A Multimodal Approach to Predicting Toe Temperature: Experimental, CFD, and LSTM-Based Methods

Abstract: For technical footwear, such as mountaineering boots, there is currently no official standard for assessing and quantifying their thermal insulation, although this is crucial for footwear designed for use at high altitudes. Thermal insulation is not only important for the comfort of the wearer but also for safety during prolonged exposure to extreme conditions. This study aims to develop a customizable simulation model (based on Computational Fluid Dynamics, CFD) for mountaineering boots that allows the evaluation of their thermal resistance (RcT in m²K/W) according to the UNI EN ISO 15831:2004 standard.The 3D geometry of the boot was reconstructed with the Rhinoceros 7 CAD software based on a realistic reproduction of the considered boot prototype. The model simplifies the design by removing details such as laces, lace holes, and the outer gaiter, which does not contribute to thermal insulation. To increase realism, the model contains an air gap between the foot and the shoe in some specific areas, which reproduces the actual conditions as accurately as possible.The computational framework uses a User Defined Database (UDD), implemented in the CFD software Ansys Fluent to manage the material composition of the boot. The database contains the thermal properties of the materials used, such as thermal conductivity (in W/mK) and thickness (in mm), evaluated according to the UNI EN ISO 9920:2007 and UNI EN ISO 5084:1998 standards. The CFD simulations were validated by comparing the results with experimental data obtained with a Newton Thermal Manikin and showed a deviation of only 12%. This discrepancy is attributed to minor differences between the CAD model and the physical prototype of the boot. The validated CFD results provides the first relevant metric describing the insulation performance of the shoe.The simulation results are also integrated into a SARIMAX machine learning algorithm that predicts the temperature of the big toe over time starting from the average skin temperature (whose strong correlation with big toe temperature has been observed and confirmed through numerous human test experimental campaigns). The data used to train and test the SARIMAX algorithm came from in vivo tests performed in a climate chamber under four different environmental and activity conditions corresponding to different Metabolic Rates (MR). All tests were performed according to strict protocols to ensure reproducibility. This included standardized clothing for all participants and a uniform test time to minimize disruption to circadian cycles in thermoregulation. Core temperature was monitored as an additional control measure.This model is then used in connection to the JOS-3 thermoregulation model, a system of 83 interconnected nodes that calculates human physiological responses and body temperatures using a numerical backward difference method. The thermoregulation model is able to return the mean skin temperature, given as an input to the previously trained SARIMAX algorithm resulting in an otherwise unavailable (to JOS-3) big toe temperature.The predicted big toe temperature serves as a secondary parameter for evaluating the insulation performance of the shoe. The maximum exposure duration is defined as the time (in minutes or hours) required for the temperature of the big toe to reach the safety limit of 15°C. This two-parameter approach improves the evaluation of technical footwear and takes into account both comfort and safety in extreme environments.

Keywords: CFD, ML, thermal model, protective equipment

DOI: 10.54941/ahfe1006027

Cite this paper:

​