Hierarchical temperature imaging using pseudoinversed convolutional neural network aided TDLAS tomography

As an in situ combustion diagnostic tool, Tunable Diode Laser Absorption Spectroscopy (TDLAS) tomography has been widely used for imaging of two-dimensional temperature distributions in reactive flows. Compared with the computational tomographic algorithms, Convolutional Neural Networks (CNNs) have been proofed to be more robust and accurate for image reconstruction, particularly in case of limited access of laser beams in the Region of Interest (RoI). In practice, flame in the RoI that requires to be reconstructed with good spatial resolution is commonly surrounded by low-temperature background. Although the background is not of high interest, spectroscopic absorption still exists due to heat dissipation and gas convection. Therefore, we propose a Pseudo-Inversed CNN (PI-CNN) for hierarchical temperature imaging that (a) uses efficiently the training and learning resources for temperature imaging in the RoI with good spatial resolution, and (b) reconstructs the less spatially resolved background temperature by adequately addressing the integrity of the spectroscopic absorption model. In comparison with the traditional CNN, the newly introduced pseudo inversion of the RoI sensitivity matrix is more penetrating for revealing the inherent correlation between the projection data and the RoI to be reconstructed, thus prioritising the temperature imaging in the RoI with high accuracy and high computational efficiency. In this paper, the proposed algorithm was validated by both numerical simulation and lab-scale experiment, indicating good agreement between the phantoms and the high-fidelity reconstructions.Comment: Submitted to IEEE Transactions on Instrumentation and Measuremen

Spectrally Resolved Absorption Tomography for Reacting, Turbulent Gas Phase Systems: Theory and Application

This work proposes tomographic absorption spectroscopy as a complementary measurement method to other non-intrusive methods that are applied in the research of reactive gas-phase flows. A coherent methodological framework based on conventional Bayesian inference is presented, that contains new methods and improvements in several key procedures. The framework relies on linear hyperspectral absorption tomography, that is favored for its higher computational efficiency compared to nonlinear tomography, and separates tomographic reconstruction and spectroscopic regression. The methods target the analysis of direct absorption spectroscopic measurements like direct tunable diode laser absorption spectroscopy. The improved key procedures include a spatial resolution measure based on a modified Maximum-a-posteriori covariance matrix. This resolution measure is applicable to sparse and dense beam arrangements alike, without inconsistencies arising from unprobed mesh nodes. The compatibility with resolution measures based on point spread functions is demonstrated in simulations. Additionally, the design question of the spatial-temporal resolution trade-off is discussed on spatio-temporal correlation maps with a constraint imposed by the effective measurement data-rate. Typical data-rates of spectrally resolved tomographic absorption spectroscopy setups often do not allow for capturing turbulent structures. In consequence, the optimum trade-off for quasi-stationary systems often is the focus on spatial resolution, neglecting temporal resolution. A regularization parameter choice method, relying on residuals of the spectroscopic regressions, is introduced. The idea is to balance noise amplification through under-regularization, and incompatibility with the spectroscopic model through excessive spatial-averaging of temperature structures due to over-regularization. This method allows to partially reclaim the informative advantage of nonlinear tomography, by inferring information on temperature structures from the nonlinear temperature dependence of the spectroscopic model. The selected prior parameters are shown to result in spatial resolutions matching spatial structures in the application cases. The same model error used to judge the compatibility with the spectroscopic model for parameter selection, leads to a temperature bias if temporally averaged data of a turbulent system is fitted by a homogeneous spectroscopic model. Ideas from methods to prevent this bias in spatial averaging are transferred to temporal averaging. The resulting temperature fluctuation model reduces the bias and additionally gives a qualitative measure of temperature fluctuations. The often neglected problem of estimating absorbance spectra from intensity traces is treated with Bayesian inference. This new Bayesian absorbance estimation method is shown to be numerically efficient if large numbers of absorbance traces are to be inferred like in tomography. Unlike fitting methods it is compatible with inhomogeneous line-of-sights without modification or computational penalties. Further, the incident intensity shape is not restricted to arbitrary model functions, but modeled with all degrees of freedom. The framework of methods is applied to practically relevant scenarios in the industrial characterization of selective catalytic reduction systems, and in the research of oxy-fuel combustion. The application cases feature different levels of complexity, with turbulent and laminar flows, stationary and instationary processes, axisymmetric and two dimensional flows, as well as homogeneous and inhomogeneous temperature distributions. Also the scalability of the methods is demonstrated by experiments with beam counts from 8 to 10440, and (pseudo) temporal resolutions of up to 5 kHz. For all application cases a specific discussion of uncertainty and spatial resolution is provided

