Reconstructed Temperature Field Research Articles

Reconstructing the Ocean State Using Argo Data and a Data-Driven Method

Abstract Over the past two decades, Argo profiles have provided unprecedented insight into the global patterns of space and time variability of ocean temperature and salinity, significantly reducing associated uncertainties. However, analyzing such assessments during the pre-Argo period remains challenging due to the scarcity of observations in many regions. From the Argo period, a set of dominant three-dimensional patterns can be estimated using Empirical Orthogonal Function (EOF) analysis, which helps to fill in observational gaps. From the associated principal components, temporal fluctuations can be observed, aiming to build a catalog of possible ocean state trajectories. To map pre-Argo observations, EOFs are used in a data assimilation framework that uses this catalog to feed an analog prediction and provide reanalysis. In this study, a new data-driven interpolation method called RedAnDA (Reduced-space Analog Data Assimilation) was tested in the tropical Pacific Ocean. RedAnDA was first validated through an Observing System Simulation Experiment (OSSE) approach, using synthetic observations extracted from a model simulation. It was subsequently applied to a real historical dataset and compared with other available reanalysis products. Overall, the reconstructed temperature field showed variability consistent with the OSSE true field and other reanalysis products in the real data application. Further improvements are needed to optimally estimate uncertainty, but RedAnDA already combines valuable information about state predictability, observational sampling, and unresolved scale issues.

2D temperature field reconstruction using optimized Gaussian radial basis function networks

Monitoring temperature fields by sensors and mapping the reconstructed temperature field holds great importance in numerous contexts. Concurrently, as sensing technologies continue to advance, there is a parallel development of temperature reconstruction algorithms. In this study, we present an enhanced Quadratic Optimization Gaussian Radial Basis Function approximation (QO-GRBF). We demonstrate the effectiveness of this algorithm by reconstructing a 10 cm x 10 cm temperature field using distributed optical fiber sensing system. The absolute error across four different temperature stages from 35 °C to 65 °C ranged from 0.21 °C to 0.45 °C, indicating a strong reconstruction ability. Furthermore, we compared the performance of QO-GRBF with GRBF in different point densities. The results reveal an over 30 % improvement in scenarios with denser data points, highlighting the efficacy of proposed algorithm. The data size chosen was quantified as well. There was a 10.22 % improvement observed when transitioning from selecting 4 points to selecting 6 points.

A simultaneous non-invasive diagnosis method for flame temperature and velocity fields based on radiation self-calibration and optical flow

The measurement of flame temperature and velocity is crucial to combustion research, hence it is of great significance to develop a non-invasive diagnosis technology for the measurement of flame temperature and velocity. In this study, a single-camera simultaneous non-invasive diagnosis technology for flame temperature and velocity field was developed, based on radiation self-calibration and optical flow method. The diagnosis method was applied to two case studies, propane diffusion flame and solid surface spread flame. The reconstructed flame temperature field was compared with measuring results by thermocouples. Results show that the reconstructed temperature field can accurately describe the symmetrical distribution characteristics and the clear high-temperature front. The combustion zone reconstruction temperature was 1250–1380 K for propane diffusion flame and the maximum reconstruction temperature was 1400 K for solid spread flame. The maximum relative error between the reconstructed temperature and the measured values by thermocouples is less than 15 %. Additionally, the flow velocity field at the flame edge was also measured, which could provide a good qualitative characterization of flame kinematic.

Real-time reconstruction of 3D transient non-uniform temperature field for thermal protection system based on machine learning

Reconstructed temperature field will provide critical input for monitoring the aerodynamic heating on the thermal protection system (TPS). In this paper, a novel data-driven method is proposed that allows real-time reconstruction of the 3D transient non-uniform temperature field in a TPS ceramic tile. The measured temperature is obtained by embedding sparse sensors at different layers of the tile. The spatial feature bases and time projection coefficients of the non-uniform temperature fields are extracted using the multi-parameter proper orthogonal decomposition (POD) method. The Fully-connected Long Short-Term Memory (FC-LSTM) networks are used to establish the prediction relationship between the measurements and the full-field temperatures. The problem to estimate the projection coefficients of the spatial feature bases is solved by optimizing the loss function using Adam algorithm. The numerical examples show an approximation error less than 5% and the reconstruction time-consuming less than 1 s in 3D temperature field reconstruction (TFR). The proposed reconstruction method is robust at different measurement noise levels and tested point arrangements.

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.

