Control Relevant System Identification Using Orthonormal Basis Filter Models

Models are extensively used in advanced process control system design and implementations. Nearly all optimal control design techniques including the widely used model predictive control techniques rely on the use of model of the system to be controlled. There are several linear model structures that are commonly used in control relevant problems in process industries. Some of these model structures are: Auto Regressive with Exogenous Input (ARX), Auto Regressive Moving Average with Exogenous Input (ARMAX), Finite Impulse Response (FIR), Output Error (OE) and Box Jenkins (BJ) models. The selection of the appropriate model structure, among other factors, depend on the consistency of the model parameters, the number of parameters required to describe a system with acceptable accuracy and the computational load in estimating the model parameters. ARX and ARMAX models suffer from inconsistency problem in most open-loop identification problems. Finite Impulse Response (FIR) models require large number of parameters to describe linear systems with acceptable accuracy. BJ, OE and ARMAX models involve nonlinear optimization in estimating their parameters. In addition, all of the above conventional linear models, except FIR, require the time delay of the system to be separately estimated and included in the estimation of the parameters. Orthonormal Basis Filter (OBF) models have several advantages over the other conventional linear models. They are consistent in parameters for most open-loop identification problems. They are parsimonious in parameters if the dominant pole(s) of the system are used in their development. The model parameters are easily estimated using the linear least square method. Moreover, the time delay estimation can be easily integrated in the model development. However, there are several problems that are not yet addressed. Some of the outstanding problems are: (i) Developing parsimonious OBF models when the dominant poles of the system are not known (ii) Obtaining a better estimate of time delay for second or higher order systems (iii) Including an explicit noise model in the framework of OBF model structures and determine the parameters and multi-step ahead predictions (iv) Closed-loop identification problems in this new OBF plus noise model frame work This study presents novel schemes that address the above problems. The first problem is addressed by formulating an iterative scheme where one or two of the dominant pole(s) of the system are estimated and used to develop parsimonious OBF models. A unified scheme is formulated where an OBF-deterministic model and an explicit AR or ARMA stochastic (noise) models are developed to address the second problem. The closed-loop identification problem is addressed by developing schemes based on the direct and indirect approaches using OBF based structures. For all the proposed OBF prediction model structures, the method for estimating the model parameters and multi-step ahead prediction are developed. All the proposed schemes are demonstrated with the help of simulation and real plant case studies. The accuracy of the developed OBF-based models is verified using appropriate validation procedures and residual analysis

Control Relevant System Identification Using Orthonormal Basis Filter Models

Models are extensively used in advanced process control system design and implementations. Nearly all optimal control design techniques including the widely used model predictive control techniques rely on the use of model of the system to be controlled. There are several linear model structures that are commonly used in control relevant problems in process industries. Some of these model structures are: Auto Regressive with Exogenous Input (ARX), Auto Regressive Moving Average with Exogenous Input (ARMAX), Finite Impulse Response (FIR), Output Error (OE) and Box Jenkins (BJ) models. The selection of the appropriate model structure, among other factors, depend on the consistency of the model parameters, the number of parameters required to describe a system with acceptable accuracy and the computational load in estimating the model parameters. ARX and ARMAX models suffer from inconsistency problem in most open-loop identification problems. Finite Impulse Response (FIR) models require large number of parameters to describe linear systems with acceptable accuracy. BJ, OE and ARMAX models involve nonlinear optimization in estimating their parameters. In addition, all of the above conventional linear models, except FIR, require the time delay of the system to be separately estimated and included in the estimation of the parameters. Orthonormal Basis Filter (OBF) models have several advantages over the other conventional linear models. They are consistent in parameters for most open-loop identification problems. They are parsimonious in parameters if the dominant pole(s) of the system are used in their development. The model parameters are easily estimated using the linear least square method. Moreover, the time delay estimation can be easily integrated in the model development. However, there are several problems that are not yet addressed. Some of the outstanding problems are: (i) Developing parsimonious OBF models when the dominant poles of the system are not known (ii) Obtaining a better estimate of time delay for second or higher order systems (iii) Including an explicit noise model in the framework of OBF model structures and determine the parameters and multi-step ahead predictions (iv) Closed-loop identification problems in this new OBF plus noise model frame work This study presents novel schemes that address the above problems. The first problem is addressed by formulating an iterative scheme where one or two of the dominant pole(s) of the system are estimated and used to develop parsimonious OBF models. A unified scheme is formulated where an OBF-deterministic model and an explicit AR or ARMA stochastic (noise) models are developed to address the second problem. The closed-loop identification problem is addressed by developing schemes based on the direct and indirect approaches using OBF based structures. For all the proposed OBF prediction model structures, the method for estimating the model parameters and multi-step ahead prediction are developed. All the proposed schemes are demonstrated with the help of simulation and real plant case studies. The accuracy of the developed OBF-based models is verified using appropriate validation procedures and residual analysis

Pressure modification index based on hydrodynamics and mass transfer effects for modeling of CO2 removal from natural gas via absorption at high pressures

In this paper, experimental works involving high concentration CO2 removal at elevated pressures are conducted using a high pressure CO2 pilot plant and the result is used to validate a simulation model based on established models in the literature. A rate based non-equilibrium model using 20 wt% aqueous monoethanolamine (MEA) is developed based on the work of Pandya (1983). The model considers reaction kinetics, mass transfer rate and heat transfer. Since the condition of CO2 removal at atmospheric and high pressure are different, a pressure modification index is proposed and incorporated in the mass transfer flux equation to account for the non-idealities. Comparative study involving the modified model with index-f, original rate-based non-equilibrium model, Aspen Plus equilibrium and non-equilibrium models has also been carried out for the CO2 loading at the top column exit of 1.505 m. It is found that the introduction of the proposed pressure modification index together with proper selection of mass transfer and effective interfacial area correlations results in an improvement in the average error from more than 100% to as low as 18% between the estimated and the pilot plant data

Simultaneous fault diagnosis based on multiple kernel support vector machine in nonlinear dynamic distillation column

Although numerous works have been done, most of the studies in fault diagnosis are limited to single fault type at a time. Majority of the works reported in the literature do not extend the diagnosis of the root cause of the fault for simultaneous faults specifically in the distillation column. However, an industrial system is susceptible to more than one fault at a time, which may or may not be interrelated. These faults not only reduce the diagnosis performance but also increase the computational complexity of the diagnosis algorithm. In this work, therefore, a multiple kernel support vector machine (MK-SVM) algorithm is proposed to diagnose simultaneous faults in the distillation column. In the developed MK-SVM algorithm, multilabel approach based on various kernel functions has been utilized for the classification of simultaneous faults. Dynamic simulation of a pilot-scale distillation column using Aspen Plus(R) is used for generating data in normal and faulty operation. Eight different fault types are considered, including valve sticking at reflux and reboiler, tray upsets, loss of feed flow, feed composition, and feed temperature changes. In the classification of simultaneous faults, a combination of two, three, and four faults is introduced for the performance evaluation of the proposed MK-SVM algorithm. The result showed that the proposed MK-SVM has a high fault detection rate (FDR) of 99.51% and a very low misclassification rate (MR) of 0.49%. The MK-SVM-based classification is better with the F1 score of >97% for all combinations of faults. Moreover, it is observed that the proposed MK-SVM shows better fault diagnosis for single, multiple, and simultaneous faults as compared to other established machine-learning algorithms