Accurate and efficient calculation of discrete correlation functions and power spectra
Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data ser...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Xu, Y.F. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015transfer abstract |
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| Umfang: |
20 |
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| Übergeordnetes Werk: |
Enthalten in: Cancer of the uterus and treatment of incontinence (CUTI) - Robison, K.M. ELSEVIER, 2015, London |
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| Übergeordnetes Werk: |
volume:347 ; year:2015 ; day:7 ; month:07 ; pages:246-265 ; extent:20 |
| Links: |
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| DOI / URN: |
10.1016/j.jsv.2015.02.026 |
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ELV03489618X |
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| 245 | 1 | 0 | |a Accurate and efficient calculation of discrete correlation functions and power spectra |
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| 520 | |a Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. | ||
| 520 | |a Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. | ||
| 700 | 1 | |a Liu, J.M. |4 oth | |
| 700 | 1 | |a Zhu, W.D. |4 oth | |
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2015 |
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10.1016/j.jsv.2015.02.026 doi GBVA2015021000017.pica (DE-627)ELV03489618X (ELSEVIER)S0022-460X(15)00160-1 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Xu, Y.F. verfasserin aut Accurate and efficient calculation of discrete correlation functions and power spectra 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Liu, J.M. oth Zhu, W.D. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:347 year:2015 day:7 month:07 pages:246-265 extent:20 https://doi.org/10.1016/j.jsv.2015.02.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 347 2015 7 0707 246-265 20 045F 530 |
| spelling |
10.1016/j.jsv.2015.02.026 doi GBVA2015021000017.pica (DE-627)ELV03489618X (ELSEVIER)S0022-460X(15)00160-1 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Xu, Y.F. verfasserin aut Accurate and efficient calculation of discrete correlation functions and power spectra 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Liu, J.M. oth Zhu, W.D. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:347 year:2015 day:7 month:07 pages:246-265 extent:20 https://doi.org/10.1016/j.jsv.2015.02.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 347 2015 7 0707 246-265 20 045F 530 |
| allfields_unstemmed |
10.1016/j.jsv.2015.02.026 doi GBVA2015021000017.pica (DE-627)ELV03489618X (ELSEVIER)S0022-460X(15)00160-1 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Xu, Y.F. verfasserin aut Accurate and efficient calculation of discrete correlation functions and power spectra 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Liu, J.M. oth Zhu, W.D. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:347 year:2015 day:7 month:07 pages:246-265 extent:20 https://doi.org/10.1016/j.jsv.2015.02.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 347 2015 7 0707 246-265 20 045F 530 |
| allfieldsGer |
10.1016/j.jsv.2015.02.026 doi GBVA2015021000017.pica (DE-627)ELV03489618X (ELSEVIER)S0022-460X(15)00160-1 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Xu, Y.F. verfasserin aut Accurate and efficient calculation of discrete correlation functions and power spectra 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Liu, J.M. oth Zhu, W.D. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:347 year:2015 day:7 month:07 pages:246-265 extent:20 https://doi.org/10.1016/j.jsv.2015.02.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 347 2015 7 0707 246-265 20 045F 530 |
| allfieldsSound |
10.1016/j.jsv.2015.02.026 doi GBVA2015021000017.pica (DE-627)ELV03489618X (ELSEVIER)S0022-460X(15)00160-1 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 610 VZ 44.11 bkl Xu, Y.F. verfasserin aut Accurate and efficient calculation of discrete correlation functions and power spectra 2015transfer abstract 20 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. Liu, J.M. oth Zhu, W.D. oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:347 year:2015 day:7 month:07 pages:246-265 extent:20 https://doi.org/10.1016/j.jsv.2015.02.026 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 347 2015 7 0707 246-265 20 045F 530 |
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Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. |
| abstractGer |
Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. |
| abstract_unstemmed |
Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis. |
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However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass–spring–damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate their natural frequencies, damping ratios, and mode shapes. Natural frequencies, damping ratios, and mode shapes of the 2-DOF system obtained from OMA agree well with theoretical ones from complex modal analysis; natural frequencies, damping ratios, and mode shapes of the beam from OMA agreed well with those from experimental modal analysis.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liu, J.M.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhu, W.D.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Academic Press</subfield><subfield code="a">Robison, K.M. ELSEVIER</subfield><subfield code="t">Cancer of the uterus and treatment of incontinence (CUTI)</subfield><subfield code="d">2015</subfield><subfield code="g">London</subfield><subfield code="w">(DE-627)ELV012704822</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:347</subfield><subfield code="g">year:2015</subfield><subfield code="g">day:7</subfield><subfield code="g">month:07</subfield><subfield code="g">pages:246-265</subfield><subfield code="g">extent:20</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.jsv.2015.02.026</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_30</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.11</subfield><subfield code="j">Präventivmedizin</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">347</subfield><subfield code="j">2015</subfield><subfield code="b">7</subfield><subfield code="c">0707</subfield><subfield code="h">246-265</subfield><subfield code="g">20</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">530</subfield></datafield></record></collection>
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