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Improved Ensemble Empirical Mode Decomposition and its Applications to Gearbox Fault Signal Processing, Keywords: Complementary Ensemble Empirical Mode Decomposition(CEEMD), Improved Complementary Ensemble Empirical Mode Decomposition(ICEEMD), Gearbox, Signal Processing.
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62604a4b090cbf2c4ec3c3b3/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62604a4b090cbf2c4ec3c3b3/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc1 ls0 ws0">I<span class="_ _0"></span>m<span class="_ _0"></span>p<span class="_ _0"></span>r<span class="_ _0"></span>o<span class="_ _0"></span>v<span class="_ _0"></span>e<span class="_ _0"></span>d<span class="_ _0"></span> <span class="_ _0"></span>E<span class="_ _0"></span>n<span class="_ _0"></span>s<span class="_ _0"></span>e<span class="_ _0"></span>m<span class="_ _0"></span>b<span class="_ _0"></span>l<span class="_ _0"></span>e<span class="_ _0"></span> <span class="_ _0"></span>E<span class="_ _0"></span>m<span class="_ _0"></span>p<span class="_ _0"></span>i<span class="_ _0"></span>r<span class="_ _0"></span>i<span class="_ _0"></span>c<span class="_ _0"></span>a<span class="_ _0"></span>l<span class="_ _0"></span> <span class="_ _0"></span>M<span class="_ _0"></span>o<span class="_ _0"></span>d<span class="_ _0"></span>e<span class="_ _0"></span> <span class="_ _0"></span>D<span class="_ _1"></span>e<span class="_ _0"></span>c<span class="_ _1"></span>o<span class="_ _0"></span>m<span class="_ _2"></span>p<span class="_ _1"></span>o<span class="_ _0"></span>s<span class="_ _0"></span>i<span class="_ _0"></span>t<span class="_ _0"></span>i<span class="_ _0"></span>o<span class="_ _0"></span>n<span class="_ _0"></span> <span class="_ _0"></span>a<span class="_ _0"></span>n<span class="_ _0"></span>d<span class="_ _0"></span> <span class="_ _0"></span>i<span class="_ _0"></span>t<span class="_ _0"></span>s<span class="_ _0"></span> </div><div class="t m0 x4 h3 y4 ff2 fs1 fc0 sc1 ls0 ws0">A<span class="_ _0"></span>p<span class="_ _0"></span>p<span class="_ _1"></span>l<span class="_ _0"></span>i<span class="_ _0"></span>c<span class="_ _0"></span>a<span class="_ _0"></span>t<span class="_ _0"></span>i<span class="_ _0"></span>o<span class="_ _0"></span>n<span class="_ _0"></span>s<span class="_ _0"></span> <span class="_ _0"></span>t<span class="_ _0"></span>o<span class="_ _0"></span> <span class="_ _0"></span>G<span class="_ _0"></span>e<span class="_ _0"></span>a<span class="_ _0"></span>r<span class="_ _0"></span>b<span class="_ _0"></span>o<span class="_ _0"></span>x<span class="_ _0"></span> <span class="_ _0"></span>F<span class="_ _0"></span>a<span class="_ _0"></span>u<span class="_ _0"></span>l<span class="_ _0"></span>t<span class="_ _0"></span> <span class="_ _0"></span>S<span class="_ _0"></span>i<span class="_ _0"></span>g<span class="_ _0"></span>n<span class="_ _0"></span>a<span class="_ _0"></span>l<span class="_ _0"></span> <span class="_ _1"></span>P<span class="_ _0"></span>r<span class="_ _0"></span>o<span class="_ _0"></span>c<span class="_ _0"></span>e<span class="_ _0"></span>s<span class="_ _0"></span>s<span class="_ _0"></span>i<span class="_ _0"></span>n<span class="_ _0"></span>g<span class="_ _0"></span> </div><div class="c x5 y5 w2 h4"><div class="t m0 x6 h5 y6 ff3 fs2 fc0 sc0 ls0 ws0">Jinshan Lin </div><div class="t m0 x7 h5 y7 ff3 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x8 h5 y8 ff3 fs2 fc0 sc0 ls0 ws0"> School of Mechatronics and Vehic<span class="ls1">le</span> <span class="_ _3"></span>Engineering<span class="ls2">, </span>Weifang University </div><div class="t m0 x9 h5 y9 ff3 fs2 fc0 sc0 ls0 ws0">Weifang<span class="ls2">, </span>261061<span