{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T01:21:26Z","timestamp":1770340886264,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T00:00:00Z","timestamp":1623369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FZSU-2020-00219, project no. 075-03-2020-051\/3 of June 9, 2020"],"award-info":[{"award-number":["FZSU-2020-00219, project no. 075-03-2020-051\/3 of June 9, 2020"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["Agreement No. 075-03-2020-051, Topic No. fzsu-2020-0020, FOKRAT"],"award-info":[{"award-number":["Agreement No. 075-03-2020-051, Topic No. fzsu-2020-0020, FOKRAT"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The work presents data treatment methods aimed at eliminating the noise in the strain sensor data induced by vibrations of the helicopter blade in flight conditions. The methods can be applied in order to enhance the metrological performance of the helicopter weight estimation system based on the deformation measurement of the main rotor blades. The experimental setup included a composite plate fixed to the vibrating stand on the one end, with six fiber-optic strain sensors attached to its surface. In this work, the procedure of the optimal linear smoothing (POLS) and 3D-invariant methods were used to obtain monotone calibration curves for each detector, thereby making it possible to distinguish the increase of load applied to the free end of the plate with an increment of 10 g. The second method associated with 3D invariants took into account 13 quantitative parameters defined as the combination of different moments and their intercorrelations up to the fourth-order inclusive. These 13 parameters allowed the calculation of the 3D surface that can serve as a specific fingerprint, differentiating one set of initial data from another one. The combination of the two data treatment methods used in this work can be applied successfully in a wide variety of applications.<\/jats:p>","DOI":"10.3390\/s21124028","type":"journal-article","created":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T02:55:28Z","timestamp":1623380128000},"page":"4028","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Noise Cancellation of Helicopter Blade Deformations Measurement by Fiber Bragg Gratings"],"prefix":"10.3390","volume":"21","author":[{"given":"Raoul R.","family":"Nigmatullin","sequence":"first","affiliation":[{"name":"Department of Radio-Electronic and Information-Measuring Tools, Kazan National Research Technical University Named after A.N. Tupolev-KAI, K. 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Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1155\/2000\/342875","article-title":"Measurement of rotorcraft blade deformation using Projection Moire Interferometry","volume":"7","author":"Fleming","year":"2000","journal-title":"Shock Vib."},{"key":"ref_6","unstructured":"Gaukroger, D.R., Payen, D.B., and Walker, A.R. (1980, January 16\u201319). Application of Strain Gauge Pattern Analysis. Proceedings of the Sixth European Rotorcraft and Powered Lift Aircraft Forum, Bristol, UK."},{"key":"ref_7","unstructured":"Leung, J.G.M., Wei, M.Y., and Aoyagi, M. (November, January 30). UH-60A airloads data acquisition and processing system. Proceedings of the AIAA\/IEEE Digital Avionics Systems Conference, 13th DASC, Phoenix, AZ, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"43","DOI":"10.4050\/1.3092877","article-title":"Validation of Structural and Aerodynamic Modeling Using UH-60A Airloads Program Data","volume":"51","author":"Datta","year":"2006","journal-title":"J. Am. Helicopter Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2605","DOI":"10.1109\/JLT.2018.2885957","article-title":"Toward Commercial Polymer Fiber Bragg Grating Sensors: Review and Applications","volume":"37","author":"Broadway","year":"2019","journal-title":"J. Lightwave Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"86930F","DOI":"10.1117\/12.2012214","article-title":"Multiplexed fibre optic sensors for monitoring resin infusion, flow, and cure in composite material processing","volume":"Volume 8693","author":"Chehura","year":"2013","journal-title":"Smart Sensor Phenomena, Technology, Networks, and Systems Integration 2013"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104001","DOI":"10.1088\/0957-0233\/27\/10\/104001","article-title":"Development and application of optical fibre strain and pressure sensors for in-flight measurements","volume":"27","author":"Lawson","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_12","unstructured":"Suesse, S., and Hajek, M. (2016, January 5\u20138). Rotor Blade Shape Estimation with Fiber-Optical Sensors for a Health and Usage Monitoring System. Proceedings of the 42nd European Rotorcraft Forum, Lille, France."