Model-based control of a molten carbonate fuel cell (MCFC) process

To improve availability and performance of fuel cells, the operating temperature of molten carbonate fuel cells (MCFC) stack should be strictly maintained within a specified operation range, and an efficient control technique should be employed to meet this objective. While most modern control strategies are based on process models, many existing models of MCFC are not ready to be applied in synthesis and operation of control systems. In this study, we developed an auto-regressive moving average (ARMA) model and machine learning methods of least squares support vector machine (LS-SVM), artificial neural network (ANN) and partial least squares (PLS) for the MCFC system based on input-output operating data. The ARMA model showed the best tracking performance. A model predictive control method for the operation of MCFC system was developed based on the proposed ARMA model. The control performance of the proposed MPC methods was compared with that of conventional controllers using numerical simulations performed on various process models including an MCFC process. Numerical results show that ARMA model based control provides improved control performance compared to other control methods.     

A model predictive functional control based on proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) using extended non-minimal state space: Application to a molten carbonate fuel cell process

The performance of most controllers, including proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) controllers, depends upon tuning of control parameters. In this study, we propose a novel tuning strategy for PID and PIPD controllers whose control parameters are tuned using the extended non-minimal state space model predictive functional control (ENMSSPFC) scheme based on the auto-regressive moving average (ARMA) model. The proposed control method is applied numerically in the operation of the MCFC process with the parameters of PID and PIPD controllers being optimized by ENMSSPFC based on the ARMA model for the MCFC process. Numerical simulations were carried out to assess the set-point tracking performance and disturbance rejection performance both for the perfect plant model, which represents the ideal case, and for the imperfect plant model, which is usual in practical applications. When there exists uncertainty in the plant model, the PIPD controller exhibits better overall control performance compared to the PID controller.     

Comparative study of estimation methods of NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> emission with selection of input parameters for a coal-fired boiler

This study focuses on estimation of NO_x emission and selection of input parameters for a coal-fired boiler in a 500 MW power generation plant. Careful selection of input parameters is required not only to improve accuracy of the estimation, but also to reduce the model dimensionality. The initial operating input parameters are determined based on operation heuristics and accumulated operation knowledge; the essential input parameters are selected by sensitivity analysis where the performance of the estimation model is assessed as one or some input parameters are successively eliminated from the computation while all other input parameters are retained. From the sequential input selection process, less than ten input parameters survived out of 36 initial input parameters. Auto-regressive moving average (ARMA) model, artificial neural networks (ANN), partial least-squares (PLS) model, and least-squares support vector machine (LSSVM) algorithm were proposed to express the relationship between the operating input parameters and the content of NO_x emission. Historical real-time data obtained from a 500 MW power plant coal-fired boiler were used to test the proposed models. It was found that principal components analysis (PCA) enhances the estimation performance of each model. Among the four proposed estimation models, the LSSVM model coupled with PCA scheme showed the minimum root-mean square error (RMSE) and the best R-square value.     

Technical Analysis of an Eco‐Friendly Hybrid Plant With a Microgas Turbine and an MCFC System

This article refers to a Molten Carbonate Fuel Cell (MCFC) system coupled to a plant with a microgas turbine and a heat recovery system for obtaining a small sized hybrid system in co‐generative arrangement. MCFC are devices capable of concentrating carbon dioxide (CO₂) produced in anode exhaust gases. If they are handled conveniently, it is possible to separate and store the surplus CO₂ produced by the plant instead of emitting it into the atmosphere. From the simulation model of the MCFC system, previously developed by the authors, a zero‐dimensional and stationary simulation model for the whole hybrid system was formulated and implemented in the same language. By the simulation model of the MCFC system it has been possible to make a parametric analysis of the hybrid plant to find some optimal operating conditions of the fuel cell(s) that maximise the performance of the entire hybrid plant. In addition, the separation of the CO₂ surplus produced by the hybrid plant was simulated by the model and then the emissions of carbon monoxide (CO) and nitrogen oxides (NO_x) from the same plant were evaluated.     

家用熔融碳酸盐燃料电池发电系统日常运行的遗传算法优化

To decrease the cost of electricity generation of a residential molten carbonate fuel cell （MCFC） power system, multi-crossover genetic algorithm （MCGA）, which is based on ＂multi-crossover＂ and ＂usefulness-based selection rule＂, is presented to minimize the daily fuel consumption of an experimental 10kW MCFC power system for residential application. Under the operating conditions obtained by MCGA, the operation constraints are satisfied and fuel consumption is minimized. Simulation and experimental results indicate that MCGA is efficient for the operation optimization of MCFC power systems.     

DIFFERENTIAL GEOMETRY OF ARMA MODELS

Abstract. A general approach for the development of a statistical inference on autoregressive moving-average (ARMA) models is presented based on geometric arguments. ARMA models are characterized as members of the curved exponential family. Geometric properties of ARMA models are computed and used to suggest parameter transformations that satisfy predetermined properties. In particular, the effect on the asymptotic bias of the maximum likelihood estimator of model parameters is illustrated. Hypothesis testing of parameters is discussed through the application of a modified form of the likelihood ratio test statistic.     

