Estimation Of Temperature Field Research Articles

Physics-Informed Fully Convolutional Networks for Forward Prediction of Temperature Field and Inverse Estimation of Thermal Diffusivity

Abstract Physics-informed neural networks (PINNs) are a novel approach to solving partial differential equations (PDEs) through deep learning. They offer a unified manner for solving forward and inverse problems, which is beneficial for various engineering problems, including heat transfer analysis. However, traditional PINNs suffer from low accuracy and efficiency due to the fully-connected neural network framework and the method to incorporate physical laws. In this paper, a novel physics-informed learning architecture, named physics-informed fully convolutional networks (PIFCNs), is developed to simultaneously solve forward and inverse problems in thermal conduction. The use of fully convolutional networks (FCNs) significantly reduces the density of connections. Thus, the computational cost is reduced. With the advantage of the nodal-level match between inputs and outputs in FCNs, the output solution can be used directly to formulate discretized PDEs via a finite difference method, which is more accurate and efficient than the traditional approach in PINNs. The results demonstrate that PIFCNs can flexibly implement Dirichlet and Neumann boundary conditions to predict temperature distribution. Remarkably, PIFCNs can also estimate unknown thermal diffusivity with an accuracy exceeding 99%, even with incomplete boundaries and limited sampling data. The results obtained from PIFCNs outperform those obtained from PINNs.

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

An analytical model for thermoelastic crack problems in a strip incorporating convective heat transfer between lateral surfaces and ambient environment

Most existing thermoelastic crack models commonly overlook the convective heat exchange occurring on the lateral surfaces of the structures being studied. Consequently, there is often a concern regarding the accurate estimation of temperature fields and the resulting thermal stresses. To address this concern, this paper presents a two-dimensional (2D) thermoelastic model for a cracked strip that incorporates convective heat transfer between the lateral surfaces and the ambient environment. The crack problem is reduced to a set of singular integral equations with Cauchy kernels which are solved numerically. Analytical solutions for temperature distribution, stress intensity factors (SIFs) and energy release rate at crack tips are obtained. The influence of the ratios of convective heat transfer coefficient to thermal conductivity and thickness to height of the strip on the key fracture parameters is investigated through the numerical results. It has been discovered that classical thermoelastic crack models often exhibit a significant underestimation of the SIFs and energy release rates for cracks located near the hot boundary of the strip. The analytical model proposed in this paper has significant potential to advance our understanding of thermoelastic fracture mechanics.

Non-destructive estimation of temperature field during laser-induced tumor hyperthermia based on Kalman filtering

Laser-induced thermal therapy (LITT) is an emerging minimally invasive treatment technique for tumors. Non-destructive acquisition of the transient temperature field in the target tissue is a key in studying and developing LITT technology. In this paper, a non-destructive temperature field estimation scheme based on Kalman filtering theory is proposed to address the challenge of temperature field monitoring during the LITT process. This scheme establishes a state space model that corresponds to the fundamental equations of heat transfer in biological tissues. Subsequently, the real-time estimation of the transient temperature field within the target tissue is conducted by integrating the temperature observations on the surface of the tissue with the state space model of heat transfer in biological tissues and the Kalman filtering theory. Numerical experiments are conducted in this study to estimate the transient temperature field inside the target tissue during the therapy of LITT. The effect of the number of temperature observation points on the surface of the target tissue, laser irradiation conditions, and measurement noise on the estimation results of the transient temperature field within the target tissue is also discussed.

Enhancing remote sensing of water temperature using acoustic tomography and 3-D-RPS algorithm

Remote sensing of water temperature and flow dynamics is of paramount importance for water environment management. Coastal acoustic tomography (CAT), an innovative method for remote sensing in underwater environments, utilizes the dual-way travel time of multiple sound paths to reconstruct the underwater temperature field. However, the transmission experiments are susceptible to data noise caused by station drift and inaccuracies in travel time extraction. In this study, a three-dimensional Rousseeuw Phase-Space (3-D-RPS) thresholding algorithm is proposed to remove outliers in the travel time data obtained from Huangcai Reservoir using three CAT systems on September 16, 2020. Additionally, this work includes grid partitioning based on sound path propagation, calculation of sound path lengths, and reference transmission time within each grid, construction of a sparse matrix, and inversion of the two-dimensional temperature field and its associated inversion error. The accuracy and applicability of the proposed method are confirmed through a comparison with data obtained from temperature–depth (TD) sensors. The results demonstrate the precision and suitability of this approach. By effectively mitigating the impact of station drift and extraction accuracy issues, this method provides a reliable temperature field estimation.

