References
Abarbanel, H., Kennel, M., & Brown, R. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A, 45, 3403–3411. Adcock, A., Carlsson, E., & Carlsson, G. (2016). The ring of algebraic functions on persistence barcodes. In Homology, homotopy and applications (Vol. 18, p. 381-403). Arnol’d, V. I. (1989). Mathematical methods of classical mechanics. Springer. Atienza, N., Gonzalez-Diaz, R., & Rucco, M. (2019). Persistent entropy for separating topological features from noise in vietoris-rips complexes. Journal of Intelligent Information Systems, 52, 637–655. Atienza, N., Gonzalez-D´ıaz, R., & Soriano-Trigueros, M. (2020). On the stability of persistent entropy and new summary functions for topological data analysis. Pattern Recognit., 107, 107509. Attali, D., Lieutier, A., & Salinas, D. (2011). Vietorisrips complexes also provide topologically correct reconstructions of sampled shapes. In Proceedings of the twenty-seventh annual symposium on computational geometry (pp. 491–500). Casolo, S. (2022). Severe slugging flow identification from topological indicators,. Digital Chemical Engineering,, 4, 100045. Chauhan, S., Vashishtha, G., Kumar, R., Zimroz, R., Gupta,
M. K., & Kundu, P. (2024). An adaptive feature mode decomposition based on a novel health indicator for bearing fault diagnosis. Measurement, 226, 114191. Chazal, F., & Michel, B. (2021). An introduction to topological data analysis: Fundamental and practical aspects for data scientists. Front. Artif. Intell., 4, 667963. Fraser, A., & Swinney, H. (1986). Independent coordinates for strange attractors from mutual information. Phys. Rev. A, 33(2), 1134–1140.
Hatcher, A. (2002). Algebraic topology. Cambridge University Press.
Jiang, Z., Zhang, K., Xiang, L., Yu, G., & Xu, Y. (2023). A time-frequency spectral amplitude modulation method and its applications in rolling bearing fault diagnosis. Mechanical Systems and Signal Processing, 185, 109832.
Khasawneh, F. A., & Munch, E. (2016). Chatter detection in turning using persistent homology. Mechanical Systems and Signal Processing, 70-71, 527-541. Khasawneh, F. A., Munch, E., & Perea, J. A. (2018). Chatter classification in turning using machine learning and topological data analysis. IFAC-PapersOnLine, 51(14), 195-200.
Perea, J. A. (2016). Persistent homology of toroidal sliding window embeddings. In 2016 IEEE international conference on acoustics, speech and signal processing (icassp) (pp. 6435–6439).
Perea, J. A., & Harer, J. (2015). Sliding windows and persistence: as application of topological methods to signal analysis. Found. of Comput. Mathematics, 15, 799. P´erez, J. B., Hauke, S., Lupo, U., Caorsi, M., & Dassatti,
A. (2021). giotto-ph: A Python library for high-performance computation of persistent homology of Vietoris-Rips filtrations. Sawalhi, N., & Randall, R. B. (2004). The application of spectral kurtosis to bearing diagnostics. Proceedings of Acoustics, 040115.
Smith, A. D., Dłotko, P., & Zavala, V. M. (2021). Topological data analysis: Concepts, computation, and applications in chemical engineering. Comput. Chem. Eng., 146, 107202. Stetco, A., Dinmohammadi, F., Zhao, X., Robu, V., Flynn, D., Barnes, M., . . . Nenadic, G. (2019). Machine learning methods for wind turbine condition monitoring: A review. Renew. Energy, 133, 620-639. Takens, F. (1981). Detecting strange attractors in turbulence. In D. A. Rand & L.-S. Young (Eds.), Dynamical systems and turbulence, lecture notes in mathematics (Vol. 898, p. 366-381). Springer-Verlag. Tchakoua, P., Wamkeue, R., Ouhrouche, M., SlaouiHasnaoui, F., Tameghe, T. A., & Ekemb, G. (2014). Wind turbine condition monitoring: State-of-the-art review, new trends, and future challenges. Energies, 7, 2595-2630. Wang, Q., Dong, Z., Li, R., & Wang, L. (2022). Renewable energy and economic growth: New insight from country risks. Energy, 238, 122018. Wang, W.-K., Wan, M., Zhang, W.-H., & Yang, Y. (2022). Chatter detection methods in the machining processes: A review. Journal of Manufacturing Processes, 77, 240-259. Wasserman, L. (2018). Fault analysis and condition monitoring of the wind turbine gearbox. Annual Review of Statistics and its Application, 5(3), 501-532. Xiao, F., Tian, C., Wait, I., Yang, Z., Still, B., & Chen, G. S. (2020). Fault analysis and condition monitoring of the wind turbine gearbox. Advances in Mechanical Engineering, 12(3). Yesilli, M. C., Khasawneh, F. A., & Otto, A. (2022a). Chatter detection in turning using machine learning and similarity measures of time series via dynamic time warping. Journal of Manufacturing Processes, 77, 190-206. Yesilli, M. C., Khasawneh, F. A., & Otto, A. (2022b). Topological feature vectors for chatter detection in turning processes. Int J Adv Manuf Technol, 119, 5687–5713. Zhang, H., Chen, X., Du, Z., & Yan, R. (2016). Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis. Mechanical Systems and Signal Processing, 80, 349-376. Zhang, Z., Verma, A., & Kusiak, A. (2012). Fault analysis and condition monitoring of the wind turbine gearbox. IEEE Transactions on Energy Conversion, 27(2), 526535.