Reconstruction Of Temperature Distribution Research Articles

Three-dimensional temperature measurement in harsh environments using quadriwave lateral shearing interferometric tomography

This paper presents Quadriwave Lateral Shearing Interferometric Tomography for reconstructing three-dimensional temperature fields in environments that pose significant challenges for interferometric measurements, such as those with ambient noise and moderate vibrations. Employing QWLSIT enables non-invasive, high-resolution measurements, facilitating precise reconstruction of temperature distributions. Accuracy was confirmed through comparative experiments using thermocouples (TC), specifically in tests that measured heated air emitted from a 3-orifice nozzle and a slit nozzle. The agreement between QWLSI and TC results emphasizes the robustness of QWLSI tomography and its potential for application applications in measuring stationary phenomena with general 3D distributions that affect the refractive index.

Distribution of the acoustobrightness temperature satisfies heat equation

Passive acoustic thermometry (PAT), a method proposed for medical applications, involves direct measurement of the acoustobrightness temperature which is the intensity of the thermal acoustic radiation expressed in degrees. The hypothesis has been proposed that the acoustobrightness temperature measured on the surface of the object under study obeys the 2D heat equation whose parameters coincide or are uniquely connected with the parameters of the 3D heat equation governing the deep temperature of the object. Since in PAT a noise signal is measured, the achievement of an acceptable error level (0.5–1 K) requires a considerable integration time (about a minute). The proposed hypothesis will enable linking together the data obtained by acoustothermometric sensors separated in space, at different points in time. This, in turn, will lower the dimensionality of the problem of temperature distribution reconstruction and enable reducing the integration time without loss of accuracy. The proposed hypothesis has been confirmed experimentally and with the aid of computer simulation for the case where local hyperthermia of soft tissues of the human organism is modeled.

Resolving nonuniform flow in gas turbines: challenges, progress, and moving forward

Abstract The flow in gas turbines exhibits a highly unsteady, complex and nonuniform manner, which presents two main challenges. Firstly, it introduces instrumentation errors, contributing to uncertainties when calculating one-dimensional performance metrics during rig or engine tests using fixed-location rakes. Secondly, it raises mechanical concerns, including high-cycle fatigue due to blade row interactions in turbomachines and thermal fatigue caused by hot-streaks at the combustor exit. Experimental characterisation of the flow nonuniformity in gas turbines is highly challenging due to the confined space and harsh environment for instrumentation. This paper presents recent efforts to address this issue by resolving the nonuniform flow in gas turbines using spatially under-sampled measurements. The proposed approach utilises discrete probe data and leverages a ‘Fourier-based approximation’ method developed by the author. The technique has undergone preliminary experimental validation involving reconstruction of the total pressure distribution in a multi-stage axial compressor and the total temperature field at the exit of the combustor and high-pressure turbine. Results show that, in the multi-stage axial compressor environment, reconstruction of inter-stage total pressure is achieved using a reduced dataset covering less than 20% of the annulus with reasonably good accuracy. The reconstructed total pressure yields almost identical mean total pressure values at all spanwise locations, with a maximum deviation of less than 0.02%. Additionally, reconstruction of the total temperature distribution at an engine-representative full annulus combustor is achieved using measurements at ten carefully selected circumferential locations. Results show that the reconstructed temperature field successfully captures the primary features associated with combustor exit temperature flow. The reconstructed temperature field yields excellent agreement in the magnitude of radial temperature distribution factor (RTDF) and overall temperature distribution factor (OTDF) predictions to the experiment, with a deviation of less than 0.5% for RTDF and less than 2.5% for OTDF. Lastly, reconstruction of the total temperature distribution at the exit of the GE E3 high-pressure turbine (HPT) is achieved using measurements at eight carefully selected circumferential locations. Results demonstrate remarkable robustness in resolving the temperature profile at the HPT exit with high fidelity, irrespective of the HPT inlet conditions. The initial validation results are promising, demonstrating that the new probe layout scheme and the Fourier-based approximation method enable effective characterisation of flow nonuniformity in gas turbines, thereby providing valuable insights into the complex flow of gas turbine engines.

