{"id":80322,"date":"2026-03-04T21:41:50","date_gmt":"2026-03-04T13:41:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/80322.html"},"modified":"2026-03-04T21:41:50","modified_gmt":"2026-03-04T13:41:50","slug":"vmd-se-grutransformer%e5%a4%9a%e5%8f%98%e9%87%8f%e6%97%b6%e5%ba%8f%e9%a2%84%e6%b5%8b%ef%bc%8cmatlab%e4%bb%a3%e7%a0%81","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/80322.html","title":{"rendered":"VMD-SE-GRU+Transformer\u591a\u53d8\u91cf\u65f6\u5e8f\u9884\u6d4b\uff0cMATLAB\u4ee3\u7801"},"content":{"rendered":"<p>\u8be5\u4ee3\u7801\u5b9e\u73b0\u4e86\u4e00\u79cd\u57fa\u4e8e VMD&#xff08;\u53d8\u5206\u6a21\u6001\u5206\u89e3&#xff09;- \u6837\u672c\u71b5 &#8211; GRU&#043;Transformer \u7684\u6df7\u5408\u591a\u53d8\u91cf\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u6a21\u578b\u3002<\/p>\n<hr \/>\n<h4>\u4e00\u3001\u7814\u7a76\u80cc\u666f<\/h4>\n<p>\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u5728\u91d1\u878d\u3001\u6c14\u8c61\u3001\u7535\u529b\u3001\u4ea4\u901a\u7b49\u9886\u57df\u5177\u6709\u91cd\u8981\u5e94\u7528\u4ef7\u503c\u3002\u4f20\u7edf\u5355\u4e00\u6a21\u578b&#xff08;\u5982ARIMA\u3001LSTM&#xff09;\u96be\u4ee5\u540c\u65f6\u6355\u6349\u65f6\u5e8f\u4e2d\u7684\u4f4e\u9891\u8d8b\u52bf\u548c\u9ad8\u9891\u6ce2\u52a8\u3002VMD\u53ef\u5c06\u539f\u59cb\u5e8f\u5217\u5206\u89e3\u4e3a\u591a\u4e2a\u672c\u5f81\u6a21\u6001\u51fd\u6570&#xff08;IMF&#xff09;&#xff0c;\u7ed3\u5408\u6837\u672c\u71b5\u533a\u5206\u9ad8\u4f4e\u9891\u6210\u5206&#xff0c;\u518d\u5206\u522b\u7528GRU&#xff08;\u95e8\u63a7\u5faa\u73af\u5355\u5143&#xff09; \u548cTransformer\u5efa\u6a21&#xff0c;\u63d0\u5347\u9884\u6d4b\u7cbe\u5ea6\u3002<\/p>\n<hr \/>\n<h4>\u4e8c\u3001\u4e3b\u8981\u529f\u80fd<\/h4>\n<li>\n<p>\u6570\u636e\u5bfc\u5165\u4e0e\u9884\u5904\u7406<\/p>\n<ul>\n<li>\u4ece Excel \u4e2d\u8bfb\u53d6\u591a\u53d8\u91cf\u6570\u636e&#xff0c;\u63d0\u53d6\u76ee\u6807\u53d8\u91cf\u548c\u7279\u5f81\u53d8\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>VMD \u5206\u89e3<\/p>\n<ul>\n<li>\u5c06\u76ee\u6807\u53d8\u91cf\u5206\u89e3\u4e3a\u591a\u4e2a IMF \u5206\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6837\u672c\u71b5\u8ba1\u7b97\u4e0e\u9ad8\u4f4e\u9891\u5212\u5206<\/p>\n<ul>\n<li>\u8ba1\u7b97\u5404\u5206\u91cf\u7684\u6837\u672c\u71b5&#xff0c;\u6839\u636e\u9608\u503c\u5212\u5206\u4e3a\u4f4e\u9891\u548c\u9ad8\u9891\u5206\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u65f6\u95f4\u5e8f\u5217\u91cd\u6784<\/p>\n<ul>\n<li>\u5c06\u7279\u5f81\u4e0e\u76ee\u6807\u53d8\u91cf&#xff08;\u4f4e\u9891\/\u9ad8\u9891&#xff09;\u7ec4\u5408&#xff0c;\u6784\u5efa\u9002\u7528\u4e8e\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u7684\u8f93\u5165\u683c\u5f0f\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>GRU \u4e0e Transformer \u5efa\u6a21<\/p>\n<ul>\n<li>\u7528 GRU \u9884\u6d4b\u4f4e\u9891\u5206\u91cf&#xff0c;\u7528 Transformer \u9884\u6d4b\u9ad8\u9891\u5206\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6a21\u578b\u878d\u5408\u4e0e\u53cd\u5f52\u4e00\u5316<\/p>\n<ul>\n<li>\u5c06\u4e24\u90e8\u5206\u9884\u6d4b\u7ed3\u679c\u76f8\u52a0&#xff0c;\u53cd\u5f52\u4e00\u5316\u5f97\u5230\u6700\u7ec8\u9884\u6d4b\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6027\u80fd\u8bc4\u4f30\u4e0e\u53ef\u89c6\u5316<\/p>\n<ul>\n<li>\u8ba1\u7b97 RMSE\u3001MAE\u3001R\u00b2 \u7b49\u6307\u6807&#xff0c;\u7ed8\u5236\u591a\u79cd\u56fe\u8868&#xff08;\u5982\u9884\u6d4b\u5bf9\u6bd4\u56fe\u3001\u6b8b\u5dee\u5206\u6790\u56fe\u3001\u7f6e\u4fe1\u533a\u95f4\u56fe\u7b49&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>\u4e09\u3001\u7b97\u6cd5\u6b65\u9aa4\u4e0e\u6280\u672f\u8def\u7ebf<\/h4>\n<li>\n<p>\u6570\u636e\u52a0\u8f7d\u4e0e\u9884\u5904\u7406<\/p>\n<ul>\n<li>\u8bfb\u53d6 data.xlsx&#xff0c;\u63d0\u53d6\u7279\u5f81\u548c\u76ee\u6807\u53d8\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>VMD \u5206\u89e3<\/p>\n<ul>\n<li>\u5c06\u76ee\u6807\u53d8\u91cf\u5206\u89e3\u4e3a K \u4e2a IMF\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6837\u672c\u71b5\u5206\u6790\u4e0e\u9ad8\u4f4e\u9891\u5212\u5206<\/p>\n<ul>\n<li>\u8ba1\u7b97\u6bcf\u4e2a IMF \u7684\u6837\u672c\u71b5&#xff0c;\u5747\u503c\u4f5c\u4e3a\u9608\u503c&#xff0c;\u5212\u5206\u4f4e\u9891&#xff08;\u71b5\u4f4e&#xff09;\u548c\u9ad8\u9891&#xff08;\u71b5\u9ad8&#xff09;\u5206\u91cf\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6570\u636e\u5f52\u4e00\u5316\u4e0e\u65f6\u95f4\u5e8f\u5217\u91cd\u6784<\/p>\n<ul>\n<li>\u5206\u522b\u5bf9\u4f4e\u9891\u3001\u9ad8\u9891\u548c\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316&#xff0c;\u6784\u5efa\u6ed1\u52a8\u7a97\u53e3\u6837\u672c&#xff08;kim \u6b65\u5386\u53f2\u6570\u636e\u9884\u6d4b zim \u6b65\u540e\u7684\u503c&#xff09;\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6a21\u578b\u6784\u5efa\u4e0e\u8bad\u7ec3<\/p>\n<ul>\n<li>GRU \u6a21\u578b&#xff1a;\u7528\u4e8e\u4f4e\u9891\u5206\u91cf&#xff0c;\u5305\u542b\u4e24\u5c42 GRU &#043; Dropout &#043; \u5168\u8fde\u63a5\u5c42\u3002<\/li>\n<li>Transformer \u6a21\u578b&#xff1a;\u7528\u4e8e\u9ad8\u9891\u5206\u91cf&#xff0c;\u5305\u542b\u4f4d\u7f6e\u5d4c\u5165\u3001\u81ea\u6ce8\u610f\u529b\u5c42\u3001\u7d22\u5f15\u5c42\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u9884\u6d4b\u4e0e\u878d\u5408<\/p>\n<ul>\n<li>\u5206\u522b\u9884\u6d4b\u4f4e\u9891\u548c\u9ad8\u9891\u5206\u91cf&#xff0c;\u76f8\u52a0\u5f97\u5230\u6700\u7ec8\u9884\u6d4b\u503c\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6027\u80fd\u8bc4\u4f30\u4e0e\u53ef\u89c6\u5316<\/p>\n<ul>\n<li>\u8ba1\u7b97\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u7684 RMSE\u3001MAE\u3001R\u00b2\u3001MAPE\u3001SMAPE \u7b49\u6307\u6807\u3002<\/li>\n<li>\u7ed8\u5236 VMD \u5206\u89e3\u56fe\u3001\u6837\u672c\u71b5\u56fe\u3001\u9884\u6d4b\u5bf9\u6bd4\u56fe\u3001\u6b8b\u5dee\u56fe\u3001\u7f6e\u4fe1\u533a\u95f4\u56fe\u3001\u96f7\u8fbe\u56fe\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>\u56db\u3001\u516c\u5f0f\u539f\u7406<\/h4>\n<li>\n<p>VMD \u5206\u89e3<\/p>\n<ul>\n<li>\u5c06\u539f\u59cb\u4fe1\u53f7 ( f(t) ) \u5206\u89e3\u4e3a K \u4e2a\u6a21\u6001 ( u_k(t) )&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>              min<\/p>\n<p>              \u2061<\/p>\n<p>              {<\/p>\n<p>               u<\/p>\n<p>               k<\/p>\n<p>              }<\/p>\n<p>              ,<\/p>\n<p>              {<\/p>\n<p>               \u03c9<\/p>\n<p>               k<\/p>\n<p>              }<\/p>\n<p>             {<\/p>\n<p>              \u2211<\/p>\n<p>              k<\/p>\n<p>               \u2225<\/p>\n<p>                \u2202<\/p>\n<p>                t<\/p>\n<p>                [<\/p>\n<p>                 (<\/p>\n<p>                 \u03b4<\/p>\n<p>                 (<\/p>\n<p>                 t<\/p>\n<p>                 )<\/p>\n<p>                 &#043;<\/p>\n<p>                  j<\/p>\n<p>                   \u03c0<\/p>\n<p>                   