Direct reconstruction of the temperature field of lithium-ion battery based on mapping characteristics

Lithium-ion (Li-ion) batteries are susceptible to the working temperature so that the monitoring is essential to the battery internal temperature. The electrochemical-thermal coupling model completely reflects the battery internal behavior. However, the high complexity and multi-field coupling make it difficult to be applied to reconstruct the battery temperature field based on state observer. Based on mapping characteristics, this work proposes a temperature field direct reconstruction scheme. And the electrochemical-thermal coupling model plays a large role in this scheme. Mapping characteristic vectors of the transient temperature field are obtained from the step response model of the Li-ion battery temperature field to charge and discharge current. Furthermore, the quantitative connection of the mapping characteristic vectors between the surface points of and the internal nodes of the battery is characterized by a relevance degree matrix. And a direct reconstruction model of the internal transient temperature field is established. The internal temperature field is reconstructed directly online and in real time via exploiting the temperature measurements on battery surface. In numerical experiments, the three-dimensional temperature field of the Li-ion battery charge and discharge processes is reconstructed. The effects of charge and discharge rates, model mismatch, and measurement errors on the reconstruction results are investigated. During the charge and discharge processes, the maximum values of the transient average error of the reconstructed temperature field are about 0.4 K and 0.3 K, respectively. And the transient average error is generally below 0.8 K when the standard deviation of measurement errors is 0.5 K.

Detection of multiple tumors through temperature response of a human brain using inverse bioheat transfer based on swarm optimization

In this article, an innovative inverse regularized framework has been proposed for a bio-medical problem to detect tumors in the human brain via temperature. Most of the thermal data obtained through infrared thermography is sensitive towards errors, thus a regularized approach is sought from the literature. The best inversion algorithm, WOA, together with a hybrid GWOCS are utilized. Pennes model is used for the formulation of heat transfer within the human brain. Using inverse analysis, the unknown blood perfusion rate ωi is retrieved in the regularized environment. The current research reported that at positions where tumor cells are present, the temperature rises. Moreover, with an increase in time, the temperature of the cancer cells increases, whereas no change in the temperature of tissue without tumor is seen. This observation marks the presence of tumor. Elastic net regularization (λ=0.1, α=10−2) for WOA and (λ=0.9, α=10−4) for GWOCS shows the least relative error. After regularization, the perfusion rate is retrieved. A clear distinction of two tumors from the brain tissue is observed. The obtained perfusion rate is used to reconstruct the temperature profile. An excellent matching of the reconstructed temperature field and the exact field is obtained, even when the forward data contain measurement errors. The obtained set of perfusion rate is appropriate for tumor detection, up to 7% error in the measured data. Thus, the proposed comparative procedure is found suitable for the bio-heat transfer problem.

Rainbow Schlieren Deflectometry for spherical fields: A new algorithm and numerical validation approach

The authors present a new algorithm for analyzing ray deflection within spherical refractive index fields. The algorithm emanates from the well-known deconvolution algorithm for axisymmetric refractive index fields using the inverse Abel transformation and can be used for experimental Rainbow Schlieren Deflectometry (RSD) data. It was numerically validated by Computational Fluid Dynamics (CFD) calculations of free convection around an isothermal sphere and successive ray tracing through the determined temperature field. The algorithm determined radial temperature profiles and local Nusselt numbers from resulting deflection angles of the ray tracing simulations. An excellent agreement between original and reconstructed temperature field within the limits of assumptions was reached. This proves the usability of the algorithm for the experimental determination of spherical refractive index fields from future heat or mass transfer experiments.

Physics-informed deep Monte Carlo quantile regression method for interval multilevel Bayesian Network-based satellite circuit board reliability analysis

Temperature field reconstruction is essential for analyzing the reliability of a high-density functionally integrated satellite circuit board (HFI-SCB). As a representative deep learning model, the deep convolutional neural network (DCNN) is a powerful tool for reconstructing the HFI-SCB temperature field. However, DCNN needs a lot of labeled data to learn its parameters, which is contrary to the fact that actual satellite engineering can only acquire noisy unlabeled data. Thus, this paper proposes an unsupervised method, i.e., the physics-informed deep Monte Carlo quantile regression method, for reconstructing the HFI-SCB temperature field and quantifying the data uncertainty caused by sensor noise. The proposed method combines a DCNN with known physics knowledge to reconstruct an accurate HFI-SCB temperature field using only monitoring point temperatures. Besides, the proposed method can quantify the data uncertainty by the Monte Carlo quantile regression. Based on the reconstructed temperature field and the quantified data uncertainty, this paper builds an interval multilevel Bayesian Network to analyze the HFI-SCB reliability. Two case studies are used to validate the proposed method.

