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Title:  Databased mathematical modeling: Development and application 
Author(s):  Banan, MahmoudReza 
Doctoral Committee Chair(s):  Hjelmstad, Keith D. 
Department / Program:  Civil Engineering 
Discipline:  Civil Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Statistics
Engineering, Civil Artificial Intelligence Computer Science 
Abstract:  This research study presents the mathematical basis for building the MCHARP dataprocessing environment. The MCHARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mappings. The constructed mapping can be modeled as a neural network. The HARP algorithm is based on a divideandconquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions, reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the constructed mapping. The tree structure of the HARP modules and the independence of both the subdomain approximations and the random partitions enable the MCHARP environment to quickly converge to a series of equally plausible solutions without user interaction. The MCHARP environment enjoys a largescale granularity produced by the Monte Carlo parallelism and the geometric parallelism achieved by partitioning the input space. Therefore this environment can exhibit good performance on parallel computers for large and complex scientific databases. The developed MCHARP philosophy for building databased approximate mappings leads to a novel model selection criterion and an original framework for classifying datafitting problems. The MCHARP environment not only can build approximate multivariate mappings with selforganization capability, noise and fault tolerance, adaptivity, generalization, highly plastic and stable learning characteristics with respect to the addition of new data points, and parallel structure but also can answer fundamental questions in databased mathematical modeling. These questions include: (1) What is the confidence level for each predicted output of the constructed model? (2) What is the approximation confidence measure for the constructed model? (3) How does the functional complexity of the actual multivariate mapping change over the input space? (4) What is the suitable structural complexity for a databased model using noisy data? (5) What is the level of noise in the data? (6) Is the amount of training data adequate? If not, which regions of the input space need more data? (7) Is the selected parametric model suitable? (8) What is the conditioning of a datafitting problem? (9) Is databased mathematical modeling promising for the given task? The developed MCHARP environment can support the diverse needs of the scientific and engineering community. It has the versatility to develop and verify parametric and nonparametric mathematical models and also global and local approximate mappings. Furthermore, It establishes an environment for unifying existing mathematical modeling techniques in statistics, approximation theory, information theory, system identification, and neural networks. 
Issue Date:  1995 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/22097 
Rights Information:  Copyright 1995 Banan, MohmoudReza 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9522079 
OCLC Identifier:  (UMI)AAI9522079 
This item appears in the following Collection(s)

Dissertations and Theses  Civil and Environmental Engineering

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois
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