t<\/p>\n<p>                 )<\/p>\n<p>                \u2217<\/p>\n<p>                 u<\/p>\n<p>                 k<\/p>\n<p>                (<\/p>\n<p>                t<\/p>\n<p>                )<\/p>\n<p>                ]<\/p>\n<p>                e<\/p>\n<p>                 \u2212<\/p>\n<p>                 j<\/p>\n<p>                  \u03c9<\/p>\n<p>                  k<\/p>\n<p>                 t<\/p>\n<p>               \u2225<\/p>\n<p>              2<\/p>\n<p>              2<\/p>\n<p>             }<\/p>\n<p>            \\\\min_{\\\\{u_k\\\\},\\\\{\\\\omega_k\\\\}} \\\\left\\\\{ \\\\sum_k \\\\left\\\\| \\\\partial_t \\\\left[ \\\\left( \\\\delta(t) &#043; \\\\frac{j}{\\\\pi t} \\\\right) * u_k(t) \\\\right] e^{-j\\\\omega_k t} \\\\right\\\\|_2^2 \\\\right\\\\} <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 3.0521em;vertical-align: -1.3021em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.309em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">{<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">}<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mopen mtight\">{<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">}<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.966em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3021em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.45em\"><span class=\"pstrut\" style=\"height: 4.4em\"><\/span><span class=\"\" style=\"width: 0.556em;height: 2.4em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right: 0.0556em\">\u2202<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0556em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0379em\">\u03b4<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3365em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.3488em;margin-left: -0.0359em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1512em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.45em\"><span class=\"pstrut\" style=\"height: 4.4em\"><\/span><span class=\"\" style=\"width: 0.556em;height: 2.4em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.654em\"><span class=\"\" style=\"top: -1.7003em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.9029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7ea6\u675f\u6761\u4ef6&#xff1a;(\\\\sum_k u_k &#061; f)\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u6837\u672c\u71b5&#xff08;Sample Entropy&#xff09;<\/p>\n<ul>\n<li>\u8861\u91cf\u65f6\u95f4\u5e8f\u5217\u590d\u6742\u5ea6&#xff0c;\u503c\u8d8a\u5927\u8868\u793a\u5e8f\u5217\u8d8a\u4e0d\u89c4\u5219\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>GRU<\/p>\n<ul>\n<li>\u66f4\u65b0\u95e8 ( z_t ) \u548c\u91cd\u7f6e\u95e8 ( r_t )&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>             z<\/p>\n<p>             t<\/p>\n<p>            &#061;<\/p>\n<p>            \u03c3<\/p>\n<p>            (<\/p>\n<p>             W<\/p>\n<p>             z<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>            &#043;<\/p>\n<p>             U<\/p>\n<p>             z<\/p>\n<p>             h<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            )<\/p>\n<p>            z_t &#061; \\\\sigma(W_z x_t &#043; U_z h_{t-1}) <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.044em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.044em\">z<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.044em\">z<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             