are modelled as DAE systems and hence state and parameter estimation of DAE systems is a significant problem. Becerra et al. (2001) proposed an extension of the extended kalman filter (EKF) for estimating the states of a system described by nonlinear differential-algebraic equations (DAE). One limitation of this approach is that it only utilizes measurements of the differential states, and is therefore not applicable to processes in which algebraic states are measured. In this paper, we address the state estimation of constrained nonlinear DAE systems. The novel aspects of this work are: (i) development of a modified EKF approach that can utilize measurements of both algebraic and differential states, (ii) development of a recursive approach for the inclusion of constraints, and (iii) development of approaches that utilize unscented sampling in state and parameter estimation of nonlinear DAE systems; this has not been attempted before. The utility of these estimators is demonstrated using electrochemical and reactive distillation processes.     

Nonlinear stochastic modeling to improve state estimation in process monitoring and control

State estimation from plant measurements plays an important role in advanced monitoring and control technologies, especially for chemical processes with nonlinear dynamics and significant levels of process and sensor noise. Several types of state estimators have been shown to provide high‐quality estimates that are robust to significant process disturbances and model errors. These estimators require a dynamic model of the process, including the statistics of the stochastic disturbances affecting the states and measurements. The goal of this article is to introduce a design method for nonlinear state estimation including the following steps: (i) nonlinear process model selection, (ii) stochastic disturbance model selection, (iii) covariance identification from operating data, and (iv) estimator selection and implementation. Results on the implementation of this design method in nonlinear examples (CSTR and large dimensional polymerization process) show that the linear time‐varying autocovariance least‐squares technique accurately estimates the noise covariances for the examples analyzed, providing a good set of such covariances for the state estimators implemented. On the estimation implementation, a case study of a chemical reactor demonstrates the better capabilities of MHE when compared with the extended Kalman filter. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

STATE ESTIMATION IN THE BATCH DRYING OF FOODS

Measurement of material moisture content is necessary for the control of product quality in batch drying. However, this variable cannot be measured on-line, and state estimation techniques are proposed. A non-linear dynamic model is developed for batch drying of foods. Process disturbances and measurement errors are modeled as stochastic processes and a hybrid extended Kalman filter is employed for state estimation. This filter is based on the local linearization of the process model around the suboptimal filter estimates. The moisture estimation approach was applied to experimental points obtained in a laboratory dryer with quite satisfactory results.     

STATE ESTIMATION IN THE BATCH DRYING OF FOODS

ABSTRACT

Measurement of material moisture content is necessary for the control of product quality in batch drying. However, this variable cannot be measured on-line, and state estimation techniques are proposed. A non-linear dynamic model is developed for batch drying of foods. Process disturbances and measurement errors are modeled as stochastic processes and a hybrid extended Kalman filter is employed for state estimation. This filter is based on the local linearization of the process model around the suboptimal filter estimates. The moisture estimation approach was applied to experimental points obtained in a laboratory dryer with quite satisfactory results.     

Nonlinear state estimation for fermentation process using cubature Kalman filter to incorporate delayed measurements☆

State estimation of biological process variables directly influences the performance of on-line monitoring and op-timal control for fermentation process. A novel nonlinear state estimation method for fermentation process is proposed using cubature Kalman filter (CKF) to incorporate delayed measurements. The square-root version of CKF (SCKF) algorithm is given and the system with delayed measurements is described. On this basis, the sample-state augmentation method for the SCKF algorithm is provided and the implementation of the proposed algorithm is constructed. Then a nonlinear state space model for fermentation process is established and the SCKF algorithm incorporating delayed measurements based on fermentation process model is presented to implement the nonlinear state estimation. Finally, the proposed nonlinear state estimation methodology is applied to the state estimation for penicillin and industrial yeast fermentation processes. The simulation results show that the on-line state estimation for fermentation process can be achieved by the proposed method with higher esti-mation accuracy and better stability.     

Distributed semi-cooperative filter for a nonlinear multi-agent system with heterogeneous and homologous unknown inputs

In this study, the simultaneous estimation of the states and unknown inputs for a nonlinear multi-agent system with homologous and heterogeneous unknown inputs is performed. The decentralized sub-filter is used to estimate the states and heterogeneous unknown inputs, whereas the distributed sub-filter is used to estimate the homologous unknown inputs. The extended Kalman filter is used to solve the estimation problem for nonlinear systems. Compared with previous studies, the distributed solution is improved to relax the existence of the homologous unknown input sub-filter. Moreover, the updating method of the residual generator is improved to relax the heterogeneous unknown input sub-filter. The practical problem of estimating the state of charge and temperature of the battery pack is used to verify the effectiveness of the proposed filter.     

Tracking of moving interfaces in sedimentation processes using electrical impedance tomography

Sedimentation monitoring is widely used to control and optimize industrial processes. In this paper we propose a novel computational method for sedimentation monitoring using electrical impedance tomography (EIT). EIT measurements consist of electric current and voltage measurements that are made on the surface of the sedimentation tank and therefore they do not interfere with the sedimentation process. The proposed computational method is based on shape estimation and state estimation formulation of the EIT problem. The sedimentation is parameterized by the locations of the phase interfaces and conductivities of the phase layers. Three different evolution models for the state parameters are considered and the state estimates are computed using the extended Kalman filter algorithm. The performance of the method and the models are evaluated using simulated data from a six electrode EIT measurement configuration. From the results a promising performance of the method can be seen.     

