Time-frequency Analysis of Natural Accelerograms
DOI:
https://doi.org/10.24160/1993-6982-2019-5-135-141Keywords:
evolutionary spectral analysis and spectral power density, seismic intensity, seismic analysis, eismic stability analysis, acceleration time historyAbstract
An example of a frequency-time analysis of a long-period accelerogram of Tohoku earthquake is considered (Tohoku earthquake, Japan, March 11, 2011) including seismic intensity definition as a function of time; evolutionary spectral power density; prevailing frequencies of seismic ground motion for different earthquake phases . The function of seismic intensity is obtained as pseudo-envelope of nonstationary seismic accelerations. The time dependent pseudo-envelope is calculated as standard deviation at small time intervals. The analysis of the time dependent prevailing frequencies is performed using the Welch’s power spectral density estimation smoothed with the Hamming windows. For the considered accelerogram, a decrease in prevailing frequencies from 0.77 Hz at the beginning to 0.38 Hz at the end of seismic motion was determined. All calculations were realized using Matlab.
The results of the research may be useful for performing seismic analysis based on accelerograms using response spectrum method, when it is necessary to estimate seismic intensity. Spectral analysis of different earthquake phases is necessary to prevent resonance phenomena in the situation, for example, when during a long-term earthquake both the natural frequencies of the structure and the prevailing frequency of the impact are reduced. In general, the understanding of the changes in the time-dependent parameters of accelerograms is relevant in the seismic analysis taking duration of the earthquake into account. Such calculation should include a preliminary time-frequency analysis of seismic impact.
References
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Для цитирования: Позняк Е.В., Радин В.П., Новикова О.В. Частотно-временной анализ акселерограмм природных землетрясений // Вестник МЭИ. 2019. № 5. С. 135—141. DOI: 10.24160/1993-6982-2019-5-135-141.
#
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2. Bolotin V.V. Primenenie Metodov Teorii Veroyatnostey i Teorii Nadezhnosti v Raschetakh Sooruzheniy. M.: Stroyizdat, 1971. (in Russian).
3. Marano G.C. Non-stationary Stochastic Modulation Function Definition Based On Process Energy Release. Physica A: Statistical Mechanics and its Appl. 2019;517: 280—289.
4. Wang D., Fan Z., Hao Sh., Zhao D. An Evolutionary Power Spectrum Model of Fully Nonstationary Seismic Ground Motion. Soil Dynamics and Earthquake Eng. 2018;105:1—10.
5. Schillinger D., Stefanov D., Stavrev А. The Method of Separation for Evolutionary Spectral Density Estimation of Multi-variate and Multi-dimensional Non-stationary Stochastic Processes. Probabilistic Eng. Mechanics. 2013; 33:58—78.
6. Canor Т., Caracoglia L., Denoël V. Perturbation Methods in Evolutionary Spectral Analysis for Linear Dynamics and Equivalent Statistical Linearization. Probabilistic Eng. Mechanics. 2016;46:1—17.
7. Zhao Y., Li Y., Zhang Y., Kennedy D. Nonstationary Seismic Response Analysis of Long-span Structures by Frequency Domain Method Considering Wave Passage Effect. Soil Dynamics and Earthquake Eng. 2018;109: 1—9.
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11. Gribanov YU.I., Mal'kov V.L. Spektral'nyy Analiz Sluchaynykh Protsessov. M.: Energiya, 1974.
12. Poznyak E.V. Sostoyatel'naya Otsenka Spektral'noy Plotnosti Moshchnosti Seysmicheskogo Uskoreniya Grunta. Vestnik MEI. 2015;5:30—36. (in Russian).
13. Lee W.H.K., Kanamori H., Jennings P., Kisslinger C. International Handbook of Earthquake & Engineering Seismology. Pt. B. Academic Press, 2003.
14. Zerva A., Zervas V. Spatial Variation of Seismic Ground Motions: an Overview. Appl. Mech. Rev. 2002;55; 3:271—296.
15. Abrahamson N.A., Schneider J.F., Stepp C. The Spatial Variation of Earthquake Ground Motion End Effects of Local Site Conditions. Proc. X World Conf. Earthquake Eng. 1992:967—972.
16. Rodda G.K., Basu D. Parameterization of Auto- spectral Density of Earthquake Induced Strong Ground Motions. Soil Dynamics and Earthquake Eng. 2019;118: 52—64.
17. Nazarov Yu.P., Travush V.I. Dlinnoperiodnye Seysmicheskie Vozdeystviya i Ikh Vliyanie na Prochnost' Konstruktsiy Vysotnykh Zdaniy, Intern. J. Computational Civil and Structural Eng. 2018;14(4):14—26. (in Russian).