A 3D thermal conductivity prediction method for deep strata based on temperature field estimation

Accurate predictions of earth’s interior thermal conductivity are essential for interpreting the mechanisms involved in geothermal systems and delineating geothermal resource targets. Existing thermal conductivity prediction methods, which typically involve measurements of rock samples and predictions based on geophysical well logging, cannot accurately predict regional thermal conductivity distributions. We develop a 3D thermal conductivity prediction based on temperature field estimation. First, the finite-element method is used for temperature forward modeling. Subsequently, the inexact Gauss-Newton method is implemented in the prediction algorithm. Synthetic studies indicate that the method can recover the true model well. The subsurface temperature distribution of the Xiong’an New Area is predicted using the coefficient correction method of the optimal temperature. Next, we obtain the 3D distribution of thermal conductivity of deep formation in the Xiong’an New Area with the predicted temperature field. The distribution of terrestrial heat flow also is estimated. In addition, the law of thermal accumulation of strata at different depths is analyzed, and the internal relation among resistivity, temperature, and thermal conductivity is studied. Thus, the 3D thermal conductivity prediction method provides the theoretical basis for interpreting mechanisms for the origin of geothermal systems and heat accumulation patterns. It could have significant utility for the analysis of geothermal fields and the sustainable development and use of geothermal resources.

Modelling the furnace temperature field of a municipal solid waste incinerator using the numerical simulation and the deep forest regression algorithm

The furnace temperature field is key information to reflect the combustion conditions and is related to process safety, equipment failure rates, and pollution emissions in municipal solid waste incinerators. However, the measurement of the actual temperature distribution of the incinerator is difficult because of the limitations of physical sensors (thermocouples). A new furnace temperature field modeling strategy was proposed to address the above problem. It included five virtual temperature points, with the numerical simulation and the deep forest regression algorithm used. First, numerical models of different benchmark conditions were established via FLIC. Second, modeling data were obtained by orthogonal experiments. Third, deep forest regression based on the fully connected cross layer (DFR-clfc) was used to establish five virtual temperature models. The five models had high prediction performance (R2 = 0.707, 0.870, 0.918, 0.895, and 0.907) and characterized the distribution of the furnace temperature. The grate speed had the greatest influence on temperature distribution, and based line condition (2) was more suitable for a stable operation. The novelties of the work are as follows. (1) Furnace temperature field estimation based on FLIC simulation and data-driven model. (2) Multi-conditions design based on micro, composition, and operating parameters. (3) Multi-dimensional visual analysis of incinerator virtual temperature field. (4) Temperature field model by using deep ensemble forest with potential interpretability.

Simultaneous estimation of heat flux and temperature field using optimal two-stage Kalman filters

Inverse estimation of unknown input heat flux and temperature field plays an important role in thermal state monitoring. Optimal two-stage Kalman filter (OTSKF) is introduced into the inverse estimation of thermal state in this work. To further improve its performance, a new method weighted optimal two-stage Kalman filter (WOTSKF) algorithm is developed, in which a forgetting factor is used to modify OTSKF. The estimation performances of OTSKF and WOTSKF are compared in a two-dimensional heat transfer system. They are employed to estimate the state with heat flux of temporal, spatial, and spatiotemporal variation. Additionally, the effects of forgetting factor and measurement noises on the estimation accuracy of heat flux and temperature are investigated. Though decreasing the forgetting factor can improve the tracking ability and estimation accuracy of WOTSKF, it should not be too low due to the reason that low α causes fluctuation of estimation results. When the standard deviation of measurement noises σr increases from 0.05 to 2.00, the mean relative error of estimated heat flux ηq using OTSKF rises from 4.03% to 10.67% and it climbs from 2.76% to 7.07% using WOTSKF. That demonstrates proposed WOTSKF has stronger robustness than OTSKF.