Numerical Analysis of Transient State Heat Transfer by Spectral Method Based on POD Reduced-Order Extrapolation Algorithm

In order to meet the requirements of high accuracy and fast algorithm for numerical heat transfer simulation, an iterative scheme of Proper Orthogonal Decomposition (for short, POD) dimension reduction based on the classical central difference Galerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. The POD dimension reduction spectral method model is constructed by taking the calculation results of classical central difference Galerkin spectral method as sample data. The numerical algorithm characteristics of flow and heat transfer are studied by using a partial differential equation as a mathematical model, and the error estimation is given. Finally, different time intervals are used as parameters to simulate experiments. The results show that the POD method is applicable to transient nonlinear heat conduction problems, and the maximum average relative error of the reconstructed temperature field is 0.89675%. Moreover, the POD method not only has a high calculation accuracy, but also has an average calculation speed as high as 310.25 times that of the central difference Galerkin algorithm. It can be seen that under the condition that the error between the solution of POD dimension reduction extrapolation algorithm and the solution of classical central difference Galerkin spectrum method is small enough, the POD method can greatly reduce the calculation amount, shorten the running time, and ensure a high accuracy of the calculation results, thus verifying the effectiveness and feasibility of the algorithm.

Approximating Gas Turbine Combustor Exit Temperature Distribution Factors Using Spatially Under-Sampled Measurements

Abstract In gas turbine engines, the temperature field at the exit plane of the combustor is highly unsteady and complex, with large radial and circumferential variations. The circumferential temperature variations (hot-streaks) are caused by the discrete nature of fuel and dilution air jets, and combustor lining coolant flow results in a strong radial temperature gradient. Two widely adopted parameters include the radial temperature distribution factor (RTDF) and the overall temperature distribution factor (OTDF) to quantify combustor exit temperature nonuniformity. The state-of-the-art approach to characterizing the combustor exit temperature nonuniformity is to carry out an extensive traverse along the circumferential direction at a spatial resolution of two to three degrees. With hundreds of measurements in place, the combustor OTDF and RTDF can be obtained. Though the approach is practical, this involves the design of complex traverse mechanisms and can be costly. To address this challenge, this paper presents a novel method for predicting combustor exit TDFs using much sparser measurements. The approach's effectiveness was examined using three engine representative combustor exit temperature measurements covering a single-burner, double-burner, and entire annulus. In all cases, the hot-streaks-related features are well resolved in the reconstructed temperature field, and the multiwavelet approximation method yields almost identical RTDF to experiment with majority variations of less than 1.0% using sparse measurements. In addition, the method's robustness was examined, and considerations for the implementation of the method were provided.

Temperature reconstruction of an axisymmetric enclosed reactive flow using simultaneous background oriented schlieren and infrared thermography

The temperature distribution of a premixed methane air flame running at a Reynolds number of 1300 on a circular burner, 12.7 diameter, enclosed in a fused silica cylindrical liner has been experimentally reconstructed using a non-invasive approach combining background oriented schlieren (BOS) and infrared (IR) thermography. BOS is used to characterize both the air ambient to the system, using an existing technique called 3D ray tracing, and the reactive flow inside the enclosure, with a novel modified version of 3D ray tracing. IR thermography is used to characterize the thermal/optical characteristics of the quartz glass enclosure itself, since the information is required as BOS is a line of sight imaging technique. Out of necessity, an approximated species independent relationship is used to calculate flow temperature from refractive index. A simulation is used to show this error is in the range of 5.8%–7%. Additionally, it is found that drastically simplifying the approach by removing the IR thermography system entirely and using the near outer wall air temperature from BOS/3D ray tracing to characterize the internal temperature of the quartz liner itself only causes a 1.5%–3.8% degradation in the accuracy of the reconstructed temperature field. The technique as presented is a relatively inexpensive, experimentally simple approach capable of determining the steady state temperature characteristics of optically accessible axisymmetric reactive flows.

A deep learning method based on partition modeling for reconstructing temperature field

Physical field reconstruction is highly desirable for the measurement and control of engineering systems. The reconstruction of the temperature field from limited observation plays a crucial role in thermal management for electronic equipment. Deep learning has been employed in physical field reconstruction, whereas the accurate estimation for the regions with large gradients is still difficult. To solve the problem, we propose a novel deep learning method based on partition modeling to accurately reconstruct the temperature field of electronic equipment from limited observation. Firstly, the temperature field reconstruction (TFR) task of electronic equipment is modeled mathematically and transformed as an image-to-image regression problem. Then a partition modeling framework consisting of an adaptive UNet and a shallow multilayer perceptron (MLP) is developed to establish the mapping from the observation to the temperature field. The adaptive UNet is utilized to reconstruct the whole temperature field, while the MLP is designed to predict the patches with large temperature gradients. Numerical case studies employing finite element simulation data are conducted to demonstrate the accuracy of the proposed method. Furthermore, the generalization is evaluated by investigating cases under different heat source layouts, power intensities, and observation point locations. The maximum absolute errors of the reconstructed temperature field are less than 1 K under the partition modeling approach.

