{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T21:27:14Z","timestamp":1769203634213,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,10]],"date-time":"2018-01-10T00:00:00Z","timestamp":1515542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Nowadays, hydropower plays an essential role in the energy market. Due to their fast response and regulation capacity, hydraulic turbines operate at off-design conditions with a high number of starts and stops. In this situation, dynamic loads and stresses over the structure are high, registering some failures over time, especially in the runner. Therefore, it is important to know the dynamic response of the runner while in operation, i.e., the natural frequencies, damping and mode shapes, in order to avoid resonance and fatigue problems. Detecting the natural frequencies of hydraulic turbine runners while in operation is challenging, because they are inaccessible structures strongly affected by their confinement in water. Strain gauges are used to measure the stresses of hydraulic turbine runners in operation during commissioning. However, in this paper, the feasibility of using them to detect the natural frequencies of hydraulic turbines runners while in operation is studied. For this purpose, a large Francis turbine runner (444 MW) was instrumented with several strain gauges at different positions. First, a complete experimental strain modal testing (SMT) of the runner in air was performed using the strain gauges and accelerometers. Then, the natural frequencies of the runner were estimated during operation by means of analyzing accurately transient events or rough operating conditions.<\/jats:p>","DOI":"10.3390\/s18010174","type":"journal-article","created":{"date-parts":[[2018,1,10]],"date-time":"2018-01-10T12:41:10Z","timestamp":1515588070000},"page":"174","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Feasibility of Detecting Natural Frequencies of Hydraulic Turbines While in Operation, Using Strain Gauges"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7125-0734","authenticated-orcid":false,"given":"David","family":"Valent\u00edn","sequence":"first","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandre","family":"Presas","sequence":"additional","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matias","family":"Bossio","sequence":"additional","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1777-1840","authenticated-orcid":false,"given":"M\u00f2nica","family":"Egusquiza","sequence":"additional","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eduard","family":"Egusquiza","sequence":"additional","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carme","family":"Valero","sequence":"additional","affiliation":[{"name":"Center for Industrial Diagnostics and Fluid Dynamics (CDIF), Polytechnic University of Catalonia (UPC), Av. Diagonal, 647, ETSEIB, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"International Energy Agency (IEA) (2016). Key World Energy Trends. Excerpt from: World Energy Balances.","DOI":"10.1787\/key_energ_stat-2016-en"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012014","DOI":"10.1088\/1755-1315\/22\/1\/012014","article-title":"Fatigue Analyses of the Prototype Francis Runners Based on Site Measurements and Simulations","volume":"22","author":"Huang","year":"2014","journal-title":"IOP Conf. Ser.: Earth Environ. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1155\/S1023621X94000059","article-title":"Case Study of Pump Failure Due to Rotor-Stator Interaction","volume":"1","author":"Ohashi","year":"1994","journal-title":"Int. J. Rotat. Mach."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.engfailanal.2012.01.012","article-title":"Failure investigation of a large pump-turbine runner","volume":"23","author":"Egusquiza","year":"2012","journal-title":"Eng. Fail. Anal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engfailanal.2017.02.021","article-title":"A review on fluid structure interaction in hydraulic turbines: A focus on hydrodynamic damping","volume":"77","author":"Trivedi","year":"2017","journal-title":"Eng. Fail. Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.measurement.2015.01.004","article-title":"Condition monitoring of pump-turbines. New challenges","volume":"67","author":"Egusquiza","year":"2015","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jfluidstructs.2014.06.006","article-title":"Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement","volume":"50","author":"Presas","year":"2014","journal-title":"J. Fluids Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"072004","DOI":"10.1088\/1755-1315\/49\/7\/072004","article-title":"Influence of the Boundary Conditions on the Natural Frequencies of a Francis Turbine","volume":"49","author":"Ramos","year":"2016","journal-title":"IOP Conf. Ser.: Earth Environ. