A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through integrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.     

A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.     

A DYNAMIC MODEL WITH ON-LINE IDENTIFICATION FOR ROTARY SUGAR DRYING PROCESSES

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to replace the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.     

A Hybrid Method for Stochastic Performance Modeling and Optimization of Chemical Engineering Processes

As chemical engineers seek to improve plant safety, reliability, and financial performance, a wide range of uncertaintyladen decisions need to be made. It is widely agreed that probabilistic approaches provide a rational framework to quantify such uncertainties and can result in improved decision making and performance when compared with deterministic approaches. This article proposes a novel method for design and performance analysis of chemical engineering processes under uncertainty. The framework combines process simulation tools, response surface techniques, and numerical integration schemes applied in structural reliability problems to determine the probability of a process achieving a performance function of interest. The approach can be used to model processes in the presence or absence of performance function(s), with or without parameter interactions, at both design and operational phases. With this, process behavior can be quantified in terms of stochastic performance measures such as reliability indices and the associated most probable process design/operating conditions, providing a simple way to analyze a wide range of decisions. To validate the applicability of the proposed framework, three case study systems are considered: a plug flow reactor, a heat exchanger, and finally a pump system. In each case, performance criteria based on the original physical model and the surrogate model are set up. Reliability analysis is then carried out based on these two models and the results are assessed. The results show that the proposed framework can be successfully applied in chemical engineering analysis with additional benefits over the traditional deterministic methods.     

Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

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.     

Stochastic optimization based on a novel scenario generation method for midstream and downstream petrochemical supply chain

A two-stage mixed integer linear programming model (MILP) incorporating a novel method of stochastic scenario generation was proposed in order to optimize the economic performance of the synergistic combination of midstream and downstream petrochemical supply chain. The uncertainty nature of the problem intrigued the parameter estimation, which was conducted through discretizing the assumed probability distribution of the stochastic parameters. The modeling framework was adapted into a real-world scale of petrochemical enterprise and fed into optimization computations. Comparisons between the deterministic model and stochastic model were discussed, and the influences of the cost components on the overall profit were analyzed. The computational results demonstrated the rationality of using reasonable numbers of scenarios to approximate the stochastic optimization problem.     

Property evaluation and control in a semibatch MMA/MA solution copolymerization reactor

This article deals with the property control of polymer product in a semibatch MMA/MA copolymerization reactor by applying the extended Kalman filter (EKF) based nonlinear model predictive control (MPC). In addition to the feeding of the more reactive monomer, the solvent is continuously supplied so as to maintain the viscosity of the reaction mixture within a reasonable range. This measure then provides favorable conditions not only for the on-line estimation with the EKF but also for the performance of the EKF based nonlinear MPC. Indeed, the improved performance of the state estimator is confirmed by experiment under isothermal and nonisothermal conditions over a prolonged reaction time. On the basis of the estimated state, the EKF based nonlinear MPC is implemented to the semibatch reactor to produce copolymers with desired properties. The experimental results clearly demonstrate the superiority of the present control strategy compared to the result of our previous work obtained without having additional feed of solvent.     

GENERIC MODEL ADAPTIVE CONTROL

Generic Model Control (GMC) is a process model based control algorithm incorporating a process model directly within the control structure. It has been shown to produce excellent control, despite reasonable modelling errors. In this paper an algorithm is developed within a GMC framework which reduces the effect of larger modelling errors by regularly updating the model parameters. This new adaptive algorithm is capable of adapting model parameters in a nonlinear model, where the parameters appear in a nonlinear manner. Several examples are presented to illustrate the principles of the technique.     

基于经济模型预测控制的金氰化浸出过程动态实时优化

针对金氰化浸出过程时间常数大、不确定性强等问题,提出了一种基于经济模型预测控制（EMPC）的动态实时优化方法。不同于传统的模型预测控制,EMPC将经济指标直接作为滚动优化的目标函数,在每个采样时刻求解滚动窗口内的最优操作序列。和稳态优化方法相比,基于EMPC的方法能保证动态最优性,提高经济收益。此外,金氰化浸出过程受随机噪声、未知参数可变等不确定性影响,提出使用扩展卡尔曼滤波（EKF）,通过构造增广系统对状态变量及不确定参数进行在线同步估计,加强EMPC的准确性和可靠性。仿真结果表明,提出的EMPC+EKF策略能有效提高金氰化浸出过程的经济性能。     

A study on the prediction of ozone formation in air pollution

Two prediction schemes-time series analysis and parameter estimation method-were investigated to predict the formation of ozone in Seoul, Korea. Moving average method and double exponential smoothing method are applied to the time-series analysis. Three typical methods, such as extended least squares (ELS), recursive maximum likelihood (RML) and generalized least squares (GLS), were used to predict ozone formation in a real time parameter estimation. Autoregressive moving average model with external input (ARMAX) is used as the model of the parameter estimation. To test the performance of the ozone formation prediction schemes proposed in the present work, the prediction results of ozone formation were compared to the real data. From the comparison it can be seen that the prediction scheme based on the parameter estimation method gives a reasonable accuracy with limited prediction horizon.     

