Machine learning applied to retrieval of temperature and concentration distributions from infrared emission measurements

Abstract

Inversion of temperature and species concentration distributions from radiometric measurements involves solving nonlinear, ill-posed and high-dimensional problems. Machine Learning approaches allow solving such highly nonlinear problems, offering an alternative way to deal with complex and dynamic systems with good flexibility. In this study, we present a machine learning approach for retrieving temperatures and species concentrations from spectral infrared emission measurements in combustion systems. The training spectra for the machine learning model were synthesized through calculations from HITEMP 2010 for gas mixtures of CO 2 , H 2 O, and CO. The method was tested for different line-of-sight temperature and concentration distributions, different gas path lengths and different spectral intervals. Experimental validation was carried out by measuring spectral emission from a Hencken flat flame burner with a Fourier-transform infrared spectrometer with different spectral resolutions. The temperature fields above the burner for combustion with equivalence ratios of φ =1, φ = 0.8, and φ = 1.4 were retrieved and were in excellent agreement with temperatures deduced from Rayleigh scattering thermometry. performed to address the inverse radiation problems using gradient-based [14] optimization methods. Griffith et al. [15,16] were the first to recognize that measurements of the transmissivity or emissivity of rotational spectral lines of a gas can reveal its temperature. In order to extract temperature, a nonlinear least-square method was used to fit the integrated transmissivity minima. Best et al. [17,18] combined tomography and Fourier transform infrared (FTIR) spectrometer transmission and emission spectra to extract temperature, concentration and soot volume fraction fields. By measuring spectral intensity of the CO 2 4.3 µm band, temperature profiles were retrieved in a number of ways [19,20]. At their time these results were not accurate enough due to lack of an accurate radiation prediction model and robust inverse algorithms. Song et al. [21,22] developed a spectral remote sensing technique to reconstruct CO 2 temperature profiles based on radiative intensity measurements. An accurate narrow band radiation model was employed and several Newton-type regression methods were tested. Due to the nonlinearity and ill-posedness of the problem, regularization of the inverse problems was applied to enforce some degree of smoothness to the solution. It is always difficult to select an appropriate regularization parameter and empirical values for the regularization parameter were employed. Ren and Modest [23] applied the Levenberg-Marquardt optimization method with Tikhonov regularization to reconstruct CO 2 temperature profiles and average concentrations from synthetic line-of-sight spectral intensity data. Two types of temperature profiles were tested for different gas path lengths and different CO 2 spectral bands. A new regularization selection method based on the combination of the L-curve criterion and the discre...

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