Calculation Of The Nusselt Number From Temperature And Velocity Data Obtained From Enhanced 3D Two-Colour LIF And 3D PTV In A Rayleigh-Benard Convection Cell

Experimental study of Rayleigh-Benard convection (RBC) requires 3D measurement of the velocity and temperature due to the complexity of the physics of this system. Using a scanning system, the application of the 3D particle image velocimetry (PTV) and 3D time-resolved two-color laser-induced fluorescence (LIF) is investigated on a slender RBC cell. Calculation of the out-of-plane velocity component by using the planar velocity components and applying the continuity law is discussed. From these observations that calculation of the dimensionless heat transfer coefficient, the Nusselt number from the 3D reconstructed temperature field close to the boundary of the fluid domain is investigated.

Variability of the Early Summer Temperature in the Southeastern Tibetan Plateau in Recent Centuries and the Linkage to the Indian Ocean Basin Mode

Abstract Although many temperature time-series reconstructions, constructed on the basis of tree-ring widths, with lengths of centuries to millennia have been published for many parts of the southeastern Tibetan Plateau (SETP), field reconstruction has been unaddressed to date. Here, we present a tree-ring network comprising 53 chronologies (one δ13C chronology, one regional maximum latewood density chronology, and 51 width chronologies). Using the modified point-by-point reconstruction method, a temperature field consisting of data from 28 meteorological stations in the SETP over the past 200–500 y (the common period was from 1730 to 1998; the longest single period was from 1480 to 2002) was reconstructed. Principal component analysis and rotated principal component analysis results indicated that the reconstructed temperature field may be representative of spatial distribution characteristics. The temperature changes in the SETP were similar. The correlation coefficients between the reconstructed regional average temperature and each observed series were 0.44–0.83 (86% were greater than 0.6, and all the significance tests reported a level of 0.01). Temperature changes were mainly synchronous with those in the middle and low latitudes of the Northern Hemisphere. We then explored the influence of possible climatic forcing and found that the Indian Ocean Basin mode may be a principal factor controlling the interannual variations in the STEP summer temperatures.

Ultrasonic measurement and methods for reconstruction of temperature fields for the use in bioreactors

Abstract When operating bioreactors, monitoring the process temperature is of great importance. Ultrasonic temperature measurement enables this without the need for sensors inside the bioreactor. The average speed of sound can be determined from the travel time of ultrasonic waves along the path of known length between a transmitter and a receiver positioned in the reactor wall. Due to the temperature dependence of the speed of sound, the average temperature along the path can be calculated from the average speed of sound. If this measurement is carried out for a sufficiently large number of measurement paths in a slice plane of the bioreactor, the temperature field in this plane can be reconstructed. In this article, a measurement setup for measuring temperature distributions is presented. Two different methods are then used to reconstruct temperature fields from the travel times measured with this setup. The first method is the Tikhonov regularization, which is widely used to solve inverse problems. The second method is derived from compressed sensing and can only be used under certain conditions. However, if these conditions are met, this method always provides better results than Tikhonov regularization. In addition to reconstruction results from measured travel times, results from simulated travel times are also presented.

Acoustic tomography of temperature and velocity fields by using the radial basis function and alternating direction method of multipliers

Considering the acoustic refraction effect, an investigation of simultaneously visualizing the temperature and velocity fields is carried out by using the combined meshfree radial basis function and alternating direction method of multipliers (RBF-ADMM). The radial basis function is introduced to recover the null-space component. It assumes that the reconstructed fields are continuous functions according to their nature, which, therefore, adds the prior information of the continuity in the fields’ reconstruction. Meanwhile, the alternating direction method of multipliers with improving anti-noise capacity is employed to iteratively resolve the inverse acoustic tomographic problem in low Mach number, which makes the parallel implementation and distributed optimization possible. Different from the traditional methods for solving boundary value problems, a fast two-point ray-tracing algorithm is introduced to trace the curved sound waves more efficiently. Proof-of-concept demonstrations including the representative temperature and aerodynamic fields are performed. For the two scenarios of two-peak and two-vortex inhomogeneous fields with 10% measurement errors, the averaged absolute errors of the reconstructed temperature fields are 120.7 K, and 39.9 K, respectively, and that of the reconstructed velocity fields are 0.24 m/s and 1.23 m/s, respectively. In addition, a data-based verification, which depicts the Karman vortex street phenomenon, is carried out to prove the ability of this method. All the results confirm the feasibility and effectiveness of the proposed RBF-ADMM in simultaneously reconstructing the temperature and velocity fields under different complicated environment. The proposed method for visualizing the arbitrary temperature and velocity fields will provide crucial input for control system such as the engines and boilers to optimize the thermal fluid and combustion process.

