Forecasting VARMA processes using VAR models and subspace-based state space models

VAR modelling is a frequent technique in econometrics for linear processes. VAR modelling offers some desirable features such as relatively simple procedures for model specification (order selection) and the possibility of obtaining quick non-iterative maximum likelihood estimates of the system parameters. However, if the process under study follows a finite-order VARMA structure, it cannot be equivalently represented by any finite-order VAR model. On the other hand, a finite-order state space model can represent a finite-order VARMA process exactly, and, for state-space modelling, subspace algorithms allow for quick and non-iterative estimates of the system parameters, as well as for simple specification procedures. Given the previous facts, we check in this paper whether subspace-based state space models provide better forecasts than VAR models when working with VARMA data generating processes. In a simulation study we generate samples from different VARMA data generating processes, obtain VAR-based and state-space-based models for each generating process and compare the predictive power of the obtained models. Different specification and estimation algorithms are considered; in particular, within the subspace family, the CCA (Canonical Correlation Analysis) algorithm is the selected option to obtain state-space models. Our results indicate that when the MA parameter of an ARMA process is close to 1, the CCA state space models are likely to provide better forecasts than the AR models. We also conduct a practical comparison (for two cointegrated economic time series) of the predictive power of Johansen restricted-VAR (VEC) models with the predictive power of state space models obtained by the CCA subspace algorithm, including a density forecasting analysis.subspace algorithms; VAR; forecasting; cointegration; Johansen; CCA

Closed-loop Identification of an Industrial Extrusion Process

This paper deals with the challenging problem of closed-loop identification for multivariable chemical processes and particularly the estimation of an open-loop plant model for a lab-scale industrial twin-screw extruder used in a powder coatings manufacturing line. The aim is to produce a low order efficient model in order to assist the scaling-up and the model-based control design of the manufacturing process. To achieve this goal, a two-stage indirect approach has been deployed which relies on the a-priori knowledge of the controller parameters in order to extract good estimates of the open-loop dynamics of the underlying process. As input excitation signals we have used multiple single variable step tests at various operating conditions (current industrial practice) carried out manually in order to generate the data-set which captures the dynamics of the extrusion process. In order to increase the efforts for obtaining a suitable plant model, we have employed various identification techniques, such as Prediction Error Methods (PEM) and Subspace Identification Methods (SIM) in order to generate candidate closed-loop models that fit to the original input-output process data. Then, a comparison of the estimated models was performed by means of the mean square error and data fitting criteria in order to select the model that best describes the dynamic behaviour of the extrusion process. Model validation based on closed-loop step responses also used as verification of the results

Detecting stationary gain changes in large process systems

Stationary process gains are critical model parameters to determine targets in commercial MPC technologies. Consequently, important savings can be reached by acceding to an early prevention method capable of detecting whether the actual process moves away from the modeled dynamics or not, particularly by indicating when the process gains are not more represented by those included in the model identified during commissioning stages. In this first approach, a subspace identification method is used under open loop process condition to develop a process gain-matrix estimator. The main reason for using the subspace identification method is that it works directly with raw data and that the development is intended for monitoring future applications under multivariable closed-loop optimizing control where the transient regime is a frequent scenario. The objective of this paper is to present a method capable of detecting those gains of a multivariable model that start moving away from the original values. The anticipated knowledge of these events could provide a warning to process engineers and prevent from targeting process conditions with wrong gain estimations. The regular follow-up of the gain matrix should also help to localize those dynamics needing an updating identification.Fil: Bustos, Germán Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

Control optimization, stabilization and computer algorithms for aircraft applications

The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory

SYSTEM IDENTIFICATION AND MODEL PREDICTIVE CONTROL FOR INTERACTING SERIES PROCESS WITH NONLINEAR DYNAMICS

This thesis discusses the empirical modeling using system identification technique and the implementation of a linear model predictive control with focus on interacting series processes. In general, a structure involving a series of systems occurs often in process plants that include processing sequences such as feed heat exchanger, chemical reactor, product cooling, and product separation. The study is carried out by experimental works using the gaseous pilot plant as the process. The gaseous pilot plant exhibits the typical dynamic of an interacting series process, where the strong interaction between upstream and downstream properties occurs in both ways. The subspace system identification method is used to estimate the linear model parameters. The developed model is designed to be robust against plant nonlinearities. The plant dynamics is first derived from mass and momentum balances of an ideal gas. To provide good estimations, two kinds of input signals are considered, and three methods are taken into account to determine the model order. Two model structures are examined. The model validation is conducted in open-loop and in closed-loop control system. Real-time implementation of a linear model predictive control is also studied. Rapid prototyping of such controller is developed using the available equipments and software tools. The study includes the tuning of the controller in a heuristic way and the strategy to combine two kinds of control algorithm in the control system. A simple set of guidelines for tuning the model predictive controller is proposed. Several important issues in the identification process and real-time implementation of model predictive control algorithm are also discussed. The proposed method has been successfully demonstrated on a pilot plant and a number of key results obtained in the development process are presented

Recursive subspace identification algorithm using the propagator based method

Subspace model identification (SMI) method is the effective method in identifying dynamic state space linear multivariable systems and it can be obtained directly from the input and output data. Basically, subspace identifications are based on algorithms from numerical algebras which are the QR decomposition and Singular Value Decomposition (SVD). In industrial applications, it is essential to have online recursive subspace algorithms for model identification where the parameters can vary in time. However, because of the SVD computational complexity that involved in the algorithm, the classical SMI algorithms are not suitable for online application. Hence, it is essential to discover the alternative algorithms in order to apply the concept of subspace identification recursively. In this paper, the recursive subspace identification algorithm based on the propagator method which avoids the SVD computation is proposed. The output from Numerical Subspace State Space System Identification (N4SID) and Multivariable Output Error State Space (MOESP) methods are also included in this paper

Application of a method to diagnose the source of performance degradation in MPC systems

Model Predictive Control systems may suffer from performance degradation mainly for two reasons: (i) external unmeasured disturbances are not estimated correctly, (ii) the (linear) dynamic model used by the MPC does not match (any longer) the actual process response. In this work we present the application of a method to detect when performance is not optimal, to diagnose the source of performance degradation and to propose appropriate corrections. In the simplest situation (i), optimal performance can be restored by recomputing the estimator parameters; in the other case (ii), re-identification becomes necessary. The method is based on analysis of the prediction error, i.e. the difference between the actual measured output and the corresponding model prediction, and uses three main tools: a statistical (whiteness) test on the prediction error sequence, a subspace identification method to detect the order of the input-to-prediction error system, and a nonlinear optimization algorithm to recompute optimal estimator parameters. We illustrate the effectiveness of the method on a large-scale rigorously simulated industrial process. Copyright © 2013, AIDIC Servizi S.r.l