This repository implements the line spectral estimators written in Python used in the published article "Real-time sinusoidal parameter estimation for damage growth monitoring during ultrasonic very high cycle fatigue tests".
Abstract:
Ultrasonic fatigue tests (UFT) are used to study the fatigue life behavior of metallic components undergoing a very high number of cycles (typically ≥ 10^7 − 10^9 cycles) under relatively low mechanical loads. By soliciting fatigue specimens at 20 kHz, ultrasonic fatigue machines are indispensable for monitoring damage growth and fatigue failures in a reasonable amount of time. As fatigue damage accumulates in the specimen, the specimen’s free-end exhibits a nonlinear dynamic response. The resulting quasi-stationary, harmonic signals have sinusoidal parameters (frequency and amplitude) which are slowly time-varying with respect to the excita- tion frequency. The discrete Fourier transform (DFT) is typically used to extract these evolving sinusoidal parameters from a window of finite data of the vibration signal. Alternative spectral estimation methods, specifically line spectra estimators (LSEs), exploit a priori information of the signal via their modeling basis and overcome limitations seen by the DFT. Many LSEs are known to have state-of-the-art results when benchmarked on purely stationary signals with unit amplitudes. However, their performances are unknown in the context of slowly time-varying signals typical of UFT, leading to a widespread use of the DFT. Thus, this paper benchmarks classical and modern LSEs against specific synthetic signals which arise in UFTs. Adequate algorithms are then recommended and made publicly available to process experimental data coming from ultrasonic fatigue tests depending on performance metrics and experimental restraints.
If you use this code, please cite this work:
[1] S. L. Kiser, M. Rébillat, M. Guskov, and N. Ranc, “Real-time sinusoidal parameter estimation for damage growth monitoring during ultrasonic very high cycle fatigue tests,” Mechanical Systems and Signal Processing, vol. 182, p. 109544, Jan. 2023, doi: 10.1016/j.ymssp.2022.109544.
We recommend the usage of the Anaconda distribution and the included Spyder IDE. Spyder is a unique Python IDE that offers a MATLAB-like experience with an integrated variable viewer.
Two zip files are provided for download due to size constraints:
| Filename (download) | Size | Description |
|---|---|---|
| lineSpectraVibration-Full-v1.1.0.zip | 756.35 MB | Includes the source code and all DeepFreq weight files for all signal lengths tested in the submitted manuscript. |
| lineSpectraVibration-Lite-v1.1.0.zip | 26.44 MB | Includes the source code and only the DeepFreq weight file corresponding to a signal length (N = 128). |
For required packages, refer to requirements.txt. The packages can be installed quickly using pip and/or in a virtual environment:
pip install -r requirements.txt
Or if using Anaconda:
conda install pip
pip install -r requirements.txt
Make sure to make the main folder the console's working directory.
example.py is a script that generates a random number of stationary cissoids K = 5 with a normalized frequency distance of d = 2/N as a discrete with a signal length N = 128 and an SNR of snr = 30. These parameters are indicated on lines 14-17:
N = 2**7
K = 5
snr = 30
d = 2/N
The script utilizes a timer class TicToc() which behaves very similarly to MATLAB's tic toc. For all 6 algorithms, results of time taken, frequency and their respective amplitude estimates are given.
At the end, a plot is created comparing the discrete Fourier Transform (via FFT), Unitary ESPRIT, and DeepFreq frequency and amplitude estimates.
The vertical black dotted lines correspond to the true normalized wrapped frequencies and the horizontal black dotted line corresponds to the correct amplitude.
The example.py script should be understood as a reference for syntax (especially for PyTorch), function calls, and the object-oriented organization.
This research was part of a PhD thesis funded by Arts et Métiers (École nationale supérieure d'arts et métiers). Laboratory equipment was provided by H2020 FastMat (fast determination of fatigue properties of materials beyond one billion cycles) project under the European Research Council (ERC) (grant agreement No 725142) at PIMM laboratory.
Distributed under the MIT License. See LICENSE for more information.