Sensor Head Temperature Distribution Reconstruction of High-Precision Gravitational Reference Sensors with Machine Learning.

Temperature fluctuations affect the performance of high-precision gravitational reference sensors. Due to the limited space and the complex interrelations among sensors, it is not feasible to directly measure the temperatures of sensor heads using temperature sensors. Hence, a high-accuracy interpolation method is essential for reconstructing the surface temperature of sensor heads. In this study, we utilized XGBoost-LSTM for sensor head temperature reconstruction, and we analyzed the performance of this method under two simulation scenarios: ground-based and on-orbit. The findings demonstrate that our method achieves a precision that is two orders of magnitude higher than that of conventional interpolation methods and one order of magnitude higher than that of a BP neural network. Additionally, it exhibits remarkable stability and robustness. The reconstruction accuracy of this method meets the requirements for the key payload temperature control precision specified by the Taiji Program, providing data support for subsequent tasks in thermal noise modeling and subtraction.

A deep-learning approach to the 3D reconstruction of dust density and temperature in star-forming regions

Aims. We introduce a new deep-learning approach for the reconstruction of 3D dust density and temperature distributions from multi-wavelength dust emission observations on the scale of individual star-forming cloud cores (<0.2 pc). Methods. We constructed a training data set by processing cloud cores from the Cloud Factory simulations with the POLARIS radiative transfer code to produce synthetic dust emission observations at 23 wavelengths between 12 and 1300 µm. We simplified the task by reconstructing the cloud structure along individual lines of sight (LoSs) and trained a conditional invertible neural network (cINN) for this purpose. The cINN belongs to the group of normalising flow methods and it is able to predict full posterior distributions for the target dust properties. We tested different cINN setups, ranging from a scenario that includes all 23 wavelengths down to a more realistically limited case with observations at only seven wavelengths. We evaluated the predictive performance of these models on synthetic test data. Results. We report an excellent reconstruction performance for the 23-wavelength cINN model, achieving median absolute relative errors of about 1.8% in log(n/m−3) and 1% in log(Tdust/K), respectively. We identify trends towards an overestimation at the low end of the density range and towards an underestimation at the high end of both the density and temperature values, which may be related to a bias in the training data. After limiting our coverage to a combination of only seven wavelengths, we still find a satisfactory performance with average absolute relative errors of about 2.8% and 1.7% in log(n/m−3) and log(Tdust/K). Conclusions. This proof-of-concept study shows that the cINN-based approach for 3D reconstruction of dust density and temperature is very promising and it is even compatible with a more realistically constrained wavelength coverage.

Numerical and Experimental Reconstruction of Temperature Distribution and Soot Concentration Field for Thin-Slice Flames Using a Charge Coupled Device Camera

This work proposed a novel model to simultaneously reconstruct temperature distribution and soot volume fraction field for two-dimensional thin-slice flames using the knowledge of monochromatic radiation intensities at two wavelengths using a CCD camera. The deduction process and numerical analysis of the model were described. Effects of wavelength combinations and measurement errors on reconstruction accuracy were considered in detail. Numerical results have proven the model’s accuracy and showed that the temperature and soot volume fraction fields can be reconstructed well even with noisy input data from flame radiation. In addition, a series of experiments were conducted on a mesoscale combustor to obtain the real thin-slice flames for further experimental reconstruction via the model. The experimental results indicated that the proposed model can successfully reconstruct the flame temperature distribution and soot volume fraction field and the main features of thin-slice flames also can be reasonably reproduced.

