Machine learning digital twin predicts electric powertrain efficiency in real time

Engineers have built a digital twin of an electromechanical powertrain that predicts its efficiency in real time using machine learning, offering an alternative to the slow and costly test bench measurements that traditionally dominate the late stages of electric vehicle development. The work, published in Advanced Modeling and Simulation in Engineering Sciences, compares six different modeling approaches for the same powertrain and identifies a hybrid strategy that balances prediction accuracy, speed and measurement effort.

Highly detailed physical simulations can be accurate but slow to run and demanding to build, while purely data-driven models are fast but may sacrifice insight into the system. Their solution was to test the entire spectrum, from a purely physical white-box model through black-box machine learning to several hybrid grey-box architectures that combine physical equations with learned components.

The physical test object was an electric powertrain consisting of a permanent magnet synchronous machine with a nominal power of 400 kW at 12,000 rpm, driving a multi-stage transmission made up of a spur gear stage and a planetary gear stage. The experiments took place on a Road-to-Rig full vehicle test bench from KS Engineers, arranged as a back-to-back setup. An asynchronous machine with 440 kW nominal power simulated the road load counter-torque at the transmission output, with both machines connected through constant-velocity drive shafts.

The sensor concept was deliberately comprehensive. Torque was measured with HBM T40B torque flanges rated at 1 kNm on the input side and 5 kNm on the output side, while rotational speeds were captured with Heidenhain angle and speed sensors. A Yokogawa WT5000 power analyzer recorded voltages and currents in all three phases of the drive motor and derived quantities such as power factor, apparent power, reactive power and active power. Oil temperature in the lubricating oil was measured with a type K thermocouple, and fresh Shell Spirax S6 AXME 75W-90 oil was filled into the system before testing.

Data collection followed carefully designed load collectives. Reproduction tests first revisited ten selected load points five times each to verify the reproducibility of the measurement configuration, and the results showed excellent repeatability for nearly all measured and calculated variables, with only the slowly changing oil temperature and low-torque operating regions showing larger relative dispersion. The main training campaign then approached 789 randomized load points spanning speeds from 0 to 580 min⁻1 and torques from 0 to 2,000 Nm, with increased point density near the 2,000 Nm torque limit. A separate, systematically arranged set of 269 load points, covering 75 to 580 min⁻1 and 270 to 2,000 Nm, was reserved exclusively for validating the models, so that training and test data never mixed.

Preprocessing converted the raw 30-second time series, sampled at 1 kHz, into one characteristic value per variable and load point. Thermal and mechanical variables were averaged, while electrical signals were low-pass filtered and reduced to root mean square values of voltage and current together with the phase shift. From these quantities the team calculated the efficiency of the energy converter, the mechanical subsystem and the overall powertrain. Correlation matrices confirmed that the data reflected the known physics of a synchronous machine and a gearbox, with motor torque strongly correlated with current and speed strongly correlated with voltage, supporting the suitability of the data set for model building.

The six models were built in MATLAB using the Regression Learner app, in which 31 candidate model variants, including linear regression, decision trees, ensembles, support vector machines, Gaussian process regression and neural networks, were trained with five-fold cross-validation so that the best variant could be chosen for each prediction task. Training ran on a notebook with an NVIDIA GeForce MX550 GPU, 32 GB RAM and an Intel Core i7-1260P processor. Performance was judged not only on mean and maximum absolute and relative errors of the overall efficiency prediction, but also on training time, model size, point-wise prediction speed in kHz and a newly introduced output-to-input quotient that captures how much information a model delivers relative to the measurement effort it demands.

The results were striking. The purely physical white-box model, which fits constants such as torque and speed constants from the training data, produced a mean absolute error of 4.36 percent and a maximum absolute error of 14.85 percent, demonstrating that limited analytical knowledge cannot capture the non-linear behavior of the real powertrain. In contrast, all machine learning-based approaches reduced the mean absolute error to between 0.34 and 0.84 percent. The dark-grey-box model with two machine learning blocks achieved the best accuracy at 0.34 percent mean absolute error, while the simplest black-box model reached 0.37 percent with a training time of only 5.57 seconds.

The final choice, however, was the bright-grey-box model with four machine learning integrations, designated Model 6. This architecture predicts the power factor from current and voltage, removing the need to measure it during operation, and raises the output-to-input quotient to 2.67, the highest among the machine learning approaches. Despite a slightly higher mean absolute error of 0.84 percent, a prediction speed of 10 to 14 kHz and a compact model size of 187 kB make it suitable for real-time integration into vehicle control systems. Detailed analysis showed the selected model predicting output torque with a mean relative error of just 0.01 percent and input torque with 0.39 percent, although the power factor remained the least accurate quantity, particularly at low rotational speeds.

The authors note that limitations remain in predicting the power factor at low speeds and in generalizing to other powertrain configurations, and future work will explore extended data sets, transfer learning and implementation on embedded hardware. Even so, the study demonstrates that data-driven digital twins with physically informed structures can deliver early, real-time efficiency predictions for electromechanical powertrains, supporting front-loading strategies that reduce development costs and shorten time to market for electrified commercial vehicles.

Subject of Research: Data-driven digital twin modeling of electromechanical powertrain efficiency using machine learning and physical modeling

Article Title: Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling

Article References: Kopp, L., Ockert, N., Cadau, L., & Kley, M. (2026). Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling. Advanced Modeling and Simulation in Engineering Sciences, 13(1), Article 13. https://doi.org/10.1186/s40323-026-00333-w

Image Credits: AI Generated

DOI: 10.1186/s40323-026-00333-w

Keywords: digital twin, electric powertrain, machine learning, hybrid modeling, efficiency prediction, permanent magnet synchronous machine, test bench, grey-box model, real-time simulation, electric vehicles, Development, digital