Yang, Y., Peng, L., Lin, W., Zhang, J. and Zhang, Z. (2025) Improved Time-Domain Hybrid Extrapolation Method for Vehicle Durability Load Spectrum Based on Load Component Decomposition. Measurement, 245, Article ID: 116660.
https://doi.org/10.1016/j.measurement.2025.116660

has been cited by the following article:

• TITLE: Fatigue-Consistent Load Extrapolation Based on Tail-Weighted Histogram-Regularized LSTM

  AUTHORS: Yu Bai, Fei Meng

  KEYWORDS: LSTM Sequence Modeling, Load Extrapolation, Rainflow Counting

  JOURNAL NAME: World Journal of Engineering and Technology, Vol.14 No.1, January 28, 2026

  ABSTRACT: This study proposes a Tail-Weighted Histogram-Regularized LSTM (TWHR-LSTM) to extend 10s load signals into longer sequences while preserving fatigue characteristics. The method removes trends, normalizes the signal, and trains a sequence-to-sequence LSTM model using overlapping windows of 2000 data points. The model’s loss function includes reconstruction error, histogram distance, variance regularization, and a penalty for large step changes to focus on extreme rainflow cycles. Compared to traditional parameter and KDE rainflow extrapolation methods, TWHR-LSTM better reproduces the tail of the load range spectrum, with a pseudo-damage ratio error of only 1.2%. It shows superior performance in maintaining fatigue characteristics and signal quality.