{"id":1383,"date":"2021-11-19T18:00:08","date_gmt":"2021-11-19T10:00:08","guid":{"rendered":"https:\/\/damakey.com\/?p=1383"},"modified":"2023-06-01T22:20:21","modified_gmt":"2023-06-01T14:20:21","slug":"%e6%95%b8%e5%ad%b8%e5%a5%b3%e5%ad%a9","status":"publish","type":"post","link":"https:\/\/damakey.com\/?p=1383","title":{"rendered":"\u6578\u5b78\u5973\u5b69"},"content":{"rendered":"

<\/a><\/p>\n

<\/p>\n

\u96d6\u7136\u4ee5\u524d\u5927\u5b78\u5538\u7684\u662f\u7406\u5de5\u79d1\u7cfb\uff0c\u4f46\u662f\u73fe\u5728\u62ff\u8d77\u300a\u6578\u5b78\u5973\u5b69\u300b\u9019\u672c\u66f8\uff0c\u9084\u4e0d\u514d\u6297\u62d2\u3002\u7ffb\u4e86\u4e00\u4e0b\uff0c\u767c\u73fe\u5176\u5be6\u4ee5\u524d\u9084\u771f\u7684\u4e0d\u66fe\u597d\u597d\u5b78\u904e\u6578\u5b78\uff0c\u800c\u5306\u5306\u4e00\u77a5\uff0c\u7121\u77e5\u4f9d\u7136\u6545\u6211\u3002<\/span><\/p>\n

 <\/p>\n

\u5176\u4e2d\uff0c\u6709\u95dc\u65bc\u6eab\u5ea6\u51b7\u537b\u548c\u653e\u5c04\u7dda\u6b98\u91cf\u7684\u6642\u9593\u51fd\u6578\uff0c\u89ba\u5f97\u9817\u70ba\u76f4\u89c0\u6709\u8da3\uff0c\u5c31\u8a18\u4e86\u4e0b\u4f86\u8ddf\u5927\u5bb6\u5206\u4eab\u3002<\/span><\/p>\n

 <\/p>\n

\u554f\u984c\u3008\u725b\u9813\u51b7\u537b\u5b9a\u5f8b\u3009<\/span><\/p>\n

 <\/p>\n

\u5728\u5ba4\u6eab\u70ba<\/span>U<\/span>\u7684\u623f\u9593\u5167\u653e\u7f6e\u4e00\u7269\u9ad4\uff0c\u8a2d\u6642\u9593\u70ba<\/span>t<\/span>\u6642\uff0c\u7269\u9ad4\u6eab\u5ea6\u70ba<\/span>u(t)<\/span>\u3002\u5df2\u77e5\u6642\u9593<\/span>t=0<\/span>\u6642\uff0c\u6eab\u5ea6<\/span>ut>U<\/span>\uff1b\u6642\u9593<\/span>t=1<\/span>\u6642\uff0c\u6eab\u5ea6\u70ba<\/span>u1<\/span>\u3002<\/span><\/p>\n

 <\/p>\n

\u8a66\u6c42\u51fd\u6578<\/span>u(t)<\/span>\uff0c\u5176\u4e2d\uff0c\u5047\u8a2d\u6eab\u5ea6\u8b8a\u5316\u901f\u5ea6\u8207\u6eab\u5dee\u6210\u6b63\u6bd4<\/span>(<\/span>\u725b\u9813\u51b7\u537b\u5b9a\u5f8b<\/span>)<\/span><\/p>\n

 <\/p>\n

\u89e3\u984c\uff1a<\/span><\/p>\n

 <\/p>\n

u’(t)<\/span>\uff1a\u4ee3\u8868\u7269\u9ad4\u7684\u300c\u6eab\u5ea6\u8b8a\u5316\u901f\u5ea6\u300d\uff1b<\/span>u(t)-U <\/span>\u4ee3\u8868\u7269\u9ad4\u8207\u5ba4\u6eab\u7684\u300c\u6eab\u5dee\u300d<\/span><\/p>\n

 <\/p>\n

\u4f9d\u64da<\/span>(<\/span>\u725b\u9813\u51b7\u537b\u5b9a\u5f8b<\/span>)<\/span>\uff0c\u5047\u8a2d\u6eab\u5ea6\u8b8a\u5316\u901f\u5ea6\u8207\u6eab\u5dee\u6210\u6b63\u6bd4\uff0c\u5247\u53ef\u5beb\u6210\uff1a<\/span><\/p>\n