Реконструктивные методы визуализации тепловых флуктуаций в тканях человека с использованием ультразвуковой томографии

Thermal therapy is an emerging non-invasive method used for cancer treatment. Implementation of this method requires non-invasive temperature monitoring during the treatment process and through-transmission ultrasonic tomography is a potential technique for such monitoring. The technique allows internal cross-sectional images of acoustic properties to be obtained. These properties change with temperature and the technique therefore allows the temperature field in the tissue to be measured non-invasively. The accuracy of this technique is significantly reduced, however, for regions of tissue which contain acoustically non-transparent objects such as medical devices or implants, because these cause missing parts in the projection data. The heated lesion itself may also distort ultrasonic rays. The present work considers and compares different methods of solving the inverse problem for ultrasonic tomographical reconstruction. A special method, which is a modification of the expectation maximization (EM) method for temperature distribution reconstruction from noisy projections with missing data, has been developed for through-transmission fan-beam tomography. The accuracy of the developed method was investigated by computer modeling and compared with the conventional EM method. It was shown that the developed method gives higher accuracy and less distortion after reconstruction than the conventional EM methods.

Real-time temperature distribution reconstruction via linear parameter-varying state-space model and Kalman filter in rack-based cooling data centers

Rapidly growing data centers (DCs) are facing challenges with energy consumption increase and thermal environmental security. Thus, this paper proposed a novel real-time temperature distribution prediction and reconstruction model for rack-based cooling DCs, in order to facilitate efficient energy consumption and thermal environment management. The parameter identification method coupling with inherent physical relationships was employed to obtain the linear parameter-varying state-space model, rapidly and approximately predicting the nonlinear thermal dynamic processes within rack-based cooling DC. Then, Kalman filter was adopted to reconstruct the temperature distribution in real-time based upon the developed linear parameter-varying state-space temperature prediction model and measurement information. This study comprehensively analyzed the temperature estimation performance of the proposed model under various model input biases, different sensor numbers and layouts. The results show that the input biases have significant impacts on the accuracy of the temperature prediction model, e.g., ±5% bias in IT workload resulting in an increase of 0.6 times in the mean absolute error (MAE) of the temperature prediction. The proposed temperature reconstruction model reveals excellent performance: compared to the original temperature prediction model, the MAE was decreased by about 5%, 10%, and 13% for reconstruction scenarios using one, two, and three sensors, respectively.

Rapid online tomograph in non-uniform complex combustion fields based on laser absorption spectroscopy

Laser absorption spectroscopy tomography is widely applied to measure the two-dimensional distribution information in complex combustion flow fields. Rapid and accurate estimation of the integrated absorption area (IA) is the key to achieving accurate online reconstruction. In this paper, a novel method is introduced with the wavelength modulation spectroscopy (WMS) for obtaining the IA, which is applied in the reconstruction of temperature and species concentrations distributions of non-uniform complex combustion flames. With this method, the traditional time-consuming line-shape fitting process is no longer required, and the IA is obtained through simple algebraic operations instead. This method has been validated via numerical simulations and field experiments on afterburner flames. The experimental results show that the measurement accuracy is comparable to that achieved with the conventional WMS with line-shape fitting (WMS-F), however the computational efficiency is improved significantly by at least two orders of magnitude, demonstrating its potential for real industrial applications, where often rapid reconstructions are desirable or required.

Thermal Sensor Allocation for Effective and Efficient Heat Transfer Measurements in Transportation Systems.