r<\/p>\n<p>             t<\/p>\n<p>            &#061;<\/p>\n<p>            \u03c3<\/p>\n<p>            (<\/p>\n<p>             W<\/p>\n<p>             r<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>            &#043;<\/p>\n<p>             U<\/p>\n<p>             r<\/p>\n<p>             h<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            )<\/p>\n<p>            r_t &#061; \\\\sigma(W_r x_t &#043; U_r h_{t-1}) <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0278em\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>              h<\/p>\n<p>              ~<\/p>\n<p>             t<\/p>\n<p>            &#061;<\/p>\n<p>            tanh<\/p>\n<p>            \u2061<\/p>\n<p>            (<\/p>\n<p>             W<\/p>\n<p>             h<\/p>\n<p>             x<\/p>\n<p>             t<\/p>\n<p>            &#043;<\/p>\n<p>             U<\/p>\n<p>             h<\/p>\n<p>            (<\/p>\n<p>             r<\/p>\n<p>             t<\/p>\n<p>            \u2299<\/p>\n<p>             h<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            )<\/p>\n<p>            )<\/p>\n<p>            \\\\tilde{h}_t &#061; \\\\tanh(W_h x_t &#043; U_h (r_t \\\\odot h_{t-1})) <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0813em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\">tanh<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2299<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>             h<\/p>\n<p>             t<\/p>\n<p>            &#061;<\/p>\n<p>            (<\/p>\n<p>            1<\/p>\n<p>            \u2212<\/p>\n<p>             z<\/p>\n<p>             t<\/p>\n<p>            )<\/p>\n<p>            \u2299<\/p>\n<p>             h<\/p>\n<p>              t<\/p>\n<p>              \u2212<\/p>\n<p>              1<\/p>\n<p>            &#043;<\/p>\n<p>             z<\/p>\n<p>             t<\/p>\n<p>            \u2299<\/p>\n<p>              h<\/p>\n<p>              ~<\/p>\n<p>             t<\/p>\n<p>            h_t &#061; (1 &#8211; z_t) \\\\odot h_{t-1} &#043; z_t \\\\odot \\\\tilde{h}_t <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.044em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2299<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9028em;vertical-align: -0.2083em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.044em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2299<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0813em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Transformer \u81ea\u6ce8\u610f\u529b\u673a\u5236<\/p>\n<ul>\n<li>\u81ea\u6ce8\u610f\u529b\u8f93\u51fa&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            Attention<\/p>\n<p>            (<\/p>\n<p>            Q<\/p>\n<p>            ,<\/p>\n<p>            K<\/p>\n<p>            ,<\/p>\n<p>            V<\/p>\n<p>            )<\/p>\n<p>            &#061;<\/p>\n<p>            softmax<\/p>\n<p>             (<\/p>\n<p>               Q<\/p>\n<p>                K<\/p>\n<p>                T<\/p>\n<p>                d<\/p>\n<p>                k<\/p>\n<p>             )<\/p>\n<p>            V<\/p>\n<p>            \\\\text{Attention}(Q, K, V) &#061; \\\\text{softmax}\\\\left(\\\\frac{QK^T}{\\\\sqrt{d_k}}\\\\right)V <\/p>\n<p>        <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">Attention<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4684em;vertical-align: -0.95em\"><\/span><span