A multiple model,state feedback strategy for robust control of non-linear processes

The major limitation of reported multiple model approaches is that robustness against process/controller disturbances cannot be addressed for processes consisting of hybrid stable/unstable regimes, or with chaotic dynamics. In this paper, a significantly modified multiple model approach is developed to achieve robust control with global stability. The new advances include: (1) stabilization of open-loop unstable plants using a state feedback strategy, (2) incorporation of an adjustable pre-filter to achieve offset-free control, (3) implementation of a Kalman filter for state estimation, and (4) connection of the multiple model approach with non-linear model predictive control to achieve a precise control objective. The improved controller design method is successfully applied to two non-linear processes with different chaotic behaviour. Compared with conventional methods without model modifications, the new approach has achieved significant improvement in control performance and robustness with a dramatically reduced number of local models.     

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.     

Subsystem decomposition of process networks for simultaneous distributed state estimation and control

An appropriate subsystem configuration is a prerequisite for a successful distributed control/state estimation design. Existing subsystem decomposition methods are not designed to handle simultaneous distributed estimation and control. In this article, we address the problem of subsystem decomposition of general nonlinear process networks for simultaneous distributed state estimation and distributed control based on community structure detection. A systematic procedure based on modularity is proposed. A fast folding algorithm that approximately maximizes the modularity is used in the proposed procedure to find candidate subsystem configurations. Two chemical process examples of different complexities are used to illustrate the effectiveness and applicability of the proposed approach. © 2018 American Institute of Chemical Engineers AIChE J, 65: 904–914, 2019     

不敏变换鲁棒Kalman滤波器在发酵过程中的应用(英文)

State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However, there are many difficulties in dealing with a non-linear system, such as the instability of process, un-modeled dynamics, parameter sensitivity, etc. This paper discusses the principles and characteristics of three different approaches, extended Kalman filters, strong tracking filters and unscented transformation based Kalman filters. By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance, an improved Kalman filter, unscented transformation based robust Kalman filter, is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process. The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.     

未知输入扩展卡尔曼滤波的收敛性分析及其非线性故障诊断

Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.     

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.     

Distributed parameter estimation and identification for system with fast and slow dynamics: A tubular,fixed-bed catalytic reactor to form styrene

A simple and efficient on-line scheme is developed to estimate temperature and compositions along a packed bed reactor in which styrene is being produced by the dehydrogenation of ethylbenzene. Slowly varying catalyst activity is also identified. The system is distributed in time and axial position and is nonlinear in the states: temperature and nine compositions. The dehydrogenation rate is augmented with a catalyst activity parameter which is assumed to undergo a long-term exponential decay.Since the decline in catalyst activity is slow when compared to state dynamics, a quasi-steady-state approach is used to derive a state filter equation neglecting process state dynamics and assuming spatially uncorrelated measurements and model uncertainty. For this filter, temperature measurements are available from four locations along the reactor and compositions are measured only at the reactor exit. A second dynamic, Kalman filter is used to identify the slowly varying catalyst activity.The two filters, one for distributed, steady-state, state estimation and the other for dynamic catalyst activity identification, are tested by computer simulation using measurements with added white noise. Several cases for numbers of sensors and noise levels are studied. The overall scheme is efficient and useable for on-line implementation. The steady-state filter is readily extended to distributed systems in more than one spatial variable such as reactor models with axial and radial dependencies. For steady-state or static models, multiple measurements yield significant improvements in the quality of the optimal estimates. Internal measurement locations allow for the subdivision of the spatial domain for the problem and improved profile estimates.     

Calorimetric estimation for a batch-loop emulsion polymerisation reactor

To facilitate the online monitoring and control of a pilot-scale polymerisation reactor, state estimation techniques are investigated. Specifically, a batch-loop reactor is employed for the emulsion polymerisation of methyl methacrylate. The reactor consists of jacketed tubular sections fitted with in-line static mixers, thus providing mixing homogeneity and improved temperature control. A direct estimation of the reaction rate is attained through measurements of process and jacket side temperatures, and thus a calorimetric method of estimation. This is compared with a Kalman filter based calorimetric approach, in which there is compensation for model uncertainties and measurement noise. For both estimation methods, no knowledge of the kinetic model for polymerisation is needed. Experimental results indicate that with an accurate model of the process energy balance, in which, for example, the recycle pump energy input is described, the Kalman filter approach is found to provide excellent prediction of conversion, for both high and low conversions, for this pilot-plant reactor system. The approach does not require any (approximate) kinetic knowledge, and is thus considerably easier in implementation than the extended Kalman filter approaches.     

Two-dimensional Bayesian monitoring method for nonlinear multimode processes

Nonlinear and multimode are two common behaviors in modern industrial processes, monitoring research studies have been carried out separately for these two natures in recent years. This paper proposes a two-dimensional Bayesian method for monitoring processes with both nonlinear and multimode characteristics. In this method, the concept of linear subspace is introduced, which can efficiently decompose the nonlinear process into several different linear subspaces. For construction of the linear subspace, a two-step variable selection strategy is proposed. A Bayesian inference and combination strategy is then introduced for result combination of different linear subspaces. Besides, through the direction of the operation mode, an additional Bayesian combination step is performed. As a result, a two-dimensional Bayesian monitoring approach is formulated. Feasibility and efficiency of the method are evaluated by the Tennessee Eastman (TE) process case study.