Weiwei Cai

Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging

We investigate the simultaneous tomographic reconstruction of temperature and species concentration using hyperspectral absorption spectroscopy. Previous work on absorption tomography has relied on a small number of wavelengths, resulting in the requirement of a large number of projections and limited measurement capability. Here we develop a tomographic inversion method to exploit the increased spectral information content enabled by recent advancement in laser technologies. The simulation results clearly demonstrate that the use of hyperspectral absorption data significantly reduces the number of projections, enables simultaneous mapping of temperature and species concentration, and provides more stable reconstruction compared with traditional absorption tomographic techniques.

Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence

Three-dimensional (3D) measurements are highly desirable both for fundamental combustion research and practical monitoring and control of combustion systems. This work discusses a 3D diagnostic based on tomographic chemiluminescence (TC) to address this measurement need. The major contributions of this work are threefold. First, a hybrid algorithm is developed to solve the 3D TC problem. The algorithm was demonstrated in extensive tests, both numerical and experimental, to yield 3D reconstruction with high fidelity. Second, an experimental approach was designed to enable quantifiable metrics for examining key aspects of the 3D TC technique, including its spatial resolution and reconstruction accuracy. Third, based on the reconstruction algorithm and experimental results, we investigated the effects of the view orientations. The results suggested that for an unknown flame, it is better to use projections measured from random orientations than restricted orientations (e.g., coplanar orientations). These findings are expected to provide insights to the fundamental capabilities of the TC technique, and also to facilitate its practical application.

Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments.

This paper describes a preliminary demonstration and validation of temperature imaging using hyperspectral H2O absorption tomography in controlled experiments. Fifteen wavelengths are monitored on each of 30 laser beams to reconstruct the temperature image in a 381 mm × 381 mm square room-temperature plane that contains a 102 mm × 102 mm square zone of lower or higher temperature. The hyperspectral tomography technique attempts to leverage multispectral information to enhance measurement fidelity. The experimental temperature images exhibit average accuracies of 2.3% or better, with pixel-by-pixel standard deviations of less than 1%. In addition, even when the internal zone is only 4 K cooler than the surroundings, its presence is still detectable; statistical analysis of the associated experimental image reveals a 98% confidence that the internal zone is in fact cooler than the surroundings.

Practical aspects of implementing three-dimensional tomography inversion for volumetric flame imaging

Instantaneous three-dimensional (3D) measurements have been long desired to resolve the spatial structures of turbulent flows and flame. Previous efforts have demonstrated tomography as a promising technique to enable such measurements. To facilitate the practical application, this work investigated four practical aspects for implementing 3D tomographic under the context of volumetric combustion diagnostics. Both numerical simulations and controlled experiments were performed to study: (1) the termination criteria of the inversion algorithm; (2) the effects of regularization and the determination of the optimal regularization factor; (3) the effects of a number of views; and (4) the impact of the resolution of the projection measurements. The results obtained have illustrated the effects of these practical aspects on the accuracy and spatial resolution of volumetric tomography. Furthermore, all these aspects are related to the complexity and implementing cost (both hardware cost and computational cost). Therefore, the results obtained in this work are expected to be valuable for the design and implementation of practical 3D diagnostics.

Application of simulated annealing for multispectral tomography

A new method based on simulated annealing is developed to obtain tomographic reconstructions based on multispectral absorption spectroscopy. The new method is able to exploit the spectral information content, to incorporate various a priori information, and to ameliorate the ill-posedness of the tomographic inversion problem. Numerical simulations are conducted to demonstrate the performance of this method for simultaneous temperature and species concentration imaging. This method is expected to enhance the practicality of multispectral tomography.

Determination of the optimal regularization parameters in hyperspectral tomography

In a previous paper, we described a novel technique to exploit hyperspectral absorption spectroscopy to retrieve tomographic imaging of temperature and species concentration simultaneously. This technique casts the tomographic inversion into a nonlinear minimization problem with regularizations. Here a simple and effective method is developed to determine the optimal regularization parameters in the nonlinear optimization problem. This method, combined with the minimization method described previously, provides a robust algorithm for hyperspectral tomography. This method takes advantage of an inherent feature of absorption and is therefore expected to be useful for other sensing techniques based on absorption spectroscopy.

