Temperature Estimates Research Articles

QCD with 2+1 flavors at the physical point in external chromomagnetic fields

We investigate full quantum chromodynamics (QCD) with (2+1)-flavor of highly improved staggered quarks fermions at the physical point in the presence of uniform Abelian chromomagnetic background fields. Our focus is to conduct an exploratory study on the renormalized light and strange chiral condensates around the pseudocritical temperature. We find that in the confined region the gauge system is subjected to the chromomagnetic catalysis that turns into the inverse catalysis in the high-temperature regime. We further observe that the chiral condensates are subjected to the so-called thermal hysteresis. Our estimate of the deconfinement temperature indicates that the critical temperature begins to decrease in the small field region, soon after it seems to saturate and finally increase with the strength of the chromomagnetic field. Published by the American Physical Society 2024

Using Google Earth Engine open-source code for land surface temperature estimation from Landsat data in Chuong My district, Hanoi city, Vietnam

Land surface temperature (LST) in association with urbanization has significantly influenced on local climates and terrestrial surface processes. By using multi-temporal Landsat data in the GEE platform, the study has found that there have been changes in land covers due to the main drivers of industrial development, urban and built-up expansion. This study estimated land surface temperature (LST) in Chuong My district from Landsat 5, 7, 8 and 9 thermal infrared sensors, using different surface emissivity sources. The Google Earth Engine (GEE), an advanced earth science data and analysis platform, offers the estimation of LST products, covering the time period from 2000 to 2024 in study site. RF algorithm for land cover classification and mapping is suggested to be applied in Chuong My district, with overall accuracy of land cover mapping in 2024 being 91.9% with Kappa coefficient of 0.89. The period 2000-2010 showed that 327.0 ha of land were converted to land for industrial development, urban and residential land, while the period 2010-2024 continued to witness a continued conversion of land to other land use purposes, with a decrease in agricultural land area (65.7 ha) and an increase in industrial land use (65.2 ha), but the rate of conversion was much lower than the previous period (2000-2024). The periods of 2000-2010 and 2010-2024 showed that there have been significant changes in land surface temperature. Most of the surface temperature in the entire region increased by over 20C, especially in the period 2003-2015 when a total area of 1424 ha had the temperature increased by above 30C. This is a consequence of the process of urbanization and industrialization, which began to take place in 2008, along with the process of changing the land cover status of the study area. Further studies are needed to better understand the thermal conductivity of surface materials and to plan how to reduce LST in such areas.

Unveiling Ecosystem Shifts in the Southern Benguela Through Otolith Biochronologies of Sardine (Sardinops sagax)

ABSTRACTSardine (Sardinops sagax) in the southern Benguela has shown substantial changes in population size over the past 70 years. Heavy fishing pressure in the 1950s to early 1970s caused the collapse of sardine stocks in South Africa. A fishery collapse happens because of significant alterations in the marine community, hindering the recovery of valuable commercial species and leading to cascading effects across multiple trophic levels in marine food webs. In this study, a robust 58‐year biochronology (1962–2019) was developed using archived sardine otoliths from the West of Cape Agulhas in South Africa. Sequential t‐test analysis of regime shifts (STARS) performed on the biochronology of fish growth indicated four regimes with three alteration points in 1986, 2006 and 2015 that correspond with periods of low, high, average and low biomass, respectively; that is, high growth rates occurred during the high biomass period and vice versa. A series of mixed effects models was developed to determine increment width response to selected environmental, prey availability and sardine biomass factors based on the assumption that otolith increment growth is a proxy for somatic growth. Predicted sardine growth positively correlated with sardine biomass, sea surface temperature and copepod abundance estimates. This observation suggests that sardine population dynamics exhibit a depensation mechanism, potentially destabilizing populations after the fishery collapse. Sea surface temperature and copepod abundance have been primary factors influencing sardine growth, partly because of depensatory population dynamics. Furthermore, the study improves understanding of how different factors have affected sardine growth following the collapse of the sardine fishery.

