Temperature Estimation Error Research Articles

Core body temperature estimation model with thermal contact resistance compensation

Continuous and accurate monitoring of core body temperature (CBT) is crucial for personal healthcare, clinical disease diagnosis, and enhancing athletic performance. Current CBT measurement methods typically ignore contact interface variation at the sensor-body interface, resulting in insufficient CBT measurement accuracy under daily wearable scenarios with varying sensor contact pressure. This study proposed a core temperature estimation model with thermal contact resistance (TCR) compensation, introducing the TCR factor into the computational equation to improve estimation accuracy in daily wearable scenarios. A numerical simulation of the temperature field between the human forehead and sensor was developed for model performance evaluation. Given the inconvenience of TCR measurement, this study proposed a method based on pressure/optical photoplethysmography (PPG) signals for updating thermal contact resistance. The mean absolute error of CBTER model under varying thermal contact resistance conditions was 0.26 °C, which was 27 % compared to traditional model errors in simulation. Using pressure updating methods, the result of human trials was 0.01±0.23 °C (with 95 % limits of agreement). Overall, the proposed method effectively compensated for errors in core body temperature estimation due to thermal contact resistance, holding potential for continuous core body temperature monitoring to meet healthcare needs scenarios.

Soil temperature detection based on acoustic method and improved Wyllie model

Soil temperature is one of the important environmental factors for the underground parts of plants. It is important to detect soil temperature in agricultural production. Acoustic waves serve as effective carriers of soil information, providing a reliable means to detect soil physical properties. In order to detect the temperature of sandy loam soil based on acoustic technology, this study extends the application of Wyllie model to the temperature measurement of sandy loam soil. The relationship between soil temperature and acoustic velocity is explored. A model of soil moisture content-soil temperature-acoustic velocity (MTV) for temperature measurement in sandy loam soil is proposed by extending the temperature–velocity of sound relationship with the introduction of a variable empirical coefficient related to soil moisture β(θ). In order to determine the parameters of proposed model, a pulsed acoustic velocity detection system was built in this paper. The influence of temperature on the acoustic velocity in sandy loam soil was analyzed through experiments. Based on the experimental results, the key parameters of the MTV model are refined. Finally, a validation experiment was carried out on sandy loam soil. The maximum estimation error of soil temperature based on the MTV model for sandy loam soil temperature estimation is 8.55 %. The results indicate that the MTV model proposed in this study can be used for temperature estimation in sandy loam soil, providing a theoretical basis for the development of acoustic soil physical information detection sensors.

Estimation of battery temperature during drive cycle operation by the time evolution of voltage and current

During the operation of electric vehicles, accurate temperature monitoring of lithium-ion batteries by battery management system is crucial to their safety. However, temperature sensors possess limitations as they necessitate regular calibration to avoid inaccuracies, which can be challenging to accomplish in certain scenarios. As an alternative, a general sensorless temperature estimation framework is developed in this study to either serve as a complementary approach alongside sensors or function independently to ensure reliable temperature measurement. The proposed framework relies solely on data regarding battery voltage and current measurements, and this information is employed to determine the parameters of the equivalent circuit model via the vector-type recursive least squares algorithm in the first step. In the second step, these parameters and the voltage/current data serve as the input to the deep neural network (DNN) to estimate the instantaneous battery surface temperature during dynamic driving cycles under various ambient temperatures and degradation scenarios. To reflect the effect of past battery operation on the current temperature, a newly defined current integral function is proposed, by which the input time length of the DNN model is suggested. Four combinations of the model input are studied, and the best input option yields an average estimation error of the battery temperature that falls below 0.5 °C.