 <\/p>\n

u’(t)=K(u(t)-U<\/span>\uff09\uff0c<\/span>K <\/span>\u70ba<\/span>(<\/span>\u6b63\u6bd4<\/span>)<\/span>\u5e38\u6578<\/span><\/p>\n

 <\/p>\n

\u9032\u4e00\u6b65\u6539\u5beb\u6210<\/span><\/p>\n

 <\/p>\n

(u(t)-U)’= K(u(t)-U<\/span>\uff09<\/span><\/p>\n

 <\/p>\n

[\u9019\u662f\u719f\u6089\u7684<\/span> f’(t)=f(t) <\/span>\u7684\u5f62\u5f0f\uff0c\u7b26\u5408\u9019\u500b\u7b49\u5f0f\u7684\u51fd\u6578\u70ba<\/span>f(t) =C*e^t<\/span>\uff1b\u800c<\/span>f’(t)=Kf(t) <\/span>\u7684<\/span>f(t) <\/span>\u5247\u70ba<\/span>C*e^Kt<\/span>]<\/span><\/p>\n

 <\/p>\n

f(t)= u(t)-U=C*e^Kt<\/span><\/p>\n

 <\/p>\n

[\u5169\u908a\u5fae\u5206\u9a57\u7b97\u4e00\u4e0b\uff1a<\/span>f’(t)=(u(t)-U)’=(C*e^Kt)’=KCe^Kt=K(u(t)-U)=Kf(t)<\/span>\uff0c\u5c0d\u5594\uff01\uff3d<\/span><\/p>\n

 <\/p>\n

\u6240\u4ee5\u6eab\u5ea6\u51fd\u6578<\/span>u(t)=C*e^Kt+U<\/span><\/p>\n

 <\/p>\n

\u5728<\/span>t=0<\/span>\u6642\uff0c\u7269\u9ad4\u6eab\u5ea6\u70ba<\/span>u0<\/span><\/p>\n

\u5728<\/span>t=1<\/span>\u6642\uff0c\u7269\u9ad4\u6eab\u5ea6\u70ba<\/span>u1<\/span><\/p>\n

 <\/p>\n

\u4ee3\u5165<\/span>u(t) <\/span>\u51fd\u6578\uff0c\u53ef\u5f97\uff1a<\/span><\/p>\n

 <\/p>\n

u0=C+U<\/span><\/p>\n

u1=Ce^K +U<\/span><\/p>\n

 <\/p>\n

\u7b2c\u4e00\u5f0f\u79fb\u9805\u5f97<\/span>C=u0-U<\/span>\u4ee3\u5165\u7b2c\u4e8c\u5f0f<\/span><\/p>\n

 <\/p>\n

u1=(u0-U)e^K+U<\/span><\/p>\n

 <\/p>\n

\u79fb\u9805\u5f97<\/span><\/p>\n

 <\/p>\n

e^K=(u1-U)\/(u0-U<\/span>\uff09<\/span><\/p>\n

 <\/p>\n

\u4ee3\u56de\u5230<\/span>u(t)=Ce^Kt+U<\/span><\/p>\n

=(u0-U)(e^K)^t+U<\/span><\/p>\n

= (u0-U)((u1-U\/(u0-U))^t+U<\/span><\/p>\n

 <\/p>\n

u(t)=(u0-U)((u1-U\/(u0-U))^t+U <\/span>\u5c31\u662f\u725b\u9813\u51b7\u537b\u5b9a\u5f8b\uff0c\u7576\u77e5\u9053\u6642\u9593\u70ba<\/span>0<\/span>\u548c<\/span>1<\/span>\u7684\u6eab\u5ea6\u70ba<\/span>u0<\/span>\u53ca<\/span>u1<\/span>\u6642\uff0c\u4ee3\u8868\u4f9d\u6642\u9593<\/span>t<\/span>\u800c\u8b8a\u5316\u7684\u6eab\u5ea6\u51fd\u6578\u3002<\/span><\/p>\n

 <\/p>\n

\u5f88\u5de7\u7684\u662f\uff0c\u9019\u500b\u51fd\u6578\u4e5f\u53ef\u4ee5\u4f86\u63cf\u8ff0\u653e\u5c04\u6027\u7269\u8cea\u7684\u8870\u8b8a\u3002<\/span><\/p>\n

 <\/p>\n

\u554f\u984c\u3008\u653e\u5c04\u6027\u7269\u8cea\u7684\u8870\u8b8a\u3009<\/span><\/p>\n