Criticality-enhanced precision in phase thermometry

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study noninvasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behavior of finite many-body systems beyond the validity of mean-field models. Published by the American Physical Society 2024

Integration of ML methods with CR model-based optical diagnostic for the estimation of electron temperature in Ga laser produced plasma

Accelerated diagnostic of plasma plays a significant role in controlling and optimizing plasma-mediated processing, particularly for plasma with higher temporal and spatial gradients, such as laser produced plasma (LPP). In the present work, two advanced machine learning (ML) algorithms, random forest regression, and gradient boosting regression are integrated with noninvasive collisional radiative (CR) model-based optical diagnostics to facilitate accurate diagnostics. A comprehensive fine-structure resolved CR model framework is developed by incorporating our consistent cross section data obtained from the Relativistic Distorted Wave method [Suresh et al., “Fully relativistic distorted wave calculations of electron impact excitation of gallium atom: Cross sections relevant for plasma kinetic modelling,” Spectrochim. Acta B: At. Spectrosc. 213, 106860 (2024)]. An extensive dataset of CR model simulated intensities is created to train and test the ML methods. The present CR model is applied to characterize the Gallium LPP coupling with the optical emission spectroscopic measurements of Guo et al. [“Time-resolved spectroscopy analysis of Ga atom in laser induced plasma,” Laser Phys. 19, 1832–1837 (2009)] at different delay times. Further, a detailed correlation study of the line intensity ratios is performed to observe the qualitative behavior of the plasma parameters. The electron temperature results obtained from the CR model, ML, and line ratio methods were compared and found to be in excellent agreement. Overall, the present study demonstrates diagnostic approaches that can benefit the LPP community significantly by providing a rapid understanding of the plasma behavior across various operating conditions.

Core temperature estimation of lithium-ion battery based on numerical model fusion deep learning

Temperature has a critical impact on the lifespan and safety of lithium batteries. This paper proposes a battery core temperature estimation method based on numerical model fused with long short-term memory (LSTM) neural network. The proposed technique extracts features from the numerical model, estimates the volume-averaged temperature by electrochemical impedance spectroscopy (EIS), uses an LSTM neural network to learn thermodynamic parameters and complex calculations, which takes advantage of the strengths of each method, and achieves accurate core temperature estimation. The effects of state of charge (SOC) and temperature on EIS are explored, impedance properties are selected on the criteria of robustness and rapidity, and the estimation of the volume-averaged temperature is achieved using the imaginary part of the impedance. The proposed method can achieve root mean squared error (RMSE) of less than 0.28 °C and mean absolute error (MAE) of less than 0.23 °C. The proposed method has advantages of high estimation accuracy and does not require an electrothermal model. It also considers the effect of ambient temperature and has a good generalization capability.

Estimation of the silicone rubbers glass transition temperature using the method of thermally stimulated depolarization currents and thermodynamic functions at the first-order phase transitions

Estimation of the silicone rubbers glass transition temperature using the method of thermally stimulated depolarization currents and thermodynamic functions at the first-order phase transitions

Heat transfer study on a stator-permanent magnet electric motor: A hybrid estimation model for real-time temperature monitoring and predictive maintenance

When electrical machines operate without a specific cooling system, the surrounding environment plays a crucial role in the rise of temperature and the duty cycle of operation. More clearly, a natural convection cooling system with a low value of heat transfer coefficient carries the risk of thermal breakdown, insufficient safety, and reliability. This paper studies the heat transfer aspects of a low-power flux switching permanent magnet (FSPM) motor under natural convection cooling to implement a novel real-time sensor-less temperature monitoring system. Thermal and electromagnetic experiments are carried out to create foundations for transient and steady-state numerical models. A data-driven, deep learning algorithm estimates the core and permanent magnet (PM) eddy current losses in real-time, besides the already available copper and friction losses. Subsequently, a two-node thermal equivalent circuit in a hybrid model with a feed-forward neural network estimates the dynamic temperature profile of windings and PMs. It is indicated that the worst-case estimation error is below 7.5%, and the configuration is applicable under a wide range of operation states and environmental conditions. Lastly, the system, including the power source, FSPM motor, and hybrid temperature estimation unit, will be implemented in MATLAB/Simulink to investigate the fault prediction and operation management capabilities.