class="ls2">, C</span>hina </div><div class="t m0 x7 h6 ya ff4 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="t m0 x1 h7 yb ff3 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 xa h7 yc ff3 fs0 fc0 sc0 ls0 ws0">Abstract </div><div class="t m0 x1 h8 yd ff1 fs2 fc0 sc0 ls0 ws0">Ensemble <span class="_"> </span>empirical <span class="_"> </span>mode <span class="_ _4"> </span>decomposition <span class="_"> </span>(EEMD) <span class="_"> </span>is <span class="_ _4"> </span>a <span class="_"> </span>noise-</div><div class="t m0 x1 h8 ye ff1 fs2 fc0 sc0 ls0 ws0">assisted <span class="_ _3"></span>method <span class="_ _5"></span>and <span class="_ _3"></span>also <span class="_ _5"></span>a <span class="_ _3"></span>significant <span class="_ _5"></span>improvement <span class="_ _3"></span>on <span class="_ _5"></span>empirical<span class="_ _3"></span> </div><div class="t m0 x1 h8 yf ff1 fs2 fc0 sc0 ls0 ws0">mode <span class="_ _3"></span>decomposition <span class="_ _3"></span>(EMD). <span class="_ _3"></span>However,<span class="_ _3"></span> <span class="_ _3"></span>the <span class="_ _3"></span>EE<span class="_ _3"></span>MD <span class="_ _3"></span>method <span class="_ _3"></span>la<span class="_ _3"></span>cks </div><div class="t m0 x1 h8 y10 ff1 fs2 fc0 sc0 ls0 ws0">a guide <span class="_ _3"></span>to <span class="_ _3"></span>choosing the <span class="_ _3"></span>appropriate <span class="_ _3"></span>amplitude <span class="_ _3"></span>of added <span class="_ _3"></span>noise and </div><div class="t m0 x1 h8 y11 ff1 fs2 fc0 sc0 ls0 ws0">its <span class="_ _6"> </span>computation <span class="_ _6"> </span>efficiency<span class="_ _3"></span> <span class="_ _6"> </span>is <span class="_ _6"> </span>fairly <span class="_ _6"> </span>low. <span class="_ _6"> </span>To <span class="_ _6"> </span>alleviate <span class="_ _6"> </span>the </div><div class="t m0 x1 h8 y12 ff1 fs2 fc0 sc0 ls0 ws0">problems <span class="_ _4"> </span>of <span class="_ _7"> </span>the <span class="_ _7"> </span>EE<span class="_ _3"></span>MD <span class="_ _7"> </span>method, <span class="_ _4"> </span>the <span class="_ _7"> </span>improved <span class="_ _4"> </span>complementary </div><div class="t m0 x1 h8 y13 ff1 fs2 fc0 sc0 ls0 ws0">EEMD <span class="_ _8"> </span>method <span class="_ _8"> </span>(ICEEMD) <span class="_ _8"> </span><span class="ls3">wa</span>s <span class="_ _8"> </span>proposed. <span class="_ _8"> </span>Furthermore, <span class="_ _8"> </span>the </div><div class="t m0 x1 h8 y14 ff1 fs2 fc0 sc0 ls0 ws0">ICEEMD <span class="_ _7"> </span>method <span class="_ _7"> </span>was <span class="_ _7"> </span>used <span class="_ _7"> </span>to <span class="_ _7"> </span>ana<span class="_ _3"></span>lyze <span class="_ _7"> </span>realisti<span class="_ _3"></span>c <span class="_ _7"> </span>gearbox <span class="_ _7"> </span>faulty<span class="_ _3"></span> </div><div class="t m0 x1 h8 y15 ff1 fs2 fc0 sc0 ls0 ws0">signals. <span class="_ _5"></span>The <span class="_ _9"></span>results <span class="_ _5"></span>i<span class="_ _3"></span>ndicate <span class="_ _9"></span>that <span class="_ _5"></span>the <span class="_ _9"></span>ICEEMD <span class="_ _9"></span>method <span class="_ _5"></span>has <span class="_ _9"></span>some </div><div class="t m0 x1 h8 y16 ff1 fs2 fc0 sc0 ls0 ws0">advantages <span class="_ _a"> </span>over <span class="_ _a"> </span>the <span class="_ _a"> </span>EEMD <span class="_ _a"> </span>method <span class="_ _b"> </span>in <span class="_ _b"> </span>al<span class="_ _3"></span>leviating <span class="_ _a"> </span>the <span class="_ _b"> </span>mode </div><div class="t m0 x1 h8 y17 ff1 fs2 fc0 sc0 ls0 ws0">mixing <span class="_ _c"></span>and <span class="_ _c"></span>splitting <span class="_ _7"></span>as <span class="_ _9"></span>well <span class="_ _c"></span>as<span class="_ _3"></span> <span class="_ _c"></span>reducing <span class="_ _c"></span>the<span class="_ _3"></span> <span class="_ _c"></span>time <span class="_ _c"></span>cost <span class="_ _7"></span>and <span class="_ _9"></span>also </div><div class="t m0 x1 h8 y18 ff1 fs2 fc0 sc0 ls0 ws0">outperforms <span class="_ _3"></span>the <span class="_ _5"></span>CEEMD <span class="_ _5"></span>method <span class="_ _3"></span>in <span class="_ _9"></span>alleviating <span class="_ _5"></span>the <span class="_ _3"></span>mode <span class="_ _5"></span>mixing </div><div class="t m0 x1 h8 y19 ff1 fs2 fc0 sc0 ls0 ws0">and <span class="_ _5"></span>splitting. <span class="_ _5"></span>The <span class="_ _5"></span>paper <span class="_ _5"></span>also <span class="_ _5"></span>indi<span class="_ _3"></span>cates <span class="_ _5"></span>that <span class="_ _5"></span>the <span class="_ _9"></span>ICEEMD <span class="_ _5"></span>method </div><div class="t m0 x1 h8 y1a ff1 fs2 fc0 sc0 ls0 ws0">seems <span class="_"> </span>to <span class="_"> </span>be <span class="_"> </span>an <span class="_"> </span>effective <span class="_"> </span>and <span class="_"> </span>efficient <span class="_"> </span>method <span class="_"> </span>for <span class="_ _4"> </span>processing </div><div class="t m0 x1 h8 y1b ff1 fs2 fc0 sc0 ls0 ws0">gearbox fault signals. </div><div class="t m0 x1 h9 y1c ff5 fs0 fc0 sc0 ls0 ws0">Keywords:<span class="ff6 fs2"> <span class="_ _d"> </span>Complementary <span class="_ _d"> </span>Ensemble <span class="_ _d"> </span>Empirical <span class="_ _d"> </span>Mode </span></div><div class="t m0 x1 ha y1d ff6 fs2 fc0 sc0 ls0 ws0">Decomposition(CEEMD)<span class="ls2">, <span class="_ _a"> </span></span>Improved <span class="_ _a"> </span>Complementary <span class="_ _e"> </span>Ensemble </div><div class="t m0 x1 ha y1e ff6 fs2 fc0 sc0 ls0 ws0">Empirical <span class="_ _6"> </span>Mode <span class="_ _6"> </span>Decomposition(ICEEMD)<span class="ls2">, <span class="_ _6"> </span></span>Gearbox<span class="ls2">, <span class="_ _f"> </span></span>Signal </div><div class="t m0 x1 h9 y1f ff6 fs2 fc0 sc0 ls0 ws0">Processing.<span class="ff5 fs0"> </span></div><div class="t m0 x1 hb y20 ff3 fs3 fc0 sc0 ls0 ws0">1. Introduction </div><div class="t m0 x1 h2 y21 ff1 fs0 fc0 sc0 ls0 ws0">It <span class="_ _8"> </span>is <span class="_ _8"> </span>a <span class="_ _8"> </span>challenging <span class="_ _8"> </span>task <span class="_ _8"> </span>to <span class="_ _8"> </span>develop <span class="_ _8"> </span>signal <span class="_ _e"> </span>pr<span class="_ _3"></span>ocessing </div><div class="t m0 x1 h2 y22 ff1 fs0 fc0 sc0 ls0 ws0">techniques <span class="_ _3"></span>for <span class="_ _3"></span>non<span class="_ _3"></span>-stationary <span class="_ _3"></span>and <span class="_ _3"></span>no<span class="_ _3"></span>isy <span class="_ _3"></span>signals, <span class="_ _3"></span>which <span class="_ _5"></span>has </div><div class="t m0 x1 h2 y23 ff1 fs0 fc0 sc0 ls0 ws0">attracted <span class="_ _10"> </span>considerable <span class="_ _10"> </span>attentions <span class="_ _10"> </span>recently <span class="_ _10"> </span>[1]. <span class="_ _10"> </span>Many </div><div class="t m0 x1 h2 y24 ff1 fs0 fc0 sc0 ls0 ws0">methods, <span class="_ _c"></span>such <span class="_ _7"></span>as <span class="_ _c"></span>short <span class="_ _7"></span>tim<span class="_ _2"></span>e <span class="_ _7"></span>frequency <span class="_ _c"></span>transform <span class="_ _7"> </span>[2] <span class="_ _11"></span>and </div><div class="t m0 x1 h2 y25 ff1 fs0 fc0 sc0 ls0 ws0">wavelet transform <span class="_ _3"></span>[3] , <span class="_ _3"></span>have <span class="_ _3"></span>been <span class="_ _3"></span>proposed <span class="_ _3"></span>for <span class="_ _3"></span>solving <span class="_ _3"></span>the </div><div class="t m0 x1 h2 y26 ff1 fs0 fc0 sc0 ls0 ws0">problem and<span class="_ _3"></span> <span class="_ _3"></span>proved <span class="_ _3"></span>us<span class="_ _3"></span>eful <span class="_ _3"></span>in <span class="_ _3"></span>some <span class="_ _3"></span>applications.