 <\/p>\n

\u8a2d\u6642\u9593\u70ba<\/span>t<\/span>\u6642\uff0c\u653e\u5c04\u6027\u7269\u8cea\u6b98\u91cf\u70ba<\/span>r(t)<\/span>\uff0c\u5df2\u77e5\u6642\u9593<\/span>t=0<\/span>\u6642\uff0c\u6b98\u91cf\u70ba<\/span>r0<\/span>\uff1b\u6642\u9593<\/span>t=1<\/span>\u6642\uff0c\u6b98\u91cf\u70ba<\/span>r1<\/span>\uff0c\u8a66\u6c42\u51fd\u6578<\/span>r(t)<\/span>\uff0c\u5176\u4e2d\uff0c\u5047\u8a2d\u653e\u5c04\u6027\u7269\u8cea\u7684\u8870\u8b8a\u901f\u5ea6\u8207\u6b98\u91cf\u6210\u6b63\u6bd4\u3002<\/span><\/p>\n

 <\/p>\n

\u89e3\u984c\uff1a<\/span><\/p>\n

 <\/p>\n

\u4ee5<\/span>r(t)<\/span>\u4ee3\u8868\u653e\u5c04\u6027\u7269\u8cea\u7684\u6b98\u91cf\uff0c\u90a3\u9ebc<\/span>r’(t)<\/span>\u5c31\u53ef\u4ee5\u8868\u793a\u653e\u5c04\u6027\u7269\u8cea\u7684\u8870\u8b8a\u901f\u5ea6\u3002<\/span><\/p>\n

 <\/p>\n

\u653e\u5c04\u6027\u7269\u8cea\u7684\u8870\u8b8a\u901f\u5ea6\u8207\u6b98\u91cf\u6210\u6b63\u6bd4\uff0c\u53ef\u4ee5\u5beb\u6210<\/span><\/p>\n

 <\/p>\n

r’(t)=Kr(t)<\/span><\/p>\n

 <\/p>\n

\u9019\u516c\u5f0f\u548c\u725b\u9813\u51b7\u537b\u5b9a\u5f8b\u985e\u4f3c\u3002<\/span><\/p>\n

 <\/p>\n

\u725b\u9813\u51b7\u537b\u5b9a\u5f8b\u6eab\u5ea6\u51fd\u6578<\/span>u(t)=(u0-U)((u1-U\/(u0-U))^t+U<\/span>\uff0c\u5982\u679c\u8a2d\u5b9a<\/span>U=0<\/span>\uff0c\u5247\u53ef\u5f97\uff1a<\/span><\/p>\n

 <\/p>\n

u(t)=u0(u1\/u0)^t<\/span><\/p>\n

 <\/p>\n

\u9019\u5c31\u8ddf\u653e\u5c04\u6027\u7269\u8cea\u7684\u6b98\u91cf\u51fd\u6578\u7684\u5f62\u5f0f\u4e00\u6a23\uff01<\/span><\/p>\n

 <\/p>\n

r(t)=r0(r1\/r0)^t<\/span><\/p>\n

 <\/p>\n

\u592a\u795e\u5947\u4e86\u3002<\/span><\/p>\n

 <\/p>\n

\u653e\u5c04\u6027\u7269\u8cea\u7684\u6b98\u91cf\u6709\u6240\u8b02\u7684\u534a\u8870\u671f\uff0c\u6c92\u6709\u60f3\u5230\u6eab\u5ea6\u7684\u51b7\u537b\u4e5f\u6709\u985e\u4f3c\u7684\u6027\u8cea\uff0c\u9019\u662f\u6578\u5b78\u544a\u8a34\u6211\u5011\u7684\u3002<\/span><\/p>\n

 <\/p>\n

\u6307\u6578\u51fd\u6578\u9084\u7b97\u6bd4\u8f03\u76f4\u89c0\uff0c\u5230\u4e86\u66f8\u4e2d\u95dc\u65bc\u5fae\u7a4d\u5206\u5c24\u5176\u4e09\u89d2\u51fd\u6578\u7684\u8f49\u63db\uff0c\u5c31\u89ba\u5f97\u90fd\u9084\u7d66\u8001\u5e2b\u4e86\uff0c\u90a3\u5c31\u66f4\u4e0d\u7528\u8aaa\u62c9\u666e\u62c9\u65af\u8f49\u63db\u3001\u5085\u7acb\u8449\u5c55\u958b\uff0c\u4ee5\u964c\u751f\u7684\u975e\u6b50\u5f0f\u5e7e\u4f55\u5b78\u4e86\u3002<\/span><\/p>\n