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6953","DOI":"10.1364\/AO.55.006953","article-title":"Vibration monitoring of a helicopter blade model using the optical fiber distributed strain sensing technique","volume":"55","author":"Wada","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_14","unstructured":"Daniell, J.G.B., and Molnar, G.A. (1993). Helicopter Weight Measurement. (5,229,956), U.S. Patent."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"060901","DOI":"10.1117\/1.OE.59.6.060901","article-title":"Fiber Bragg grating sensors for monitoring of physical parameters: A comprehensive review","volume":"59","author":"Sahota","year":"2020","journal-title":"Opt. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1088\/0964-1726\/1\/1\/006","article-title":"Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structure critical issues","volume":"1","author":"Melle","year":"1992","journal-title":"Smart Mater. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1117\/12.184861","article-title":"Structural strain mapping using a wavelength\/time division addressed fiber Bragg grating array","volume":"2361","author":"Davis","year":"1994","journal-title":"Proc. SPIE"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e2118","DOI":"10.1002\/stc.2118","article-title":"Measurement of strains by optical fiber Bragg grating sensors embedded into polymer composite material","volume":"25","author":"Matveenko","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Qiao, X., Shao, Z., Bao, W., and Rong, Q. (2017). Fiber Bragg grating sensors for the oil industry. Sensors, 17.","DOI":"10.3390\/s17030429"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ma, Z., and Chen, X. (2019). Fiber Bragg gratings sensors for aircraft wing shape measurement: Recent applications and technical analysis. Sensors, 19.","DOI":"10.3390\/s19010055"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Agliullin, T., Gubaidullin, R., Sakhabutdinov, A., Morozov, O., Kuznetsov, A., and Ivanov, V. (2020). Addressed Fiber Bragg Structures in Load-Sensing Wheel Hub Bearings. Sensors, 20.","DOI":"10.20944\/preprints202009.0017.v1"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"767","DOI":"10.3103\/S1068799820040261","article-title":"Implementation of the Radiophotonic Method for Measuring Blade Deformations of a Helicopter Main Rotor Model","volume":"63","author":"Ledyankin","year":"2020","journal-title":"Russ. Aeronaut."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Morozov, O., Sakhabutdinov, A., Anfinogentov, V., Misbakhov, R., Kuznetsov, A., and Agliullin, T. (2020). Multi-Addressed Fiber Bragg Structures for Microwave-Photonic Sensor Systems. Sensors, 20.","DOI":"10.3390\/s20092693"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.chaos.2011.02.003","article-title":"NAFASS: Discrete spectroscopy of random signals","volume":"44","author":"Nigmatullin","year":"2011","journal-title":"Chaos Solitons Fractals"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1002\/lapl.200710067","article-title":"Detection of the OH band fine structure in a liquid water by means of new treatment procedure based on the statistics of the fractional moments","volume":"4","author":"Pershin","year":"2007","journal-title":"Lazer Phys. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1007\/s11760-012-0386-1","article-title":"NIMRAD: Novel technique for respiratory data treatment","volume":"8","author":"Nigmatullin","year":"2014","journal-title":"J. Signal Image Video Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"013717","DOI":"10.1063\/1.3525582","article-title":"Stress-induced traps in multilayed structures","volume":"109","author":"Ciurea","year":"2011","journal-title":"J. Appl. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5712","DOI":"10.1016\/j.tsf.2011.04.021","article-title":"Chemical Bonding Structure of TiO2 Thin Films grown on N-Type Si","volume":"519","author":"Cetin","year":"2011","journal-title":"Thin Solid Film."},{"key":"ref_29","first-page":"729","article-title":"New method and treatment technique applied to interband transition in GaAs1-x Px ternary alloys","volume":"9","author":"Nigmatullin","year":"2011","journal-title":"Cent. Eur. J. Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4028\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:13:11Z","timestamp":1760163191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,11]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21124028"],"URL":"https:\/\/doi.org\/10.3390\/s21124028","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,11]]}}}