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.ymssp.2015.05.034","article-title":"Analysis of the dynamic response of pump-turbine impellers","volume":"68","author":"Egusquiza","year":"2016","journal-title":"Influence of the rotor. Mech. Syst. Sign. Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1016\/j.compfluid.2006.08.007","article-title":"Numerical simulation of fluid added mass effect on a francis turbine runner","volume":"36","author":"Liang","year":"2007","journal-title":"Comput. Fluids"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Egusquiza, E., Valero, C., Liang, Q., Coussirat, M., and Seidel, U. (2009, January 2). Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Impeller. Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, San Diego, CA, USA.","DOI":"10.1115\/DETC2009-86830"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.jsv.2014.10.032","article-title":"Influence of the rotation on the natural frequencies of a submerged-confined disk in water","volume":"337","author":"Presas","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.ymssp.2015.01.013","article-title":"On the detection of natural frequencies and mode shapes of submerged rotating disk-like structures from the casing","volume":"60","author":"Presas","year":"2015","journal-title":"Mech. Syst. Sign. Process."},{"key":"ref_14","unstructured":"Mao, Z., and Wang, Z. (2016, January 10\u201315). Structural Characteristic in Prototype Runner of Francis Turbine Analysis. Proceedings of the International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"012107","DOI":"10.1088\/1755-1315\/12\/1\/012107","article-title":"Impact of startup scheme on Francis runner life expectancy","volume":"12","author":"Gagnon","year":"2010","journal-title":"IOP Conf. Ser.: Earth Environ. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"032055","DOI":"10.1088\/1755-1315\/22\/3\/032055","article-title":"Challenges in Dynamic Pressure and Stress Predictions at No-Load Operation in Hydraulic Turbines","volume":"22","author":"Nennemann","year":"2014","journal-title":"IOP Conf. Ser.: Earth Environ. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6968","DOI":"10.1016\/j.jsv.2013.08.015","article-title":"The mass normalization of the displacement and strain mode shapes in a strain experimental modal analysis using the mass-change strategy","volume":"332","author":"Kranjc","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3389","DOI":"10.1177\/0954406215614599","article-title":"On the comparison between displacement modal testing and strain modal testing","volume":"230","author":"Mucchi","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.rser.2015.09.025","article-title":"A review on fatigue damage mechanism in hydro turbines","volume":"54","author":"Liu","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.rser.2016.09.121","article-title":"Fluid-structure interactions in Francis turbines: A perspective review","volume":"68","author":"Trivedi","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_21","first-page":"012036","article-title":"Dynamic Response of the MICA Runner. Experiment and Simulation","volume":"813","author":"Presas","year":"2017","journal-title":"J. Phys.: Conf. Ser."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.jfluidstructs.2006.04.001","article-title":"Experimental investigation of added mass effects on a Francis turbine runner in still water","volume":"22","author":"Rodriguez","year":"2006","journal-title":"J. Fluids Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"303","DOI":"10.5293\/IJFMS.2009.2.4.303","article-title":"Dynamic Analysis of Francis Runners\u2014Experiment and Numerical Simulation","volume":"2","author":"Lais","year":"2009","journal-title":"Int. J. Fluids Mach. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"28","DOI":"10.4236\/wjm.2012.21004","article-title":"A fatigue analysis of a hydraulic Francis turbine runner","volume":"2","author":"Flores","year":"2012","journal-title":"World J. Mech."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Woon, C., and Mitchell, L.D. (1996). Second International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Temperature-Induced Variations in Structural Dynamic Characteristicspart II: Analytical.","DOI":"10.1117\/12.248684"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.jfluidstructs.2017.05.008","article-title":"Numerical study on the influence of acoustic natural frequencies on the dynamic behaviour of submerged and confined disk-like structures","volume":"73","author":"Bossio","year":"2017","journal-title":"J. Fluids Struct."