<span class="_ _3"></span> <span class="_ _3"></span>Ho<span class="_ _3"></span>wever, </div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls0 ws0">because <span class="_ _4"> </span>these <span class="_ _4"> </span>methods <span class="_ _4"> </span>usually <span class="_ _4"> </span>need <span class="_ _4"> </span>a <span class="_ _4"> </span>priori <span class="_"> </span>knowledge </div><div class="t m0 x1 h2 y28 ff1 fs0 fc0 sc0 ls0 ws0">about <span class="_ _c"></span>the <span class="_ _c"></span>researched <span class="_ _11"></span>signals, <span class="_ _c"></span>they <span class="_ _c"></span>naturally <span class="_ _11"></span>lack <span class="_ _c"></span>the <span class="_ _c"></span>self<span class="_ _3"></span>-</div><div class="t m0 x1 h2 y29 ff1 fs0 fc0 sc0 ls0 ws0">adaption <span class="_ _e"> </span>for <span class="_ _8"> </span>the <span class="_ _e"> </span>researched <span class="_ _8"> </span>signals. <span class="_ _e"> </span>The <span class="_ _e"> </span>W<span class="_ _3"></span>igner-Ville </div><div class="t m0 x1 h2 y2a ff1 fs0 fc0 sc0 ls0 ws0">distribution <span class="_ _a"> </span>has <span class="_ _a"> </span>high <span class="_ _e"> </span>time-frequency <span class="_ _a"> </span>resolution, <span class="_ _a"> </span>but <span class="_ _a"> </span>its </div><div class="t m0 x1 h2 y2b ff1 fs0 fc0 sc0 ls0 ws0">cross <span class="_ _d"> </span>terms <span class="_ _12"> </span>is <span class="_ _12"> </span>unbear<span class="_ _3"></span>able <span class="_ _d"> </span>[4]. <span class="_ _12"> </span>Empirical <span class="_ _12"> </span>mode </div><div class="t m0 x1 h2 y2c ff1 fs0 fc0 sc0 ls0 ws0">decomposition <span class="_ _f"> </span>(EMD) <span class="_ _6"> </span>is <span class="_ _6"> </span>a <span class="_ _f"> </span>self<span class="_ _3"></span>-adaptive <span class="_ _f"> </span>method <span class="_ _6"> </span>and </div><div class="t m0 x1 h2 y2d ff1 fs0 fc0 sc0 ls0 ws0">suitable <span class="_ _e"> </span>to <span class="_ _8"> </span>analyzing <span class="_ _e"> </span>the <span class="_ _8"> </span>non-stationary <span class="_ _e"> </span>and <span class="_ _8"> </span>nonlinear </div><div class="t m0 x1 h2 y2e ff1 fs0 fc0 sc0 ls0 ws0">signals <span class="_ _3"></span>[4], <span class="_ _3"></span>which <span class="_ _3"></span>has <span class="_ _3"></span>been <span class="_ _3"></span>successfully <span class="_ _3"></span>applied <span class="_ _3"></span>to <span class="_ _3"></span>various </div><div class="t m0 x1 h2 y2f ff1 fs0 fc0 sc0 ls0 ws0">fields <span class="_ _5"></span>[4]. <span class="_ _9"></span>Nevertheless, <span class="_ _9"></span>when <span class="_ _9"></span>the <span class="_ _5"></span>EMD <span class="_ _9"></span>algor<span class="_ _3"></span>ithm <span class="_ _5"></span>is <span class="_ _5"></span>us<span class="_ _3"></span>ed </div><div class="t m0 x1 h2 y30 ff1 fs0 fc0 sc0 ls0 ws0">to <span class="_ _9"></span>deal <span class="_ _5"></span>with <span class="_ _9"></span>a <span class="_ _9"></span>signal <span class="_ _9"></span>with <span class="_ _9"></span>intermittency, <span class="_ _9"></span>the <span class="_ _9"></span>mode <span class="_ _5"></span>mixing </div><div class="t m0 x1 h2 y31 ff1 fs0 fc0 sc0 ls0 ws0">often emerges