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---
For citation: Poznyak E.V., Radin V.P., Novikova O.V. Time-frequency Analysis of Natural Accelerograms. Bulletin of MPEI. 2019;5:135—141. (in Russian). DOI: 10.24160/1993-6982-2019-5-135-141.
2. Болотин В.В. Применение методов теории вероятностей и теории надежности в расчетах сооружений. М.: Стройиздат, 1971.
3. Marano G.C. Non-stationary Stochastic Modulation Function Definition Based On Process Energy Release // Physica A: Statistical Mechanics and its Appl. 2019. V. 517. Pp. 280—289.
4. Wang D., Fan Z., Hao Sh., Zhao D. An Evolutionary Power Spectrum Model of Fully Nonstationary Seismic Ground Motion // Soil Dynamics and Earthquake Eng. 2018. V. 105. Pp. 1—10.
5. Schillinger D., Stefanov D., Stavrev А. The Method of Separation for Evolutionary Spectral Density Estimation of Multi-variate and Multi-dimensional Non-stationary Stochastic Processes // Probabilistic Eng. Mechanics. 2013. V. 33. Pp. 58—78.
6. Canor Т., Caracoglia L., Denoël V. Perturbation Methods in Evolutionary Spectral Analysis for Linear Dynamics and Equivalent Statistical Linearization // Probabilistic Eng. Mechanics. 2016. V. 46. Pp. 1—17.
7. Zhao Y., Li Y., Zhang Y., Kennedy D. Nonstationary Seismic Response Analysis of Long-span Structures by Frequency Domain Method Considering Wave Passage Effect // Soil Dynamics and Earthquake Eng. 2018. V. 109. Pp. 1—9.
8. Котюк А.Ф, Цветков Э.И. Спектральный и корреляционный анализ нестационарных случайных процессов. М.: Изд-во Комитета стандартов мер и измерительных приборов при Совете Министров СССР, 1970.
9. Пугачев В.С., Синицын И.Н. Стохастические дифференциальные системы. Анализ и фильтрация. М.: Наука, 1990.
10. Бендат Дж., Пирсол А. Прикладной анализ случайных данных. М.: Мир, 1989.
11. Грибанов Ю.И., Мальков В.Л. Спектральный анализ случайных процессов. М.: Энергия, 1974.
12. Позняк Е.В. Состоятельная оценка спектральной плотности мощности сейсмического ускорения грунта // Вестник МЭИ. 2015. № 5. С. 30—36.
13. Lee W.H.K., Kanamori H., Jennings P., Kisslinger C. International Handbook of Earthquake & Engineering Seismology. Pt. B. Academic Press, 2003.
14. Zerva A., Zervas V. Spatial Variation of Seismic Ground Motions: an Overview // Appl. Mech. Rev. 2002. V. 55. No. 3. Pp. 271—296.
15. Abrahamson N.A., Schneider J.F., Stepp C. The Spatial Variation of Earthquake Ground Motion End Effects of Local Site Conditions // Proc. X World Conf. Earthquake Eng. 1992. Pp. 967—972.
16. Rodda G.K., Basu D. Parameterization of Auto- spectral Density of Earthquake Induced Strong Ground Motions // Soil Dynamics and Earthquake Eng. 2019. V. 118. Pp. 52—64.
17. Назаров Ю.П., Травуш В.И. Длиннопериодные сейсмические воздействия и их влияние на прочность конструкций высотных зданий // Intern. J. Computational Civil and Structural Eng. 2018. V. 14(4). Pp. 14—26.
18. Назаров Ю.П. Аналитические основы расчета сооружений на сейсмические воздействия. М.: Наука, 2010.
19. Назаров Ю.П., Позняк Е.В. О пространственной изменчивости сейсмических движений грунта при расчете сооружений // Основания, фундаменты и механика грунтов. 2014. № 5. С. 17—20.
20. Назаров Ю.П., Позняк Е.В. Определение коэффициента динамичности в расчетах на сейсмостойкость // Строительство: наука и образование. 2015. № 1. Ст. 2. [Электрон. ресурс] http://www.nso-journal.ru (дата обращения 25.01.2019).
---
Для цитирования: Позняк Е.В., Радин В.П., Новикова О.В. Частотно-временной анализ акселерограмм природных землетрясений // Вестник МЭИ. 2019. № 5. С. 135—141. DOI: 10.24160/1993-6982-2019-5-135-141.
#
1. Bolotin V.V. Statisticheskie Metody v Stroitel'noy Mekhanike. M.: Stroyizdat, 1961. (in Russian).
2. Bolotin V.V. Primenenie Metodov Teorii Veroyatnostey i Teorii Nadezhnosti v Raschetakh Sooruzheniy. M.: Stroyizdat, 1971. (in Russian).
