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

Tao Ren, Michael F. Modest, Alexander Fateev, Gavin Sutton, Weijie Zhao, Florin Rusu
2019 Applied Energy  
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
more » ... stems. 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 discrepancy principle was proposed and shows good generality for different temperature profile inversions. However, the accuracy of retrieved temperatures are highly dependent on initial guesses and "measurement" noise level. The optical diagnostics described so far all deal with a single line-of-sight measurement. Researchers attempted to relax this restriction and focused on axisymmetric flames [24, 25] , in which optical data were collected at uniformly-spaced, parallel lines-of-sight. These data are related to an unknown radial distribution. The most common approach used to deconvolve axisymmetric flames in the combustion literature is the Abel three-point inversion [26] , which works by smoothing data in the axial direction but does not treat the underlying ill-posedness of Abel's equation directly, thereby limiting the accuracy and stability of the solution. Liu et al. [27] reported 2-D measurements of temperature and CO 2 concentration profiles of a laminar co-flow sooting flame obtained by line-of-sight high-resolution absorption spectroscopy with Tikhonov regularization and assuming the co-flow flame to be axisymmetric. Multiline measurements were performed to reconstruct 2-D temperature and species concentration fields. Deconvolution of line-of-sight data from nonaxisymmetric flames requires more elaborate tomography algorithms, which are either based on Fourier transforms, or algebraic reconstruction [28] . Most recently, hyperspectral imaging devices [29] have been applied to combustion diagnostics [30, 31] . Hyperspectral imaging is a promising technology, which contains a two-dimensional array of pixels and each pixel of the spectrometer measures radiation at a large number of continuous wavenumbers along multiple linesof-sight, providing spatially and spectrally resolved radiation images. However, due to lack of advanced 3-D tomographic algorithms, only 2-D combustion fields were reconstructed with path-averaged scalar fields in these studies [12, 30] . A widely used method for 3-D measurements (reconstructions) is computed tomography (CT) [28] . By simultaneously measuring the target at different angles and directions through low-dimensional sensors, high-dimensional flow fields can be reconstructed through inversion algorithms [32] . Such CT method requires multiple detectors installed at different angles and positions. The newly developed light field camera technology [33] is another way to achieve 3-D flame measurements. Light field cameras add a series of micro-lenses in front of the sensor, which are able to capture both intensity and direction of emitted light. Compared to CT, the light field camera approach reduces the complexity of the measurement system and eliminates the use of multiple detectors. However, the application of a light field camera only reduces the measurement complexity, reconstruction algorithms
doi:10.1016/j.apenergy.2019.113448 fatcat:772lipim5redvjhvrdniwyrfqe