Tomographic Laser Absorption Imaging of Combustion Gases in the Mid-wave Infrared

This dissertation describes advancements in mid-infrared laser absorption tomography for spatio-temporal measurements of thermochemistry in reacting flows relevant to combustion systems. Tunable laser absorption spectroscopy is combined with tomographic reconstruction techniques to resolve small diameter ( < 1 cm) non-uniform flow fields with steep spatial gradients, leveraging emerging mid-wave infrared photonics. Multiple novel measurement methods, hardware configurations, and image processing techniques were investigated. Initially, a mid-infrared laser absorption tomography sensing method was developed for quantitative measurement of CO and CO2 concentrations and temperature distributions in turbulent premixed jet flames using a translation-stage-mounted optical system. This sensing approach was used to examine effects of varying fuel structure on carbon oxidation over a range of Reynolds number regimes. It was found that spatial and temporal resolution is limited in this method due to the finite laser beam size (~ 1 mm) and the slow mechanical translation of the optical system. To address these limitations, a novel laser absorption imaging (LAI) technique, that expands a single laser beam and replaces the detector with a high-speed infrared camera, was introduced to achieve enhanced spatial and temporal resolution for thermo-chemical imaging. As a demonstration of this new technique, distributions of combustion species were imaged in both axisymmetric and non-axisymmetric flow fields using linear tomography algorithms. For non-axisymetric flows, the limited view tomography problem often results in a blurring effect and artifacts in the reconstructed flow-field. In an effort to address these issues, state-of-the-art deep learning neural networks were developed and applied to solve the limited angle inversion. Initial results suggest that deep neural networks have potential to more accurately predict flame structures with fewer projection angles than linear tomography. This work provides a foundation for a new approach to quantitative time-resolved 3D thermo-chemical imaging in high-temperature reacting flows

High spatial resolution laser cavity extinction and laser-induced incandescence in low-soot-producing flames

Abstract Accurate measurement techniques for in situ determination of soot are necessary to understand and monitor the process of soot particle production. One of these techniques is line-of-sight extinction, which is a fast, low-cost and quantitative method to investigate the soot volume fraction in flames. However, the extinction-based technique suffers from relatively high measurement uncertainty due to low signal-to-noise ratio, as the single-pass attenuation of the laser beam intensity is often insufficient. Multi-pass techniques can increase the sensitivity, but may suffer from low spatial resolution. To overcome this problem, we have developed a high spatial resolution laser cavity extinction technique to measure the soot volume fraction from low-soot-producing flames. A laser beam cavity is realised by placing two partially reflective concave mirrors on either side of the laminar diffusion flame under investigation. This configuration makes the beam convergent inside the cavity, allowing a spatial resolution within 200 μm, whilst increasing the absorption by an order of magnitude. Three different hydrocarbon fuels are tested: methane, propane and ethylene. The measurements of soot distribution across the flame show good agreement with results using laser-induced incandescence (LII) in the range from around 20 ppb to 15 ppm.B. Tian is funded through a fellowship provided by China Scholarship Council. Y. Gao and S. Balusamy are funded through a grant from EPSRC EP/K02924X/1 and EP/G035784/1, respectively.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00340-015-6156-

