rcada_eemd--快速eemd算法

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<On the computational complexity of the empirical mode decomposition algorithm>2014 快速eemd算法,收敛速度与传统eemd相比有很大改进
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内容介绍
<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/627edac49b6e2b6d55553e29/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/627edac49b6e2b6d55553e29/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Physica<span class="_ _0"> </span>A<span class="_ _0"> </span>400<span class="_ _0"> </span>(2014)<span class="_ _0"> </span>159&#8211;167</div><div class="t m0 x2 h3 y2 ff2 fs1 fc1 sc0 ls0 ws0">Contents<span class="_ _1"> </span>lists<span class="_ _1"> </span>available<span class="_ _1"> </span>at<span class="_ _1"> </span><span class="fc0">ScienceDirect</span></div><div class="t m0 x3 h4 y3 ff1 fs2 fc1 sc0 ls0 ws0">Physica<span class="_ _2"> </span>A</div><div class="t m0 x4 h3 y4 ff2 fs1 fc1 sc0 ls0 ws0">journal<span class="_ _1"> </span>homepage:<span class="_ _1"> </span><span class="fc0">www.elsevier.com/locate/physa</span></div><div class="t m0 x5 h5 y5 ff1 fs3 fc1 sc0 ls0 ws0">On<span class="_ _2"> </span>the<span class="_ _2"> </span>computational<span class="_ _2"> </span>complexity<span class="_ _2"> </span>of<span class="_ _2"> </span>the<span class="_ _2"> </span>empirical<span class="_ _2"> </span>mode</div><div class="t m0 x5 h5 y6 ff1 fs3 fc1 sc0 ls0 ws0">decomposition<span class="_ _2"> </span>algorithm</div><div class="t m0 x5 h6 y7 ff1 fs4 fc1 sc0 ls0 ws0">Yung-Hung<span class="_ _3"> </span>Wang</div><div class="t m0 x6 h7 y8 ff1 fs5 fc0 sc0 ls0 ws0">a</div><div class="t m0 x7 h6 y7 ff1 fs4 fc1 sc0 ls0 ws0">,<span class="_ _3"> </span>Chien-Hung<span class="_ _3"> </span>Yeh</div><div class="t m0 x8 h7 y8 ff1 fs5 fc0 sc0 ls0 ws0">a<span class="fc1">,</span>b</div><div class="t m0 x9 h6 y7 ff1 fs4 fc1 sc0 ls0 ws0">,<span class="_ _3"> </span>Hsu-Wen<span class="_ _3"> </span>Vincent<span class="_ _3"> </span>Young</div><div class="t m0 xa h7 y8 ff1 fs5 fc0 sc0 ls0 ws0">a</div><div class="t m0 xb h6 y7 ff1 fs4 fc1 sc0 ls0 ws0">,<span class="_ _3"> </span>Kun<span class="_ _3"> </span>Hu</div><div class="t m0 xc h7 y8 ff1 fs5 fc0 sc0 ls0 ws0">c</div><div class="t m0 xd h6 y7 ff1 fs4 fc1 sc0 ls0 ws0">,</div><div class="t m0 x5 h6 y9 ff1 fs4 fc1 sc0 ls0 ws0">Men-Tzung<span class="_ _3"> </span>Lo</div><div class="t m0 xe h7 ya ff1 fs5 fc0 sc0 ls0 ws0">a<span class="fc1">,</span><span class="ff3 fs6">&#8727;</span></div><div class="t m0 x5 h8 yb ff1 fs7 fc1 sc0 ls0 ws0">a</div><div class="t m0 xf h9 yc ff4 fs0 fc1 sc0 ls0 ws0">Research<span class="_ _0"> </span>Center<span class="_ _0"> </span>for<span class="_ _0"> </span>Adaptive<span class="_ _0"> </span>Data<span class="_ _0"> </span>Analysis,<span class="_ _0"> </span>National<span class="_ _0"> </span>Central<span class="_ _0"> </span>University,<span class="_ _0"> </span>Chungli,<span class="_ _0"> </span>Taiwan,<span class="_ _0"> </span>ROC</div><div class="t m0 x5 h8 yd ff1 fs7 fc1 sc0 ls0 ws0">b</div><div class="t m0 xf h9 ye ff4 fs0 fc1 sc0 ls0 ws0">Department<span class="_ _0"> </span>of<span class="_ _0"> </span>Electrical<span class="_ _0"> </span>Engineering,<span class="_ _0"> </span>National<span class="_ _0"> </span>Central<span class="_ _0"> </span>University,<span class="_ _0"> </span>Chungli,<span class="_ _0"> </span>Taiwan,<span class="_ _0"> </span>ROC</div><div class="t m0 x5 h8 yf ff1 fs7 fc1 sc0 ls0 ws0">c</div><div class="t m0 xf h9 y10 ff4 fs0 fc1 