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基于模糊规则的模型优化方法.doc
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Evolving Fuzzy Rule-Based Models
Plamen Angelov
Civil and Building Engineering Department, Loughborough University,
Ashby Road, Loughborough LE11 3TU, Leicestershire, UK
tel: +44 (1509) 222 609 fax: +44 (1509) 223 981 e-mail: P.P.Angelov@Lboro.ac.UK
Abstract
An approach to auto-generation of fuzzy
rule-based models is proposed in the paper. Its
main advantage is the high flexibility: no a priory
information about the model structure is
necessary. A new efficient coding procedure is
proposed instead of usually used coding of all
possible fuzzy rules into a chromosome.
Parameter and structure identifications are
realized by optimization at two stages. First, the
best k rules are determined such that to minimize
the root square error. At the second stage, GA
tunes parameters of the membership functions
and singletons.
Software, which realizes the approach in the
framework of Matlab� v.5.2, is designed.
Modeling of thermal load of a building is
considered in order to illustrate the applicability
of the approach.
.
1. Introduction
The so-called classical models (which are
usually based on differential equations, mass-
balance principles and neglect qualitative and
subjective information) are in many cases
insufficient or practically difficult to be used [1].
In the last decade fuzzy models have been
widely used in different fields like economy,
biotechnology, civil engineering etc. They have a
very important advantage in comparison with
neural-network-based models, which also have
been intensively developed, that they are
interpretable, i.e. that they content expressible
knowledge about the object of modeling.
Although the identification criterion (minimal
root square error between the target and predicted
outputs) is the same, the design of fuzzy models is
different from the design of conventional models
[1]: determination of fuzzy rules as well as of
membership functions of fuzzy sets is based,
usually, on subjective estimations. In many cases it
is a complex and ambiguous process.
In the last few years the methods for fuzzy
membership functions tuning, adjustment, learning,
and rule extraction [2-13] has been intensively
developed. A part of them [3,5-6,9], however, treat
parameter identification only (parameters of
membership functions). Some of others [2,7]
consider minimization of an exhausted rule-base by
GA. The length of the chromosome there is
determined, however, on the base of all possible
combinations of linguistic variables. This is not
effective and could become unnecessarily complex.
In this paper a two-stage identification
procedure is proposed which uses significantly
smaller chromosome and allows to increase the
number of fuzzy rules used stage-by-stage. Thus
the minimal number of fuzzy rules could be
determined which describe the process at a pre-
defined level of precision. This approach is very
flexible: no a priory information about the model
structure is necessary. The knowledge extracted
from the data is fully interpretable and could help
for better understanding of the intimate nature of
the process modeled. In the same time, the expert
could add his own knowledge or to suppress some
of them either at the initialization either during the
modeling process.
Modeling of heat load of a building is
considered as a matter of illustration. Software,
which realizes the approach in the framework of
Matlab� v.5.2, is designed.
2. Fuzzy rule-based model
Fuzzy 'IF-THEN' models of the following type are
considered:
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