Data-Based Mathematical Modeling: Development and Application, or How to Build a Mapping Neural Network

Banan, Mahmoud-Reza; Hjelmstad, K.D.

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https://hdl.handle.net/2142/14211 Copy

Description

Title

Data-Based Mathematical Modeling: Development and Application, or How to Build a Mapping Neural Network

Author(s)

• Banan, Mahmoud-Reza
• Hjelmstad, K.D.

Issue Date

1994-04

Keyword(s)

• Neural networks
• Fuzzy subsets
• Mathematical modeling

Abstract

This report presents a general method for developing data-based mathematical models for complex problems with large data bases. The method uses the Monte Carlo method in conjunction with a hierarchical adaptive random partitioning scheme with fuzzy sub domains (Me-HARP). Me-HARP provides an environment for simultaneously building and training a mapping neural network. The method is self-organizing and can operate with minimal external adjustment. It can interactively accept knowledge and provide guidance for efficiently improving the model and the data base. The Me-HARP environment enjoys a large-scale granularity produced by the Monte Carlo parallelism and the geometric parallelism achieved by partitioning the input space. We study the performance of the Me-HARP method by applying it to an experimental data base on pavement performance under a variety of environmental and traffic conditions. Numerical simulations are used throughout the report to demonstrate that the method is able to deal with high-dimensional, noisy, non-homogeneous data. The Me-HARP method leads to a novel model selection criterion and an original framework for classifying data-fitting problems, and can be used to answer fundamental questions in data-based mathematical modeling. These questions include: What is the confidence level in the constructed model and the data base? What is the optimal functional structure of the model for noisy data? How appropriate is a particular parametric model for the given data? The Me-HARP method established an environment for unifying existing mathematical modeling techniques in statistics, approximation theory, information theory, system identification, and neural networks.

Publisher

University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-Champaign.

Series/Report Name or Number

Civil Engineering Studies SRS-590

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/14211

Sponsor(s)/Grant Number(s)

• National Science Foundation Grant CES 86-58019
• Army Research Office Contracts DAAL-03-87-K-006, DAAL-03-86-G-0186, and DAAL-03-86-0188

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