Machine-learning-assisted long-term G functions for bidirectional aquifer thermal energy storage system operation

Optimization of aquifer thermal energy storage (ATES) performance in a building system is an important topic for maximizing the seasonal offset between energy demand and supply and minimizing the building's primary energy consumption. To evaluate ATES performance with bidirectional operation, this study develops an analytical solution-based model to simulate the spatiotemporal thermal response in an aquifer. The model consists of three temperature response functions, similar to the G functions in borehole thermal energy storage (BTES), to estimate the transient temperature profile in the aquifer during seasonally varying injection and extraction of hot/cold water. Applying machine learning (ML) based data classification and regression techniques to the results of a series of finite element (FE) benchmark simulations of typical ATES configurations, model input parameters are linked to the subsurface thermal, hydrogeological, and ATES operational properties. Compared to the benchmark simulation results, the errors of the proposed model in estimating the annual energy storage and locating the thermally affected area are about 3 % and 1 %, respectively. The model was applied to a previous short-term case study, and the error in the transient production temperature estimation is about 1 %. The long-term heat recovery ratio estimated from the model also compares well to those calculated from the previous study and the validated numerical model. Because of its fast computation, the proposed model can be coupled with the individual building system simulation and used for preliminary ATES design, and this will allow for greater exploration of ATES operational space and, therefore, better choices of ATES operating conditions. The proposed model can also be coupled with the district heating and cooling network simulation for computationally efficient city-scale long-term ATES potential assessment.

Multi-index-weighted geothermometer estimation of geothermal reservoir temperature: Applications and future directions

Geothermal reservoir temperature (GRT) is an important factor for estimation of geothermal resources and exploitative potential. Errors in the estimated temperature of a geothermal reservoir can likely result from the use of a single geothermometer or the average. Therefore, there is an urgent need for novel and more accurate methods for estimating GRT. Taking Yitong Basin, China as the study area, this study collected water samples and measured the geothermal water temperature of 26 geothermal wells. After application of the improved entropy method (IEM) to the collected data, a multi-index weighted geothermometer (MIWG) was proposed. The MIWG provided the most accurate estimation of temperature, with average errors in temperature estimation for quartz, chalcedony, Na–K, K–Mg, and MIWG of 57.58 %, 15.86 %, 29.92 %, 42.03 %, and 11.94 %, respectively. This novel approach to estimating GRT has clear advantages, including wide applicability, and can provide a new pathway for future related research.

Novel method to remotely measure air temperature distribution for indoor environments with heat sources using thermal infrared spectroradiometer

Air temperature is an important physical indicator of a built space. A novel method for remotely measuring the air temperature distribution using a thermal infrared spectroradiometer is evaluated, and an experiment using the maximum a posteriori method, which uses a priori information, is conducted with a heat source. The a priori information is the probabilistic information that the observer knows about the air temperature prior to the observation. Assuming an indoor scale (10 m), the air temperature distribution is estimated (i.e., retrieved) by discretizing the space into four layers. Accordingly, our method reduces the error in the air temperature estimation compared to the a priori information. When the layer of the heat source is known, the air temperature estimation is sensitive to the air temperature of the heated layer, even when the heat source is away from the sensor (2nd to 4th layers). The root-mean-square error (RMSE) of the heated layer decreased from 10 K (a priori) to 4.8 K. Although the RMSE of the temperature distribution was approximately the same regardless of the number of spectral channels used in the retrieval, the RMSE of the heated layer was smaller when ten spectral channels were used. In the case of a target space and spectrometer, as in this study, ten spectral channels were sufficient. These findings indicate the possibility of remotely measuring the air temperature distribution in a space with a local heat source (e.g., data centers), which is a relatively difficult case for remote sensing methods.