Geochemical constraints on reaction temperature and pressure and heat- and mass-transfer efficiency at Rainbow Hydrothermal Field

Seafloor vent fluids hosted by oceanic core complexes (OCCs) are thought to represent circulation of seawater-derived hydrothermal fluid along deeply penetrating, low-angle detachment faults. However, estimation of the source temperatures and pressures of such fluids has been limited because geochemical methods typically require vent fluid silica concentrations to be buffered by quartz, a condition not often met at oceanic core complexes. Here, we extend the calculation of the Si-Cl geothermobarometer to enable predictions of fluid Si concentrations in equilibrium with any Si-buffering mineral assemblage, rather than being restricted to quartz. We apply this method to Rainbow Hydrothermal Field vent fluid compositions and find that they are consistent with buffering by a plagioclase+talc+chlorite+tremolite mineral assemblage at conditions ranging from (430 °C, 359 bar) to (470 °C, 468 bar), which correspond to depths of 1.3–2.4 km below the seafloor. These estimates agree well with the locations of seismically imaged magma chambers within the Rainbow Massif. Additionally, calculations of fluxibility and Fe solubility support this relatively shallow origin for Rainbow vent fluids and imply relatively efficient heat and Fe extraction from the seafloor. We estimate that only 24–30 % of the heat content and almost no Fe is lost during upflow of Rainbow vent fluids.Compared to other OCC-hosted seafloor vents, the source region of Rainbow vent fluids is anomalously shallow, an observation consistent with geological interpretations of the Rainbow Massif. Vent fluids at Rainbow Hydrothermal Field have exhibited apparently stable and greater-than-seawater salinity for over two decades. We interpret these vent fluids as vapors derived from a higher-salinity source fluid that developed over multiple cycles of magma injection and phase-separation inherent to the formation of oceanic crust along slow-spreading, non-volcanic segments of oceanic spreading centers. Alternatively, higher-salinity source fluids could be derived from mineral hydration reactions associated with serpentinization of ultramafic rocks. The occurrence of greater-than-seawater salinity vent fluids is thus predicted to be a common feature of OCC-hosted vent fields, as indicated by several known examples, including the TAG, Kairei, and Edmond vent fields.

Population of excited levels of Fe+, Ni+, and Cr+ in exocomets’ gaseous tails

The star β Pictoris is widely known for harbouring a large population of exocomets, which create variable absorption signatures in the stellar spectrum as they transit the star. Although the physical and chemical properties of these objects have long been elusive, the recently developed exocomet curve of growth technique has, for the first time, enabled estimates of exocometary column densities and excitation temperatures, based on absorption measurements in mutliple spectral lines. Using this new tool, we present a refined study of a β Pic exocomet observed on December 6, 1997 with the Hubble Space Telescope. We first show that the comet’s signature in Fe II lines is well explained by the transit of two gaseous components, with different covering factors and opacities. Then, we show that the studied comet is detected in the lines of other species, such as Ni II and Cr II. These species are shown to experience similar physical conditions as Fe II (same radial velocity profiles and same excitation temperatures), hinting that they are well mixed. Finally, using almost 100 Fe II lines rising from energy levels between 0 and 33 000 cm–1, we derive the complete excitation diagram of Fe+ in the comet. The transiting gas is found to be populated at an excitation temperature of 8190 ± 160 K, very close to the stellar effective temperature (8052 K). Using a model of radiative and collisional excitation, we show that the observed excitation diagram is compatible with a radiative regime, associated with a close transit distance (≤60 R⋆ ∼ 0.43 au) and a low electronic density (≤107 cm–3). In this regime, the excitation of Fe+ is controlled by the stellar flux, and does not depend on the local electronic temperature or density. These results allow us to derive the Ni+/Fe+ and Cr+/Fe+ ratios in the December 6, 1997 comet, at 8.5 ± 0.8 ⋅ 10–2 and 1.04 ± 0.15 ⋅10–2, respectively, close to solar abundances.

New constraints to subduction zone arc and backarc mantle temperatures: a test of the corner flow model