sc0 ls0 ws0">Medical<span class="_ _0"> </span>Biodynamics<span class="_ _0"> </span>Program,<span class="_ _0"> </span>Division<span class="_ _0"> </span>of<span class="_ _0"> </span>Sleep<span class="_ _0"> </span>Medicine,<span class="_ _0"> </span>Brigham<span class="_ _0"> </span>and<span class="_ _0"> </span>Women&#8217;s<span class="_ _0"> </span>Hospital,<span class="_ _0"> </span>Harvard<span class="_ _0"> </span>Medical<span class="_ _0"> </span>School,</div><div class="t m0 x5 h9 y11 ff4 fs0 fc1 sc0 ls0 ws0">Boston,<span class="_ _0"> </span>MA<span class="_ _0"> </span>02115,<span class="_ _0"> </span>United<span class="_ _0"> </span>States</div><div class="t m0 x5 ha y12 ff5 fs8 fc1 sc0 ls0 ws0">h<span class="_ _2"> </span>i<span class="_ _2"> </span>g<span class="_ _2"> </span>h<span class="_ _2"> </span>l<span class="_ _4"> </span>i<span class="_ _4"> </span>g<span class="_ _2"> </span>h<span class="_ _2"> </span>t<span class="_ _2"> </span>s</div><div class="t m0 x5 hb y13 ff3 fs9 fc1 sc0 ls0 ws0">&#8226;<span class="_ _5"> </span><span class="ff1 fsa">The<span class="_ _0"> </span>order<span class="_ _1"> </span>of<span class="_ _0"> </span>the<span class="_ _6"> </span>computational<span class="_ _0"> </span>complexity<span class="_ _6"> </span>of<span class="_ _6"> </span>the<span class="_ _6"> </span>EMD<span class="_ _0"> </span>is<span class="_ _6"> </span>equivalent<span class="_ _6"> </span>to<span class="_ _6"> </span>FFT.</span></div><div class="t m0 x5 hb y14 ff3 fs9 fc1 sc0 ls0 ws0">&#8226;<span class="_ _5"> </span><span class="ff1 fsa">Optimized<span class="_ _0"> </span>program<span class="_ _6"> </span>is<span class="_ _6"> </span>proposed<span class="_ _6"> </span>to<span class="_ _0"> </span>speed<span class="_ _6"> </span>up<span class="_ _6"> </span>the<span class="_ _6"> </span>computation<span class="_ _0"> </span>of<span class="_ _6"> </span>EMD<span class="_ _6"> </span>up<span class="_ _6"> </span>to<span class="_ _6"> </span>1000<span class="_ _0"> </span>times.</span></div><div class="t m0 x5 hb y15 ff3 fs9 fc1 sc0 ls0 ws0">&#8226;<span class="_ _5"> </span><span class="ff1 fsa">Fast<span class="_ _0"> </span>HHT<span class="_ _6"> </span>with<span class="_ _6"> </span>optimized<span class="_ _6"> </span>EMD/EEMD<span class="_ _0"> </span>algorithm<span class="_ _6"> </span>can<span class="_ _6"> </span>operate<span class="_ _6"> </span>in<span class="_ _0"> </span>real-time.</span></div><div class="t m0 x5 hc y16 ff5 fsb fc1 sc0 ls0 ws0">a<span class="_ _2"> </span>r<span class="_ _5"> </span>t<span class="_ _2"> </span>i<span class="_ _2"> </span>c<span class="_ _5"> </span>l<span class="_ _4"> </span>e<span class="_ _7"> </span>i<span class="_ _2"> </span>n<span class="_ _5"> </span>f<span class="_ _2"> </span>o</div><div class="t m0 x5 h9 y17 ff4 fs0 fc1 sc0 ls0 ws0">Article<span class="_ _0"> </span>history:</div><div class="t m0 x5 h2 y18 ff1 fs0 fc1 sc0 ls0 ws0">Received<span class="_ _0"> </span>30<span class="_ _0"> </span>October<span class="_ _0"> </span>2013</div><div class="t m0 x5 h2 y19 ff1 fs0 fc1 sc0 ls0 ws0">Received<span class="_ _0"> </span>in<span class="_ _8"> </span>revised<span class="_ _8"> </span>form<span class="_ _0"> </span>30<span class="_ _8"> </span>December<span class="_ _0"> </span>2013</div><div class="t m0 x5 h2 y1a ff1 fs0 fc1 sc0 ls0 ws0">Available<span class="_ _0"> </span>online<span class="_ _0"> </span>21<span class="_ _0"> </span>January<span class="_ _0"> </span>2014</div><div class="t m0 x5 h9 y1b ff4 fs0 