281 research outputs found
Some Results on the Identification and Estimation of Vector ARMAX Processes
This paper addresses the problem of identifying echelon canonical forms for a vector autoregressive moving average model with exogenous variables using finite algorithms. For given values of the Kronecker indices a method for estimating the structural parameters of a model using ordinary least squares calculations is presented. These procedures give rise, rather naturally, to a technique for the determination of the structural indices based on the use of conventional model selection criteria. A detailed analysis of the statistical properties of the estimation and identification procedures is given and some evidence on the practical significance of the results obtained is also provided. Modifications designed to improve the performance of the methods are presented. Some discussion of the practical significance of the results obtained is also provided.ARMAX model, consistency, echelon canonical form, efficiency, estimation, identification, Kronecker invariants, least squares, selection criterion, structure determination, subspace algorithm.
Modeling and Prediction in Diabetes Physiology
Diabetes is a group of metabolic diseases characterized by the inability of the organism to autonomously regulate the blood glucose levels. It requires continuing medical care to prevent acute complications and to reduce the risk of long-term complications. Inadequate glucose control is associated with damage, dysfunction and failure of various organs. The management of the disease is non trivial and demanding. With today’s standards of current diabetes care, good glucose regulation needs constant attention and decision-making by the individuals with diabetes. Empowering the patients with a decision support system would, therefore, improve their quality of life without additional burdens nor replacing human expertise. This thesis investigates the use of data-driven techniques to the purpose of glucose metabolism modeling and short-term blood-glucose predictions in Type I Diabetes Mellitus (T1DM). The goal was to use models and predictors in an advisory tool able to produce personalized short-term blood glucose predictions and on-the-spot decision making concerning the most adequate choice of insulin delivery, meal intake and exercise, to help diabetic subjects maintaining glycemia as close to normal as possible. The approaches taken to describe the glucose metabolism were discrete-time and continuous-time models on input-output form and statespace form, while the blood glucose short-term predictors, i.e., up to 120 minutes ahead, used ARX-, ARMAX- and subspace-based prediction
Structural dynamics analysis in the presence of unmeasured excitations
Methods for comprehensive structural dynamic analysis generally employ input-output
modal analysis with a mathematical model of structural vibration using excitation and
response data. Recently operational modal analysis methods using only vibration
response data have been developed. In this thesis, both input-output and operational
modal analysis, in the presence of significant unmeasured excitations, is considered.
This situation arises when a test structure cannot be effectively isolated from ambient
excitations or where the operating environment imposes dynamically-important
boundary conditions.
The limitations of existing deterministic frequency-domain methods are assessed. A
novel time-domain estimation algorithm, based on the estimation of a discrete-time
autoregressive moving average with exogenous excitation (ARMAX) model, is
proposed. It includes a stochastic component to explicitly account for unmeasured
excitations and measurement noise. A criterion, based on the sign of modal damping, is
incorporated to distinguish vibration modes from spurious modes due to unmeasured
excitations and measurement noise, and to identify the most complete set of modal
parameters from a group of estimated models.
Numerical tests demonstrate that the proposed algorithm effectively identifies vibration
modes even with significant unmeasured random and periodic excitations. Random
noise is superimposed on response measurements in all tests. Simulated systems with
low modal damping, closely spaced modes and high modal damping are considered
independently. The accuracy of estimated modal parameters is good except for degreesof-
freedom with a low response level but this could be overcome by appropriate
placement of excitation and response measurement points.
These observations are reflected in experimental tests that include unmeasured periodic
excitations over 200% the level of measured excitations, unmeasured random
excitations at 90% the level of measured excitations, and the superposition of periodic
and random unmeasured excitations. Results indicate advantages of the proposed
algorithm over a deterministic frequency domain algorithm. Piezoceramic plates are
used for structural excitation in one experimental case and the limitations of distributed
excitation for broadband analysis are observed and characterised in terms of actuator
geometry and modal deformation.
The ARMAX algorithm is extended for use with response measurements exclusively.