Power plants, electric generators, high-frequency controllers, battery storage, and control units are essential in current transportation and energy distribution networks. To improve the performance and guarantee the endurance of such systems, it is critical to control their operational temperature within certain regimes. Under standard working conditions, those elements become heat sources either during their entire operational envelope or during given phases of it. Consequently, in order to maintain a reasonable working temperature, active cooling is required. The refrigeration may consist of the activation of internal cooling systems relying on fluid circulation or air suction and circulation pulled from the environment. However, in both scenarios pulling surrounding air or making use of coolant pumps increases the power demand. The augmented power demand has a direct impact on the power plant or electric generator autonomy, while instigating higher power demand and substandard performance from the power electronics and batteries' compounds. In this manuscript, we present a methodology to efficiently estimate the heat flux load generated by internal heat sources. By accurately and inexpensively computing the heat flux, it is possible to identify the coolant requirements to optimize the use of the available resources. Based on local thermal measurements fed into a Kriging interpolator, we can accurately compute the heat flux minimizing the number of sensors required. Considering the need for effective thermal load description toward efficient cooling scheduling. This manuscript presents a procedure based on temperature distribution reconstruction via a Kriging interpolator to monitor the surface temperature using a minimal number of sensors. The sensors are allocated by means of a global optimization that minimizes the reconstruction error. The surface temperature distribution is then fed into a heat conduction solver that processes the heat flux of the proposed casing, providing an affordable and efficient way of controlling the thermal load. Conjugate URANS simulations are used to simulate the performance of an aluminum casing and demonstrate the effectiveness of the proposed method.

Reconstruction of the Thermal Load of a Functionally Graded Hollow Sphere by Surface Displacements

We formulate and solve a problem of reconstruction of the unknown time-dependent temperature distribution on one boundary surface of a functionally graded hollow sphere according to the temperature and radial displacements on the other boundary surface. We suggest a procedure reducing the formulated problem to the inverse thermoelasticity problem. By applying the finite-difference method, we construct a numerical algorithm aimed at solving the obtained inverse problem. By using the solution of the direct thermoelasticity problem, we analyze the stability of the obtained solution of the inverse problem and the distributions of displacements and stresses obtained on the basis of this solution against the errors of the input data.

Online tomography algorithm based on laser absorption spectroscopy

Conventional calibration-free wavelength modulation spectroscopy generally requires complex absorption spectrum simulations in combination with spectral databases and laser modulation parameters, placing high demands on the accuracy of a priori spectral parameters and hardware parameters. Meanwhile, inappropriate initial values can increase the computation time and even lead to local optimal solutions. In order to improve the computational efficiency, a rapid calibration-free wavelength modulation spectroscopy to obtain the integrated absorbance is presented in this work. First, this method is computationally efficient, requiring only algebraic calculations by using the 2nd, 4th, and 6th harmonic center peak height parameters to obtain the integrated absorbance, eliminating the need for computationally intensive harmonic fitting calculations. Secondly, this method has low dependence on the spectral database, requiring only line intensity and low-state energy level spectral parameters. Finally, this method is highly adaptable and does not require scanning the complete absorption spectral line shape, which solves the problem of incomplete harmonic signals caused by the conventional method at high temperature and high pressure due to the broadening of the absorption spectral line. This method has previously been used only for line-of-sight measurements at low-frequency experimental signals in stable environments, and for calculating the integrated absorbance at average temperature, concentration and pressure states. In this work, the method is applied to non-uniform complex combustion field tomography and combined with the proposed tomographic system to achieve online reconstructing temperature and concentration distributions. The accuracy and computational efficiency of the method in obtaining the integrated absorbance are verified by numerical simulations and experiments on the butane burner flame. The results show that the presented method is consistent with the reconstructed distribution compared with the conventional wavelength modulation method, with a maximum relative deviation of only 0.94% from the measurement and 3.5% from the thermocouple measurement, verifying the accuracy of the method. The computational efficiencies of the two methods for obtaining the integrated absorbance are analyzed. The average calculation time per path is 0.15 s for the present method and 21.10 s for the conventional method. The calculation efficiency of the present method is at least two orders of magnitude higher than that of the conventional method, which provides a fast and reliable research method and technical means to realize the industrial-grade online reconstruction of temperature and concentration distribution of combustion fields.

Temperature Field Reconstruction Method for Acoustic Tomography Based on Multi-Dictionary Learning.

