{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:15:05Z","timestamp":1772583305620,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,11]],"date-time":"2020-04-11T00:00:00Z","timestamp":1586563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index \u03b1. Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by \u03b1H &gt; 1.<\/jats:p>","DOI":"10.3390\/sym12040605","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T03:10:01Z","timestamp":1586833801000},"page":"605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction"],"prefix":"10.3390","volume":"12","author":[{"given":"Shouwu","family":"Duan","sequence":"first","affiliation":[{"name":"School of Electronic &amp; Electrical Engineering, Shanghai University of Science Engineering, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanqing","family":"Song","sequence":"additional","affiliation":[{"name":"School of Electronic &amp; Electrical Engineering, Shanghai University of Science Engineering, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 1007 Baku, Azerbaijan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yakufu","family":"Yasen","sequence":"additional","affiliation":[{"name":"State Grid Kashi Electric Power Supply Company, 156 Renmin West Road, Kashi City 844099, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"He","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic &amp; Electrical Engineering, Shanghai University of Science Engineering, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,11]]},"reference":[{"key":"ref_1","first-page":"62","article-title":"Analysis of wind power value to power system operation","volume":"5","author":"Lei","year":"2002","journal-title":"Power Syst. 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