as <span class="_ _3"></span>an annoying<span class="_ _3"></span> problem <span class="_ _3"></span>[5-7]. <span class="_ _3"></span>To ov<span class="_ _3"></span>ercome </div><div class="t m0 x1 h2 y32 ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _f"> </span>mode <span class="_ _f"> </span>mixing <span class="_ _f"> </span>problem, <span class="_ _f"> </span>ensemble <span class="_ _f"> </span>empirical <span class="_ _f"> </span>mode </div><div class="t m0 x1 h2 y33 ff1 fs0 fc0 sc0 ls0 ws0">decomposition <span class="_ _3"></span>(EEMD) <span class="_ _5"></span>is <span class="_ _3"></span>pr<span class="_ _3"></span>esented <span class="_ _5"></span>in <span class="_ _3"></span>place <span class="_ _5"></span>of <span class="_ _5"></span>EMD <span class="_ _9"></span>[8]<span class="ls4">. </span></div><div class="t m0 x1 h2 y34 ff1 fs0 fc0 sc0 ls0 ws0">The <span class="_ _7"> </span>EEMD <span class="_ _4"> </span>met<span class="_ _2"></span>ho<span class="_ _3"></span>d <span class="_ _7"> </span>adds <span class="_ _4"> </span>some <span class="_ _11"></span>wh<span class="_ _3"></span>ite <span class="_ _7"> </span>noise <span class="_ _7"> </span>with <span class="_ _7"> </span>limited </div><div class="t m0 x1 h2 y35 ff1 fs0 fc0 sc0 ls0 ws0">amplitude <span class="_ _b"> </span>to <span class="_ _e"> </span>the <span class="_ _b"> </span>research<span class="_ _3"></span>ed <span class="_ _a"> </span>signals, <span class="_ _a"> </span>sufficiently <span class="_ _a"> </span>taking </div><div class="t m0 xb h2 y36 ff1 fs0 fc0 sc0 ls0 ws0">advantage <span class="_ _7"> </span>of <span class="_ _7"> </span>the <span class="_ _7"> </span>statistical <span class="_ _7"></span>characteristics <span class="_ _11"></span>of <span class="_ _7"> </span>white <span class="_ _7"> </span>noise </div><div class="t m0 xb h2 y37 ff1 fs0 fc0 sc0 ls0 ws0">whose <span class="_ _c"></span>energy <span class="_ _9"></span>den<span class="_ _3"></span>sity <span class="_ _9"></span>is <span class="_ _c"></span>uniformly <span class="_ _9"></span>distributed <span class="_ _c"></span>throug<span class="_ _3"></span>hout </div><div class="t m0 xb h2 y38 ff1 fs0 fc0 sc0 ls0 ws0">the frequency domain, then <span class="_ _3"></span>projects <span class="_ _3"></span>the signal components </div><div class="t m0 xb h2 y39 ff1 fs0 fc0 sc0 ls0 ws0">onto <span class="_ _4"> </span>the <span class="_ _7"> </span>prop<span class="_ _3"></span>er <span class="_ _4"> </span>frequency <span class="_ _7"> </span>bands<span class="_ _3"></span> <span class="_ _4"> </span>and, <span class="_ _7"> </span>finally, <span class="_ _4"> </span>the <span class="_ _7"> </span>added </div><div class="t m0 xb h2 y3a ff1 fs0 fc0 sc0 ls0 ws0">white <span class="_ _11"></span>noise <span class="_ _11"></span>can <span class="_ _11"></span>been <span class="_ _7"> </span>counteracted <span class="_ _11"></span>by <span class="_ _7"> </span>ensemble <span class="_ _11"></span>mean <span class="_ _11"></span><span class="ls2">of </span></div><div class="t m0 xb h2 y3b ff1 fs0 fc0 sc0 ls0 ws0">enough <span class="_ _f"> </span>corresponding <span class="_ _f"> </span>components <span class="_ _f"> </span>[8]. <span class="_ _8"> </span>Therefore, <span class="_ _f"> </span>the </div><div class="t m0 xb h2 y3c ff1 fs0 fc0 sc0 ls0 ws0">EEMD <span class="_ _3"></span>method <span class="_ _3"></span>is <span class="_ _3"></span>considered <span class="_ _3"></span>as <span class="_ _5"></span>a <span class="_ _3"></span>significant <span class="_ _5"></span>improvement </div><div class="t m0 xb h2 y3d ff1 fs0 fc0 sc0 ls0 ws0">on <span class="_ _5"></span>the <span class="_ _5"></span>EMD <span class="_ _9"></span>method <span class="_ _5"></span>and <span class="_ _5"></span>recommended <span class="_ _5"></span>as <span class="_ _5"></span>a <span class="_ _9"></span>substitute <span class="_ _5"></span>for </div><div class="t m0 xb h2 y3e ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _a"> </span>EMD <span class="_ _a"> </span>method <span class="_ _a"> </span>[8]. <span class="_ _a"> </span>Indeed<span class="_ _3"></span>, <span class="_ _a"> </span>the <span class="_ _a"> </span>EEMD <span class="_ _a"> </span>method <span class="_ _a"> </span>has </div><div class="t m0 xb h2 y3f ff1 fs0 fc0 sc0 ls0 ws0">shown <span class="_ _e"> </span>its <span class="_ _e"> </span>superiority <span class="_ _e"> </span>over <span class="_ _e"> </span>the <span class="_ _e"> </span>EMD <span class="_ _e"> </span>method <span class="_ _a"> </span>in <span class="_ _e"> </span>some </div><div class="t m0 xb h2 y40 ff1 fs0 fc0 sc0 ls0 ws0">applications [9]. </div><div class="t m0 xb h2 y41 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 xb h2 y42 ff1 fs0 fc0 sc0 ls5 ws0">How<span class="ls0">ever, <span class="_ _b"> </span>the <span class="_ _b"> </span>EEMD <span class="_ _b"> </span>method <span class="_ _b"> </span>lacks <span class="_ _b"> </span>a <span class="_ _b"> </span>guide <span class="_ _b"> </span>to <span class="_ _b"> </span>how <span class="_ _a"> </span>to </span></div><div class="t m0 xb h2 y43 ff1 fs0 fc0 sc0 ls0 ws0">choose <span class="_ _11"></span>the <span class="_ _11"></span>appropriate <span class="_ _11"></span>amplitude <span class="_ _c"></span>of <span class="_ _11"></span>the <span class="_ _11"></span>added <span class="_ _11"></span>noise <span class="_ _11"></span>and </div><div class="t m0 xb h2 y44 ff1 fs0 fc0 sc0 ls0 ws0">its <span class="_ _7"> </span>computation <span class="_ _7"> </span>eff<span class="_ _3"></span>iciency <span class="_ _7"> </span>is <span class="_ _4"> </span>fairly <span class="_ _7"> </span>low. <span class="_ _4"> </span>As <span class="_ _7"> </span>a <span class="_ _4"> </span>result, <span class="_ _7"> </span>the </div><div class="t m0 xb h2 y45 ff1 fs0 fc0 sc0 ls0 ws0">inappropriate <span class="_ _11"></span>amplitude <span class="_ _11"></span>of <span class="_ _11"></span>the <span class="_ _11"></span>added <span class="_ _11"></span>wh<span class="_ _3"></span>ite <span class="_ _11"></span>noise <span class="_ _11"></span>for <span class="_ _7"> </span>the </div><div class="t m0 xb h2 y46 ff1 fs0 fc0 sc0 ls0 ws0">EEMD <span class="_ _4"> </span>method <span class="_ _4"> </span>is <span class="_ _4"> </span>go<span class="_ _3"></span>ing <span class="_ _4"> </span>to <span class="_"> </span>cause <span class="_ _4"> </span>the <span class="_ _4"> </span>mode <span class="_ _4"> </span>mixing <span class="_ _4"> </span>and </div><div class="t m0 xb h2 y47 ff1 fs0 fc0 sc0 ls0 ws0">splitting <span class="_ _4"> </span>that <span class="_ _4"> </span>often <span class="_"> </span>exists <span class="_ _7"> </span>in <span class="_"> </span>the <span class="_ _4"> </span>EMD <span class="_ _4"> </span>method <span class="_ _4"> </span>[<span class="ls2">10<span class="ls4">, <span class="_ _4"> </span></span>11</span>]<span class="ls4">. </span></div><div class="t m0 xb h2 y48 ff1 fs0 fc0 sc0 ls0 ws0">Although <span class="_ _3"></span>the <span class="_ _3"></span>reference <span class="_ _3"></span>[<span class="_ _3"></span>8] <span class="_ _3"></span>suggested <span class="_ _3"></span>that <span class="_ _3"></span>the <span class="_ _5"></span>amplitude of </div><div class="t m0 xb h2 y49 ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _7"> </span>add<span class="_ _3"></span>ed <span class="_ _4"> </span>white <span class="_ _7"> </span>noise <span class="_ _4"> </span>should <span