An inverse problem for estimating the time-dependent reaction coefficient in an autocatalytic reaction pathway

An inverse algorithm based on the Iterative Regularization Method (IRM) is applied in this study in determining the unknown time-dependent reaction coefficient for an autocatalytic reaction pathway by using measurements of concentration components. Since no prior information is available on the functional form of the unknown reaction coefficient, thus it can be classified as function estimation for the inverse calculations. The accuracy of this inverse problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the time-dependent reaction coefficient can be obtained within a very short CPU time on a Pentium IV 1.4 GHz personal computer.     

具有预测校正的固定床反应器状态估计

本文建立了基于后集中方法的固定床反应器的非线性状态估计算法，并分别用正交配置法集中偏微分方程、Gear法积分常微分方程、Hybrid法求解非线性代数方程，实现状态估计器的在线估计．针对工业实际过程中浓度测量滞后较大、采样时间间隔较长的特点，提出了浓度估计的预测校正，进一步提高了状态估计器对模型误差的克服能力．同时，在实验和仿真两方面考察了固定床反应器状态估计器的性能，无论是收敛性还是鲁棒性，其品质都令人满意．     

具有预测校正的固定床反应器状态估计

本文建立了基于后集中方法的固定床反应器的非线性状态估计算法，并分别用正交配置法集中偏微分方程、Gear法积分常微分方程、Hybrid法求解非线性代数方程，实现状态估计器的在线估计．针对工业实际过程中浓度测量滞后较大、采样时间间隔较长的特点，提出了浓度估计的预测校正，进一步提高了状态估计器对模型误差的克服能力．同时，在实验和仿真两方面考察了固定床反应器状态估计器的性能，无论是收敛性还是鲁棒性，其品质都令人满意．     

Nonlinear observers for parameter estimation in a solution polymerization process using infrared spectroscopy

Adaptive and high gain nonlinear observers are used for state and parameter estimation in an industrial polymerization process. The solution homopolymerization of acrylic acid is considered. The process is monitored online by near infrared spectroscopy giving the residual amount of monomer. Using this measurement, a continuous adaptive observer is first constructed to estimate the concentration of radicals. A second high gain continuous-discrete observer uses off-line measurements of the polymer molecular weight to estimate the termination rate coefficient that might be time varying due to the gel effect. The transfer to solvent rate coefficient is estimated under steady-state conditions and is assumed to be constant during the reaction. The identified model is validated by varying the process parameters: the concentrations of solvent, monomer, radicals and the residence time in the reactor with interest of their impact on the polymer molecular weight.     

Predicting conversion using temperature as the measured variable in the RIM process. Part I: Simulation and measurement structure

In general the monitoring and control of many industrial processes is so complicated by problems associated with the on-line measurement of the desired objectives that they must be inferred from available measurements. This leads to a state estimation problem in which the selection and adaptation of the structure of the measurements plays an important role. In particular, in the reaction injection molding (RIM) process, an accurate on-line estimate of the conversion field is highly desirable. Since conversions cannot be determined readily by direct measurements, and a thermocouple can provide reliable dynamic temperature data, we can predict the conversion field from the solution of a state estimation problem using temperature as the measured variable. In this article, we describe an algorithm for designing the optimal arrangement of measuring sensors and analyze the RIM process dynamics which influence the structure depending on the operating conditions. The search for the optimal measurement structure for the purpose of state estimation makes up the bulk of the results. No particular estimation-control strategy is investigated in this paper. Work is underway to develop the on-line corrective system, which will use the temperature measurements to correct model predictions. The results of that work will appear in part II of this series.     

Recursive least squares scheme for operating a class of continuous fermentation processes at optimal steady state productivity

This paper has developed a recursive least squares scheme for operating a class of continuous fermentation processes at the optimal steady state productivity. More precisely, the class of continuous fermentation processes under investigation is described by a widely accepted non-segregated fermentation process model. Based on a recursive least squares algorithm, an on-line estimation scheme for estimating the optimal set points for feed substrate concentration and dilution rate is developed. Finally, via simulation, it is shown that this on-line estimation scheme is robust against measurement time (sampling time). © 1998 Society of Chemical Industry     

On controlling an autothermal fixed-bed reactor at an unstanble state—IV: Model fitting and control of the laboratory reactor

This study describes in detail model fitting and experimental control implementation for a tubular autothermal reactor running the water-gas shift reaction. The reactor is interfaced to a real-time computer for data logging and control purposes. Certain unknown reaction and heat transport parameters are either evaluated through indirect measurements or estimated from steady-state temperature and concentration data. The heat capacity of the catalyst bed is then adjusted so as to improve the agreement between simulated and measured transient responses.The control approach is purposely kept very simple: measurement of only a few bed temperatures, no state estimation scheme, and use of a single manipulated input. Operation of the reactor at an unstable steady state is clearly demonstrated by several independent tests. Finally, excellent agreement between experimental and simulation results are observed for various cases of pulse perturbation of the heat input at the catalyst bed entrance.     