Subset ARMA Model Identification Using Genetic Algorithms

Subset models are often useful in the analysis of stationary time series. Although subset autoregressive models have received a lot of attention, the same attention has not been given to subset autoregressive moving-average (ARMA) models, as their identification can be computationally cumbersome. In this paper we propose to overcome this disadvantage by employing a genetic algorithm. After encoding each ARMA model as a binary string, the iterative algorithm attempts to mimic the natural evolution of the population of such strings by allowing strings to reproduce, creating new models that compete for survival in the next population. The success of the proposed procedure is illustrated by showing its efficiency in identifying the true model for simulated data. An application to real data is also considered.     

熔融碳酸盐燃料电池(MCFC)系统建模与控制的研究现状与发展

首先详细介绍MCFC的电极，单电池，电堆，系统四个层次的建模以及MCFC控制的研究现状，并指出现有模型的不足，然后讨论电堆和系统两级建模的发展方向；最后，分析MCFC系统的非线性，大时滞，分布参数，从输入多输出，有约束和随机干扰等特征，并根据这些特征，提出两种适宜的控制方法。     

A State space approach to bootstrapping conditional forecasts in arma models

A bootstrap approach to evaluating conditional forecast errors in ARMA models is presented. The key to this method is the derivation of a reverse-time state space model for generating conditional data sets that capture the salient stochastic properties of the observed data series. We demonstrate the utility of the method using several simulation experiments for the MA( q ) and ARMA( p, q ) models. Using the state space form, we are able to investigate conditional forecast errors in these models quite easily whereas the existing literature has only addressed conditional forecast error assessment in the pure AR( p ) form. Our experiments use short data sets and non-Gaussian, as well as Gaussian, disturbances. The bootstrap is found to provide useful information on error distributions in all cases and serves as a broadly applicable alternative to the asymptotic Gaussian theory.     

Model algorithmic control of grade change operations in paper mills

In this work, the Model Algorithmic Control (MAC) method is applied to control the grade change operations in paper mills. The neural network model for the grade change operations is identified first and the impulse model is extracted from the neural network model. Results of simulations for MAC control of grade change operations are compared with plant operation data. The major contribution of the present work is the application of MAC in the industrial plants based on the identification of neural network models. We can confirm that the proposed MAC method exhibits faster responses and less oscillatory behavior compared to the plant operation data in the grade change operations.     

An experimental study for property control in a continuous styrene polymerization reactor using a polynomial ARMA model

By using a multivariable nonlinear model predictive controller (NLMPC), the control experiments for the monomer conversion and the weight-average molecular weight are conducted in a continuous styrene polymerization reactor. Instead of a complex first-principles model, a polynomial auto-regressive moving average model (ARMA) is used to describe the nonlinear behavior of the polymerization reactor. The pseudorandom multilevel input signals mounted on the jacket inlet temperature and the feed flow rate are applied to the polymerization reaction system to identify a polynomial ARMA model. In the experiments of identification and control, the monomer conversion and the weight-average molecular weight are measured by on-line densitometer and viscometer with appropriate correlations. The on-line measurements are found to be in good agreement with the off-line analysis by the gravimetry and the gel permeation chromatography. Since a polynomial ARMA model is expected to give a higher order objective function of input variables, we employ the extended Kalman filter based NLMPC scheme to reduce the computational requirement in the control experiments. The NLMPC based on the polynomial ARMA model is found to perform satisfactorily for the control of the polymer properties during a grade-transition period as well as under the steady-state operation.     

ASYMPTOTIC INFERENCE FOR NON-INVERTIBLE MOVING-AVERAGE TIME SERIES

Abstract. This paper is concerned with statistical inference of nonstationary and non-invertible autoregressive moving-average (ARMA) processes. It makes use of the fact that a derived process of an ARMA( p, q ) model follows an AR( q ) model with an autoregressive (AR) operator equivalent to the moving-average (MA) part of the original ARMA model. Asymptotic distributions of least squares estimates of MA parameters based on a constructed derived process are obtained as corresponding analogs of a nonstationary AR process. Extensions to the nearly non-invertible models are considered and the limiting distributions are obtained as functionals of stochastic integrals of Brownian motions and Ornstein-Uhlenbeck processes. For application, a two-stage procedure is proposed for testing unit roots in the MA polynomial. Examples are given to illustrate the application.     

A GENERALIZED LEAST-SQUARES APPROACH FOR ESTIMATION OF AUTOREGRESSIVE MOVING-AVERAGE MODELS

Abstract. In this paper we present a generalized least-squares approach for estimating autoregressive moving-average (ARMA) models. Simulation results based on different model structures with varying numbers of observations are used to contrast the performance of our procedure with that of maximum likelihood estimates. Existing software packages can be utilized to derive these estimates.     