The heat source for the hot volcanic arc of subduction zones and the uniformly warm backarc is not well understood, particularly where backarc extension is absent. In the widely studied corner flow model, the traction of the underthrusting plate drags down the overlying viscous mantle, and the induced shallower seaward flow brings in heat from the landward and deeper asthenosphere. However, earlier comparisons with observations, especially backarc heat flow, gave poor agreement. There are several new constraints to the temperatures and structures above the underthrusting plate and in the backarc, especially those in western North America, for comparison with model predictions. Seismic receiver functions map horizontal boundaries, including the lithosphere-asthenosphere boundary (LAB). Seismic shear wave tomography gives mantle velocity-depth that provides an approximate proxy for temperature. Attenuation of seismic wave speed indicates high temperature or partial melting. The presence of recent backarc volcanics and their geochemistry give the depth and temperature of the LAB. From these constraints in western North America, the LAB reflects ponding of partial melt, is consistently at a depth of 65±3 km and temperature of 1350±25°C, and overlies nearly constant temperature (adiabatic) asthenosphere across the backarc from Mexico to Alaska. These depth and temperature estimates are greatly different from corner flow model predictions. An alternative hypothesis more consistent with these constraints is vigorous small-scale convection in the backarc asthenosphere. Whether or how this convection coexists with the large-scale flow patterns inferred from the interpretation of seismic anisotropy analyses, and to what degree it prevails in the arc-forearc region, deserve further research.

Deciphering the properties of UV upturn galaxies in the Virgo cluster

Abstract The UV upturn refers to the increase in UV flux at wavelengths shorter than 3000 Å observed in quiescent early-type galaxies (ETGs), which still remains a puzzle. In this study, we aim to identify ETGs showing the UV upturn phenomenon within the Virgo galaxy cluster. We utilized a color-color diagram to identify all potential possible UV upturn galaxies. The Spectral Energy Distributions (SED) of these galaxies were then analyzed using the CIGALE software; we confirmed the presence of UV upturn in galaxies within the Virgo cluster. We found that the SED fitting method is the best tool to visualize and confirm the UV upturn phenomenon in ETGs. Our findings reveal that the population distributions regarding stellar mass and star formation rate properties are similar between UV upturn and red sequence galaxies. We suggest that the UV contribution originates from old stellar populations and can be modeled effectively without a burst model. Moreover, by estimating the temperature of the stellar population responsible for the UV emission, we determined it to be 13,000 K to 18,000 K. These temperature estimates support the notion that the UV upturn likely arises from the contribution of low mass evolved stellar populations (extreme horizontal branch stars). Furthermore, the Mg2 index, a metallicity indicator, in the confirmed upturn galaxies shows higher strength and follows a similar trend to previous studies. This study sheds light on the nature of UV upturn galaxies within the Virgo cluster and provides evidence that low-mass evolved stellar populations are the possible mechanisms driving the UV upturn phenomenon.

Occurrences of the Rare, REE Minerals Daqingshanite, Törnebohmite, Biraite, Sahamalite, and Ferriperbøeite from the Sheep Creek Area, Montana, USA

Over 30 small, discontinuous, tabular carbonatite bodies are located in the Sheep Creek area, Ravalli County, southwest Montana. The age and origin of these REE-Nb-rich deposits are currently being investigated. The purpose of this paper is to document the occurrence of several rare minerals, including daqingshanite, törnebohmite, biraite, sahamalite, and ferriperbøeite, in two of the carbonatite bodies. These minerals are found in association with monazite, hydroxylbastnäsite, ferriallanite, calcite, dolomite, baryte, quartz, actinolite, apatite, celsian, and Sr-rich aragonite. Automated SEM-EDS was used to target the areas of interest in polished specimens for more detailed spot SEM-EDS and electron probe microanalysis. Raman spectra were also acquired for each of the rare minerals. The complex mineralogy of the Sheep Creek carbonatites is most likely due to several overlapping thermal events, including primary magmatic, overprinting hydrothermal, and supergene weathering stages. The rare minerals described in this study are believed to be hydrothermal and/or carbothermal in origin, although no estimates of temperature are available at this time.

Application of meta-heuristic hybrid models in estimating the average air temperature of Caspian sea coast of Iran

The rise of industrial societies leads to higher greenhouse gas emissions, profoundly affecting the climate in coastal regions. Consequently, air temperature readings from standard meteorological stations are key indicators of the Earth's environmental condition. Therefore, accurate estimation of daily temperature in each region is one of the important prerequisites for agricultural planning as well as water resources management and drought prevention, which can be done in different ways such as experimental, semi-experimental and intelligent models. In this research, WSVR, AIG-SVR, GWO-SVR and BAT-SVR hybrid models were investigated and evaluated in order to estimate the average daily air temperature on the shores of the Caspian Sea located in the north of Iran. For modeling, weather station data from Babolsar meteorological station located in Mazandaran province were used. During the water year from 2012 to 2022, daily parameters including relative humidity, maximum temperature, minimum temperature, wind speed, and evaporation were selected as network inputs, with the average daily air temperature as the network output. To assess and compare model performances, several criteria were employed including correlation coefficient, root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NSE), and percentage bias. Comparative analysis revealed that the WSVR model surpassed other models, demonstrating the highest correlation coefficient (0.992), lowest RMSE (0.096), and lowest MAE (0.042). The highest Nash Sutcliffe criterion (0.996) and bias percentage (0.001) were prioritized in the validation stage.

