joshi@wuche2.wustl.edu (Amol Joshi) (04/30/91)
The following tech report is available. This work was presented
at the AIChE Spring Meeting, April 1991, Houston, TX. The
departmental policy requires that requests for the tech report
be official (e.g. on the company letterhead). The cost of
the tech report is US$5.00 (check payable to `Department
of Chemical Engineering').
A. Joshi
(ps: We would like to express our gratitude to *Prof. Eugene Norris* of
West Virginia U. whose backprop simulator, BPS, was used in this work.)
___________________________________________________________________
Process Trend Analysis Using
the Frazier-Jawerth Transform
and Neural Networks
A. Joshi and R. Motard
Department of Chemical Engineering
Washington University in St. Louis
St. Louis, MO 63130.
Keywords:
abnormality detection, multiresolution descriptions,
pattern recognition, signal interpretation,
time-frequency analysis
ABSTRACT
This work employs a novel signal processing technique, the
Frazier-Jawerth transform (FJT) [1,2], in conjunction with
an artificial feedforward neural network (FFN) to detect trends
in process operational data. Two trained neural networks
are employed --- one to assign a qualitative descriptive term
to each signal and the other to detect process abnormalities
by associating patterns among multiple signals. These tasks are
critical to many applications of the AI technology to process
control.
A time-domain description obscures frequency characteristics
of a signal whereas the information about its evolution in
time is hidden in its Fourier domain representation.
FJT coefficients provide a *joint* time-frequency description
and thus make both time and frequency domain features in signals
explicit. The paper argues that generating concise, explicit
input data representations is an important step in improving
the generalization properties of FFNs. Less importantly, the
convergence properties of the FFNs are also improved.
In this work, transformed signals are fed to a trained FFN
that employs the conventional back-propagation algorithm.
The FJT is closely related to the wavelet transform
which is receiving much attention in the engineering community
lately [3]. The advantage of using the FJT is that it is rather
easy to construct the FJ analyzing functions such that they
have small essential supports in both time and frequency
domains. FJT can be used on-line and yields *multiresolution*
descriptions [4]. An appropriate resolution can then be
chosen to examine the trends. This is crucial in situations
where signals have different characteristic time constants
(e.g. signals from distillation columns). The FJT and neural nets
together provide a promising paradigm for extracting information
from sensor data for on-line applications.
REFERENCES:
[1] Frazier, M. and Jawerth, B., "Decomposition of Besov
Spaces," Indiana U. Math J., Volume 34, No. 3,
pp. 777-799, 1985.
[2] Kumar, A., Fuhrmann, D., Frazier, M. and Jawerth, B.,
"A New Transform for Time-Frequency Analysis,"
submitted to IEEE Trans. Acoustics, Speech, and Signal
Processing.
[3] "A New Wave in Applied Mathematics," Science, Volume 249,
pp. 858-859, August 1990.
[4] Joshi, A., Kumar, A. and Motard, R.,"The Frazier-Jawerth
Transform and its On-line Implementation," submitted to
Computers and Chemical Engineering.
--
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Amol Joshi | joshi@wuche2.wustl.edu
Department of Chemical Engineering |
Washington University in St. Louis.|enorris@gmuvax2.gmu.edu (Gene Norris) (05/01/91)
In article <1991Apr29.201633.13203@wuche2.wustl.edu> joshi@wuche2.wustl.edu (Amol Joshi) writes: > > >(ps: We would like to express our gratitude to *Prof. Eugene Norris* of >West Virginia U. whose backprop simulator, BPS, was used in this work.) Reports concerning Prof Norris' affiliation with West Virginia University are somewhat obsolete. Though he was a member of the WVU faculty from 1969 until 1972, he has been at George Mason University since 1980. Bps is available via ftp from gmuvax2.gmu.edu (129.174.1.8). Connect via anonymous ftp, cd to nn, read and take what you find. Executables for SUN 3, Sparc 1.0, MS-DOS, Ultrix, and Macintosh (old version) are there. Source licenses are available from the undersigned, who should be contacted for details. Prof. Eugene M. Norris CS Dept George Mason University Fairfax, VA 22032 (703)323-2713 enorris@gmuvax2.gmu.edu FAX: 703 323 2630