A dynamic thermal model for a photovoltaic module under varying atmospheric conditions

Operating temperature strongly affects the performance of the photovoltaic module. Thus, the accurate estimation of the module temperature plays an important role in the assessment of photovoltaic system generation. In this article, it was shown that the existing empirical models are characterized by a limited accuracy in determining the module temperature under varying atmospheric conditions, and the estimation error exceeded 25 °C. This feature of empirical models results from the neglect of the thermal inertia of the module. To solve this problem, a dynamic thermal model for the photovoltaic module was proposed. The proposed model is based on the Finite Difference Method and only uses data on the ambient temperature, solar irradiation, and wind speed. The model coefficients were optimized using the Particle Swarm Optimization method. Developed model was benchmarked against field measurements at the Silesian University of Technology, Poland. The performance of the proposed model was also compared with the performance of the dynamic thermal model proposed by Barry et al., using measurements from systems located in the Allgäu region, Germany. The results demonstrated the effectiveness of the proposed dynamic thermal model for the correct calculation of the photovoltaic module temperature under varying weather conditions. The temperature estimation error did not exceed 9 °C.

Laser-induced fluorescence spectroscopy for kinetic temperature measurement of xenon neutrals and ions in the discharge chamber of a radiofrequency ion source

Application of single-photon absorption laser-induced fluorescence (LIF) spectroscopy for non-intrusive measurement of neutral xenon and singly charged xenon ion kinetic temperatures in the discharge chamber of a gridded radiofrequency ion source is demonstrated. A LIF spectrum analysis approach including hyperfine structure reconstruction and inverse filtering (Fourier deconvolution) is outlined. Special focus is set on optimization of post-deconvolution filtering as well as retracing of deconvolution result imperfection due to hyperfine structure parameter uncertainty, incorrect natural linewidth, and saturation of the LIF signal. The corresponding contributions to the kinetic temperature estimation error are quantified via simulation of spectral lineshapes. Deconvolution of almost unsaturated LIF spectra recorded in the center of the ion source discharge chamber reveals that the neutral xenon and xenon ion kinetic temperatures range between approximately 500 and 700 K and, respectively, 700 and 1000 K depending on the radiofrequency power supplied to the discharge.

Computational fluid dynamics modelling of microclimate for a vertical agrivoltaic system

The increasing worldwide population is leading to a continuous increase in energy and food demand. These increasing demands have led to fierce land-use conflicts as we need agricultural land for food production while striving towards renewable energy systems such as large-scale solar photovoltaic (PV) systems, which also require in most of the cases agricultural flat land for implementation. It is therefore essential to identify the interrelationships between the food, and energy sectors and develop sustainable solutions to achieve global goals such as food and energy security. A technology that has shown promising potential in supporting food and energy security, as well as supporting water security, is agrivoltaic (AV) systems. This technology combines conventional farm activities with PV systems on the same land. Understanding the microclimatic conditions in an AV system is essential for an accurate assessment of crop yield potential as well as for the energy performance of the PV systems. Nevertheless, the complex mechanisms governing the microclimatic conditions under agrivoltaic systems represent an underdeveloped research area. In this study, a computational fluid dynamics (CFD) model for a vertical AV system is developed and validated. The CFD model showed PV module temperature estimation errors in the order of 0–2 °C and ground temperature errors in the order of 0–1 °C. The shading caused by the vertical PV system resulted in a reduction of solar irradiance by 38%. CFD modelling can be seen as a robust approach to analysing microclimatic parameters and assessing AV system performance.

Static sensor assisted rotor temperature estimation of permanent magnet machine for the low‐speed servo applications

AbstractA permanent magnet synchronous machine (PMSM) temperature estimation method fusing the classic lumped‐parameter thermal network (LPTN) and the stator sensor temperature information is investigated. With respect to the industrial servo applications, it is important to monitor the rotor magnet temperature to extend the machine thermal utilisation. A simple LPTN is developed and the quadratic programming is applied to identify the model parameters. The research work shows that the rotor temperature is sensitive to the rotor speed even at low speeds, and this simple estimation network can provide an accurate estimation. The winding sensor information can further improve the performance. A compound mechanism is built, by which the winding temperature estimation error is used as feedback to suppress the model‐based temperature estimation error accumulation. The estimation performance is compared with a regular constant LPTN‐based method. Experimental results based on a PMSM are presented to validate the proposed method.

