Testing for finite variance with applications to vibration signals from rotating machines

Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedur...
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Autor*in:	Skowronek, Katarzyna [verfasserIn] Zimroz, Radosław [verfasserIn] Wyłomańska, Agnieszka [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Testing Finite variance Heavy-tailed distribution Monte Carlo simulations Condition monitoring

Anmerkung:	© The Author(s) 2024

Übergeordnetes Werk:	Enthalten in: Journal of mathematics in industry - Springer Berlin Heidelberg, 2011, 14(2024), 1 vom: 27. Aug.
Übergeordnetes Werk:	volume:14 ; year:2024 ; number:1 ; day:27 ; month:08

Links:	Volltext

DOI / URN:	10.1186/s13362-024-00157-6

Katalog-ID:	SPR057113424

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520			\|a Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains.
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allfields	10.1186/s13362-024-00157-6 doi (DE-627)SPR057113424 (SPR)s13362-024-00157-6-e DE-627 ger DE-627 rakwb eng 510 VZ Skowronek, Katarzyna verfasserin (orcid)0000-0003-1021-8962 aut Testing for finite variance with applications to vibration signals from rotating machines 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. Testing (dpeaa)DE-He213 Finite variance (dpeaa)DE-He213 Heavy-tailed distribution (dpeaa)DE-He213 Monte Carlo simulations (dpeaa)DE-He213 Condition monitoring (dpeaa)DE-He213 Zimroz, Radosław verfasserin aut Wyłomańska, Agnieszka verfasserin aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 27. Aug. (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:27 month:08 https://dx.doi.org/10.1186/s13362-024-00157-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 27 08
spelling	10.1186/s13362-024-00157-6 doi (DE-627)SPR057113424 (SPR)s13362-024-00157-6-e DE-627 ger DE-627 rakwb eng 510 VZ Skowronek, Katarzyna verfasserin (orcid)0000-0003-1021-8962 aut Testing for finite variance with applications to vibration signals from rotating machines 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. Testing (dpeaa)DE-He213 Finite variance (dpeaa)DE-He213 Heavy-tailed distribution (dpeaa)DE-He213 Monte Carlo simulations (dpeaa)DE-He213 Condition monitoring (dpeaa)DE-He213 Zimroz, Radosław verfasserin aut Wyłomańska, Agnieszka verfasserin aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 27. Aug. (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:27 month:08 https://dx.doi.org/10.1186/s13362-024-00157-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 27 08
allfields_unstemmed	10.1186/s13362-024-00157-6 doi (DE-627)SPR057113424 (SPR)s13362-024-00157-6-e DE-627 ger DE-627 rakwb eng 510 VZ Skowronek, Katarzyna verfasserin (orcid)0000-0003-1021-8962 aut Testing for finite variance with applications to vibration signals from rotating machines 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. Testing (dpeaa)DE-He213 Finite variance (dpeaa)DE-He213 Heavy-tailed distribution (dpeaa)DE-He213 Monte Carlo simulations (dpeaa)DE-He213 Condition monitoring (dpeaa)DE-He213 Zimroz, Radosław verfasserin aut Wyłomańska, Agnieszka verfasserin aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 27. Aug. (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:27 month:08 https://dx.doi.org/10.1186/s13362-024-00157-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 27 08
allfieldsGer	10.1186/s13362-024-00157-6 doi (DE-627)SPR057113424 (SPR)s13362-024-00157-6-e DE-627 ger DE-627 rakwb eng 510 VZ Skowronek, Katarzyna verfasserin (orcid)0000-0003-1021-8962 aut Testing for finite variance with applications to vibration signals from rotating machines 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. Testing (dpeaa)DE-He213 Finite variance (dpeaa)DE-He213 Heavy-tailed distribution (dpeaa)DE-He213 Monte Carlo simulations (dpeaa)DE-He213 Condition monitoring (dpeaa)DE-He213 Zimroz, Radosław verfasserin aut Wyłomańska, Agnieszka verfasserin aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 27. Aug. (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:27 month:08 https://dx.doi.org/10.1186/s13362-024-00157-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 27 08
allfieldsSound	10.1186/s13362-024-00157-6 doi (DE-627)SPR057113424 (SPR)s13362-024-00157-6-e DE-627 ger DE-627 rakwb eng 510 VZ Skowronek, Katarzyna verfasserin (orcid)0000-0003-1021-8962 aut Testing for finite variance with applications to vibration signals from rotating machines 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2024 Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. Testing (dpeaa)DE-He213 Finite variance (dpeaa)DE-He213 Heavy-tailed distribution (dpeaa)DE-He213 Monte Carlo simulations (dpeaa)DE-He213 Condition monitoring (dpeaa)DE-He213 Zimroz, Radosław verfasserin aut Wyłomańska, Agnieszka verfasserin aut Enthalten in Journal of mathematics in industry Springer Berlin Heidelberg, 2011 14(2024), 1 vom: 27. Aug. (DE-627)718611039 (DE-600)2660490-5 2190-5983 nnns volume:14 year:2024 number:1 day:27 month:08 https://dx.doi.org/10.1186/s13362-024-00157-6 X:SPRINGER Resolving-System kostenfrei Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_2129 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 14 2024 1 27 08
language	English
source	Enthalten in Journal of mathematics in industry 14(2024), 1 vom: 27. Aug. volume:14 year:2024 number:1 day:27 month:08
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author	Skowronek, Katarzyna
spellingShingle	Skowronek, Katarzyna ddc 510 misc Testing misc Finite variance misc Heavy-tailed distribution misc Monte Carlo simulations misc Condition monitoring Testing for finite variance with applications to vibration signals from rotating machines
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topic	ddc 510 misc Testing misc Finite variance misc Heavy-tailed distribution misc Monte Carlo simulations misc Condition monitoring
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title	Testing for finite variance with applications to vibration signals from rotating machines
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title_sort	testing for finite variance with applications to vibration signals from rotating machines
title_auth	Testing for finite variance with applications to vibration signals from rotating machines
abstract	Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. © The Author(s) 2024
abstractGer	Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. © The Author(s) 2024
abstract_unstemmed	Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains. © The Author(s) 2024
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title_short	Testing for finite variance with applications to vibration signals from rotating machines
url	https://dx.doi.org/10.1186/s13362-024-00157-6
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Testing for finite variance with applications to vibration signals from rotating machines

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