fc1 sc0 ls0 ws0">Keywords:</div><div class="t m0 x5 h2 y1c ff1 fs0 fc1 sc0 ls0 ws0">EMD</div><div class="t m0 x5 h2 y1d ff1 fs0 fc1 sc0 ls0 ws0">EEMD</div><div class="t m0 x5 h2 y1e ff1 fs0 fc1 sc0 ls0 ws0">Time</div><div class="t m0 x5 h2 y1f ff1 fs0 fc1 sc0 ls0 ws0">Space</div><div class="t m0 x5 h2 y20 ff1 fs0 fc1 sc0 ls0 ws0">Complexity</div><div class="t m0 x10 ha y21 ff5 fs8 fc1 sc0 ls0 ws0">a<span class="_ _4"> </span>b<span class="_ _2"> </span>s<span class="_ _2"> </span>t<span class="_ _2"> </span>r<span class="_ _2"> </span>a<span class="_ _4"> </span>c<span class="_ _2"> </span>t</div><div class="t m0 x2 hb y22 ff1 fsa fc1 sc0 ls0 ws0">It<span class="_ _8"> </span>has<span class="_ _8"> </span>been<span class="_ _8"> </span>claimed<span class="_ _8"> </span>that<span class="_ _8"> </span>the<span class="_ _8"> </span>empirical<span class="_ _8"> </span>mode<span class="_ _8"> </span>decomposition<span class="_ _8"> </span>(EMD)<span class="_ _8"> </span>and<span class="_ _8"> </span>its<span class="_ _8"> </span>improved<span class="_ _8"> </span>version</div><div class="t m0 x2 hb y23 ff1 fsa fc1 sc0 ls0 ws0">the<span class="_ _3"> </span>ensemble<span class="_ _3"> </span>EMD<span class="_ _3"> </span>(EEMD)<span class="_ _3"> </span>are<span class="_ _3"> </span>computation<span class="_ _4"> </span>intensive.<span class="_ _3"> </span>In<span class="_ _3"> </span>this<span class="_ _3"> </span>study<span class="_ _3"> </span>we<span class="_ _3"> </span>will<span class="_ _3"> </span>prove<span class="_ _3"> </span>that</div><div class="t m0 x2 hb y24 ff1 fsa fc1 sc0 ls0 ws0">the<span class="_ _6"> </span>time<span class="_ _6"> </span>complexity<span class="_ _6"> </span>of<span class="_ _1"> </span>the<span class="_ _6"> </span>EMD/EEMD,<span class="_ _6"> </span>which<span class="_ _1"> </span>has<span class="_ _6"> </span>never<span class="_ _6"> </span>been<span class="_ _6"> </span>analyzed<span class="_ _1"> </span>before,<span class="_ _6"> </span>is<span class="_ _6"> </span>actually</div><div class="t m0 x2 hb y25 ff1 fsa fc1 sc0 ls0 ws0">equivalent<span class="_ _1"> </span>to<span class="_ _3"> </span>that<span class="_ _1"> </span>of<span class="_ _3"> </span>the<span class="_ _1"> </span>Fourier<span class="_ _3"> </span>Transform.<span class="_ _1"> </span>Numerical<span class="_ _3"> </span>examples<span class="_ _1"> </span>are<span class="_ _9"> </span>presented<span class="_ _1"> </span>to<span class="_ _9"> </span>verify</div><div class="t m0 x2 hb y26 ff1 fsa fc1 sc0 ls0 ws0">that<span class="_ _0"> </span>EMD/EEMD<span class="_ _6"> </span>is,<span class="_ _6"> </span>in<span class="_ _6"> </span>fact,<span class="_ _0"> </span>a<span class="_ _6"> </span>computationally<span class="_ _6"> </span>efficient<span class="_ _6"> </span>method.</div><div class="t m0 x11 hb y27 ff6 fsc fc1 sc0 ls0 ws0">&#169;<span class="_ _0"> </span><span class="ff1 fsa">2014<span class="_ _6"> </span>Elsevier<span class="_ _6"> </span>B.V.<span class="_ _6"> </span>All<span class="_ _0"> </span>rights<span class="_ _6"> </span>reserved.</span></div><div class="t m0 x5 hd y28 ff7 fsd fc1 sc0 ls0 ws0">1.<span class="_ _5"> </span>Introduction</div><div class="t m0 x12 he y29 ff1 fsd fc1 sc0 ls0 ws0">EMD<span class="_ _1"> </span>[<span class="fc0">1</span>]<span class="_ _1"> </span>is<span class="_ _1"> </span>a<span class="_ _9"> </span>nonlinear<span class="_ _1"> </span>and<span class="_ _1"> </span>nonstationary<span class="_ _9"> </span>time<span class="_ _1"> </span>domain<span class="_ _1"> </span>decomposition<span class="_ _1"> </span>method.