Applications of critical temperature in minimizing functions of continuous variables with simulated annealing algorithm

The simulated annealing (SA) algorithm has been recognized as a powerful technique for minimizing complicated functions. However, a critical disadvantage of the SA algorithm is its high computational cost. Therefore, it is the goal of this paper to investigate the use of the critical temperature in SA to reduce its computational cost. This paper presents a systematic study of the critical temperature and its applications in the minimization of functions of continuous variables with the SA algorithm. Based on this study, a new algorithm was developed to exploit the unique feature of the critical temperature in SA. The new algorithm combines SA and local search to determine global minimum effectively. Extensive tests on a variety of functions demonstrated that the new algorithm provides comparable performance to well-established SA techniques. Furthermore, the new algorithm also improves the determination of the starting temperature for the SA algorithm. The results obtained in this study are expected to be useful for improving the efficiency of SA algorithms, and for facilitating the development of temperature parallel SA algorithms.

Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows

A series of previous studies, both numerical and experimental, have demonstrated the advantages of hyperspectral tomography (HT) as a promising technique to measure the two-dimensional distributions of temperature and species concentration in reacting flows. This paper intends to prepare the mathematical groundwork for extended use of the HT technique for three-dimensional and/or time-correlated measurements. Direct application of the methods developed previously encounters both experimental and computational difficulties. Numerical studies reported in this paper suggest that the use of proper orthogonal decomposition (POD) is effective to overcome these difficulties. The use of POD in HT significantly reduces the computational cost, enhances the fidelity of the tomographic reconstructions, and improves the stability of the reconstruction in the presence of measurement noise. Implications of these results for practical applications are also discussed.

Comparison of approaches based on optimization and algebraic iteration for binary tomography

Binary tomography represents a special category of tomographic problems, in which only two values are possible for the sought image pixels. The binary nature of the problems can potentially lead to a significant reduction in the number of view angles required for a satisfactory reconstruction, thusly enabling many interesting applications. However, the limited view angles result in a severely underdetermined system of equations, which is challenging to solve. Various approaches have been proposed to address such a challenge, and two categories of approaches include those based on optimization and those based on algebraic iteration. However, the relative strengths, limitations, and applicable ranges of these approaches have not been clearly defined in the past. Therefore, it is the main objective of this work to conduct a systematic comparison of approaches from each category. This comparison suggested that the approaches based on algebraic iteration offered both superior reconstruction fidelity and computation efficiency at low (two or three) view angles, and these advantages diminished at high view angles. Meanwhile, this work also investigated the application of regularization techniques, the selection of optimal regularization parameter, and the use of a local search technique for binary problems. We expect the results and conclusions reported in this work to provide valuable guidance for the design and development of algorithms for binary tomography problems.

Uncertainty in velocity measurement based on diode-laser absorption in nonuniform flows.

This work investigates the error caused by nonuniformities along the line-of-sight in velocity measurement using tunable diode-laser absorption spectroscopy (TDLAS). Past work has demonstrated TDLAS as an attractive diagnostic technique for measuring velocity, which is inferred from the Doppler shift of two absorption features using two crossing laser beams. However, because TDLAS is line-of-sight in nature, the obtained velocity is a spatially averaged value along the probing laser beams. As a result, nonuniformities in the flow can cause uncertainty in the velocity measurement. Therefore, it is the goal of this work to quantify the uncertainty caused by various nonuniformities typically encountered in practice, including boundary layer effects, the divergence/convergence of the flow, and the methods used to fit the Doppler shift. Systematic analyses are performed to quantify the uncertainty under various conditions, and case studies are reported to illustrate the usefulness of such analysis in interpreting experimental data obtained from a scramjet facility. We expect this work to be valuable for the design and optimization of TDLAS-based velocimetry, and also for the quantitative interpretation of the measurements.