},{"key":"ref_27","unstructured":"Jazar, R.N. (2005). Advanced Vibrations: A Modern Approach, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"289","DOI":"10.5293\/IJFMS.2011.4.2.289","article-title":"Vibration behavior and dynamic stress of runners of very high head reversible pump-turbines","volume":"4","author":"Tanaka","year":"2011","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_29","unstructured":"Nicolet, C., Ruchonnet, N., and Avellan, F. (2006, January 17\u201321). One-Dimensional Modeling of Rotor Stator Interaction in Francis Turbine. Proceedings of the 23rd IAHR Symposium, Yokohama, Japan."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/BF00537373","article-title":"\u00dcber die Erregung infolge der Periodizit\u00e4t von Turbomaschinen","volume":"54","author":"Dubas","year":"1984","journal-title":"M. Ing. Arch."},{"key":"ref_31","first-page":"8","article-title":"Monitoring of Rotor-Stator Interaction in Pump-Turbine Using Vibrations Measured with On-Board Sensors Rotating with Shaft","volume":"2014","author":"Rodriguez","year":"2014","journal-title":"Shock Vib."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1428","DOI":"10.1115\/1.2786489","article-title":"Frequencies in the Vibration Induced by the Rotor Stator Interaction in a Centrifugal Pump Turbine","volume":"129","author":"Rodriguez","year":"2007","journal-title":"J. Fluids Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"11919","DOI":"10.3390\/s140711919","article-title":"Feasibility of Using PZT Actuators to Study the Dynamic Behavior of a Rotating Disk due to Rotor-Stator Interaction","volume":"14","author":"Presas","year":"2014","journal-title":"Sensors"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1016\/j.ymssp.2004.08.006","article-title":"Detection of cavitation in hydraulic turbines","volume":"20","author":"Escaler","year":"2006","journal-title":"Mechan. Syst. Sign. Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.rser.2009.07.024","article-title":"Study of cavitation in hydro turbines\u2014A review","volume":"14","author":"Kumar","year":"2010","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Valent\u00edn, D., Presas, A., Egusquiza, E., Valero, C., Egusquiza, M., and Bossio, M. (2017). Power Swing Generated in Francis Turbines by Part Load and Overload Instabilities. Energies, 10.","DOI":"10.3390\/en10122124"},{"key":"ref_37","first-page":"012038","article-title":"Detection and Analysis of Part Load and Full Load Instabilities in a Real Francis Turbine Prototype","volume":"813","author":"Presas","year":"2017","journal-title":"J. Phys.: Conf. Ser."},{"key":"ref_38","unstructured":"Ewins, D.J. (1984). Modal Testing: Theory and Practice, Research Studies Press."},{"key":"ref_39","unstructured":"Grein, H. (October, January 28). Vibration Phenomena in Francis Turbines: Their Causes and Prevention. Proceedings of the 10th IAHR Symposium in Hydraulic Machinery Equipments and Cavitation, Tokyo, Japan."},{"key":"ref_40","unstructured":"Aguila, H., Egusquiza, E., Jou, E., Estevez, A., and Cabrera, J. (1999, January 7\u20139). Detection of Rotor Natural Frequencies in Hydro Powerplants. Proceedings of the 9th International Meeting of the Working Group on the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions, Brno, Czech Republic."},{"key":"ref_41","first-page":"012014","article-title":"Dynamic Stresses in a Francis Model Turbine at Deep Part Load","volume":"813","author":"Weber","year":"2017","journal-title":"J. Phys.: Conf. Ser."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"072016","DOI":"10.1088\/1755-1315\/49\/7\/072016","article-title":"Stress Predictions in a Francis Turbine at No-Load Operating Regime","volume":"49","author":"Morissette","year":"2016","journal-title":"IOP Conf. Ser.: Earth Environ. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jfluidstructs.2013.01.008","article-title":"Experimental investigation of added mass effects on a hydrofoil under cavitation conditions","volume":"39","author":"Escaler","year":"2013","journal-title":"J. Fluids Struct."},{"key":"ref_44","unstructured":"(2017, September 15). I HYdropower Plants PERformance and Flexible Operation towards Lean Integration of New Renewable Energies. Available online: https:\/\/hyperbole.epfl.ch."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1115\/1.2930443","article-title":"Wavelet Analysis of Vibration: Part 1\u2014Theory","volume":"116","author":"Newland","year":"1994","journal-title":"J. Vib. Acoust."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/174\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:50:44Z","timestamp":1760194244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,10]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["s18010174"],"URL":"https:\/\/doi.org\/10.3390\/s18010174","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,10]]}}}