A reconstruction algorithm is proposed, based on multi-dictionary learning (MDL), to improve the reconstruction quality of acoustic tomography for complex temperature fields. Its aim is to improve the under-determination of the inverse problem by the sparse representation of the sound slowness signal (i.e., reciprocal of sound velocity). In the MDL algorithm, the K-SVD dictionary learning algorithm is used to construct corresponding sparse dictionaries for sound slowness signals of different types of temperature fields; the KNN peak-type classifier is employed for the joint use of multiple dictionaries; the orthogonal matching pursuit (OMP) algorithm is used to obtain the sparse representation of sound slowness signal in the sparse domain; then, the temperature distribution is obtained by using the relationship between sound slowness and temperature. Simulation and actual temperature distribution reconstruction experiments show that the MDL algorithm has smaller reconstruction errors and provides more accurate information about the temperature field, compared with the compressed sensing and improved orthogonal matching pursuit (CS-IMOMP) algorithm, which is an algorithm based on compressed sensing and improved orthogonal matching pursuit (in the CS-IMOMP, DFT dictionary is used), the least square algorithm (LSA) and the simultaneous iterative reconstruction technique (SIRT).

Reconstruction Optimization Algorithm of 3D Temperature Distribution Based on Tucker Decomposition

For the purpose of solving the large temperature field reconstruction error caused by different measuring point arrangements and the problem that the prior dataset cannot be built due to data loss or distortion in actual measurement, a three-dimensional temperature profile reconstruction optimization algorithm is proposed to repair the empirical dataset and optimize the arrangement of temperature measuring points based on Tucker decomposition, the minimum condition number method, the greedy algorithm, and the hill climbing algorithm. We used the Tucker decomposition algorithm to repair the missing data and obtain the complete prior dataset and the core tensor. By optimizing the dimension of the core tensor and the number and position of the measuring points calculated by the minimum condition number method, the greedy algorithm, and the mountain climbing algorithm, the real-time three-dimensional distribution of the temperature field is reconstructed. The results show that the Tucker decomposition optimization algorithm could accurately complete the prior dataset, and compared with the original algorithm, the proposed optimal placement algorithm improves the reconstruction accuracy by more than 20%. At the same time, the algorithm has strong robustness and anti-noise, and the relative error is less than 4.0% and 6.0% with different signal-to-noise ratios. It indicates that the proposed method can solve the problem of building an empirical dataset and 3D temperature distribution reconstruction more accurately and stably in industry.

Heat diffusion blurs photothermal images with increasing depth

In this Tutorial, we aim to directly recreate some of our “aha” moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function. The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction.

Temperature Distribution Reconstruction Method for Acoustic Tomography Based on Compressed Sensing.

Acoustic tomography (AT) is one of a few non-contact measurement techniques that can present information about the temperature distribution. Its successful application greatly depends on the performance of the reconstruction algorithm. In this paper, a temperature distribution reconstruction method based on compressed sensing (CS) is proposed. Firstly, a measurement matrix of an AT system in a CS framework is established. Secondly, a sparse basis is selected based on the mutual coherence between the measurement matrix and sparse basis. Thirdly, an improvement of the orthogonal matching pursuit (OMP) algorithm, called the IMOMP algorithm, is proposed for pursuing efficiency in recovering sparse signals. Reconstruction experiments of Gaussian sparse signals showed that IMOMP was better than OMP in both success ratio and running time, and the selection method of sparse basis was effective. Finally, a temperature distribution reconstruction algorithm based on compressed sensing, that is, the CS-IMOMP algorithm, is proposed. Simulation and experiment results show that, compared with the least square algorithm and the Simultaneous Iterative Reconstruction Technique algorithm, the CS-IMOMP algorithm has smaller reconstruction errors and provides more accurate information about the temperature distribution.

