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.     

Data reconciliation for input-output models in linear dynamic systems

Sequential data reconciliation algorithms have been developed for input-output models in linear dynamic systems. Existing filtering methods do not treat the case where there are measurement errors in the input variables. In our approach, the measurement errors in the input variables are optimally handled by the least squares method. This method shows good performance for input-output models.     

Deconstructing principal component analysis using a data reconciliation perspective

Data reconciliation (DR) and principal component analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from erroneous measurements. PCA is primarily used as a method for reducing the dimensionality of high dimensional data and as a preprocessing technique for denoising measurements. These techniques have been developed and deployed independently of each other. The primary purpose of this article is to elucidate the close relationship between these two seemingly disparate techniques. This leads to a unified framework for applying PCA and DR. Further, we show how the two techniques can be deployed together in a collaborative and consistent manner to process data. The framework has been extended to deal with partially measured systems and to incorporate partial knowledge available about the process model.     

Gross error modeling and detection in plant linear dynamic reconciliation

This paper presents a method to identify and estimate gross errors in plant linear dynamic data reconciliation. An integral dynamic data reconciliation method presented in a previous paper (Bagajewicz and Jiang, 1997) is extended to allow multiple gross error estimation. The dynamic integral measurement test is extended to identify hold-up measurements as suspects of gross error. A series of theorems are used to show the equivalencies of gross errors and to discuss the issue of exact identification. A serial approach for gross error identification and estimation is then presented. Gross errors are identified without the need for measurement elimination. The strategy is capable of effectively identifying a large number of gross errors.     

基于约束强跟踪滤波器的动态数据协调

引言 在实际工业过程中,由于过程测量数据的不平衡性和不完备性,给过程分析和研究工作带来了很多困难,甚至失败.因此必须对过程数据进行校正,然而目前的数据校正方法大部分是面对稳态过程的,但实际情况中过程的条件更多地是处在变化之中,此时稳态数据校正方法已不能满足要求.     

基于Kalman滤波的换热器非线性状态参数校正

炼化工艺系统中换热网络数据的准确提取将直接影响到集成优化方案和优化控制的性能。针对换热器非线性状态参数的数据校正,构建了换热器分段线性集总参数传热过程模型,有效地解决了换热器流股物性非线性变化所引起的非线性状态空间方程求解的问题;提出了分段线性的Kalman滤波状态空间方程建立和换热器状态参数校正方法,并通过蜡油加氢装置反应流出物高压换热器工业实例阐述了所提出方法的实现过程和效果。研究表明：换热器分段线性集总参数模型中分段数对Kalman滤波的计算收敛性具有重要影响,随着分段数的增大,换热器状态参数收敛于固定值,分段数需根据计算精度通过试差确定。本文方法可对换热器非线性状态参数实施有效的数据校正,对流股物性进行分段线性化处理具有较高的计算精度,可用于大温差或物性变化较剧烈情况下换热器非线性状态参数的数据校正。     

一种混杂系统数据校正新方法

对于既包含连续生产过程又包含离散事件的混杂系统,尤其是对于带有生产方案切换的实际生产过程,通过在物料平衡模型中引入随机调度方程,从而构造出包含随机调度方程参数变量θ的新型协调模型,然后利用一种不确定模型的协调算法对此模型进行求解,最后,通过仿真研究证实了该方法的有效性和鲁棒性.     

CLOSED-LOOP DATA RECONCILIATION FOR THE CONTROL OF A BINARY DISTILLATION COLUMN

Data reconciliation is a procedure that makes use of process models along with process measurements to give more precise and consistent estimates for process variables. Data reconciliation has been traditionally used to provide a more representative set of data to calculate steady-state inventories and process yields. For dynamic systems, the use of data reconciliation is relatively nascent. This article examines the potential use of data reconciliation in closed-loop control as a filter to attenuate the noise in measurements of the controlled variables so that the controllers can access more accurate sets of data. Data reconciliation filters were implemented in simulations of a PID control system for a binary distillation column. Results showed that data reconciliation could efficiently reduce the propagation of measurement noise in control loops, so that the overall performance of the controller is enhanced.     