class=\"mord text\"><span class=\"mord\">softmax<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5183em\"><span class=\"\" style=\"top: -2.2528em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8572em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8172em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                       <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1828em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.93em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<hr \/>\n<h4>\u4e94\u3001\u53c2\u6570\u8bbe\u5b9a<\/h4>\n<table>\n<tr>\u53c2\u6570\u503c\u8bf4\u660e<\/tr>\n<tbody>\n<tr>\n<td>alpha<\/td>\n<td>2000<\/td>\n<td>VMD \u60e9\u7f5a\u56e0\u5b50<\/td>\n<\/tr>\n<tr>\n<td>K<\/td>\n<td>5<\/td>\n<td>\u6a21\u6001\u6570\u91cf<\/td>\n<\/tr>\n<tr>\n<td>m<\/td>\n<td>2<\/td>\n<td>\u6837\u672c\u71b5\u5d4c\u5165\u7ef4\u5ea6<\/td>\n<\/tr>\n<tr>\n<td>r_coefficient<\/td>\n<td>0.2<\/td>\n<td>\u6837\u672c\u71b5\u9608\u503c\u7cfb\u6570<\/td>\n<\/tr>\n<tr>\n<td>kim<\/td>\n<td>2<\/td>\n<td>\u5386\u53f2\u6b65\u957f<\/td>\n<\/tr>\n<tr>\n<td>zim<\/td>\n<td>1<\/td>\n<td>\u9884\u6d4b\u6b65\u957f<\/td>\n<\/tr>\n<tr>\n<td>num_size<\/td>\n<td>0.7<\/td>\n<td>\u8bad\u7ec3\u96c6\u6bd4\u4f8b<\/td>\n<\/tr>\n<tr>\n<td>GRU \u9690\u85cf\u5c42<\/td>\n<td>64, 32<\/td>\n<td>GRU \u5355\u5143\u6570<\/td>\n<\/tr>\n<tr>\n<td>Transformer head<\/td>\n<td>4<\/td>\n<td>\u591a\u5934\u6ce8\u610f\u529b\u5934\u6570<\/td>\n<\/tr>\n<tr>\n<td>\u5b66\u4e60\u7387<\/td>\n<td>0.001<\/td>\n<td>\u521d\u59cb\u5b66\u4e60\u7387<\/td>\n<\/tr>\n<tr>\n<td>\u8bad\u7ec3\u8f6e\u6570<\/td>\n<td>80<\/td>\n<td>\u6700\u5927\u8fed\u4ee3\u6b21\u6570<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h4>\u516d\u3001\u8fd0\u884c\u73af\u5883<\/h4>\n<ul>\n<li>MATLAB \u7248\u672c&#xff1a;\u5efa\u8bae R2024b \u53ca\u4ee5\u4e0a<\/li>\n<\/ul>\n<hr \/>\n<h4>\u4e03\u3001\u5e94\u7528\u573a\u666f<\/h4>\n<ul>\n<li>\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b&#xff08;\u5982\u80a1\u7968\u4ef7\u683c\u3001\u6c47\u7387&#xff09;<\/li>\n<li>\u80fd\u6e90\u8d1f\u8377\u9884\u6d4b&#xff08;\u5982\u7535\u529b\u8d1f\u8377\u3001\u98ce\u7535\u529f\u7387&#xff09;<\/li>\n<li>\u6c14\u8c61\u9884\u6d4b&#xff08;\u5982\u6e29\u5ea6\u3001\u964d\u6c34\u91cf&#xff09;<\/li>\n<li>\u4ea4\u901a\u6d41\u91cf\u9884\u6d4b<\/li>\n<li>\u5de5\u4e1a\u8bbe\u5907\u72b6\u6001\u76d1\u6d4b\u4e0e\u5269\u4f59\u5bff\u547d\u9884\u6d4b<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134137-69a836918b924.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134138-69a83692d6d17.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134139-69a83693b88fe.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134140-69a8369441240.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134141-69a836951921d.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134142-69a8369612fc6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134143-69a8369746fa8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134144-69a836985c863.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134144-69a83698cf277.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134145-69a836992016f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134146-69a8369a05020.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260304134146-69a8369adee71.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" 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