Temperature measurements of long sparks in air using time-resolved moiré deflectometry

This paper presents an original investigation into time-resolved moiré deflectometry (MD) for gas temperature measurements of long sparks in air. In order to perform a rigorous comparative investigation with the widely used quantitative schlieren (QS) method, we set up an orthogonal optical measurement system. The impacts of spatial resolution and exposure time on the measurement accuracy are investigated by comparing the measured radial distribution of the gas temperature and its time evolution during the same spark discharge event. It is found that the time-resolved MD with an exposure time of 1.0 μs can accurately measure the gas temperature evolution during the isobaric heating and relaxation process of long sparks. The measured results of the expansion rate of cross-section and average temperature T g confirms that the energy loss is dominated by thermal conduction during the isobaric heating and relaxation process after the extinction of discharge current. The MD can achieve a finer spatial resolution than the QS method, which is beneficial to the reconstruction of steep radial temperature distribution and the suppression of measured temperature fluctuation. Moreover, the MD can obtain a sub-microsecond exposure time by increasing the power of continuous-wave laser source, which shows its potential to capture the rapid changes in gas temperature during the fast-heating process.

Application of Tucker Decomposition in Temperature Distribution Reconstruction

Constrained by cost, measuring conditions and excessive calculation, it is difficult to reconstruct a 3D real-time temperature field. For the purpose of solving these problems, a three-dimensional temperature distribution reconstruction algorithm based on Tucker decomposition algorithm is proposed. The Tucker decomposition algorithm is used to reduce the dimension of the measured data, and the processed core tensor is used for the temperature field reconstruction of sparse data. Theoretical analysis and simulations show that the proposed method is feasible; the overall optimization is realized by selecting the appropriate core tensor dimensions; and the reconstruction error is less than 3%. Results indicate that the proposed method can yield a reliable reconstruction solution and can be applied to real-time applications.

Tomographic reconstruction from planar thermal imaging using convolutional neural network

In this study, we investigate perspectives for thermal tomography based on planar infrared thermal images. Volumetric reconstruction of temperature distribution inside an object is hardly applicable in a way similar to ionizing-radiation-based modalities due to its non-penetrating character. Here, we aim at employing the autoencoder deep neural network to collect knowledge on the single-source heat transfer model. For that purpose, we prepare a series of synthetic 3D models of a cylindrical phantom with assumed thermal properties with various heat source locations, captured at different times. A set of planar thermal images taken around the model is subjected to initial backprojection reconstruction, then passed to the deep model. This paper reports the training and testing results in terms of five metrics assessing spatial similarity between volumetric models, signal-to-noise ratio, or heat source location accuracy. We also evaluate the assumptions of the synthetic model with an experiment involving thermal imaging of a real object (pork) and a single heat source. For validation, we investigate objects with multiple heat sources of a random location and temperature. Our results show the capability of a deep model to reconstruct the temperature distribution inside the object.

A Fast Tomographic Reconstruction Method for Flame Temperature Distribution Measurement Based on Direct Solution Algorithm

The rapid and accurate measurement of the flame temperature distribution is of great significance to the structural design and health diagnosis of the engine. Aiming at the low reconstruction efficiency of traditional flame temperature distribution reconstruction algorithms, a Direct Solution algorithm for flame temperature distribution reconstruction is proposed in this paper based on the structural characteristics of the reconstruction equations. By setting several numerical cases, the performance of the Direct Solution algorithm and some commonly used traditional algorithms, such as Simultaneous Algebraic Reconstruction Technique (SART), Least Squares QR-factorization (LSQR) algorithm, Non-Negative Least Squares QR-factorization (NNLS) algorithm, is compared in the reconstruction of the flame temperature distribution. The results show that the efficiency of the Direct Solution method is 169.4, 7.4, and 3483.3 times higher than that of the SART, LSQR, and NNLS algorithms under the condition of 40 × 40 grids. In addition, with the increase of the number of grids, the growth rate of the reconstruction time of the Direct Solution algorithm is much lower than that of other algorithms. The overall reconstruction accuracy of the Direct Solution algorithm is better than that of SART and LSQR algorithms. This shows that it has an excellent comprehensive performance and has a great application prospect in the rapid reconstruction of the temperature distribution.