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Optimization of Time Series Using Parallel, Adaptive, and Neural Techniques
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In this work we present an adaptive parallel methodology to optimize the identification of time series through parametric
models, applying it to the case of sunspot series. We employ high precision computation of system identification algorithms,
and use recursive least squares processing and ARMAX (Autoregressive Moving Average Extensive) parametric modelling. This
methodology could be very useful when the high precision mathematical modelling of dynamic complex systems is required. After
explaining the proposed heuristics and the tuning of its parameters, we show the results we have found for several solar series
using different implementations. Thus, we demonstrate how the result precision improves.
There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom
in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given
function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization
of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and
provides an unfamiliar perspective on traditional optimization problems and methods.
Two MATLAB packages have been implemented: the Neural Network Based System Identification toolbox (NNSYSID) and the Neural Network Based Control System Design Toolkit (NNCTRL). The NNSYSID toolbox has been developed to assist identification of nonlinear dynamic systems and it offers the possibility to work with a number of different nonlinear model structures based on neural networks. The NNCTRL toolkit is an add-on to the NNSYSID toolbox and contains tools for design and simulation of control systems based on neural networks. This paper gives an overview of the contents of NNSYSID and NNCTRL.
Since January 1981, the Royal Observatory of Belgium (ROB) has operated the Sunspot Index Data Center (SIDC), the World Data
Center for the Sunspot Index. From 2000, the SIDC obtained the status of Regional Warning Center (RWC) of the International
Space Environment Service (ISES) and became the “Solar Influences Data analysis Center”. As a data analysis service of the
Federation of Astronomical and Geophysical data analysis Services (FAGS), the SIDC collects monthly observations from worldwide
stations in order to calculate the International Sunspot Number, R
i
. The center broadcasts the daily, monthly, yearly sunspot numbers, with middle-range predictions (up to 12 months). Since
August 1992, hemispheric sunspot numbers are also provided.
The sections in this article are1The Problem2Background and Literature3Outline4Displaying the Basic Ideas: Arx Models and the Linear Least Squares Method5Model Structures I: Linear Models6Model Structures Ii: Nonlinear Black-Box Models7General Parameter Estimation Techniques8Special Estimation Techniques for Linear Black-Box Models9Data Quality10Model Validation and Model Selection11Back to Data: The Practical Side of Identification
In this work1 we present the use of neural networks to implement processing units of a parallel adaptative algorithm for high precision
system identification. The proposed algorithm uses recursive least squares processing and ARMAX modeling. After explaining
the algorithm and the tunning of its parameters, we show the system identification for four benchmarks with different implementations
of this algorithm, demonstrating how neural networks improve the result precision.
MoorA database for identification of systems
- I Markovsky
- J Willems