Optimal-Sensing-Based Recursive Estimation for Temperature Distribution of Pouch-Type Batteries

Real-time monitoring of the battery temperature distribution is essential in developing advanced thermal management systems. This work proposes a recursive temperature field estimation methodology for pouch-type batteries under optimal deployment of limited sensing. First, we utilize the time/space (T/S) spectral expansion to mathematically derive a physics-based dynamic model considering uncertainty from the complex thermal process. Then we find the optimal sensor placement through the observability degree of the system quantified by the attenuation rate of estimation error (AREE). Finally, we perform model-based temperature field estimation, whose performance is boosted by favorable measurements from layout-optimized sensors. Experimental studies indicate the validity of the proposed method.

Simultaneous estimation of time-varying temperature field and boundary heat flux in participating medium by the improved Kalman filter algorithm

Simultaneous estimation of time-varying temperature field and boundary heat flux in participating medium by the improved Kalman filter algorithm

Real-time estimation of thermal boundary conditions and internal temperature fields for thermal protection system of aerospace vehicle via temperature sequence

Aerospace vehicles go through extremely aerothermal heating upon entry into the atmospheric, which need to employ the reliable thermal protection system (TPS). The boundary heat flux and inner temperature information for aerospace vehicles are required to design the TPS. The direct measurement for temperature and heat fluxes is quite difficult mission. In this study, unscented Kalman filtering, is an indirect measurement method based on inner surface temperature information and is introduced to reconstruct the transient heat flux and inner temperature fields of TPS in real-time, which is regarded as a graded index medium. The finite volume method and discrete ordinate method are utilized to solve the energy equation and radiative transfer equation to obtain measurement temperature, respectively. Based on the measurement temperature signal, the unscented Kalman filtering technique is applied to reconstruct the surface heat flux and inner temperature field of the TPS. Simulation results indicate the time-dependent boundary heat flux and inner temperature fields can be estimated using proposed method. The effects of thickness, refractive index, measurement noise, and process noise on the reconstructed results are studied in detail. Retrieval results show the proposed technique is more precise and robust than Kalman filtering method in the nonlinear system.

Thermal error prediction of ball screw feed system based on inverse heat transfer analysis

The thermal error of the ball screw feed system will reduce the positioning accuracy of the machine tool, and the main reason for the thermal error is the friction heat generated by bearings and screw nut in the feed system. Therefore, a time-varying thermal error prediction method of the ball screw feed system based on the inverse method is proposed in this paper. Based on data-driven and dynamic thermal network model, the heat source estimation method of ball screw feed system under unsteady thermal effect is established, and the thermodynamic equilibrium equation is deduced into explicit form for heat source load identification. Aiming at the common matrix ill-conditioned problem of load identification, the regularization algorithm is used to identify the heat source load, and the optimal selection method of regularization parameters is proposed based on Monte Carlo algorithm. Using the collected temperature experiment data and the position data of the moving nut, the dynamic heat source load, temperature field, and thermal error of the feed system under the actual working condition are predicted and analyzed by using the inverse method. Finally, the accuracy and effectiveness of the prediction method are verified by experiment. The inverse method proposed in this paper has great application potential for the prediction and estimation of heat source and temperature field of machine tools and various mechanical structures.

A computational framework based on FEA, ML and GA for estimation of welding residual stresses