Adaptive method for sensorless temperature estimation over the lifetime of lithium-ion batteries

Over the last decade, several impedance-based temperature estimation methods for lithium-ion cells have been proposed in the literature. However, the influence of cell degradation on these methods is rarely considered. In this paper, we therefore investigate the influence of aging on the temperature estimation method, presented in our previous work, by tracking the capacity fade and resistance change of a 6s1p module over 200 cycles. Both capacity fade and resistance change were found to affect the accuracy of the temperature estimation method, leading to a root mean square error (RMSE) of up to 15 K without adaptation to cell aging. Fitting the reference used for temperature estimation with linear operations and a nonlinear least-squares solver (NLS) to the aging data proved to be a valid method of compensating for the effects of aging. Derived from the fitting results, an online applicable aging adjustment scheme based on the checkup values is proposed to maintain a stable temperature estimation over battery lifetime. Using a simple resistance offset correction and an accurate state of charge and health estimation, the temperature estimation error stabilizes at an average RMSE of below 2 K for each cell in the module over its entire lifetime. • Sensorless method for resistance-based temperature estimation for lithium-ion batteries. • Investigation of the effects of cell aging on temperature estimation in a battery module. • Aging compensation with offset correction and accurate estimation of state of charge. • Stable temperature estimation over battery lifetime with online adaptation scheme.

A heat balance model of zinc pot and its application

In this paper, the problem of stripe temperature at the entrance of the zinc pot is addressed in a novel way. Based on in-depth analysis of thermal features of hot-dip galvanization, a generalized heat-balance mode has been established that has wider adaptivity within the production lines. The relationship between the pot load, the galvanization load and the productivity has been re-characterized by introducing a new concept of line-area ratio. Subsequently, the stripe temperature can be estimated based on the model. The effectiveness of the proposed model has been verified by real-time application to the production lines with temperature estimation error within ± 3 °C. As such, effective temperature compensation can be implemented that significantly improves the galvanization quality.

Online Junction Temperature and Current Simultaneous Extraction for SiC MOSFETs With Electroluminescence Effect

In this letter, a junction-temperature and current extraction method is presented based on the electroluminescence mechanism of the SiC <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mosfet</small> body diode. Starting from the observation of two characteristic peaks in the emitted light spectrum, we proved that the junction temperature and the drain current can be simultaneously measured. This novel method consists of decoupling the relationship between the intensity of the electroluminescence peaks, the current, and the temperature. Through this optical method with inherent electrical isolation, the junction temperature and current in the SiC chip can be simultaneously measured with high precision. The total error of the junction temperature estimation is within ±3 °C, and the error of the current estimation is about ±0.2 A.

A Novel Electro-Thermal Model of Lithium-Ion Batteries Using Power as the Input

Considering that use of measured current as input of a battery model may cause distortion of the model due to low accuracy of the on-board current sensor and that power can be used to indicate energy transmission in an electric vehicle model, the power input internal resistance model is widely used in simulation of whole electric vehicles. However, since no consideration is given to battery polarization and electro-thermal coupling characteristics, the foregoing model cannot be used to describe the internal temperature change of batteries under working conditions. Three contributions are made in the present study: (1) ternary lithium-ion batteries were taken as the research objects and a second-order RC equivalent circuit model with power as the input was established in the present study; (2) A dynamic heat generation rate model suitable for RC equivalent circuits was built based on coupled electrical and thermal characteristics of lithium-ion batteries; (3) An electric model and a two-state equivalent thermal network model were further built and combined by using the heat generation rate model to form a power input electro-thermal model. Parameters of the model so formed were identified offline, and the battery model was verified with respect to accuracy under seven working conditions. The results show that the maximum root mean square error in voltage estimation, current estimation, and surface temperature estimation is 19.38 mV, 9.51 mA, and 0.19 °C respectively, which indicates that the power input electro-thermal model can describe the electrical and thermal dynamic behavior of batteries more accurately and comprehensively than the traditional power input internal resistance model.