Bayesian Methods for Gas-Phase Tomography

Gas-phase tomography refers to a set of techniques that determine the 2D or 3D distribution of a target species in a jet, plume, or flame using measurements of light, made around the boundary of a flow area. Reconstructed quantities may include the concentration of one or more species, temperature, pressure, and optical density, among others. Tomography is increasingly used to study fundamental aspects of turbulent combustion and monitor emissions for regulatory compliance. This thesis develops statistical methods to improve gas-phase tomography and reports two novel experimental applications. Tomography is an inverse problem, meaning that a forward model (calculating measurements of light for a known distribution of gas) is inverted to estimate the model parameters (transforming experimental data into a gas distribution). The measurement modality varies with the problem geometry and objective of the experiment. For instance, transmittance data from an array of laser beams that transect a jet may be inverted to recover 2D fields of concentration and temperature; and multiple high-resolution images of a flame, captured from different angles, are used to reconstruct wrinkling of the 3D reacting zone. Forward models for gas-phase tomography modalities share a common mathematical form, that of a Fredholm integral equation of the first-kind (IFK). The inversion of coupled IFKs is necessarily ill-posed, however, meaning that solutions are either unstable or non-unique. Measurements are thus insufficient in themselves to generate a realistic image of the gas and additional information must be incorporated into the reconstruction procedure. Statistical inversion is an approach to inverse problems in which the measurements, experimental parameters, and quantities of interest are treated as random variables, characterized by a probability distribution. These distributions reflect uncertainty about the target due to fluctuations in the flow field, noise in the data, errors in the forward model, and the ill-posed nature of reconstruction. The Bayesian framework for tomography features a likelihood probability density function (pdf), which describes the chance of observing a measurement for a given distribution of gas, and prior pdf, which assigns a relative plausibility to candidate distributions based on assumptions about the flow physics. Bayes’ equation updates information about the target in response to measurement data, combining the likelihood and prior functions to form a posterior pdf. The posterior is usually summarized by the maximum a posteriori (MAP) estimate, which is the most likely distribution of gas for a set of data, subject to the effects of noise, model errors, and prior information. The framework can be used to estimate credibility intervals for a reconstruction and the form of Bayes’ equation suggests procedures for improving gas tomography. The accuracy of reconstructions depends on the information content of the data, which is a function of the experimental design, as well as the specificity and validity of the prior. This thesis employs theoretical arguments and experimental measurements of scalar fluctuations to justify joint-normal likelihood and prior pdfs for gas-phase tomography. Three methods are introduced to improve each stage of the inverse problem: to develop priors, design optimal experiments, and select a discretization scheme. First, a self-similarity analysis of turbulent jets—common targets in gas tomography—is used to construct an advanced prior, informed by an estimate of the jet’s spatial covariance. Next, a Bayesian objective function is proposed to optimize beam positions in limited-data arrays, which are necessary in scenarios where optical access to the flow area is restricted. Finally, a Bayesian expression for model selection is derived from the joint-normal pdfs and employed to select a mathematical basis to reconstruct a flow. Extensive numerical evidence is presented to validate these methods. The dissertation continues with two novel experiments, conducted in a Bayesian way. Broadband absorption tomography is a new technique intended for quantitative emissions detection from spectrally-convolved absorption signals. Theoretical foundations for the diagnostic are developed and the results of a proof-of-concept emissions detection experiment are reported. Lastly, background-oriented schlieren (BOS) tomography is applied to combustion for the first time. BOS tomography employs measurements of beam steering to reconstruct a fluid’s optical density field, which can be used to infer temperature and density. The application of BOS tomography to flame imaging sets the stage for instantaneous 3D combustion thermometry. Numerical and experimental results reported in this thesis support a Bayesian approach to gas-phase tomography. Bayesian tomography makes the role of prior information explicit, which can be leveraged to optimize reconstructions and design better imaging systems in support of research on fluid flow and combustion dynamics