The present work describes a computational framework based on finite element (FE) analysis and machine learning (ML) and genetic algorithm (GA) to accurately estimate and minimize the residual stresses in welding. The FE analysis comprises of sequentially coupled thermal and mechanical analyses that are nonlinear due to temperature-dependent thermal/mechanical properties. In the FE analysis, the effective stress function (ESF) algorithm is used for accurate computation of the temperature-induced elasto-plastic stress field during welding. The ESF algorithm accounts for the large variation of yield curves due to temperature changes in welding. To improve the accuracy of the thermal and mechanical analyses, an optimization process combining supervised machine learning and binary coded genetic algorithm is utilized. This optimization technique is implemented to derive an accurate phase-change model for the thermal FE analysis of SS304, which is otherwise a burdensome and costly task to obtain from calorimetric experiments. The results obtained through the derived phase-change model are validated through welding time-temperature distribution reported for a welding experiment in literature. The same optimization process is further used to obtain a set of weld operating conditions (such as weld voltage, current, welding speed, and the gap between plates) for SS304 that reduce the tensile residual stresses. It is found that the accurate estimation and reduction of welding residual stresses can be realized by using the present computational framework. • A detailed FE analysis is presented for the estimation of residual stresses in welding. • ESF algorithm implemented in the FE analysis is found very useful. • An optimization methodology is proposed based on machine learning and genetic algorithm. • Proposed optimization scheme is used to estimate the phase-change model and weld parameters. • Accuracy in estimation of welding temperature field is improved and tensile residual stress is minimized to a certain extent.

Temperature Estimation during Pulsed Laser Sintering of Silver Nanoparticles

During the thermal sintering of metal nanoparticles (NPs) the process temperature plays the most important role in the outcome of the sintering results and the selection of a suitable substrate. Here, temperature calculation during pulsed laser sintering of silver (Ag) nanoparticles (NPs) inkjet-printed on glass substrates is presented. During the pulsed laser sintering of Ag NPs, a minimum line resistivity less than twice the bulk silver resistivity was obtained within around 52 s under a laser power of 276 mW. The temperature field during the pulsed laser sintering of Ag NPs was estimated via a three-dimensional numerical model in which a temperature-dependent thermal conductivity of Ag NPs was adopted. An algorithm for treating the thermal conductivity of the heated Ag NPs in a region by a previous laser shot was devised for the improvement of the temperature field estimation. A maximum temperature of approximately 204 °C over the Ag NPs line was obtained with a 276 mW laser power and a scanning speed of 135 μm/s.

Direct estimation of transient temperature field of heat transfer system based on mapping characteristics fuzzy clustering

In many engineering fields involving heat transfer process, real-time estimation of temperature fields is a fundamental task with significantly practical requirements. In this paper, a direct estimation method for retrieving the transient temperature field is developed based on mapping characteristics fuzzy clustering (MCFC). Mapping eigenvectors of the heat transfer system are determined by the heat transfer equations without specific system input information. According to the fuzzy clustering of the mapping eigenvectors, a temperature field predictive model space is reduced to cover the mapping relationship of the temperature field by finite representative spatial points, and to establish a fuzzy membership relationship between the mapping characteristics of the representative spatial points and that of the temperature field. The temperature field is estimated in real-time by synthesizing the temperature measurements of the representative spatial points. For the proposed method, the effectiveness as well as the adaptability is analyzed and verified by the achieved results on the preheating process of a steel casting mold. Furthermore, comparisons between the present method and other methods are conducted.

Research on numerical simulation of wear temperature field of vehicle brake disc based on SIFI feature

In order to overcome the problems of low simulation accuracy and long time in traditional numerical simulation method of vehicle brake disc wear temperature field, a numerical simulation method of vehicle brake disc wear temperature field based on SIFI characteristics is proposed. The temperature field simulation model of vehicle brake disc wear is built, and the temperature field estimation results are obtained. On this basis, after the Gaussian scale space is generated by using SIFI features, the key point descriptor is generated by determining the key extreme points and the direction of the key points, so as to extract the characteristics of the vehicle brake disc wear temperature field. According to the feature extraction results, the numerical simulation of the vehicle brake disc wear temperature field is carried out. The experimental results show that the simulation accuracy of this method is more than 92%, the average simulation time is 33.9 ms, and the comprehensive performance is better.

