Download Use of Neural Network Based Auto

Use of Neural Network Based
Auto-Associative Memory as a Data Compressor
for Pre-Processing Optical Emission Spectra
in Gas Thermometry
with the Help of Neural Network
S.A.Dolenko1,
A.V.Filippov2, A.F.Pal3,
I.G.Persiantsev1, and
A.O.Serov3
1SINP
MSU, Computer Lab.
2Troitsk Institute of Innovation and
Fusion Research
3SINP MSU, Microelectronics Dept.
Measured and calculated spectra
of the vibrational band 0-1
of CO (B1A1) Angstrom system
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Solid: measured
Dashed: calculated
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Left: 5%CO+H2
Right: 5%CO+4%Kr+H2
Spectra modeling
In’v’J’n”v”J” = const.(J’J”)4.Seqv’v”SJ’J” exp(hcF’(J’)kT)
J’J” is the wave number of rovibronic transition n’v’J’n”v”J”,
n denotes the electronic state,
v’J’ and v”J” are vibrational and rotational quantum numbers of
upper n’ and lower n” electronic states,
Se is the electronic moment of the transition,
qv’v” is the Franck-Condon factor,
SJ’J” is the Honl-London factor,
F’(J’) is the rotational energy of the upper state in cm-1.
0.125 A/step, 1000 steps, 125 A total range.
Convolution with real apparatus function
Sample model spectra
Data preparation
and design of ANN and GMDH algorithm
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Temperature range: 500 - 2500 K
Apparatus function: trapeziform, 5 - 1 - 5 A
Averaging: over 5 points
Number of inputs: 200
Number of patterns: 200 (510…2500 K with 10 K step),
40 in test set (each 5th), 160 in training set
Main production set: 200 patterns (505…2495 step 10 K)
Additional production sets with noise: 1%, 3%, 5%, 10%
Noise calculated:
a) as a fraction of total spectrum intensity (PE)
b) as a fraction of spectrum intensity in each point (PM)
Architectures used without compression
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3-layer perceptron backpropagation network
with standard connections - 16 hidden neurons,
logistic activation function in the hidden layer,
linear in the output layer, =0.01, =0.9.
General Regression Neural Network (GRNN),
with iterative search of the smoothing factor.
Group Method of Data Handling (GMDH) –
full cubic polynoms within each layer,
Regularity criterion,
Extended linear models included
Performance estimators
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Standard deviation (SD), square root of the mean
squared error, in degrees Kelvin (K):
SD =

1
N
~ 2
 (T  T )
Mean absolute error (MAE), in degrees Kelvin (K):
MAE =
1
~
|
T

T
|

N
~
T – actual value, T – predicted value
Results without compression
Data set
SD, K
MLP
SD, K
GRNN
SD, K
GMDH
MAE, K
MLP
MAE, K
GRNN
MAE, K
GMDH
TRN
4.1
157.8
0.05
2.8
89.8
0.04
TST
4.2
158.1
0.03
2.8
89.3
0.02
PRO
4.0
157.9
0.06
2.8
89.8
0.05
PE1
246.0
157.6
9.2
181.1
92.3
6.5
PM1
276.2
–
18.0
200.0
–
14.3
PE3
287.4
159.5
39.2
225.6
102.4
28.3
PM3
312.6
–
115.0
243.8
–
92.3
PE5
349.6
162.7
79.9
281.4
112.7
57.3
PM5
402.8
–
291.8
319.2
–
232.1
PE10
–
179.3
225.4
–
141.3
162.0
PM10
–
–
–
–
–
–
Data compression
using NN-based auto-associative memory
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Linear PCA – 3-layer perceptron
X1
X2
..
.
XN
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Non-linear PCA – 5-layer perceptron
X1
X2
..
.
XN
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X’1
X’ 2
..
.
X’N
X’1
X’2
..
.
X’N
8-10 neurons in the bottleneck
Best results with and without compression
Data set
SD, K
w/o cmp
SD, K
lin cmp
SD, K
nln cmp
MAE, K
w/o cmp
MAE, K
lin cmp
MAE, K
nln cmp
TRN
0.05
0.89
0.70
0.04
0.74
0.54
TST
0.03
0.85
0.72
0.02
0.67
0.56
PRO
0.06
0.86
0.67
0.05
0.71
0.53
PE1
9.2
2.5
2.4
6.5
1.8
1.8
PM1
18.0
3.5
3.4
14.3
2.7
2.6
PE3
39.2
6.8
6.8
28.3
4.9
5.0
PM3
115.0
10.4
10.2
92.3
7.8
7.8
PE5
79.9
11.6
11.8
57.3
8.4
8.7
PM5
291.8
17.2
16.9
232.1
12.9
12.9
PE10
225.4
22.1
22.8
162.0
15.9
17.1
PM10
–
34.4
34.3
–
25.8
26.1
Conclusions
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ANN can solve the inverse problem of plasma
thermometry with sufficient precision
(<35 K at 10% multiplicative noise)
These results can be achieved only with data
compression
Compression with non-linear PCA gives no
advantage compared to that with linear PCA for
this problem