High Moment Partial Sum Processes of Residuals in ARMA Models and their Applications

Abstract. In this article, we study high moment partial sum processes based on residuals of a stationary autoregressive moving average (ARMA) model with known or unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the i.i.d. errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. When properly normalized, this additional term will vanish. Thus the processes converge weakly to the same Gaussian processes as if the residuals were i.i.d. Applications to change‐point problems and goodness‐of‐fit are considered, in particular, cumulative sum statistics for testing ARMA model structure changes and the Jarque–Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.     

Testing for a Unit Root in Autoregressive Moving-average Models with Missing Data

Testing for a single autoregressive unit root in an autoregressive moving-average (ARMA) model is considered in the case when data contain missing values. The proposed test statistics are based on an ordinary least squares type estimator of the unit root parameter which is a simple approximation of the one-step Newton–Raphson estimator. The limiting distributions of the test statistics are the same as those of the regression statistics in AR(1) models tabulated by Dickey and Fuller (Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc . 74 (1979), 427–31) for the complete data situation. The tests accommodate models with a fitted intercept and a fitted time trend.     

ARMA MODELS WITH ARCH ERRORS

Abstract. This paper considers the class of ARMA models with ARCH errors. Maximum Likelihood and Least Squares estimates of the parameters of the model and their covariance matrices are noted and incorporated into techniques for model building based upon the application of the usual Box-Jenkins methodology of identification, estimation and diagnostic checking to the ARMA equation, the ARCH equation, and the full model. The techniques are applied to 16 U.S. macroeconomic time series and it is seen that in many of the series, models from this class can be constructed.     

一种基于多模型融合软测量建模方法

针对锌湿法冶炼净化过程中钴离子浓度LS-SVM软测量建模方法精度低的问题,将最小二乘支持向量机（LS-SVM）和自回归滑动平均模型（ARMA）融合建立钴离子浓度融合软测量模型,首先通过离子浓度序列的小波变换获得序列的低频和高频子序列,对各子序列分别进行相空间重构,并在相空间中分别建立最小二乘支持向量机模型,然后将各模型的输出利用小波重构整合得到钴离子基于LS-SVM软测量结果,利用自回归滑动平均模型对基于LS-SVM模型输出误差信息进行建模,通过对两个模型的融合,获得融合模型的软测量估计值。将该方法应用于锌液净化除钴段入口钴离子浓度的软测量,结果表明该方法比单一的LS-SVM方法具有更好的泛化性能和测量精度,显示出良好的应用潜力。     

Some Results on Specification Search and Pre-testing in an ARMA(1,1) Process

In this study we consider simple autoregressive moving-average (ARMA) models of order at most 1. Pre-testing, on the moving-average coefficient θ, is used to choose between an ARMA(1,1) and an AR(1) in a Monte Carlo design. We find that the pre-test estimator is not always dominated by the others, and that the bias and the mean square error of the estimate of the autoregressive coefficient φ very often depend on the sign of the autoregressive and moving-average parameters of the ARMA(1,1) model in the data-generating process. Further, we note that the degrees of size and power distortion of the t test on φ, after pre-testing for θ, are generally associated with model misspecification.     

ESTIMATION OF MULTIVARIATE TIME SERIES

Abstract. The algorithm proposed here is a multivariate generalization of a procedure discussed by Pearlman (1980) for calculating the exact likelihood of a univariate ARMA model. Ansley and Kohn (1983) have shown how the Kalman filter can be used to calculate the exact likelihood function when not all the observations are known. In Shea (1983) it is shown that this algorithm is much quicker than that of Ansley and Kohn (1983) for all ARMA models except an ARMA (2, 1) and a couple of low-order AR processes and therefore when we have no missing observations this algorithm should be used instead. The Fortran subroutine G13DCF in the NAG (1987) Library fits a vector ARMA model using an adaptation of this algorithm. Experience in the use of this routine suggests that having reasonably good initial estimates of the ARMA parameter matrices, and in particular the residual error covariance matrix, can not only substantially reduce the computing time but more important improve the convergence properties of the minimization procedure. We therefore propose a method of calculating initial estimates of the ARMA parameters which involves using a generalization of the concept of inverse cross covariances from the univariate to the multivariate case. Finally theory is put into practice with the fitting of a bivariate model to a couple of real-life time series.     

PERIODIC CORRELATION IN STRATOSPHERIC OZONE DATA

Abstract. A 50-year time series of monthly stratospheric ozone readings from Arosa, Switzerland, is analyzed. The time series exhibits the properties of a periodically correlated (PC) random sequence with annual periodicities. Spectral properties of PC random sequences are reviewed and a test to detect periodic correlation is presented. An autoregressive moving-average (ARMA) model with periodically varying coefficients (PARMA) is fitted to the data in two stages. First, a periodic autoregressive model is fitted to the data. This fit yields residuals that are stationary but non-white. Next, a stationary ARMA model is fitted to the residuals and the two models are combined to produce a larger model for the data. The combined model is shown to be a PARMA model and yields residuals that have the correlation properties of white noise.