A data fusion approach with high spatiotemporal resolution for wall temperature measurement upon jet impingement

A high spatial and temporal resolution of wall temperature measurement is beneficial for liquid film cooling design for thermal protection of rocket engine combustor chamber. The conventional thermocouple method has a high sampling frequency up to 50 kHz, but it is based on point measurement. The infrared (IR) thermal technique can achieve a two-dimensional surface temperature measurement, but the current sampling frequency is limited to a few hundreds of Hz. Here we report the application of the data fusion approach, which is integrated with proper orthogonal decomposition (POD) and compressed sensing (CS) to reconstruct the temperature field of a wall with high spatiotemporal resolution. In this approach, the low-frequency IR thermal camera data was analyzed by POD to acquire the POD modes. The high-frequency thermocouple data with the POD modes were utilized to get the high-frequency mode coefficients by CS. Subsequently, the temperature information reconstruction was completed with POD modes and the mode coefficients. The data fusion method was applied to reconstruct the 250 × 400 pixels temperature field with a frequency of 100 Hz. Using 10 thermocouples and the IR camera with sampling frequency f = 2 Hz, the root mean square error (RMSE) of the reconstructed temperature field is 1.11%, which shows the reliability of the present approach. The less thermocouple and the lower IR camera sampling frequency leads to poorer reconstruction quality, though the effect of IR camera sampling frequency is less significant than the number of thermocouples. The optimized sensor number and sampling frequency were determined by the RMSE in this paper. The RMSE of the data fusion method with the initial temperature T0 from 40 °C to 120 °C and the flow rate Q from 45 mL/min to 120 mL/min are less than 1.4%, which shows wide applicability of the present approach.

Improved Two-Color Method for Temperature Measurement of Soot Flames

An improved two-color method, which originates from an approximate emissivity ratio model based on the empirical emissivity formula by Hottel and Broughton, was developed to measure the temperature field of soot flames generated on a McKenna burner in the present study. In conjunction with the onion-peeling method and Tikhonov regularization, the reconstructed temperature fields of rich soot flames under varied equivalence ratios were obtained by calculating the 550 and 650 nm spontaneous emission signal images, which were recorded by an intensified charge coupled device, respectively. At the same time, an autoscanning R-type thermocouple was used to measure flame temperature for validating the reconstructed data. The results show that the reconstructed temperature distributions agreed well with the measured data by thermocouple, and the reconstructed temperature is more precise by the present improved two-color method than by the classic two-color method based on a constant emissivity assumption.

Multi-scale simulation of temperature on braided fibers reinforced composite plate considering the fluctuations

The direct simulation based on the braided model of a whole fibers reinforced composite (FRC) component puts forward too high request on the calculating ability. So a multi-scale simulating method of the temperature on braided FRC plate is built in this paper, considering the temperature fluctuations of braided structures. The effective model of braided plate and the periodic braided structure are built, to obtain the homogenized temperature field and the fluctuations of temperature, respectively. The Fourier series is applied to build the functions of temperature fluctuations. Then the reconstructed temperature field of braided FRC plate could be obtained based on the homogenized temperature field and the functions of temperature fluctuations. Finally, the temperature field with fluctuations based on the braided model of whole plate is also simulated and compared with the reconstructed temperature field, to validate the accuracy of multi-scale thermal analysis method. Additionally, the experiment of temperature test on the braided FRC plate is also carried out to validate the accuracy of simulation, which presented good accuracy. The results show that, the temperature distribution of the braided FRC plate has significant fluctuating characteristics, the temperature in the region with braided yarns is relatively lower comparing with that in the matrix region, and the distributions of fluctuations are highly similar to the braided structures. The homogenized model based on the effective thermal conductivities could not obtain the temperature fluctuations of braided FRC plate. The maximum temperature difference between the braided model and the homogenized model reaches 25.37 K. Finally the maximum relative variation between the reconstructed temperature distribution and the temperature distribution based on the braided model is 3.18%, so the multi-scale thermal analysis method in this paper has good accuracy in simulating the temperature distribution of braided FRC plate with fluctuations.