Estimation of catalytic activity using an unscented Kalman filtering in condensation reaction

The catalytic activity of cation exchange resins will be continuously reduced with its use time in a condensation reaction for bisphenol A (BPA). For online estimation of the catalytic activity, a catalytic deactivation model is studied for a production plant of BPA, state equation and observation equation are proposed based on the axial temperature distribution of the reactor and the acetone concentration at reactor entrance. A hybrid model of state equation is constructed for improving estimation precision. The unknown parameters in observation equation are calculated with sample data. The unscented Kalman filtering algorithm is then used for on-line estimation of the catalytic activity. The simulation results show that this hybrid model has higher estimation accuracy than the mechanism model and the model is effective for production process of BPA.     

A technique for analysing integral rate data in non-ideal flow reactors to estimate unknown parameters

A technique is described for analysing integral rate data taken from a non-ideal flow chemical reactor characterised by the axial dispersion model, using a weighted residual approach. This approach avoids the formidable computational difficulties involved with the solution of the boundary value problem associated with the model differential equations. The measured concentration profile is approximated by a series of orthogonal polynomials. Model parameters are estimated by specifying that the fitting polynomial satisfy certain moment relations derived from the mass balance equation and boundary conditions. If the form of the rate equation is known, a priori, the estimation of the rate constant and the dispersion coefficient becomes explicit. In the more general case, in which the reaction order is also unknown, the estimation problem reduces to a uni-dimensional search for the reaction order parameter (or the adsorption parameter in the case of complex kinetics). The method is applied to both linear and non-linear systems and conclusions are drawn regarding the sensitivity of the chemical kinetic and transport parameters to experimental error.     

Study of auto-accelerated reactions in heterogeneous liquid/liquid mixture: Reaction products effects on mass transfer kinetics

The alkaline hydrolysis of aromatic esters exhibits auto-accelerated kinetics when performed under two phase conditions. This auto-acceleration behavior is linked to reaction products effects (surfactant and co-solvent) on mass transfer kinetics. The co-solvent increases the equilibrium concentration of organic compounds in aqueous solution, while the surfactant modifies the mass transfer coefficient and interfacial area. In this research work, the selected reaction is the alkaline hydrolysis of methyl benzoate carried out in a calorimetric reactor Mettler RC1 in isothermal semi-batch mode. The parameters estimation of mass transfer and chemical kinetics has been conducted using thermal power profile. Two functions—giving the evolution during reaction of the mass transfer coefficient and the equilibrium concentration—are proposed accordingly to surfactant and co-solvent concentrations.     

A maximum-likelihood method for estimating parameters,stochastic disturbance intensities and measurement noise variances in nonlinear dynamic models with process disturbances

An improved approximate maximum likelihood algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear stochastic differential equation (SDE) models. This algorithm uses a Laplace approximation and B-spline basis functions for approximating the likelihood function of the parameters given the measurements. The resulting Laplace approximation maximum likelihood estimation (LAMLE) algorithm is tested using a nonlinear continuous stirred tank reactor (CSTR) model. Estimation results for four model parameters, two process disturbance intensities and two measurement noise variances are obtained using LAMLE and are compared with results from two other maximum-likelihood-based methods, the continuous-time stochastic method (CTSM) of Kristensen and Madsen (2003) and the Fully Laplace Approximation Estimation Method (FLAEM) (Karimi and McAuley, 2014). Parameter estimations using 100 simulated data sets reveal that the LAMLE estimation results tend to be more precise and less biased than corresponding estimates obtained using CTSM and FLAEM.     

Improved Estimation of the Langmuir Adsorption Isotherm Using Multiscale Filtering

Abstract

Adsorption isotherms play an important role in the design and analysis of adsorption processes. These isotherms are estimated empirically from measurements of adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet-based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Langmuir adsorption isotherm in the presence of measurement noise in the data by developing a multiscale isotherm estimation algorithm. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms, and then select among all scales the isotherm that best represent the data based on a cross-validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.     

Simultaneous Measurement Bias Correction and Dynamic Data Reconciliation

The presence of measurement bias and random noise significantly deteriorates the information quality of plant data. Data reconciliation techniques for steady-state processes have been widely applied to processing industries to improve the accuracy and precision of the raw measurements. This paper develops an algorithm for simultaneous bias correction and data reconciliation for dynamic processes. The algorithm considers process model error as an important contributing factor in the estimation of the measurement bias and process state variables. It employs black-box models for the process as would be done when phenomenological models are difficult or impractical to obtain. Simulation results of a distillation column demonstrated that this algorithm effectively compensates constant and non-constant measurement biases yielding much improved reconciled values of process variables. It has computational advantages over previously proposed algorithms based on non-linear dynamic data reconciliation because an analytical solution is available when using linear process models to approximate the process.     