class="_ _4"> </span>be <span class="_ _7"> </span>a<span class="_ _3"></span>bout <span class="_ _4"> </span>0.2 <span class="_ _4"> </span>times <span class="_ _7"> </span>of <span class="_ _4"> </span>the </div><div class="t m0 xb h2 y4a ff1 fs0 fc0 sc0 ls0 ws0">standard deviation <span class="_ _3"></span>of the <span class="_ _3"></span>investigated sign<span class="_ _3"></span>al, unfo<span class="_ _3"></span>rtunately, </div><div class="t m0 xb h2 y4b ff1 fs0 fc0 sc0 ls0 ws0">with <span class="_ _c"></span>the <span class="_ _11"></span>suggested <span class="_ _c"></span>value, <span class="_ _11"></span>the <span class="_ _c"></span>decomposition <span class="_ _11"></span>results <span class="_ _c"></span>from </div><div class="t m0 xb h2 y4c ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _13"> </span>EEMD <span class="_ _13"> </span>method <span class="_ _13"> </span>often <span class="_ _13"> </span>deviate <span class="_ _14"> </span>from <span class="_ _14"> </span>the <span class="_ _13"> </span>realistic </div><div class="t m0 xb h2 y4d ff1 fs0 fc0 sc0 ls0 ws0">contents <span class="_ _3"></span>of <span class="_ _5"></span>the <span class="_ _5"></span>signals <span class="_ _5"></span>[<span class="ls2">11</span>]. <span class="_ _3"></span>In<span class="_ _3"></span> <span class="_ _3"></span>add<span class="_ _3"></span>ition, <span class="_ _5"></span>to <span class="_ _3"></span>fu<span class="_ _3"></span>rther <span class="_ _5"></span>remove </div><div class="t m0 xb h2 y4e ff1 fs0 fc0 sc0 ls0 ws0">the residual of the added white noise and red<span class="_ _3"></span>uce a waste of </div><div class="t m0 xb h2 y4f ff1 fs0 fc0 sc0 ls0 ws0">time <span class="_ _3"></span>fo<span class="_ _3"></span>r <span class="_ _5"></span>the <span class="_ _9"></span>EEMD <span class="_ _5"></span>method, <span class="_ _9"></span>the <span class="_ _5"></span>complementary <span class="_ _5"></span>ensemble </div><div class="t m0 xb h2 y50 ff1 fs0 fc0 sc0 ls0 ws0">empirical <span class="_ _10"> </span>mode <span class="_ _10"> </span>deco<span class="_ _3"></span>mposition <span class="_ _10"> </span>(CEEMD) <span class="_ _15"> </span>has <span class="_ _10"> </span>been </div><div class="t m0 xb h2 y51 ff1 fs0 fc0 sc0 ls0 ws0">addressed <span class="_ _a"> </span>to <span class="_ _b"> </span>replace <span class="_ _a"> </span>the <span class="_ _a"> </span>EEMD <span class="_ _b"> </span>method <span class="_ _a"> </span>as <span class="_ _a"> </span>a <span class="_ _b"> </span>standard </div><div class="t m0 xb h2 y52 ff1 fs0 fc0 sc0 ls0 ws0">version <span class="_"> </span>of <span class="_ _4"> </span>the <span class="_"> </span>EMD <span class="_ _4"> </span>method <span class="_"> </span>[<span class="ls2">10</span>]. <span class="_"> </span>Notwithsta<span class="_ _2"></span>nd<span class="_ _3"></span>ing, <span class="_"> </span>the </div><div class="t m0 xb h2 y53 ff1 fs0 fc0 sc0 ls0 ws0">CEEMD <span class="_"> </span>method <span class="_ _a"> </span>only <span class="_"> </span>partly <span class="_ _a"> </span>enhances <span class="_"> </span>the <span class="_ _a"> </span>computation </div><div class="t m0 xb h2 y54 ff1 fs0 fc0 sc0 ls0 ws0">efficiency <span class="_ _e"> </span>of <span class="_ _8"> </span>the <span class="_ _e"> </span>EEMD <span class="_ _8"> </span>met<span class="_ _2"></span>ho<span class="_ _3"></span>d, <span class="_ _8"> </span>and <span class="_ _e"> </span>the <span class="_ _e"> </span>abo<span class="_ _3"></span>ve <span class="_ _e"> </span>first </div><div class="t m0 xb h2 y55 ff1 fs0 fc0 sc0 ls0 ws0">problem <span class="_ _13"> </span>reg<span class="_ _3"></span>arding <span class="_ _16"> </span>the <span class="_ _16"> </span>EEMD <span