复合粒子群优化算法在模型参数估计中的应用

化工非线性模型的参数估计是较为困难的寻优问题，经典方法常会陷入局部极值。粒子群算法操作简便、容易实现且全局搜索功能较强，适用于非线性参数估计。但其参数值的确定与问题相关，若设定不当，会严重影响全局搜索的性能。今提出引入遗传算法，在粒子群算法的搜索过程中，逐代优选参数，包括惯性权值，加速常数，以此构建为复合粒子群优化算法。分析与测试表明，其全局搜索性能有显著改善。进一步的工作又将两种粒子群算法成功地应用于重油热解模型的参数估计。采用复合粒子群优化算法估计参数构建的重油热解模型，其预报相对误差比常规粒子群优化算法降低了8.97％，比简单遗传算法降低了23.21％，效果明显。     

Model for a cascade continuous epoxidation process

A steady-state mathematical model was developed to analyze the performance of a cascade continuous epoxidation process that was applied to the epoxidation of unsaturated compounds with in-situ-formed performic acid. The model equations were nonlinear, and the model prediction was calculated by solving the model equations using a numerical solution procedure. The experimental results supported the model prediction in that good agreement between the model predictions and experimental results was achieved. The model is necessary for precise operation control, process estimation, and operating parameter optimization and regulation, and will provide a theoretical foundation and research method for automatic control and engineering scale-up.     

Composition estimation of multicomponent reactive batch distillation with optimal sensor configuration

An inferential state estimation scheme based on extended Kalman filter (EKF) with optimal selection of sensor locations using principal component analysis (PCA) is presented for composition estimation in multicomponent reactive batch distillation. The properties of PCA are exploited to provide the most sensitive dynamic temperature measurement information of the process to the estimator for accurate estimation of compositions. The state estimator is supported by a simplified dynamic model of reactive batch distillation that includes component balance equations together with thermodynamic relations and reaction kinetics. The performance of the proposed scheme is evaluated by applying it for composition estimation on all trays, reboiler, reflux drum and products of a reactive batch distillation column, in which ethyl acetate is produced through an esterification reaction between acetic acid and ethanol. This quaternary system with azeotropism is highly nonlinear and typically suited for implementation of the proposed scheme. The results demonstrate that the proposed EKF estimation scheme with optimal temperature sensor configuration is effective for inferential estimation of compositions in multicomponent reactive batch distillation.     

Estimation of void boundaries in flow field using expectation–maximization algorithm

Phase distribution in the flow field provides an insight into the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase boundaries. Electrical impedance tomography (EIT), which has high temporal characteristics, has been used as an imaging modality to estimate the void boundaries, using the prior knowledge of conductivities. The voids formed within the process vessel are not stable and their movement is random in nature, thus dynamic estimation schemes are necessary to track the fast changes. Kalman-type estimators like extended Kalman filter (EKF) assume the knowledge of model parameters, such as the initial states, state transition matrix and the covariance of process and measurement noise. In real situations, we do not have the prior information of the model parameters; therefore, in such circumstances the estimation performance of the Kalman-type filters is affected. In this paper, the expectation–maximization (EM) algorithm is used as an inverse algorithm to estimate the model parameters as well as non-stationary void boundary. The uncertainties caused in Kalman-type filters, due to the inaccurate selection of model parameters are overcome using an EM algorithm. The performance of the method is tested with numerical and experimental data. The results show that an EM has better estimation of the void boundary as compared to the conventional EKF.     

Observer-based control algorithms for a distillation column

This paper studies the synthesis of nonlinear observer-based globally linearizing control (GLC) algorithms for a multivariable distillation column. Two closed-loop observers/estimators, namely extended Kalman filter (EKF) and adaptive state observer (ASO), have been designed within the GLC framework to estimate the state variables along with the poorly known parameters. Exactly same basic model structure was used for developing the observers. The model structure is so simple that the estimator design was performed based on only two component balance equations around the condenser-reflux drum and the reboiler-column base systems of the distillation column. To construct these observers, the poorly known parameters, namely component vapor flow rate leaving top tray, component liquid flow rate leaving bottom tray and distribution coefficient in the reboiler, were considered as extra states with no dynamics. The comparative study has been carried out between the proposed GLC in conjunction with ASO (GLC-ASO) and that coupled with EKF (GLC-EKF). The GLC-ASO control scheme showed comparatively better performance in terms of set point tracking and disturbance as well as noise rejections. The control performance of GLC-ASO and a dual-loop proportional integral derivative (PID) controller was also compared under set point step changes and modeling uncertainty. The proposed GLC-ASO structure provided better closed-loop response than the PID controller.     

一种自适应多策略差分进化算法及其应用

针对差分进化算法由于固定参数设置而易早熟或陷入局部最优的问题,提出了一种自适应多策略差分进化算法（SMDE）。该方法以基本差分进化为框架,首先引入一个变异策略候选集合,一个缩放因子候选集合和一个交叉参数候选集合,然后在搜索过程中,以过去的搜索信息为基础,自适应地为下一时刻进化群体中的每个个体从候选集合中选择一组合适的变异策略和控制参数,以便在不同的进化时刻设置合适的变异策略和控制参数。对10个常用的标准测试函数进行优化计算,并与其他算法的结果进行了比较,实验结果表明,SMDE具有较好的搜索精度和更快的收敛速度。将SMDE用于化工过程动态系统不确定参数估计问题,实验结果表明该算法能较好地处理实际工程优化问题。     

Estimation of time-dependent reaction coefficient with extended Kalman filter approach

This work introduces an extended Kalman filter (EKF) to the estimation of the unknown time-dependent reaction coefficient based on the concentration measurement data. An autocatalytic reaction pathway is chosen as a model problem. This inverse estimation algorithm does not assume any functional form of the reaction coefficient. The performance of the proposed algorithm is verified through the numerical experiments with the exact and the contaminated concentration measurement data.     

水煤气水洗塔填料层高度计算模型的简化

针对气液两相在填料塔内同时传热传质的过程,提出了水洗冷却填料塔填料层高度的工程设计计算模型。研究过程基于C语言编程运算,从公式的选择、热力学数据的取值、步长的选择三方面将现有数学模型简化,提出适于工程设计的简化模型。与现有数学模型相比,简化模型的计算结果误差在±10%以内,计算量减少96%以上,符合工程设计的安全性要求。与传统的经验估算方法相比,简化模型提高了科学性和经济性。