Predicting Temporal Friction Torque of Drum Brake Systems: A Mixed-Effects Random Forest Approach

Drum brake systems are becoming increasingly important in electric vehicles (EV) and purpose-built vehicles due to cost competitiveness and EURO-7 particulate emission regulations. Despite this trend, drum brake friction behavior remains incompletely characterized due to its dependence on multiple coupled variables: temperature history, braking conditions, and component interactions. To address this gap, this study presents a method for developing a time-series friction torque prediction model using the Mixed-effects Random Forest (MERF) machine learning framework. Time-series data collected from sensors during drum brake dynamometer tests were analyzed to identify the key variables that govern the friction torque. Significant inputs were selected through Exploratory Data Analysis (EDA), considering test-to-test variability and potential mixed effects, and were then used to train and tune the MERF model. Model performance was evaluated by comparing predicted friction torque with measured torque, and prediction error was quantified by using Mean Absolute Error (MAE) to check whether predicted model is reliable. The proposed prediction model demonstrates a high level of agreement with experimental measurements, confirming that the MERF approach can effectively capture the non-linear and transient characteristics of drum brake friction torque from time-series sensor signals. These results indicate that friction torque estimation is feasible using only sensor signals already available from conventional test instrumentation, without additional dedicated sensors. This capability is expected to support broader applications, including brake performance prediction for vehicles equipped with drum brakes and enhanced simulation of drum brake thermal performance across operating conditions.