class="_ _13"> </span>method <span class="_ _16"> </span>still <span class="_ _13"> </span>remains </div><div class="t m0 xb h2 y56 ff1 fs0 fc0 sc0 ls0 ws0">untouched. Ad<span class="_ _3"></span>ditionally, if the <span class="_ _3"></span>researched <span class="_ _3"></span>signal is <span class="_ _3"></span>a <span class="_ _3"></span>noisy </div><div class="t m0 xb h2 y57 ff1 fs0 fc0 sc0 ls0 ws0">signal <span class="_ _7"> </span>in <span class="_ _7"> </span>itself, <span class="_ _7"> </span>its <span class="_ _7"> </span>intrinsic <span class="_ _4"> </span>noise <span class="_ _7"> </span>will <span class="_ _7"> </span>inevitably <span class="_ _7"> </span>interact </div><div class="t m0 xb h2 y58 ff1 fs0 fc0 sc0 ls0 ws0">with <span class="_ _11"></span>the <span class="_ _7"> </span>noise <span class="_ _7"> </span>added <span class="_ _7"> </span>through <span class="_ _7"> </span>the <span class="_ _7"> </span>EEMD <span class="_ _7"> </span>method, <span class="_ _11"></span>wh<span class="_ _3"></span>ich </div><div class="t m0 xb h2 y59 ff1 fs0 fc0 sc0 ls0 ws0">may <span class="_ _9"></span>further <span class="_ _9"></span>complicate <span class="_ _9"></span>the <span class="_ _c"></span>above <span class="_ _c"></span>first <span class="_ _9"></span>prob<span class="_ _3"></span>lem <span class="_ _9"></span>regarding </div><div class="t m0 xb h2 y5a ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _b"> </span>EEMD <span class="_ _a"> </span>method. <span class="_ _b"> </span>In<span class="_ _3"></span> <span class="_ _b"> </span>particular, <span class="_ _a"> </span>when <span class="_ _a"> </span>the <span class="_ _b"> </span>researched </div><div class="t m0 xb h2 y5b ff1 fs0 fc0 sc0 ls0 ws0">signals <span class="_ _6"> </span>become <span class="_ _6"> </span>ver<span class="_ _3"></span>y <span class="_ _6"> </span>noisy, <span class="_ _6"> </span>the <span class="_ _14"> </span>above <span class="_ _6"> </span>first <span class="_ _14"> </span>problem </div><div class="t m0 xb h2 y5c ff1 fs0 fc0 sc0 ls0 ws0">regarding the EEMD method leaves a gap. </div><div class="t m0 xb h2 y5d ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 xb h2 y5e ff1 fs0 fc0 sc0 ls0 ws0">This <span class="_ _7"> </span>paper <span class="_ _4"> </span>explores <span class="_ _7"> </span>the <span class="_ _7"> </span>above <span class="_ _7"> </span>two <span class="_ _4"> </span>problems <span class="_ _11"></span>con<span class="_ _3"></span>cerning </div><div class="t m0 xb h2 y5f ff1 fs0 fc0 sc0 ls0 ws0">the <span class="_ _17"> </span>EEMD <span class="_ _17"> </span>method. <span class="_ _15"> </span>Then<span class="_ _3"></span>, <span class="_ _17"> </span>the <span class="_ _15"> </span>improved <span class="_ _17"> </span>CEEMD </div><div class="t m0 xb h2 y60 ff1 fs0 fc0 sc0 ls0 ws0">(ICEEMD) method was pr<span class="_ _3"></span>oposed. Ap<span class="_ _3"></span>plications to analysis </div><div class="c xc y61 w3 hc"><div class="t m0 x0 hd y62 ff7 fs4 fc1 sc0 ls0 ws0">IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012<span class="fc2 sc0"> </span></div><div class="t m0 x0 hd y63 ff7 fs4 fc1 sc0 ls0 ws0">ISSN (Online): 1694-0814 </div><div class="t m0 x0 hd y64 ff7 fs4 fc1 sc0 ls0 ws0">www.IJCSI.org</div></div><div class="c xd y65 w4 he"><div class="t m0 x0 hd y64 ff7 fs4 fc1 sc0 ls0 ws0">194</div></div><div class="c xe y66 w5 he"><div class="t m0 x0 hd y64 ff7 fs4 fc1 sc0 ls0 ws0">Copyright (c) 2012 International Journal of Computer Science Issues. All Rights Reserved.</div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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  • SaliGPH 2019-04-04 11:54:01
    i want this code
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