Arbabi, H., & Mezic, I. (2017). Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the koopman operator. 
SIAM Journal on Applied Dynamical Systems, 
16(4), 2096–2126. 
https://doi.org/10.1137/17M1125236
                                                                                                                 Chang, X., & Gao, D. (2023). A comparative study of data-driven modal decomposition analysis of unforced and forced cylinder wakes. 
Journal of Visualization, 
26(4), 755–777. 
https://doi.org/10.1007/s12650-023-00912-8
                                                                                                                 Cheng, Y., & Chen, Q. (2021). Large eddy simulation and dynamic mode decomposition of turbulent mixing layers. 
Applied Sciences, 
11(24), 12127. 
https://doi.org/10.3390/app112412127
                                                                                                                 Dehghan, A. A., & Shojaeefard, M. H. (2022). Experimental and numerical optimization of a centrifugal pump volute and its effect on head and hydraulic efficiency at the best efficiency point. 
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 
236(9), 4577–4598. 
https://doi.org/10.1177/09544062211056019
                                                                                                                 Dehghan, A. A., Shojaeefard, M. H., & Roshanaei, M. (2024). Exploring a new criterion to determine the onset of cavitation in centrifugal pumps from energy-saving standpoint; experimental and numerical investigation. 
Energy, 
293, 130681. 
https://doi.org/10.1016/j.energy.2024.130681
                                                                                                                 François, B., Hingray, B., Raynaud, D., Borga, M., & Creutin, J. D. (2016). Increasing climate-related-energy penetration by integrating run-of-the river hydropower to wind/solar mix. 
Renewable Energy, 
87, 686–696. 
https://doi.org/10.1016/j.renene.2015.10.064
                                                                                                                                                                                                                                 Hao, Z., Shi, G., Peng, X., Chai, H., Lv, W., & Huang, Z. (2024). Study on the influence of vortex spatial-temporal evolution on the causes of hump region of Pump-Turbine and the characteristics of vortex dynamics. 
Journal of Energy Storage, 
92, 112297. 
https://doi.org/10.1016/j.est.2024.112297
                                                                                                                 Heng, Y., Yuan, S., Hong, F., Yuan, J., Si, Q., & Hu, B. (2014). A hybrid method for flow-induced noise in centrifugal pumps based on LES and FEM. Proceedings of the ASME Fluids Engineering Division Summer Meeting, 2013, 1b: Symposia, V01BT10A034.
                                                                                                                Jin, F., Luo, Y., Bi, H., Wang, H., Wang, Z., Lin, K., Lei, X., & Yang, X. (2023). Transient simulation of reversible pump turbine during pump mode’s starting up. 
Journal of Energy Storage, 
68, 107678. 
https://doi.org/10.1016/j.est.2023.107678
                                                                                                                 Karapici, V., Trojer, A., Lazarevikj, M., Pluskal, T., Chernobrova, A., Neziric, E., Zuecco, G., Alerci, A. L., Seydoux, M., Doujak, E., & Rudolf, P. (2024). Opportunities of hidden hydropower technologies towards the energy transition. 
Energy Reports, 
12, 5633–5647. 
https://doi.org/10.1016/j.egyr.2024.11.039
                                                                                                                 Lai, X., Chen, X., Liang, Q., Ye, D., Gou, Q., Wang, R., & Yan, Y. (2023). Experimental and numerical investigation of vortex flows and pressure fluctuations in a high-head pump-turbine. 
Renewable Energy, 
211, 236–247. 
https://doi.org/10.1016/j.renene.2023.04.092
                                                                                                                 Li, D., Wang, H., Qin, Y., Wei, X., & Qin, D. (2018). Numerical simulation of hysteresis characteristic in the hump region of a pump-turbine model. 
Renewable Energy, 
115, 433–447. 
https://doi.org/10.1016/j.renene.2017.08.081
                                                                                                                 Liang, A., Li, H., Zhang, W., Yao, Z., Zhu, B., & Wang, F. (2024). Study on pressure fluctuation and rotating stall characteristics in the vaneless space of a pump-turbine in pump mode. 
Journal of Energy Storage, 
94, 112385. 
https://doi.org/10.1016/j.est.2024.112385
                                                                                                                 Liang, W., Chen, T., Wang, G., & Huang, B. (2020). Investigation of unsteady liquid nitrogen cavitating flows with special emphasis on the vortex structures using mode decomposition methods.