 <\/p>\n

\u56de\u9867\u5728\u904e\u53bb\u7684\u5de5\u4f5c\u4e2d\uff0c\u9664\u4e86\u78b0\u5230\u4e00\u4e9b\u6a5f\u7387\u7d71\u8a08\u62bd\u6a23\u7684\u5be6\u52d9\u4e4b\u5916\uff0c\u9023\u5713\u5468\u7387\u90fd\u6c92\u6709\u7528\u904e\u5462\uff01\u66f4\u9051\u8ad6\u5176\u4ed6\u3002<\/span><\/p>\n

 <\/p>\n

\u6700\u5e38\u7528\u7684\u662f\u52a0\u6e1b\u4e58\u9664\u3002\u8a2d\u5b9a\u696d\u7e3e\u76ee\u6a19\uff0c\u62fc\u547d\u7528\u4e58\u6cd5\u548c\u52a0\u6cd5\u3002\u522a\u6e1b\u9810\u7b97\u3001\u4eba\u529b\u3001\u6210\u672c\uff0c\u62fc\u547d\u7528\u6e1b\u6cd5\u3002\u8001\u95c6\u89ba\u5f97\u8981\u597d\u597d\u8003\u6838\u4f60\uff0c\u5c31\u7528\u9664\u6cd5\u4f86\u9a57\u7b97\u5404\u7a2e\u6bd4\u7387\u6240\u4ee3\u8868\u7684\u6548\u7387\u3002\u5509<\/span>…..<\/span>\u4e00\u500b\u300c\u6b63\u5e38\u300d\u7684\u4e0a\u73ed\u65cf\uff0c\u8981\u61c2\u7684\u53ea\u662f\u52a0\u6e1b\u4e58\u9664\u7684\u56db\u5247\u7b97\u8853\uff0c\u800c\u4e0d\u662f\u5b78\u6821\u88cf\u9762\u6559\u7684\u6df1\u5967\u96e3\u61c2\u7684\u6578\u5b78\u3002\u9664\u4e86\u70ba\u4e86\u5347\u5b78\uff0c\u9084\u771f\u4e0d\u61c2\u70ba\u4ec0\u9ebc\u90a3\u500b\u6642\u5019\u8981\u5b78\u90a3\u9ebc\u591a\u5462\uff01<\/span><\/p>\n

 <\/p>\n

\u6578\u5b78\u81f3\u4eca\u6559\u6703\u6211\u7684\uff0c\u5c31\u662f\u7e31\u4f7f\u5c0d\u9019\u500b\u4e16\u754c\u7e3d\u662f\u6709\u90a3\u9ebc\u591a\u7684\u4e0d\u61c2\uff0c\u4e5f\u4e0d\u898b\u5f97\u6709\u592a\u5927\u7684\u95dc\u4fc2\u3002\u5c24\u5176\uff0c\u73fe\u5728<\/span>Google<\/span>\u4e00\u4e0b\uff0c\u4ec0\u9ebc\u90fd\u6709\u4e86\u3002<\/span><\/p>\n

 <\/p>\n

\u9019\u500b\u4e16\u754c\u6700\u91cd\u8981\u7684\uff0c\u662f\u6211\u5011\u5728\u7db2\u8def\u4e0a<\/span>Google<\/span>\u4e0d\u5230\u7684\u90a3\u4e00\u500b\u90e8\u5206\u3002<\/span><\/p>\n

 <\/p>\n

*<\/span>\uff1a\u300a\u6578\u5b78\u5973\u5b69\u300b\uff0c\u7d50\u57ce\u6d69<\/span> <\/span>\u8457\uff0c\u9673\u8054\u7586<\/span> <\/span>\u8b6f<\/span><\/p>\n

 <\/p>\n

2021\/11\/19 <\/span>\u6578\u5b78\u5973\u5b69<\/span> Damakey<\/span><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u96d6\u7136\u4ee5\u524d\u5927\u5b78\u5538\u7684\u662f\u7406\u5de5\u79d1\u7cfb\uff0c\u4f46\u662f\u73fe\u5728\u62ff\u8d77\u300a\u6578\u5b78\u5973\u5b69\u300b\u9019\u672c\u66f8\uff0c…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-1383","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/1383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1383"}],"version-history":[{"count":1,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions"}],"predecessor-version":[{"id":28620,"href":"https:\/\/damakey.com\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions\/28620"}],"wp:attachment":[{"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/damakey.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}