Acoustic Pyrometry Robustness to Time-of-Flight Estimation Errors

Abstract Acoustic pyrometry is a widely used technique for contactless temperature measurement. It may be used in several applications, especially when high temperatures and harsh environments are involved. For instance, it has been applied to measure the temperature distribution at gas turbine outlet. This technique is based on the measurement of the time of flight of an acoustic wave through a medium. If multiple emitter-receiver couples are used, using a computational procedure a reconstruction of a temperature map is possible. On the other hand, a full assessment of the robustness of this technique to potential errors in TOF estimation is still missing. In this study, the impact of an inaccuracy in TOF estimation on the reconstruction of a correct temperature map is investigated by means of a statistical approach. As a general result, it was found that when the TOF was measured without inaccuracies, temperature estimation errors may be lowered by simply increasing the number of cells in which the estimation is performed. However, when the estimation of the TOF is affected by errors, an optimal configuration exists that minimize the temperature estimation errors.

Sensorless Cell Temperature Estimation over the Lifetime of Lithium-Ion Batteries

The temperature distribution within a battery pack has a major impact on capacity loss, power degradation and safety issues. Therefore, monitoring the temperature of the cells in the battery pack is an essential task of a battery management system. Temperature is usually measured with external temperature sensors attached to a few crucial cells throughout the battery pack, leaving the majority of cells in larger battery packs unattended. In our recent work, we developed a method to determine cell temperatures using the temperature dependent voltage response to a current change in the load of the battery [1]. Thereby the temperature of each cell in a battery can be monitored without the need for additional temperature sensors as long as current and voltage values of the cell are available. The method relies on a DC resistance (RDC) reference to relate the voltage response to a temperature value. Since the resistance of a cell changes with the aging of the cell, the reference, and ultimately the temperature estimation method, loses its applicability with proceeding cell degradation. For this reason, we investigated the estimation method’s behavior during aging and possible ways to adjust the RDC reference. For the aging experiment, we used the same setting as in our initial work. A 6s1p module was cycled for 200 cycles, with every 5th discharge cycle being a randomized current profile, which is used for the evaluation of the temperature estimation method. The state of health (SOH) and a RDC offset are used to scale and shift the RDC reference. SOH and RDC offset were gained from checkup cycles, which were performed every 20th cycle. To maintain the online applicability of the method, only this values (SOH and RDC offset), which can be monitored by a battery management system (BMS), are considered for the adjustment of the RDC reference. We assume the SOH is a given value from the BMS and the RDC offset can be calculated from a defined or randomized pulse. The RDC offset can be used for the adjustment under the following two terms: (1) The system is in a thermal equilibrium, e.g. an electric vehicle that is parked for several hours. (2) There is at least one temperature sensor in the system. This sensor is needed to relate the RDC offset to a certain temperature. This simple adjustment strategy increased the estimation accuracy and allows the method from [1] to be used for the entire lifetime of the battery module with an average temperature estimation error of 2 K. To our knowledge, this is the first approach for resistance/impedance based temperature estimation of lithium-ion cells considering aging.[1] S. Ludwig, I. Zilberman, M.F. Horsche, T. Wohlers, A. Jossen - Pulse resistance based online temperature estimation for lithium-ion cells; Journal of Power Sources; 2021; DOI: https://doi.org/10.1016/j.jpowsour.2021.229523. Figure 1

Thermal Modeling of Large Electrolytic Capacitors Using FEM and Considering the Internal Geometry

This article focuses on developing a finite-element method (FEM) model for large capacitors’ thermal modeling and reliability analysis. Thermal modeling for capacitors is critical since the capacitor’s lifetime depends on the capacitor’s maximum temperature. Typically, capacitors have been modeled as a solid element, not considering the capacitor’s internal geometry, leading to temperature estimation errors and requiring extensive testing to adjust the model. The presented methodology to develop the model considers the internal geometry to obtain a reliable model, with sufficient simplicity to adapt the methodology to any electrolytic capacitor. To achieve good results, the capacitor’s winding is modeled as an anisotropic material to reproduce appropriately the behavior of the layers of aluminum and paper soaked in electrolyte. The results of the simulations match the experimental results closely, therefore validating the utility of the model.

