This paper investigates the application of artificial intelligence (AI) to create virtual sensors as cost-effective alternatives to physical sensors, specifically for temperature estimation in electric machines (e-machines), aiming to reduce system complexity and cost. It addresses the critical need for robust AI systems in high-stakes scenarios, ensuring reliability under noisy data conditions, which aligns with emerging regulatory frameworks like the EU AI Act. The study positions itself within the state-of-the-art by reviewing and comparing advanced machine learning (ML) algorithms—namely Uncertainty Quantification (UQ), Scientific Machine Learning (SML), Formal Guarantees, and Symbolic Regression—for their robustness and predictive guarantees over noisy inputs, extending beyond traditional approaches that often focus on adversarial attacks 4, 9. Unlike much of the existing literature, which emphasizes AI implementation for embedded systems 1, 2, this work prioritizes prediction robustness and formal guarantees, contributing to the growing field of trustworthy AI, including concepts like explainability and transparency 3. Using a dataset from twelve temperature sensors in an e-machine test rig, collected over 360 hours, the study trains neural network models with a consistent multi-layer perceptron architecture, optimized using Mean Squared Error (MSE) and the Adam optimizer. Robustness is assessed by introducing random noise to test inputs and evaluating metrics such as mean absolute deviation, maximum absolute deviation, and MSE. The paper provides a novel comparative analysis of these metrics alongside guarantee levels for each ML approach, offering insights into their suitability for reliable virtual sensor applications in automotive systems. This positions the work as a significant contribution to advancing robust AI-driven virtual sensing, particularly for real-time, safety-critical applications in the automotive industry.
Desmet et al. (Tue,) studied this question.
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