<span class="_ _9"> </span>It<span class="_ _1"> </span>is<span class="_ _1"> </span>an<span class="_ _1"> </span>adaptive,<span class="_ _9"> </span>data-driven<span class="_ _1"> </span>algorithm</div><div class="t m0 x5 he y2a ff1 fsd fc1 sc0 ls0 ws0">that<span class="_ _5"> </span>decomposes<span class="_ _a"> </span>a<span class="_ _5"> </span>time<span class="_ _a"> </span>series<span class="_ _5"> </span>into<span class="_ _a"> </span>multiple<span class="_ _5"> </span>empirical<span class="_ _a"> </span>modes,<span class="_ _5"> </span>known<span class="_ _a"> </span>as<span class="_ _5"> </span>intrinsic<span class="_ _a"> </span>mode<span class="_ _5"> </span>functions<span class="_ _a"> </span>(IMFs).<span class="_ _5"> </span>Each<span class="_ _a"> </span>IMF</div><div class="t m0 x5 he y2b ff1 fsd fc1 sc0 ls0 ws0">represents<span class="_ _1"> </span>a<span class="_ _9"> </span>narrow<span class="_ _1"> </span>band<span class="_ _9"> </span>frequency&#8211;amplitude<span class="_ _9"> </span>modulation<span class="_ _1"> </span>that<span class="_ _9"> </span>is<span class="_ _1"> </span>often<span class="_ _9"> </span>related<span class="_ _1"> </span>to<span class="_ _9"> </span>a<span class="_ _9"> </span>specific<span class="_ _1"> </span>physical<span class="_ _9"> </span>process.<span class="_ _1"> </span>For<span class="_ _9"> </span>signals</div><div class="t m0 x5 he y2c ff1 fsd fc1 sc0 ls0 ws0">with<span class="_ _2"> </span>intermittent<span class="_ _2"> </span>oscillations,<span class="_ _4"> </span>one<span class="_ _2"> </span>intrinsic<span class="_ _2"> </span>mode<span class="_ _2"> </span>can<span class="_ _2"> </span>comprise<span class="_ _2"> </span>oscillations<span class="_ _2"> </span>with<span class="_ _2"> </span>a<span class="_ _2"> </span>variety<span class="_ _2"> </span>of<span class="_ _2"> </span>wavelengths<span class="_ _2"> </span>at<span class="_ _4"> </span>different</div><div class="t m0 x5 he y2d ff1 fsd fc1 sc0 ls0 ws0">temporal<span class="_ _9"> </span>locations.<span class="_ _9"> </span>Collectively,<span class="_ _9"> </span>the<span class="_ _9"> </span>simultaneous<span class="_ _9"> </span>exhibition<span class="_ _9"> </span>of<span class="_ _9"> </span>these<span class="_ _9"> </span>disparate<span class="_ _9"> </span>oscillations<span class="_ _9"> </span>is<span class="_ _9"> </span>known<span class="_ _9"> </span>as<span class="_ _9"> </span>the<span class="_ _9"> </span>mode<span class="_ _9"> </span>mixing</div><div class="t m0 x5 he y2e ff1 fsd fc1 sc0 ls0 ws0">phenomenon,<span class="_ _5"> </span>which<span class="_ _5"> </span>can<span class="_ _5"> </span>complicate<span class="_ _5"> </span>analyses<span class="_ _5"> </span>and<span class="_ _a"> </span>obscure<span class="_ _5"> </span>physical<span class="_ _5"> </span>meanings.<span class="_ _5"> </span>To<span class="_ _5"> </span>overcome<span class="_ _5"> </span>this<span class="_ _a"> </span>problem,<span class="_ _5"> </span>the<span class="_ _5"> </span>EEMD</div><div class="t m0 x5 he y2f ff1 fsd fc1 sc0 ls0 ws0">algorithm<span class="_ _9"> </span>[<span class="fc0">2</span>]<span class="_ _9"> </span>and<span class="_ _9"> </span>the<span class="_ _3"> </span>noise-assisted<span class="_ _9"> </span>MEMD<span class="_ _9"> </span>[<span class="fc0">3</span>]<span class="_ _3"> </span>have<span class="_ _9"> </span>been<span class="_ _9"> </span>proposed.