Battery internal temperature estimation via a semilinear thermal PDE model

Accurate Lithium-ion (Li-ion) battery internal temperature information enables high-fidelity monitoring and safe operation in battery management systems, thus prevents thermal faults that could cause catastrophic failures. This paper proposes an online temperature estimation scheme for cylindrical Li-ion batteries based on a one-dimensional semilinear parabolic partial differential equation (PDE) model subject to in-domain and output uncertainties, using temperature measurements at the battery surface only. The thermal state observer design exploits PDE backstepping method, with a mild assumption on the Lipschitz continuity of the nonlinear heat generation rate. A sufficient condition on the Lipschitz constant to achieve exponential convergence is derived. Furthermore, when the thermal system uncertainties are present, an analytic bound on the temperature estimation error is formulated in the sense of spatial L2 norm, in terms of Lipschitz constant, design parameters, and bounds on system uncertainties. Simulation studies on various practical current profiles are demonstrated to illustrate the effectiveness of the proposed thermal estimation framework on a commercial cylindrical Li-ion battery cell.

Building Heat Load Estimation Method Including Parameter Estimation from Actual Data

In recent years, various method of air conditioning control and making operation plans have been developed. They require a building thermal model, but for making the model detailed design data is needed. Several model construction methods have been proposed up to now, but they are for buildings surrounded by walls made with one material. In this situation for deriving the room temperature and air conditioner power consumption, a parameter estimation method for estimating heat capacities and resistances of walls with different physical properties was developed. This method consists of two steps. At the first step, in steady temperature state, the least‐squares method is used to derive thermal resistances. In the second step, in non‐steady temperature state, an Unscented Kalman Filter (UKF) is used to derive heat capacities and solar‐radiation shading coefficients. UKF is adopted for numerical stability and short operation time. With this method, it is possible to obtain the independent parameters of each wall by repeating the evaluation using a simple model. These steps were applied to data obtained by simulation. As a result, the physical parameter error of the inner and outer walls was sometimes 10–60%. On the other hand, regarding to the estimation target, the error of the indoor temperature estimation was 0.3 °C, and the error of power consumption estimation was less than 4%, so high estimation accuracy was obtained. This confirmed the effectiveness of the proposed method. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Li-ion battery temperature estimation based on recurrent neural networks

The monitoring of Li-ion battery temperatures is essential to ensure high efficiency and safety. In this work, two types of recurrent neural networks (RNNs), which are long short-term memory-RNN (LSTM-RNN) and gated recurrent unit-RNN (GRU-RNN), are proposed to estimate the surface temperature of 18650 Li-ion batteries during the discharging processes under different ambient temperatures. The datasets acquired from the Prognostics Center of Excellence (PCoE) of NASA are used to train, validate and test the networks. In previous work, temperature has been set as the output of the networks; however, here the temperature difference along the time axis is adopted as the output. The net heat generated results in net temperature change, which is more closely aligned with electrochemical and thermodynamic laws. Extensive simulation results show that the two RNNs can achieve accurate real-time battery temperature estimation. The maximum absolute error in temperature estimation is approximately 0.75°C and the correlation coefficient between the estimated and measured temperature curves is greater than 0.95. The influences of three crucial parameters, which are the number of hidden neurons, initial learning rate and maximum number of iterations, are also assessed in terms of training time, root mean square error and mean absolute error.