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S.A.Dolenko 1 , A.V.Filippov 2 , A.F.Pal 3 , I.G.Persiantsev 1 , and A.O.Serov 3

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.

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S.A.Dolenko 1 , A.V.Filippov 2 , A.F.Pal 3 , I.G.Persiantsev 1 , and A.O.Serov 3

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  1. 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.

  2. Measured and calculated spectra of the vibrational band 0-1 of CO (B1A1) Angstrom system • Solid: measured • Dashed: calculated • Left: 5%CO+H2 • Right: 5%CO+4%Kr+H2

  3. 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

  4. Sample model spectra

  5. 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 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)

  6. 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

  7. 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

  8. Results without compression

  9. X1 X’1 X2 X’2 . . . . . . X1 X’1 XN X’N X2 X’2 . . . . . . XN X’N 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

  10. Best results with and without compression

  11. 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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