PSI - Issue 75

Sébastien Boudevin et al. / Procedia Structural Integrity 75 (2025) 72–84 Author name / Structural Integrity Procedia (2025)

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In post-processing analysis, these metrics are typically derived from the Hilbert transformation of a continuous time signal x(t) is defined as: ̂( ) = [ ( )] = 1 ∫ (− ) − + ∞∞ (2) For discrete signals, the Hilbert transform can be implemented using the FFT algorithm because it has a particularly simple representation in the frequency domain, so that if X(f) is the Fourier transform of x(t), then the function: ( ) = {2 ( 0 ( ) ) <= 0 0 >0 (3) S a (f) is the Fourier transform of x a (t), the analytic signal of x(t), which imaginary part is x̂(t) , the Hilbert Transform of x(t). Using the Hilbert transform, we define the following quantities: ( ) = 1 2 ( ( ). ( ) + ̂( ). ̂( )) (4) ( ) = 1 2 ( ( ). ( ) − ̂( ). ̂( )) (5) ( ) = √ ( ) 2 + ( ) ² (6) T hese quantities are typically averaged over a time interval Δt , with apparent power S is the magnitude of the vector sum of AC active P(t) and AC reactive powers Q(t). ( ) = ∆ 1 ∫ ( ) +∆ (7) ( ) = ∆ 1 ∫ ( ) +∆ (8) At the end, the power metrics are directly integrated to turn into energy consumption. The consistency of produced channels is carried out through calibration cases 3.3. Statistics Once all test data and new channel for analysis are created, the general statistics may be calculated for each channel (Min, Max, time of Max, time of Min, Mean, RMS, Skewness, Kurtosis), and saved as metadata. Other engineering interesting metrics are extracted (Energy consumed, distance traveled, time spent), and saved as well as metadata for later use in dashboards. 3.4. Data crunching A clever way of extracting relevant information for mission profile or any usage is to construct histograms, such as Rainflow cycle count, Level Crossing, FDS, RDS, or time at level, used by Chojnacki et al. (2019). All these compressed data may be mixed later into a mission profile, assuming linear combination of events (histograms) multiplied with their respective number of repeats or proportion in target usage. As part of event description, we need to characterize the uncertainty based on a collection of tests, using statistical and probabilistic tools.