CLOSED-LOOP DATA RECONCILIATION FOR THE CONTROL OF A BINARY DISTILLATION COLUMN

Data reconciliation is a procedure that makes use of process models along with process measurements to give more precise and consistent estimates for process variables. Data reconciliation has been traditionally used to provide a more representative set of data to calculate steady-state inventories and process yields. For dynamic systems, the use of data reconciliation is relatively nascent. This article examines the potential use of data reconciliation in closed-loop control as a filter to attenuate the noise in measurements of the controlled variables so that the controllers can access more accurate sets of data. Data reconciliation filters were implemented in simulations of a PID control system for a binary distillation column. Results showed that data reconciliation could efficiently reduce the propagation of measurement noise in control loops, so that the overall performance of the controller is enhanced.     

Disjunctive modeling for optimal control of hybrid systems

In this contribution, a novel approach for the modeling and numerical optimal control of hybrid (discrete–continuous dynamic) systems based on a disjunctive problem formulation is proposed. It is shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible, intuitive and effective way to formulate hybrid (discrete–continuous dynamic) optimization problems. The structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of optimal control of hybrid systems embedding linear discrete–continuous dynamic models.     

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.     

基于参数估计的动态系统过失误差侦破与识别

The detection and identification of gross errors, especially measurement bias, plays a vital role in data reconciliation for nonlinear dynamic systems. Although parameter estimation method has been proved to be a powerful tool for bias identification, without a reliable and efficient bias detection strategy, the method is limited in efficiency and cannot be applied widely. In this paper, a new bias detection strategy is constructed to detect the presence of measurement bias and its occurrence time. With the help of this strategy, the number of parameters to be estimated is greatly reduced, and sequential detections and iterations are also avoided. In addition, the number of decision variables of the optimization model is reduced, through which the influence of the parameters estimated is reduced. By incorporating the strategy into the parameter estimation model, a new methodology named IPEBD (Improved Parameter Estimation method with Bias Detection strategy) is constructed. Simulation studies on a continuous stirred tank reactor (CSTR) and the Tennessee Eastman (TE) problem show that IPEBD is efficient for eliminating random errors, measurement biases and outliers contained in dynamic process data.     

Bayesian method for simultaneous gross error detection and data reconciliation

Process measurements collected from daily industrial plant operations are essential for process monitoring, control, and optimization. However, those measurements are generally corrupted by errors, which include gross errors and random errors. Conventionally, those two types of errors were addressed separately by gross error detection and data reconciliation. Solving the simultaneous gross error detection and data reconciliation problem using the hierarchical Bayesian inference technique is focused. The proposed approach solves the following problems in a unified framework. First, it detects which measurements contain gross errors. Second, the magnitudes of the gross errors are estimated. Third, the covariance matrix of the random errors is estimated. Finally, data reconciliation is performed using the maximum a posteriori estimation. The proposed algorithm is applicable to both linear and nonlinear systems. For nonlinear case, the algorithm does not involve any linearization or approximation steps. Numerical case studies are provided to demonstrate the effectiveness of the proposed method. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3232–3248, 2015     

含反应节点过程数据校正的扩展独立物流法

Among the techniques developed for bilinear data reconciliation problems, the method based on independent flows is well known in terms of both accuracy and efficiency. However, the independent flow method is not effective when reactor units are present in the process. In this paper, an extended independent flow method is proposed for the data reconciliation of the process with chemical reaction. By the new method, the independent flows finding algorithm is adjusted to avoid the difficulties caused by the reactors in the process, and the reaction constraints are introduced into the objective function of data reconciliation. As a result, the new method can be applied to the process with chemical reaction while retaining high solution accuracy. To test the performance, the new method and the most typical Crowe‘s projection method are used in the data reconciliation of a typical industrial process. The results show that the new method can effectively accomplish the data reconciliation of the muhicomponent process with chemical reaction and gives more accurate estimates than the Crowe‘s method.     

Model predictive control: past,present and future

More than 15 years after model predictive control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for non-linear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty ‘rigorously’ an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, non-linear state estimation, and batch system control. Many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated systematically and effectively into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program. Efficient techniques for solving these problems are becoming available.     