3. Marano G.C. Non-stationary Stochastic Modulation Function Definition Based On Process Energy Release. Physica A: Statistical Mechanics and its Appl. 2019;517: 280—289.
4. Wang D., Fan Z., Hao Sh., Zhao D. An Evolutionary Power Spectrum Model of Fully Nonstationary Seismic Ground Motion. Soil Dynamics and Earthquake Eng. 2018;105:1—10.
5. Schillinger D., Stefanov D., Stavrev А. The Method of Separation for Evolutionary Spectral Density Estimation of Multi-variate and Multi-dimensional Non-stationary Stochastic Processes. Probabilistic Eng. Mechanics. 2013; 33:58—78.
6. Canor Т., Caracoglia L., Denoël V. Perturbation Methods in Evolutionary Spectral Analysis for Linear Dynamics and Equivalent Statistical Linearization. Probabilistic Eng. Mechanics. 2016;46:1—17.
7. Zhao Y., Li Y., Zhang Y., Kennedy D. Nonstationary Seismic Response Analysis of Long-span Structures by Frequency Domain Method Considering Wave Passage Effect. Soil Dynamics and Earthquake Eng. 2018;109: 1—9.
8. Kotyuk A.F, TSvetkov E.I. Spektral'nyy i Korrelyatsionnyy Analiz Nestatsionarnykh Sluchaynykh Protsessov. M.: Izd-vo Komiteta Standartov Mer i Izmeritel'nykh Priborov pri Sovete Ministrov SSSR, 1970. (in Russian).
9. Pugachev V.S., Sinitsyn I.N. Stokhasticheskie Differentsial'nye Sistemy. Analiz i Fil'tratsiya. M.: Nauka, 1990. (in Russian).
10. Bendat Dzh., Pirsol A. Prikladnoy Analiz Sluchaynykh Dannykh. M.: Mir, 1989. (in Russian).
11. Gribanov YU.I., Mal'kov V.L. Spektral'nyy Analiz Sluchaynykh Protsessov. M.: Energiya, 1974.
12. Poznyak E.V. Sostoyatel'naya Otsenka Spektral'noy Plotnosti Moshchnosti Seysmicheskogo Uskoreniya Grunta. Vestnik MEI. 2015;5:30—36. (in Russian).
13. Lee W.H.K., Kanamori H., Jennings P., Kisslinger C. International Handbook of Earthquake & Engineering Seismology. Pt. B. Academic Press, 2003.
14. Zerva A., Zervas V. Spatial Variation of Seismic Ground Motions: an Overview. Appl. Mech. Rev. 2002;55; 3:271—296.
15. Abrahamson N.A., Schneider J.F., Stepp C. The Spatial Variation of Earthquake Ground Motion End Effects of Local Site Conditions. Proc. X World Conf. Earthquake Eng. 1992:967—972.
16. Rodda G.K., Basu D. Parameterization of Auto- spectral Density of Earthquake Induced Strong Ground Motions. Soil Dynamics and Earthquake Eng. 2019;118: 52—64.
17. Nazarov Yu.P., Travush V.I. Dlinnoperiodnye Seysmicheskie Vozdeystviya i Ikh Vliyanie na Prochnost' Konstruktsiy Vysotnykh Zdaniy, Intern. J. Computational Civil and Structural Eng. 2018;14(4):14—26. (in Russian).
18. Nazarov Yu.P. Analiticheskie Osnovy Rascheta Sooruzheniy na Seysmicheskie Vozdeystviya. M.: Nauka, 2010. (in Russian).
19. Nazarov Yu.P., Poznyak E.V. O Prostranstvennoy Izmenchivosti Seysmicheskikh Dvizheniy Grunta pri Raschete Sooruzheniy. Osnovaniya, Fundamenty i Mekhanika Gruntov. 2014;5:17—20. (in Russian).
20. Nazarov Yu.P., Poznyak E.V. Opredelenie Koeffitsienta Dinamichnosti v Raschetakh na Seysmostoykost'. Stroitel'stvo: Nauka i Obrazovanie. 2015;1;2. [Elektron. Resurs] http://www.nso-journal.ru (Data Obrashcheniya 25.01.2019). (in Russian).
---
For citation: Poznyak E.V., Radin V.P., Novikova O.V. Time-frequency Analysis of Natural Accelerograms. Bulletin of MPEI. 2019;5:135—141. (in Russian). DOI: 10.24160/1993-6982-2019-5-135-141.
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Published
2019-02-25
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Section
Mathematical Modeling, Numerical Methods and Program Complexe (05.13.18)