Spatial Analysis of the Impacts Caused by Changes in Land Use on the Estimation of Surface Temperature in the The City of Paracatu (MG)

The increase in built-up areas, coupled with the suppression of vegetation without the necessary mitigating measures to curb the effects of urbanization, causes changes in the microclimate and directly impacts the health of the local population. In this sense, the present study aims to analyze the influence of land cover type on the variation of Land Surface Temperature (LST) estimation in the city of Paracatu, Minas Gerais (MG), in the years 1990 and 2020.For this, the maps provided by the Annual Mapping of Land Cover and Land Use of Brazil (MapBiomas) and images from the LANDSAT-5 (1990) and LANDSAT-8 (2020) satellites were used. Four images, distributed across seasons, were utilized to estimate LST for these periods, aiming to obtain a representative LST estimate for that year. For the calculation of the LST with bands 6 and 10, respectively of the LANDSAT-5 and 8 satellites, the SCP plugin of the QGIS software was used, and the process of recovery of the LST in the scenes used occurred through conversion of the values of the Digital Number (DN) into radiance at the Top of the Atmosphere (ToA), conversion of radiance into brightness temperature in ToA, correction of atmospheric effects and obtaining LST in Kelvin and, subsequently, in degrees Celsius. After that, the average between them was performed by means of normalization of each of the scenes, obtaining a representative mosaic for the LST of each year,thus enabling the estimation of the spatial behavior of the minimum, mean, and maximum values.. Finally, in order to verify the influence of Changes in Use and Occupation (LULC) on the spatial variation of the LST, the classes found in Vegetation, Exposed Soil, Urban Area and Water Resources were segmented, and it was found that, while the urban area of Paracatu had its territorial extension practically doubled, the vegetation class decreased by almost 25%, a fact that implied in the average increase of the LST by more than 5º C. the minimum and maximum values of these classes varied around 4.5 and 3º C, and it is possible to conclude that, in this interval of 30 years, Paracatu had no urban growth occurring exponentially and without the proper mitigations for the transformation of the microclimate, implying the need for measures that can curb these changes in strategic points of the municipality, as in the Bom Pastor neighborhood, which had its use and occupation totally changed in this temporal hiatus. In addition, in view of the estimates of economic growth in the city, it is believed that these measures should be taken as a matter of urgency, so that the results presented here can support the decisions of the managing public agencies.

Direct estimates of nitrogen abundance for Seyfert 2 nuclei

Abstract We derive the nitrogen and oxygen abundances in the Narrow Line Regions (NLRs) of a sample of 38 local (z < 0.4) Seyfert 2 nuclei. For that, we consider narrow optical emission line intensities and direct estimates of the electron temperatures (Te-method). We obtain a new theoretical expression for the nitrogen Ionization Correction Factor [ICF($\rm N^{+}$)] for NLRs. Applying this new ICF, we unexpectedly find that NLRs and disk H ii regions exhibit similar ICF distributions. We find nitrogen abundances in the range $7.6 \: < \: \rm 12+log(N/H) \: < \: 8.6$ (mean value 8.06 ± 0.22) or $\rm 0.4 \: < \: (N/N_{\odot }) \: < 4.7$, in the metallicity regime $8.3 \: < \: \rm 12+log(O/H) \: < \: 9.0$. Our results indicate that the dispersion in N/H abundance for a fixed O/H value in AGNs of ∼0.2 dex agrees with that for disc H ii regions with similar metallicity. We show that Seyfert 2 nuclei follow a similar (N/O)-(O/H) relation to the one followed by star-forming objects. Finally, we find that active galaxies called as ”nitrogen-loud” observed at very high redshift (z > 5) show N/O values in consonance with those derived for local NLRs. This result indicates that the main star-formation event is completed in the early evolution stages of active galaxies.