基于一种新的鲁棒目标函数的化工过程数据校正

给出了一种基于新鲁棒目标函数的数据校正方法,分析了目标函数的性质及其影响函数,表明了该方法对显著误差具有较强的鲁棒性。对一个线性和非线性化工过程进行了仿真研究,并与常用的Huber鲁棒估计法和Fair鲁棒估计法进行了对比分析。     

Inference of chemical reaction networks using mixed integer linear programming

The manual determination of chemical reaction networks (CRN) and reaction rate equations is cumbersome and becomes workload prohibitive for large systems. In this paper, a framework is developed that allows an almost entirely automated recovery of sets of reactions comprising a CRN using experimental data. A global CRN structure is used describing all feasible chemical reactions between chemical species, i.e. a superstructure. Network search within this superstructure using mixed integer linear programming (MILP) is designed to promote sparse connectivity and can integrate known structural properties using linear constraints. The identification procedure is successfully demonstrated using simulated noisy data for linear CRNs comprising two to seven species (modelling networks that can comprise up to forty two reactions) and for batch operation of the nonlinear Van de Vusse reaction. A further case study using real experimental data from a biodiesel reaction is also provided.     

Data‐based linear Gaussian state‐space model for dynamic process monitoring

This article develops a data‐based linear Gaussian state‐space model for monitoring of dynamic processes under noisy environment. The Kalman filter is introduced for construction of the linear Gaussian state‐space model, and an iterative expectation‐maximization algorithm is used for model parameters learning. With the incorporation of the dynamic data information, a new fault detection and identification approach is proposed. The feasibility and effectiveness of the two monitoring statistics in the new method are theoretically evaluated and further confirmed through two case studies. Furthermore, detailed fault smearing effect analysis of the proposed method is provided and compared with other identification methods. Based on the simulation results of two case studies, the superiority of the proposed method is explored. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Effect on modified nanoclay on dynamic mechanical and thermomechanical properties of natural fiber/polypropylene biocomposites

This study was conducted to investigate the effect of nanoclay addition on thermal and dynamic mechanical properties of polypropylene (PP) biocomposites reinforced with bleached red algae fiber (BRAF), kenaf fiber (KF), and cotton pulp fiber (CPF). The nano-biocomposites were fabricated with 40?wt.% loading of all natural fibers and addition of nanoclay at 5 or 10?wt.% loading by the melting compounding and compression molding techniques. The nanoclay effects on the thermal and dynamic mechanical properties of the biocomposites were analyzed as a function of properties of natural fibers such as chemical composition, fiber length, and surface morphology. Although the thermal decomposition temperature of nano-biocomposites decreased with the addition of nanoclay, the dimensional stability of biocomposites greatly improved with increasing nanoclay loading. Also, the dynamic mechanical properties of nano-biocomposites for the PP reinforced with BRAF, KF, and CPF were enhanced with the addition of 5?wt% nanoclay compared to those of biocomposites without nanoclay. The highest enhancement in dimensional stability was obtained for the nano-biocomposites reinforced with BRAF natural fiber. These increases can be attributed to a uniform distribution of nanoclay and to a good interfacial adhesion between the reinforcement and PP matrix. The well dispersed nanoclay particles can have good interactions with both natural fibers and polymer matrix, with the incorporation of the reinforcing natural fibers restricting the mobility of the polymer molecules resulting in the raised storage modulus values.     

Development of a heuristic methodology for precise sensor network design

This paper develops a heuristic methodology for designing precise sensor/measurement networks for linear material flow circuits based on the general principle of variance reduction through data reconciliation. Firstly, the paper develops a new ‘flowsheet-independent’ formula for estimating the adjusted variance of process streams on linear material flow circuits. Here, the weighted least squares problem is symbolically optimised to obtain a generalized ‘flowsheet-independent’ formula, which depends only on the measured variances of process streams. Secondly, this formula is used to develop a set of generic design principles/heuristics for maximising the variance reduction of process streams. These design principles/heuristics can be used for making a priori design decisions in selecting optimal flowsheets and/or measurement schemes for reducing the variance of process streams on linear material flow circuits. A precise knowledge of material flow rates is critical to areas such as process accounting and quality control which is important to, for example, large process industries such as the petrochemical and mining industries. Process streams are divided into two categories: (i) terminal and (ii) interacting (interconnecting) streams. The design principles/heuristics illustrate the importance of precise measurement of interacting streams and the benefits of highly interconnected flowsheets and/or measurement schemes in maximising variance reduction. The generalized formula and the design principles/heuristics are tested numerically using an industrial case study.