Data-based mechanistic modelling, forecasting, and control.

This article briefly reviews the main aspects of the generic data based mechanistic (DBM) approach to modeling stochastic dynamic systems and shown how it is being applied to the analysis, forecasting, and control of environmental and agricultural systems. The advantages of this inductive approach to modeling lie in its wide range of applicability. It can be used to model linear, nonstationary, and nonlinear stochastic systems, and its exploitation of recursive estimation means that the modeling results are useful for both online and offline applications. To demonstrate the practical utility of the various methodological tools that underpin the DBM approach, the article also outlines several typical, practical examples in the area of environmental and agricultural systems analysis, where DBM models have formed the basis for simulation model reduction, control system design, and forecastin

Numerical Analysis

Acknowledgements: This article will appear in the forthcoming Princeton Companion to Mathematics, edited by Timothy Gowers with June Barrow-Green, to be published by Princeton University Press.\ud \ud In preparing this essay I have benefitted from the advice of many colleagues who corrected a number of errors of fact and emphasis. I have not always followed their advice, however, preferring as one friend put it, to "put my head above the parapet". So I must take full responsibility for errors and omissions here.\ud \ud With thanks to: Aurelio Arranz, Alexander Barnett, Carl de Boor, David Bindel, Jean-Marc Blanc, Mike Bochev, Folkmar Bornemann, Richard Brent, Martin Campbell-Kelly, Sam Clark, Tim Davis, Iain Duff, Stan Eisenstat, Don Estep, Janice Giudice, Gene Golub, Nick Gould, Tim Gowers, Anne Greenbaum, Leslie Greengard, Martin Gutknecht, Raphael Hauser, Des Higham, Nick Higham, Ilse Ipsen, Arieh Iserles, David Kincaid, Louis Komzsik, David Knezevic, Dirk Laurie, Randy LeVeque, Bill Morton, John C Nash, Michael Overton, Yoshio Oyanagi, Beresford Parlett, Linda Petzold, Bill Phillips, Mike Powell, Alex Prideaux, Siegfried Rump, Thomas Schmelzer, Thomas Sonar, Hans Stetter, Gil Strang, Endre Süli, Defeng Sun, Mike Sussman, Daniel Szyld, Garry Tee, Dmitry Vasilyev, Andy Wathen, Margaret Wright and Steve Wright

Development of advanced techniques for rotorcraft state estimation and parameter identification

An integrated methodology for rotorcraft system identification consists of rotorcraft mathematical modeling, three distinct data processing steps, and a technique for designing inputs to improve the identifiability of the data. These elements are as follows: (1) a Kalman filter smoother algorithm which estimates states and sensor errors from error corrupted data. Gust time histories and statistics may also be estimated; (2) a model structure estimation algorithm for isolating a model which adequately explains the data; (3) a maximum likelihood algorithm for estimating the parameters and estimates for the variance of these estimates; and (4) an input design algorithm, based on a maximum likelihood approach, which provides inputs to improve the accuracy of parameter estimates. Each step is discussed with examples to both flight and simulated data cases

Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV

Markov-Switching MIDAS Models

This paper introduces a new regression model - Markov-switching mixed data sampling (MS-MIDAS) - that incorporates regime changes in the parameters of the mixed data sampling (MIDAS) models and allows for the use of mixed-frequency data in Markov-switching models. After a discussion of estimation and inference for MS-MIDAS, and a small sample simulation based evaluation, the MS-MIDAS model is applied to the prediction of the US and UK economic activity, in terms both of quantitative forecasts of the aggregate economic activity and of the prediction of the business cycle regimes. Both simulation and empirical results indicate that MSMIDAS is a very useful specification.Business cycle, Mixed-frequency data, Non-linear models, Forecasting, Nowcasting

Satellite Data and Supervised Learning to Prevent Impact of Drought on Crop Production: Meteorological Drought

Reiterated and extreme weather events pose challenges for the agricultural sector. The convergence of remote sensing and supervised learning (SL) can generate solutions for the problems arising from climate change. SL methods build from a training set a function that maps a set of variables to an output. This function can be used to predict new examples. Because they are nonparametric, these methods can mine large quantities of satellite data to capture the relationship between climate variables and crops, or successfully replace autoregressive integrated moving average (ARIMA) models to forecast the weather. Agricultural indices (AIs) reflecting the soil water conditions that influence crop conditions are costly to monitor in terms of time and resources. So, under certain circumstances, meteorological indices can be used as substitutes for AIs. We discuss meteorological indexes and review SL approaches that are suitable for predicting drought based on historical satellite data. We also include some illustrative case studies. Finally, we will survey rainfall products existing at the web and some alternatives to process the data: from high-performance computing systems able to process terabyte-scale datasets to open source software enabling the use of personal computers

Development of Adaptive and Factorized Neural Models for MPC of Industrial Systems

Many industrial processes have non-linear and time-varying dynamics, for which the control and optimization require further investigations. Adaptive modelling techniques using radial basis function (RBF) networks often provide competitive modelling performances but encounter slow recovery speed when processes operating regions are shifted largely. In addition, RBF networks based model predictive control results as a non-linear programming problem, which restricts the application to fast dynamic systems. To these targets, the thesis presents the development of adaptive and factorized RBF network models. Model predictive control (MPC) based on the factorized RBF model is applied to a non-linear proton exchange membrane fuel cell (PEMFC) stack system. The main contents include three parts: RBF model adaptation; model factorization and fast long-range prediction; and MPC for the PEMFC stack system. The adaptive RBF model employs the recursive orthogonal least squares (ROLS) algorithm for both structure and parameter adaptation. In decomposing the regression matrix of the RBF model, the R matrix is obtained. Principles for adding centres and pruning centres are developed based on the manipulation of the R matrix. While the modelling accuracy is remained, the developed structure adaptation algorithm ensures the model size to be kept to the minimum. At the same time, the RBF model parameters are optimized in terms of minimum Frobenius norm of the model prediction error. A simulation example is used to evaluate the developed adaptive RBF model, and the model performance in output prediction is superior over the existing methods. Considering that a model with fast long-range prediction is needed for the MPC of fast dynamic systems, a f-step factorization algorithm is developed for the RBF model. The model structure is re-arranged so that the unknown future process outputs are not required for output prediction. Therefore, the accumulative error caused by recursive calculation in normal neural network model is avoided. Furthermore, as the information for output prediction is explicitly divided into the past information and the future information, the optimization of the control variable in the MPC based on this developed factorized model can be solved much faster than the normal NARX-RBF model. The developed model adaptation algorithm can be applied to this f-step factorized model to achieve fast and adaptive model prediction. Finally, the developed factorized RBF model is applied to the MPC of a PEMFC stack system with a popular industrial benchmark model in Simulink developed at Michigan University. The optimization algorithms for quadratic and non-linear system without and with constraints are presented and discussed for application purpose in the NMPC. Simulation results confirm the effectiveness of the developed model in both smooth tracking performance and less optimization time used. Conclusions and further work are given at the end of the thesis. Major contributions of the research have been outlined and achievements are checked against the objectives assigned. Further work is also suggested to extend the developed work to industrial applications in real-time simulation. This is to further examine the effectiveness of developed models. Extensive investigations are also recommended on the optimization problems to improve the existing algorithms