Development of a thermodynamically consistent kinetic model for reactions in the solid oxide fuel cell

The parameter estimation using the traditional kinetic modeling of complex reaction systems will give incorrect results if the reaction mechanism contains a loop. In this work, a thermodynamically consistent kinetic model of the anodic electrochemical hydrogen oxidation reaction mechanism of a solid oxide fuel cell (SOFC) is formulated. An iterative algorithm for estimating the reaction rate constants using the thermodynamically consistent model formulation is developed. The kinetic parameters estimated using the proposed method gives a better fit to the experimental data. Using the concept of ‘Degree of rate control’ it is found that the surface reactions may have a greater role in deciding the overall rate. The proposed iterative parameter estimation algorithm developed in this work can also be adapted to other complex chemical and biochemical reaction networks for which the reaction rate constants need to be estimated using the experimental data.     

Calibration of adhesion models based on the extended Kalman filtering

ABSTRACT

This paper presents a strategy to be used for the calibration of adhesion models using a modified extended Kalman filter algorithm. A constitutive model coupling unilateral contact, adhesion and damage is considered for the analysis. The effect of the uncertainties in the constitutive adhesion parameters onto the adhesion reaction force is performed considering four uncertain scenarios. Furthermore, the effect of the speed in the loading-unloading of the system is also taken into account for these analyses. The parameter estimation strategy is assessed considering noise-corrupted synthetic data, two loading profiles and two possible measurement scenarios. The results indicate the key-role played by the sensitivity analysis when estimating the constitutive adhesion parameters and highlights the low sensitivity of system responses with respect to the viscous parameter when compared to the elastic parameter and also to the parameter associated with the energy of decohesion.     

基于迭代算法的信号频率快速估算

提出一种正弦信号频率估算的快速迭代算法，它可以保证在不知信号频率的确切值的情形下在2个周波内以0．1％的测量准确度来估算信号频率的实际值。本算法是一个迭代计算过程，仅利用一个采样周期信号采样序列值中的任何两个相邻的采样值，并通过构造信号幅值、频率和相位与这两个采样值有关的影响系数来实现。在迭代计算中，通过设定不同数值的迭代系数，可以在不同的计算时间内获得不同的估算精确度。并给出一个实际应用系统的实例计算，仿真结果证明这种算法的可靠性、准确性和快速性。     

Concentration-dependent molecular diffusion coefficient of gaseous ethane in liquid toluene

We report new experimental data on concentration-dependent molecular diffusion coefficient of ethane in toluene at temperatures ranging from 21 to 125°C and pressures up to 4.14 MPa. An analytical model has also been developed for estimation of the diffusion coefficient utilizing the experimental data of the interface velocity as a result of swelling and the rate of gas dissolution in the liquid phase. It is shown that the diffusion coefficient of ethane in toluene is dependent on the initial mass fraction of the gaseous component in the liquid. In addition, the effect of concentration dependency of the molecular diffusion coefficient on diffusive mass flux is quantified. The results reveal that the assumption of a constant diffusion coefficient introduces ~10–60% error in calculation of diffusional mass transfer flux. The developed methodology finds application in estimation of the concentration-dependent molecular diffusion coefficient of gases in liquids.     

基于STA-K均值聚类的电化学废水处理过程离子浓度软测量

针对电化学废水处理过程出口离子浓度无法在线检测的问题,提出了一种基于状态转移的K均值聚类算法的软测量建模方法。在分析内部反应机理的基础上,结合物料平衡和吸附动力学定理建立电化学过程的机理模型;由于单一的软测量模型难以满足实际的精度要求,提出一种基于状态转移的K均值聚类算法将原始数据集进行聚类,应用状态转移算法对K均值算法的初始聚类中心进行优化,同时,引入离群值矩阵动态迭代同时实现数据聚类和异常值检测;最后,对聚类后的不同训练子集分别建立子模型,综合各子模型得到基于多模型切换方法的软测量模型。通过某废水处理厂的现场数据进行实例验证,结果证明了所建立的电化学废水处理过程离子浓度软测量模型合理有效。     

有滞后环节的系统的闭环鲁棒辨识方法

提出一种新的针对带滞后环节的任意阶系统的闭环辨识方法。通过“三步法”，实现在闭环条件下的被控制对象的传递函数参数的辨识，所提出方法具有很强的鲁棒性。仿真例子表明该方法的有效性。     

Modelling of combined mass transfer-kinetic effects in an enzyme membrane reactor system with a direct approach to the identification of intrinsic rate parameters

A methodology for identifying non-linear parameters in a generalised Briggs-Haldane rate expression for immobilised enzyme membrane flow reactors has been developed for the intermediate case where mutually rate-controlling processes of mass transfer and enzymatic reaction prevail. The technological significance of the estimation procedure lies in the ability of the algorithm to handle parameter identification in non-linear, two-point boundary value problems which are prevalent in both immobilised enzyme and non-enzymic heterogeneous catalysed reactor systems. The methodology was successfully implemented on an experimental level using quasi-steady-state conversion data for the model system of urea/collagen-urease in a spiral-wound, biocatalytic reactor module. By using a novel procedure of pepsin pretreatment of the collagen host membrane before enzyme impregnation, followed by glutaraldehyde crosslinking, it was possible to enhance the activity and stability of the immobilised enzyme complex to relatively high levels where interphase and intraphase diffusional limitations mutually controlled the rate of reaction. Information on the coefficient of mass transfer at the interface between solid and fluid phases was also obtained as part of the estimation procedure.