<span class="_ _9"> </span>In<span class="_ _3"> </span>particular,<span class="_ _9"> </span>the<span class="_ _9"> </span>EEMD<span class="_ _9"> </span>has<span class="_ _3"> </span>drawn<span class="_ _9"> </span>a<span class="_ _9"> </span>lot<span class="_ _3"> </span>of<span class="_ _9"> </span>attention</div><div class="t m0 x12 h2 y30 ff4 fs0 fc1 sc0 ls0 ws0">Abbreviations:<span class="_ _4"> </span><span class="ff1">EMD,<span class="_ _4"> </span>empirical<span class="_ _2"> </span>mode<span class="_ _4"> </span>decomposition;<span class="_ _4"> </span>EEMD,<span class="_ _2"> </span>ensemble<span class="_ _4"> </span>empirical<span class="_ _4"> </span>mode<span class="_ _2"> </span>decomposition;<span class="_ _4"> </span>IMFs,<span class="_ _4"> </span>intrinsic<span class="_ _2"> </span>mode<span class="_ _4"> </span>functions;<span class="_ _4"> </span>MEMD,</span></div><div class="t m0 x5 h2 y31 ff1 fs0 fc1 sc0 ls0 ws0">multivariate<span class="_ _0"> </span>empirical<span class="_ _0"> </span>mode<span class="_ _0"> </span>decomposition;<span class="_ _0"> </span>ADD,<span class="_ _0"> </span>addition;<span class="_ _0"> </span>MUL,<span class="_ _0"> </span>multiplication;<span class="_ _0"> </span>DIV,<span class="_ _0"> </span>division;<span class="_ _0"> </span>COMP,<span class="_ _0"> </span>comparison;<span class="_ _0"> </span>BFV,<span class="_ _0"> </span>blood<span class="_ _0"> </span>flow<span class="_ _0"> </span>velocity<span class="_ _0"> </span>signal.</div><div class="t m0 xf hf y32 ff3 fse fc1 sc0 ls0 ws0">&#8727;</div><div class="t m0 x12 h2 y33 ff1 fs0 fc1 sc0 ls0 ws0">Correspondence<span class="_ _8"> </span>to:<span class="_ _0"> </span>Research<span class="_ _8"> </span>Center<span class="_ _0"> </span>for<span class="_ _0"> </span>Adaptive<span class="_ _8"> </span>Data<span class="_ _0"> </span>Analysis/National<span class="_ _8"> </span>Central<span class="_ _0"> </span>University,<span class="_ _8"> </span>No.<span class="_ _0"> </span>300,<span class="_ _8"> </span>Jhongda<span class="_ _0"> </span>Rd.,<span class="_ _8"> </span>Jhongli<span class="_ _0"> </span>City,<span class="_ _0"> </span>Taoyuan<span class="_ _8"> </span>County<span class="_ _0"> </span>32001,</div><div class="t m0 x5 h2 y34 ff1 fs0 fc1 sc0 ls0 ws0">Taiwan,<span class="_ _0"> </span>ROC.<span class="_ _0"> </span>Tel.:<span class="_ _0"> </span>+886<span class="_ _0"> </span>3<span class="_ _0"> </span>426<span class="_ _0"> </span>9734;<span class="_ _0"> </span>fax:<span class="_ _0"> </span>+886<span class="_ _0"> </span>3<span class="_ _0"> </span>426<span class="_ _0"> </span>9736.</div><div class="t m0 x12 h2 y35 ff4 fs0 fc1 sc0 ls0 ws0">E-mail<span class="_ _0"> </span>address:<span class="_ _0"> </span><span class="ff1 fc0">mzlo@ncu.edu.tw<span class="_ _0"> </span><span class="fc1">(M.-T.<span class="_ _0"> </span>Lo).</span></span></div><div class="t m0 x5 h2 y36 ff1 fs0 fc1 sc0 ls0 ws0">0378-4371/$<span class="_ _0"> </span>&#8211;<span class="_ _0"> </span>see<span class="_ _0"> </span>front<span class="_ _0"> </span>matter<span class="_ _0"> </span><span class="ff6 fsf">&#169;<span class="_ _0"> </span></span>2014<span class="_ _0"> </span>Elsevier<span class="_ _0"> </span>B.V.<span class="_ _0"> </span>All<span class="_ _0"> </span>rights<span class="_ _0"> </span>reserved.</div><div class="t m0 x5 h2 y37 ff1 fs0 fc0 sc0 ls0 ws0">http://dx.doi.org/10.1016/j.physa.2014.01.020</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 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