Reducing Laser Exposure Time of PBF-LB/P by Providing High Energy Without Thermal Degradation and Its Effect on Part Strength and Process Time

Abstract One of the most promising additive manufacturing technologies for the production of end-use parts is powder bed fusion of polymer with laser beam (PBF-LB/P). This technology can reduce production costs by increasing process efficiency and production speed. As PBF-LB/P is a layer-wise additive manufacturing process, the production speed can be increased by reducing the layering time. Although some operations such as recoating are performed during the layering process, considerable time is spent on laser scanning. To reduce the laser exposure time while maintaining proper powder melting, a high-power beam should be irradiated to the powder layer to prevent energy shortage. However, as the laser beam power increases, the irradiance at the beam center increases significantly, causing powder degradation such as thermal decomposition or sublimation. In this study, an appropriate input energy range was determined by obtaining an input energy limit that does not cause powder deterioration via experimental observations and temperature estimations during the process. Furthermore, the influence of the scanning parameters on the mechanical properties of built specimens was investigated to reduce the layering time within an indicated range. Results show that the mechanical strength of the built parts decreases slightly as the scan spacing increases following the expansion of the beam diameter. This study also validated the effects of scanning parameters on layering time. As a result, by doubling the scan speed and spacing, the layering time can be reduced by up to 1/3.

Temperature measurement in laser–metal processing using optical sensing: Radiometric calibration and validation of a multispectral camera

In laser–metal processing such as Laser-based Powder Bed Fusion of Metals (PBF-LB/M), the quality of the final product is significantly influenced by the thermal behaviour of the melt pool. Accurate temperature measurements are challenging due to high temperature gradients and rapid cooling. This study introduces Multispectral Imaging (MSI) as a highly effective thermometry technique to address these demanding conditions. MSI captures multiple bands of radiation, enabling the simultaneous determination of absolute temperature and surface emissivity. This capability is crucial for ensuring high-quality outcomes in laser–metal processing such as PBF-LB/M, contingent upon robust radiometric calibration.To enhance reliability, two radiometric calibration models were developed: an empirical model based on linear sensor data correlations and an analytical model leveraging sensor behaviour. An efficient calibration was found for both models across a range of signal-to-noise ratios in the black body calibrator, where the analytical model even performs robust under a high noise level.Additionally, the temperature accuracy in the solid-state case was tested with a thermo-mechanical simulator. Results showed that the empirical and analytical models achieved mean relative errors of 2.0% and 1.6%, respectively, outperforming the state-of-the-art. Further, laser irradiation experiments highlighted the analytical model’s ability to accurately determine the emissivity decrease during the solid-to-liquid transition, allowing for accurate melt pool temperature estimations. Conversely, the empirical model struggled to estimate temperature effectively in the liquid phase.This study not only proposed a robust methodology of MSI in temperature measurement but also confirmed the accuracy and reliability of the system, broadening the scope for further investigation into the intricate thermal dynamics involved in laser–metal interactions.

Remotely Sensed Estimation of Daily Near-Surface Air Temperature: A Comparison of Metop and MODIS

Remotely Sensed Estimation of Daily Near-Surface Air Temperature: A Comparison of Metop and MODIS

An Approach to Estimate the Temperature of an Induction Motor under Nonlinear Parameter Perturbations Using a Data-Driven Digital Twin Technique

To monitor temperature as a function of varying inductance and resistance, we propose a data-driven digital twin approach for the rapid and efficient real-time estimation of the rotor temperature in an induction motor. By integrating differential equations with online signal processing, the proposed data-driven digital twin approach is structured into three key stages: (1) transforming the nonlinear differential equations into discrete algebraic equations by substituting the differential operator with the difference quotient based on the sampled voltage and current; (2) deriving approximate analytical solutions for rotor resistance and stator inductance, which can be utilized to estimate the rotor temperature; and (3) developing a general procedure for obtaining approximate analytical solutions to nonlinear differential equations. The feasibility and validity of the proposed method were demonstrated by comparing the test results with a 1.5 kW AC motor. The experimental results indicate that our method achieves a minimum estimation error that falls within the standards set by IEC 60034-2-1. This work provides a valuable reference for the overheating protection of induction motors where direct temperature measurement is challenging.