 International Journal of Heat and Mass Transfer, 
157, 119880. 
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119880
                                                                                                                 Liao, Z. Y., Yang, J., Liu, X. H., Hu, W. L., & Deng, X. R. (2020). Analysis of unsteady flow structures in a centrifugal impeller using proper orthogonal decomposition. 
Journal of Applied Fluid Mechanics, 
14(1), 89–101. 
https://doi.org/10.47176/jafm.14.01.31299
                                                                                                                 Liu, D., Xun, H., Wang, Z., Li, G., Zheng, J., Liu, X., & Hao, Z. (2024). Analysis of vortex characteristics in hump region of reversible pump-turbine based on omega vortex identification method. 
AIP Advances, 
14(3), 035130. 
https://doi.org/10.1063/5.0199021
                                                                                                                                                                                                                                                                                                                                                 Long, Y., Guo, X., & Xiao, T. (2024). Research, application and future prospect of mode decomposition in fluid mechanics. 
Symmetry, 
16(2), 155. 
https://doi.org/10.3390/sym16020155
                                                                                                                                                                                                                                                                                                                                                 Magionesi, F., Dubbioso, G., Muscari, R., & Mascio, A. D. (2018). Modal analysis of the wake past a marine propeller. 
Journal of Fluid Mechanics, 
855, 469–502. 
https://doi.org/10.1017/jfm.2018.631
                                                                                                                 Mahfoud, R. J., Alkayem, N. F., Zhang, Y., Zheng, Y., Sun, Y., & Alhelou, H. H. (2023). Optimal operation of pumped hydro storage-based energy systems: A compendium of current challenges and future perspectives.
 Renewable and Sustainable Energy Reviews, 
178, 113267. 
https://doi.org/10.1016/j.rser.2023.113267
                                                                                                                 Mariappan, S., Gardner, A. D., Richter, K., & Raffel, M. (2014). Analysis of dynamic stall using dynamic mode decomposition technique. 
AIAA Journal, 
52(11), 2427–2439. 
https://doi.org/10.2514/1.J052858
                                                                                                                 Mohsin, M., Orynbassarov, D., Anser, M. K., & Oskenbayev, Y. (2023). Does hydropower energy help to reduce CO2 emissions in European Union countries? Evidence from quantile estimation. 
Environmental Development, 
45, 100794. 
https://doi.org/10.1016/j.envdev.2022.100794
                                                                                                                 Muld, T. W., Efraimsson, G., & Henningson, D. S. (2012). Flow structures around a high-speed train extracted using proper orthogonal decomposition and dynamic mode decomposition.
 Computers & Fluids, 
57, 87–97. 
https://doi.org/10.1016/j.compfluid.2011.12.012
                                                                                                                 Nasir, J., Javed, A., Ali, M., Ullah, K., & Kazmi, S. A. A. (2022). Capacity optimization of pumped storage hydropower and its impact on an integrated conventional hydropower plant operation. 
Applied Energy, 
323, 119561. 
https://doi.org/10.1016/j.apenergy.2022.119561
                                                                                                                 Proctor, J. L., Brunton, S. L., & Kutz, J. N. (2016). Dynamic mode decomposition with control. 
SIAM Journal on Applied Dynamical Systems, 
15(1), 142–161. 
https://doi.org/10.1137/15M1013857
                                                                                                                 Qin, Y., Li, D., Wang, H., Liu, Z., Wei, X., & Wang, X. (2023). Mechanism of runner high-pressure side on stall characteristics at typical unsteady operating points in both modes of a pump turbine. 
Physics of Fluids, 
35(7), 074102. 
https://doi.org/10.1063/5.0155655
                                                                                                                 Renhui, Z., Chen, X., & Luo, J. (2020). Knowledge mining of low specific speed centrifugal pump impeller based on proper orthogonal decomposition method. 
Journal of Thermal Science, 
30. 
https://doi.org/10.1007/s11630-020-1356-5
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Sirovich, L. (1987). Turbulence and the dynamics of coherent structures. I. Coherent structures. 
Quarterly of Applied Mathematics, 
45, 561–571. 
https://doi.org/10.1090/qam/910462
                                                                                                                 Subramanya, K., & Chelliah, T. R. (2023). Capability of synchronous and asynchronous hydropower generating systems: A comprehensive study. 
