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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.Dolenko 1, A.V.Filippov 2, A.F.Pal 3, I.G.Persiantsev 1, and A.O.Serov 3 1 SINP MSU, Computer Lab. 2 Troitsk Institute of Innovation and Fusion Research 3 SINP MSU, Microelectronics Dept.

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Measured and calculated spectra of the vibrational band 0-1 of CO (B 1 A 1 ) Angstrom system Solid: measured Dashed: calculated Left: 5%CO+H 2 Right: 5%CO+4%Kr+H 2

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Spectra modeling I nvJ nvJ = const. ( JJ ) 4. S e q vv S JJ exp( hcF(J) kT) JJ is the wave number of rovibronic transition nvJ nvJ, n denotes the electronic state, vJ and vJ are vibrational and rotational quantum numbers of upper n and lower n electronic states, S e is the electronic moment of the transition, q vv is the Franck-Condon factor, S JJ 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

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Sample model spectra

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Data preparation and design of ANN and GMDH algorithm 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 5 th ), 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)

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Architectures used without compression 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

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Performance estimators Standard deviation (SD), square root of the mean squared error, in degrees Kelvin (K): SD = Mean absolute error (MAE), in degrees Kelvin (K): MAE = T – actual value, – predicted value

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Results without compression Data setSD, K MLP SD, K GRNN SD, K GMDH MAE, K MLP MAE, K GRNN MAE, K GMDH TRN4.1157.80.052.889.80.04 TST4.2158.10.032.889.30.02 PRO4.0157.90.062.889.80.05 PE1246.0157.69.2181.192.36.5 PM1276.2–18.0200.0–14.3 PE3287.4159.539.2225.6102.428.3 PM3312.6–115.0243.8–92.3 PE5349.6162.779.9281.4112.757.3 PM5402.8–291.8319.2–232.1 PE10–179.3225.4–141.3162.0 PM10––––––

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Data compression using NN-based auto-associative memory Linear PCA – 3-layer perceptron Non-linear PCA – 5-layer perceptron 8-10 neurons in the bottleneck X1X1 X2X2 XNXN... X 1 X 2 X N... X1X1 X2X2 XNXN... X 1 X 2 X N...

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Best results with and without compression Data setSD, 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 TRN0.050.890.700.040.740.54 TST0.030.850.720.020.670.56 PRO0.060.860.670.050.710.53 PE19.22.52.46.51.8 PM118.03.53.414.32.72.6 PE339.26.8 28.34.95.0 PM3115.010.410.292.37.8 PE579.911.611.857.38.48.7 PM5291.817.216.9232.112.9 PE10225.422.122.8162.015.917.1 PM10–34.434.3–25.826.1

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Conclusions 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

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