PSI - Issue 75

Mohamed El Yazrhi et al. / Procedia Structural Integrity 75 (2025) 262–275 Mohamed El Yazrhi , Jean-Yves Disson / Structural Integrity Procedia (2025)

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split the data into training and validation sets. The goal is to provide a clear and reproducible framework for evaluating each method under the same conditions.

5.1. Methodology for Data Preparation and Comparison (1) Test conditions and signal acquisition

To evaluate the performance of the three prediction methods, two vibration datasets were used. The first was recorded under controlled laboratory conditions using a vibrating electrodynamic shaker. The second, which is the main focus of the results, was collected during highway driving. An accelerometer was placed inside a vehicle, and the acceleration was recorded continuously while driving. For this study, only the highway sections were retained, as they better represent real-world use cases. The accelera tion signals were sampled at 10 kHz, which is high enough to

capture fine-grained dynamic behavior. (2) Signal filtering and spike removal

Before analyzing the signals, a dedicated filtering step was applied to remove abnormal peaks (spikes) that could distort the damage calculations. This process was carried out in two stages. First, points where both the amplitude and the derivative exceeded predefined thresholds were identified. These regions were considered as spikes and replaced using linear interpolation. Then, a second pass was performed using a peak detection algorithm to catch remaining high-amplitude peaks, which were also removed and interpolated. This two-step filtering ensured that the signal used in later stages was clean and representative of actual vibration, not corrupted by short-term artifacts. (3) FDS Computation The filtered signals were split into 1-second windows (each containing 10,000 samples), and the fatigue damage spectrum (FDS) was computed for each window with NOMAD. FDS was calculated using a set of virtual oscillators For each window, two pieces of information were extracted: the instantaneous FDS, and the cumulative FDS. This dual representation allows both local and global analysis of damage progression and forms the basis for the prediction methods. (5) Splitting data into training and validation sets The data was split in chronological order into two parts: the first 20% was used to train or calibrate the models, while the remaining 80% was used for validation. This forward-looking setup simulates how damage prediction would work in real-time, using only past data to forecast future damage. In total, the training duration corresponded to approximately 0.67 hours, while the validation phase covered around 2.68 hours. This clear separation ensures reliable and unbiased performance evaluation for each method. (6) Controlled comparison across methods To ensure a fair comparison, all three methods were tested using the same setup. The SDF was computed over 200 frequencies from 10 Hz to 1 000 Hz. A confidence level of 95% (α = 0.05) was applied in probabilistic methods, and the same data blocks and window sizes were used across methods. This consistent setup ensures that differences in performance come from the prediction models themselves — not from the preprocessing steps. with natural frequencies ranging from 10 to 1000 Hz. (4) Structure of the data and cumulative analysis