Renewable and Sustainable Energy Reviews, 
188, 113863. 
https://doi.org/10.1016/j.rser.2023.113863
                                                                                                                 Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V., & Ukeiley, L. S. (2017). Modal analysis of fluid flows: An overview. 
AIAA Journal, 
55(12), 4013–4041. 
https://doi.org/10.2514/1.J056060
                                                                                                                 Taira, K., Hemati, M. S., Brunton, S. L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S. T. M., & Yeh, C.-A. (2020). Modal analysis of fluid flows: applications and outlook. 
AIAA Journal, 
58(3), 998–1022. 
https://doi.org/10.2514/1.J058462
                                                                                                                 Towne, A., Schmidt, O. T., & Colonius, T. (2018). Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. 
Journal of Fluid Mechanics, 847, 821–867. 
https://doi.org/10.1017/jfm.2018.283
                                                                                                                 Wang, Z., Fang, G., Wen, X., Tan, Q., Zhang, P., & Liu, Z. (2023a). Coordinated operation of conventional hydropower plants as hybrid pumped storage hydropower with wind and photovoltaic plants. 
Energy Conversion and Management, 
277, 116654. 
https://doi.org/10.1016/j.enconman.2022.116654
                                                                                                                 Wang, J., Wang, C., Liu, C., & Wu, J. (2023b).
 Numerical study on stall characteristics of a triangular airfoil in low Reynolds number compressible flow. 17th Asian Congress of Fluid Mechanics (ACFM 2023), 2023, 182–189. 
https://doi.org/10.1049/icp.2023.1947
                                                                                                                 Williams, M. O., Kevrekidis, I. G., & Rowley, C. W. (2015). A data-driven approximation of the koopman operator: extending dynamic mode decomposition. 
Journal of Nonlinear Science, 
25(6), 1307–1346. 
https://doi.org/10.1007/s00332-015-9258-5
                                                                                                                                                                                                                                 Xu, L., Kan, K., Zheng, Y., Liu, D., Binama, M., Xu, Z., Yan, X., Guo, M., & Chen, H. (2024a). Rotating stall mechanism of pump-turbine in hump region: An insight into vortex evolution. 
Energy, 
292, 130579. 
https://doi.org/10.1016/j.energy.2024.130579
                                                                                                                 Yang, J., Feng, X., Liao, Z., Pan, K., & Liu, X. (2023). Analysis on the mechanism of rotating stall inner a pump turbine in pump mode based on the proper orthogonal decomposition. 
Journal of Fluids Engineering, 
145 (9), 091202. 
https://doi.org/10.1115/1.4062345
                                                                                                                 Yang, Z., Wang, F., & Zhou, P. (2012). Evaluation of subgrid-scale models in large-eddy simulations of turbulent flow in a centrifugal pump impeller. 
Chinese Journal of Mechanical Engineering, 
25(5), 911–918. 
https://doi.org/10.3901/CJME.2012.05.911
                                                                                                                 Ye, W., Qian, Z., Zeng, Y., Ma, W., Geng, X., Luo, X., & Wang, H. (2024). Numerical investigation on the unstable flow and its interaction with the hump characteristic in a pump turbine at pump mode. 
Journal of Energy Storage, 
101, 113853. 
https://doi.org/10.1016/j.est.2024.113853
                                                                                                                 Yin, X., Huang, X., Zhang, S., Bi, H., & Wang, Z. (2023). Numerical investigation of flow and structural characteristics of a large high-head prototype pump-turbine during turbine start-up. 
Energies, 
16(9), 3743. 
https://doi.org/10.3390/en16093743
                                                                                                                 Zhang, F., Chen, Z., Han, S., & Zhu, B. (2024). Study on the unsteady flow characteristics of a pump turbine in pump mode. 
Processes, 
12(1), 41. 
https://doi.org/10.3390/pr12010041
                                                                                                                 Zheng, Y., Tang, K., Xu, L., Ren, S., Xu, J., Wang, Y., An, D., & Ye, C. (2024). Stability analysis of pump-turbine in hump zone based on omega vortex identification method. 
Water, 
16(23), 3443. 
https://doi.org/10.3390/w16233443