Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes
Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon proce...
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Veröffentlicht in: | Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-10 |
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description | Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes. |
doi_str_mv | 10.1155/2015/870420 |
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Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2015/870420</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Civil engineering ; Closed form solutions ; Decomposition ; Density ; Evolutionary ; Exact solutions ; Fourier transforms ; Frequency distribution ; Functions (mathematics) ; Mathematical analysis ; Methods ; Power spectral density ; Signal processing ; Spectra ; Stochastic models ; Time dependence ; Time domain analysis ; Typhoons ; Wavelet ; Wavelet transforms ; Wind</subject><ispartof>Mathematical problems in engineering, 2015-01, Vol.2015 (2015), p.1-10</ispartof><rights>Copyright © 2015 Guang-Dong Zhou et al.</rights><rights>Copyright © 2015 Guang-Dong Zhou et al. Guang-Dong Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c347t-6a54652a605fa94bddd9392124417d76fce87f098d4a2ec9093c8db14de723f13</cites><orcidid>0000-0002-1628-8286</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><contributor>Yi, Ting-Hua</contributor><creatorcontrib>Zhou, Guang-Dong</creatorcontrib><creatorcontrib>Li, Aiqun</creatorcontrib><creatorcontrib>Ding, You-Liang</creatorcontrib><title>Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes</title><title>Mathematical problems in engineering</title><description>Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.</description><subject>Civil engineering</subject><subject>Closed form solutions</subject><subject>Decomposition</subject><subject>Density</subject><subject>Evolutionary</subject><subject>Exact solutions</subject><subject>Fourier transforms</subject><subject>Frequency distribution</subject><subject>Functions (mathematics)</subject><subject>Mathematical analysis</subject><subject>Methods</subject><subject>Power spectral density</subject><subject>Signal processing</subject><subject>Spectra</subject><subject>Stochastic models</subject><subject>Time dependence</subject><subject>Time domain analysis</subject><subject>Typhoons</subject><subject>Wavelet</subject><subject>Wavelet transforms</subject><subject>Wind</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>BENPR</sourceid><recordid>eNqF0EtLw0AQB_AgCtbqybsEvIgSu89s9qilPqA-wIre4jY7a1PSbNxNKvn2pkRBvHjaYefHMPMPgkOMzjHmfEQQ5qNEIEbQVjDAPKYRx0xsdzUiLMKEvu4Ge94vESKY42QQvL2oNRRQR5fKgw7voF5YbQv73obGunCytkVT57ZUrg2fKshqp8KJr_OV2vyG1oT3tvS1-jGztlrYrvHobAbeg98PdowqPBx8v8Pg-WoyG99E04fr2_HFNMooE3UUK85iTlSMuFGSzbXWkkqCCWNYaBGbDBJhkEw0UwQyiSTNEj3HTIMg1GA6DE76uZWzHw34Ol3lPoOiUCXYxqc4TrgQRIoNPf5Dl7ZxZbddp2LKpEgE79RZrzJnvXdg0sp1Z7s2xSjdpJ1u0k77tDt92utFXmr1mf-Dj3oMHQGjfmHBJBX0C5JviPE</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>Zhou, Guang-Dong</creator><creator>Li, Aiqun</creator><creator>Ding, You-Liang</creator><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>7SP</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-1628-8286</orcidid></search><sort><creationdate>20150101</creationdate><title>Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes</title><author>Zhou, Guang-Dong ; Li, Aiqun ; Ding, You-Liang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-6a54652a605fa94bddd9392124417d76fce87f098d4a2ec9093c8db14de723f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Civil engineering</topic><topic>Closed form solutions</topic><topic>Decomposition</topic><topic>Density</topic><topic>Evolutionary</topic><topic>Exact solutions</topic><topic>Fourier transforms</topic><topic>Frequency distribution</topic><topic>Functions (mathematics)</topic><topic>Mathematical analysis</topic><topic>Methods</topic><topic>Power spectral density</topic><topic>Signal processing</topic><topic>Spectra</topic><topic>Stochastic models</topic><topic>Time dependence</topic><topic>Time domain analysis</topic><topic>Typhoons</topic><topic>Wavelet</topic><topic>Wavelet transforms</topic><topic>Wind</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhou, Guang-Dong</creatorcontrib><creatorcontrib>Li, Aiqun</creatorcontrib><creatorcontrib>Ding, You-Liang</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>Electronics & Communications Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhou, Guang-Dong</au><au>Li, Aiqun</au><au>Ding, You-Liang</au><au>Yi, Ting-Hua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2015-01-01</date><risdate>2015</risdate><volume>2015</volume><issue>2015</issue><spage>1</spage><epage>10</epage><pages>1-10</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2015/870420</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-1628-8286</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Civil engineering Closed form solutions Decomposition Density Evolutionary Exact solutions Fourier transforms Frequency distribution Functions (mathematics) Mathematical analysis Methods Power spectral density Signal processing Spectra Stochastic models Time dependence Time domain analysis Typhoons Wavelet Wavelet transforms Wind |
title | Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes |
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