Numerical and experimental tests demonstrate its performance using time series data
and correlation functions calculated from response measurements
Some results on the identification and estimation of vector ARMAX processes
This paper addresses the problem of identifying echelon canonical forms for a vector autoregressive moving average model with exogenous variables using finite algorithms. For given values of the Kronecker indices a method for estimating the structural parameters of a model using ordinary least squares calculations is presented. These procedures give rise, rather naturally, to a technique for the determination of the structural indices based on the use of conventional model selection criteria. A detailed analysis of the statistical properties of the estimation and identification procedures is given and some evidence on the practical significance of the results obtained is also provided. Modifications designed to improve the performance of the methods are presented. Some discussion of the practical significance of the results obtained is also provided
Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future
Regularization and Bayesian methods for system identification have been
repopularized in the recent years, and proved to be competitive w.r.t.
classical parametric approaches. In this paper we shall make an attempt to
illustrate how the use of regularization in system identification has evolved
over the years, starting from the early contributions both in the Automatic
Control as well as Econometrics and Statistics literature. In particular we
shall discuss some fundamental issues such as compound estimation problems and
exchangeability which play and important role in regularization and Bayesian
approaches, as also illustrated in early publications in Statistics. The
historical and foundational issues will be given more emphasis (and space), at
the expense of the more recent developments which are only briefly discussed.
The main reason for such a choice is that, while the recent literature is
readily available, and surveys have already been published on the subject, in
the author's opinion a clear link with past work had not been completely
clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual
Reviews in Contro
Modal identification using optimization approach.
In this thesis, the modal identification problem is pursued using two different optimization approaches. The first approach is a deterministic optimization approach that minimizes the output model error in the time domain between a direct solution using the modal model and the measured response. Examples of single-input single-output identification are used to illustrate this method; it has been shown this approach is robust against noise and can be used to fine-tune the modal parameter, especially for the damping. The second approach is based on probabilistic optimization; the objective function is defined as the a posteriori probabilistic density of the parameters given observations/measurements. The conditional probability density is computed using the Bayesian theory of minimum-mean-square-error estimation. Examples of single-output under ambient excitation are simulated to demonstrate this approach. This methodology allows one to obtain not only the estimated parameters in the form of probabilistic mean but also the uncertainties in the form of covariance. The optimization approaches works though the minimization of an objective function which can be calculated from given set of modal/model parameters. Since there is no gradient or Hessian available for the objective functions defined in this thesis, two direct optimization methods: Nelder-Mead simplex and the Genetic Algorithm are adopted to search the minimum of defined objective functions and thus find the structural parameters. (Abstract shortened by UMI.)Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .L52. Source: Masters Abstracts International, Volume: 44-03, page: 1437. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005
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
Training Echo State Networks with Regularization through Dimensionality Reduction
In this paper we introduce a new framework to train an Echo State Network to
predict real valued time-series. The method consists in projecting the output
of the internal layer of the network on a space with lower dimensionality,
before training the output layer to learn the target task. Notably, we enforce
a regularization constraint that leads to better generalization capabilities.
We evaluate the performances of our approach on several benchmark tests, using
different techniques to train the readout of the network, achieving superior
predictive performance when using the proposed framework. Finally, we provide
an insight on the effectiveness of the implemented mechanics through a
visualization of the trajectory in the phase space and relying on the
methodologies of nonlinear time-series analysis. By applying our method on well
known chaotic systems, we provide evidence that the lower dimensional embedding
retains the dynamical properties of the underlying system better than the
full-dimensional internal states of the network
A review of modeling approaches in activated sludge systems
The feasibility of using models to understand processes, predict and/or simulate, control, monitor and optimize WasteWater Treatment Plants (WWTPs) has been explored by a number of researchers. Mathematical modeling provides a powerful tool for design, operational assistance, forecast future behavior and control. A good model not only elucidates a better understanding of the complicated biological and chemical fundamentals but is also essential for process design, process start-up, dynamics predictions, process control and process optimization. This paper reviews developments and the application of different modeling approaches to wastewater treatment plants, especially activated sludge systems and processes therein in the last decade. In addition, we present an opinion on the wider wastewater treatment related research issues that need to be addressed through modeling.Key words: Mathematical modeling, water, wastewater, wastewater treatment plants, activated sludge systems
Linear System Identification - A Survey
In this paper we give an introductory survey on the theory of identification of (in general MIMO) linear systems from (discrete) time series data. The main parts are: Structure theory for linear systems, asymptotic properties of maximum likelihood type estimators, estimation of the dynamic specification by methods based on information criteria and finally, extensions and alternative approaches such as identification of unstable systems and errors-in-variables
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