Sparsity measures are effective indicators for quantifying the sparsity of data sequences. They are often used for fault feature characterization in condition monitoring and fault diagnosis of rotating machinery. This function file and Demo script file provide the code and corresponding numerical examples of traditional and recently developed typical sparsity measures, including kurtosis (Kurt), negentropy (NE), D-norm (DN), ratio of 2-norm to 1-norm (L2/L1), Gini index (GI), modified smoothness index (MSI), Gini index 2 (GI2), Gini index 3 (GI3), generalized Gini index (GGI), fully generalized Gini index (FGGI), and power function-based Gini indices 1,2 and 3 (PFGI1, PFGI2 and PFGI3). It is hoped that these results will help to understand sparsity measures. The relevant references are as follows:
[1] B. Chen, D. Song, F. Gu, W. Zhang, Y. Cheng, A.D. Ball, A. Bevan, J. Xi Gu, A full generalization of the Gini index for bearing condition monitoring, Mech. Syst. Signal Process. 188 (2023) 109998. https://doi.org/10.1016/j.ymssp.2022.109998.
[2] B. Chen, F. Gu, W. Zhang, D. Song, Y. Cheng, Z. Zhou, Power function-based Gini indices: New sparsity measures using power for bearing condition monitoring, Struct. Heal. Monit. (2023). https://doi.org/10.1177/14759217221149745.
[3] B. Chen, D. Song, Y. Cheng, W. Zhang, B. Huang, Y. Muhamedsalih, IGIgram: An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis, J. Dyn. Monit. Diagnostics. 1 (2022) 111–124. https://doi.org/10.37965/jdmd.2022.65.
[4] B. Chen, Y. Cheng, W. Zhang, F. Gu, Investigations on improved Gini indices for bearing fault feature characterization and condition monitoring, Mech. Syst. Signal Process. 176 (2022) 109165. https://doi.org/10.1016/j.ymssp.2022.109165.
Chen, Bingyan, et al. “A Full Generalization of the Gini Index for Bearing Condition Monitoring.” Mechanical Systems and Signal Processing, vol. 188, Elsevier BV, Apr. 2023, p. 109998, doi:10.1016/j.ymssp.2022.109998.
Chen, Bingyan, et al. “A Full Generalization of the Gini Index for Bearing Condition Monitoring.” Mechanical Systems and Signal Processing, vol. 188, Elsevier BV, Apr. 2023, p. 109998, doi:10.1016/j.ymssp.2022.109998.
APA
Chen, B., Song, D., Gu, F., Zhang, W., Cheng, Y., Ball, A. D., Bevan, A., et al. (2023). A full generalization of the Gini index for bearing condition monitoring. Mechanical Systems and Signal Processing, 188, 109998. Elsevier BV. Retrieved from https://doi.org/10.1016%2Fj.ymssp.2022.109998
BibTeX
@article{Chen_2023,
doi = {10.1016/j.ymssp.2022.109998},
url = {https://doi.org/10.1016%2Fj.ymssp.2022.109998},
year = 2023,
month = {apr},
publisher = {Elsevier {BV}},
volume = {188},
pages = {109998},
author = {Bingyan Chen and Dongli Song and Fengshou Gu and Weihua Zhang and Yao Cheng and Andrew D. Ball and Adam Bevan and James Xi Gu},
title = {A full generalization of the Gini index for bearing condition monitoring},
journal = {Mechanical Systems and Signal Processing}
}
Chen, Bingyan, et al. “Power Function-Based Gini Indices: New Sparsity Measures Using Power Function-Based Quasi-Arithmetic Means for Bearing Condition Monitoring.” Structural Health Monitoring, SAGE Publications, Mar. 2023, p. 147592172211497, doi:10.1177/14759217221149745.
Chen, Bingyan, et al. “Power Function-Based Gini Indices: New Sparsity Measures Using Power Function-Based Quasi-Arithmetic Means for Bearing Condition Monitoring.” Structural Health Monitoring, SAGE Publications, Mar. 2023, p. 147592172211497, doi:10.1177/14759217221149745.
