@misc{9244498,
  abstract     = {{Virtual sensors implemented in vehicles enable the prediction of forces experienced during their operational lifetime and thus allow an extension of durability assessment into the operational phase of customer vehicles.

Due to limited computational capacity of onboard electronic control units, full-scale deep learning models are often too expensive for real-time operation. As a result, compact neural network architectures are employed. However, their limited model capacity prevents them from capturing all relevant characteristics of the underlying load history, leading to significant deviations in fatigue damage estimation based on
Rainflow Counting compared to the true damage.

To address this limitation, this thesis proposes a fatigue damage surrogate for Rainflow Counting based on the spectral method by Dirlik. The underlying spectral estimates, in particular the periodogram and the Welch method, are investigated with respect to their influence on the resulting damage, their computational efficiency, and their differentiability. Ensuring differentiability down to the spectral estimation level enables the integration of the damage surrogate as an additional loss term within the deep learning training process.

It is shown that the physics-informed Dirlik formulation produces extremely small gradients, introducing a bottleneck in the training process due to vanishing-gradient-like behaviour. By adapting the loss function, this issue is mitigated through effective gradient rescaling, allowing stable optimization.

The results demonstrate that training with a multitask-like loss improves the prediction of fatigue damage during inference. These findings provide a framework for enhancing virtual sensor predictions with respect to fatigue damage assessment.}},
  author       = {{Conrad, Katharina}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{Differentiable Fatigue Damage Modeling for Neural-Network-Based Virtual Sensing}},
  year         = {{2026}},
}