Numerical modelling of non-premixed biogas and LPG combustion to study carbon nanostructures formation in flame

This work presents the numerical simulation of biogas and LPG fuelled diffusion flames in an axisymmetric chamber to study in-depth, the formation mechanism of soot and carbon nanostructures in these flames. The simulation is formulated on the set of transport equations that involve the equations for conservation of mass (the continuity equation), momentum (Navier-Stokes equation), energy, and chemical species. The governing equations are solved using ANSYS FLUENT, which is centered on the finite volume method. To predict the soot formation, one step soot model has been incorporated. The solution of these equations permits the estimation of temperature field and species concentrations inside the flame. Simulation is conducted at fixed fuel flow rate and varied oxygen flow rates. The results reveal that the formation of soot and carbon nanostructures is strongly dependent on peak flame temperature and concentration of precursor species formed in the flame. Since two fuels produce an exclusive chemical environment in the flame, the flame temperature and CO concentration that is conducive to the growth of carbon nanostructures is higher for LPG fuel as compared to that for biogas. Hence, the nucleation process of carbon nanostructures is faster for LPG than biogas. Moreover, the reactions taking place inside the flame at different locations can also be predicted from flame temperature and species concentration at that location. Pyrolysis of fuel occur near the burner exit, followed by the nucleation and surface growth of carbon nanostructures in the nearby region and oxidation of formed carbon nanostructures near the flame tip.

Temperature field estimation of an axisymmetric laminar flame via time-of-arrival measurements of acoustic waves, and machine learning

In this study, temperature field estimation was performed via time-of-arrival measurements of acoustic waves and using machine learning. An axisymmetric combustion field created by a McKenna burner was chosen as the measurement region. Electrical discharges served as the acoustic point source, and the acoustic travel times were measured using microphones installed along the periphery of the measurement region. In particular, acoustic waves refract under a temperature gradient, which makes it difficult to obtain an explicit analytic expression for the solution. Hence, a model that predicts the profile from the acoustic travel times was acquired through machine learning. As the number of acoustic paths with different travel times was four, the radial temperature profile was first parameterized by four variables. Then, big data of acoustic travel times corresponding to a set of variable values were produced using a simulator that calculates acoustic trajectories and the corresponding travel times. Finally, the model, in the form of the simplest artificial neural network with a single hidden layer, was trained with the generated big data. The temperature fields were obtained from the measured acoustic travel times using the model and found to match well with those measured using a thermocouple.

Real‐time temperature estimation method for electromagnetic performance improvement of a large axisymmetric radio telescope under solar radiation

The temperature field caused by solar radiation can seriously affect the electromagnetic (EM) performances of large-aperture and high-frequency radio telescopes, and achieving the EM performance improvements under solar radiation is of great importance. In this study, combining temperature simulation and measurement, a fast estimation method of the temperature field is presented. First, a temperature database based on transient temperature field simulation is constructed in advance, and by utilising the telescope's axisymmetric structure, the dimension of the database can be greatly reduced. Then, a small number of temperature sensors are installed and the real-time measured data are applied to correct the simulation temperature field extracted from the above temperature database by the table look-up method, which can ensure the temperature field estimation speed. Thus, based on the real-time estimated temperature field and the telescope's finite element model, thermal deformations can be calculated in real-time and used for deformation compensation. A 7.3 m reflector antenna with 21 temperature sensors is adopted to verify the proposed strategy, and the results show the effectiveness and feasibility of the strategy. This study can provide helpful guidance for the real-time compensation of thermal deformations derived from large axisymmetric telescopes.

Investigation of suspended nanoliquid flow of Eyring–Powell fluid with gyrotactic microorganisms and density number

The aim of the current investigation is to discuss the behavior of mixed convection magnetohydrodynamic flow of Eyring–Powell nanoliquid subjected to gyrotactic microorganisms over a stretchable cylinder. Energy communication is developed through the first law of thermodynamics and deliberated in the manifestation of viscous dissipation. Furthermore, Brownian motion and thermophoresis effects are also considered. Nonlinear system of partial differential equations is altered into ordinary one due to employing transformations. The given systems are then solved through ND-solve technique. Impact of influential variables on velocity, motile microorganism’s temperature, and concentration is deliberated graphically. Skin friction coefficient, mass transfer rate, density number, and Nusselt number are numerically computed versus different influential variables. Velocity and temperature have opposite impact for curvature parameter. For higher estimation of fluid parameter, temperature and velocity fields boost up.