APA
Chen, B., Gu, F., Zhang, W., Song, D., Cheng, Y., & Zhou, Z. (2023). Power function-based Gini indices: New sparsity measures using power function-based quasi-arithmetic means for bearing condition monitoring. Structural Health Monitoring, 147592172211497. SAGE Publications. Retrieved from https://doi.org/10.1177%2F14759217221149745
BibTeX
@article{Chen_2023,
doi = {10.1177/14759217221149745},
url = {https://doi.org/10.1177%2F14759217221149745},
year = 2023,
month = {mar},
publisher = {{SAGE} Publications},
pages = {147592172211497},
author = {Bingyan Chen and Fengshou Gu and Weihua Zhang and Dongli Song and Yao Cheng and Zewen Zhou},
title = {Power function-based Gini indices: New sparsity measures using power function-based quasi-arithmetic means for bearing condition monitoring},
journal = {Structural Health Monitoring}
}
Chen, Bingyan, et al. “IGIgram: An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis.” Journal of Dynamics, Monitoring and Diagnostics, Intelligence Science and Technology Press Inc., June 2022, pp. 111–24, doi:10.37965/jdmd.2022.65.
Chen, Bingyan, et al. “IGIgram: An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis.” Journal of Dynamics, Monitoring and Diagnostics, Intelligence Science and Technology Press Inc., June 2022, pp. 111–24, doi:10.37965/jdmd.2022.65.
APA
Chen, B., Song, D., Cheng, Y., Zhang, W., Huang, B., & Muhamedsalih, Y. (2022). IGIgram: An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis. Journal of Dynamics, Monitoring and Diagnostics, 111–124. Intelligence Science and Technology Press Inc. Retrieved from https://doi.org/10.37965%2Fjdmd.2022.65
BibTeX
@article{Chen_2022,
doi = {10.37965/jdmd.2022.65},
url = {https://doi.org/10.37965%2Fjdmd.2022.65},
year = 2022,
month = {jun},
publisher = {Intelligence Science and Technology Press Inc.},
pages = {111--124},
author = {Bingyan Chen and Dongli Song and Yao Cheng and Weihua Zhang and Baoshan Huang and Yousif Muhamedsalih},
title = {{IGIgram}: An Improved Gini Index-Based Envelope Analysis for Rolling Bearing Fault Diagnosis},
journal = {Journal of Dynamics, Monitoring and Diagnostics}
}
Chen, Bingyan, et al. “Investigations on Improved Gini Indices for Bearing Fault Feature Characterization and Condition Monitoring.” Mechanical Systems and Signal Processing, vol. 176, Elsevier BV, Aug. 2022, p. 109165, doi:10.1016/j.ymssp.2022.109165.
Chen, Bingyan, et al. “Investigations on Improved Gini Indices for Bearing Fault Feature Characterization and Condition Monitoring.” Mechanical Systems and Signal Processing, vol. 176, Elsevier BV, Aug. 2022, p. 109165, doi:10.1016/j.ymssp.2022.109165.
APA
Chen, B., Cheng, Y., Zhang, W., & Gu, F. (2022). Investigations on improved Gini indices for bearing fault feature characterization and condition monitoring. Mechanical Systems and Signal Processing, 176, 109165. Elsevier BV. Retrieved from https://doi.org/10.1016%2Fj.ymssp.2022.109165
BibTeX
@article{Chen_2022,
doi = {10.1016/j.ymssp.2022.109165},
url = {https://doi.org/10.1016%2Fj.ymssp.2022.109165},
year = 2022,
month = {aug},
publisher = {Elsevier {BV}},
volume = {176},
pages = {109165},
author = {Bingyan Chen and Yao Cheng and Weihua Zhang and Fengshou Gu},
title = {Investigations on improved Gini indices for bearing fault feature characterization and condition monitoring},
journal = {Mechanical Systems and Signal Processing}
}
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