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   -> Volume 5, Issue 10


Preprint: Preprints form Bao Liu on Basis Selection
 
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Liu Bao (matliub@leonis.nus.sg)
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PostPosted: Tue Dec 03, 1996 5:16 pm    
Subject: Preprint: Preprints form Bao Liu on Basis Selection
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#8 Preprint: Preprints form Bao Liu on Basis Selection

1.

Title: On the Optimal Selection of Task Dependent Wavelet Packet Basis
with Genetic Algorithms

Authors: Bao Liu, Department of Mathematics, NUS, Singapore 119260
Shih-Fu Ling, School of MPE, NTU, Singapore 639798

Abstract: A genetic algorithm for the optimal selection of various
task dependent wavelet packet bases is proposed. We introduce a
transform operator to convert the hard combinatorial selection problem
to a continuous numerical optimization problem. Each individual in a
population is transformed to a corresponding basis, e.g., its best
basis. The 'fitness' of each corresponding basis is then evaluated
with the objective function of the task. According to the fitness of
the individuals, parents are selected from this population to produce
the children that constitute the next generation by using
reproduction, crossover and mutation operators. This algorithm offers
a great deal of flexibility for the optimal selection of both complete
and incomplete (without pruning) bases in terms of different fitness
criteria for different tasks and does not need an additive cost
function. The performance of this algorithm has been tested with good
results on practical machinery diagnosis problems.

2.

Title: Tree Structured Local Basis Selection Using Genetic Algorithms

Authors: Bao Liu, Department of Mathematics, NUS, Singapore 119260
Shih-Fu Ling, School of MPE, NTU, Singapore 639798

Abstract: A genetic algorithm for the optimal selection of tree structured
local bases for various tasks is proposed. We introduce a transform
operator to convert the hard combinatorial selection problem to a
continuous numerical optimization problem. Each individual in a population
is transformed to a corresponding basis, e.g., its best basis. The
'fitness' of each corresponding basis to a given task is then evaluated
with the task objective function. According to the fitness of the
individuals, parents are selected from this population to produce the
children that constitute the next generation by using reproduction,
crossover and mutation operators. This algorithm offers a great deal of
flexibility for the optimal selection of both complete and incomplete
(without pruning) bases in terms of different fitness criteria for
different tasks and does not need an additive cost function. The
performance of this algorithm has been tested with good results on
practical machinery diagnosis problems.

Keywords: wavelet packets, local trigonometric transforms, orthonormal
basis construction, genetic algorithms

3.

Title: On the Selection of Informative Wavelets for Machinery Diagnosis

Authors: Bao Liu, Department of Mathematics, NUS, Singapore 119260
Shih-Fu Ling, School of MPE, NTU, Singapore 639798

Abstract: An application of wavelet analysis to machinery fault
diagnosis is presented. We introduce an extension to Mallat and
Zhang's matching pursuit for signal classification problems. Instead
of the 'best matching' criterion, a mutual information measure is used
to search a wavelet library for the set of wavelets that carry
meaningful information about class differences. With these informative
wavelets treated as feature extractors, this approach effectively
facilitates the diagnosis of machinery faults of a non-stationary
nature. We have applied this approach to the detection of diesel
engine malfunctions. The results show that both the sensitivity and
the reliability of this approach are good. Besides machinery fault
diagnosis, this approach can also be applied to other signal
classification tasks, such as speech recognition, etc.. In addition,
it can also be used to initialize the parameters of wavelet networks.

For Postscript format copy, E-mail a request to

Liu Bao
lb@haar.math.nus.sg
All times are GMT + 1 Hour
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