{"id":742100,"date":"2024-09-10T03:59:17","date_gmt":"2024-09-10T02:59:17","guid":{"rendered":"https:\/\/www.thermal-engineering.org\/?p=742100"},"modified":"2024-09-10T03:59:17","modified_gmt":"2024-09-10T02:59:17","slug":"%e4%bf%a1%e6%81%af%e8%ae%ba%e4%b8%8e%e7%bc%96%e7%a0%81%e4%b8%ad%e7%9a%84%e7%86%b5","status":"publish","type":"post","link":"https:\/\/www.thermal-engineering.org\/zh-hans\/%e4%bf%a1%e6%81%af%e8%ae%ba%e4%b8%8e%e7%bc%96%e7%a0%81%e4%b8%ad%e7%9a%84%e7%86%b5\/","title":{"rendered":"\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5"},"content":{"rendered":"<p class=\"sidekick\">\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5\uff1a\u89e3\u91ca\u71b5\u5728\u4fe1\u606f\u4f20\u9012\u4e2d\u7684\u4f5c\u7528\uff0c\u5982\u4f55\u8861\u91cf\u4fe1\u606f\u7684\u4e0d\u786e\u5b9a\u6027\u4ee5\u53ca\u7f16\u7801\u6548\u7387\u4f18\u5316\u7684\u91cd\u8981\u6027\u3002\u9002\u5408\u521d\u5b66\u8005\u7684\u57fa\u7840\u4ecb\u7ecd\u3002<\/p>\n<p><img src=\"https:\/\/www.thermal-engineering.org\/wp-content\/uploads\/2024\/07\/\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5.png\" alt=\"\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5\" style=\"display: block; margin-left: auto; margin-right: auto;\"\/><\/p>\n<h2>\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5<\/h2>\n<p>\u5728\u4fe1\u606f\u8bba\u4e2d\uff0c\u71b5\u662f\u8861\u91cf\u4fe1\u606f\u4e0d\u786e\u5b9a\u6027\u7684\u91cd\u8981\u6982\u5ff5\u3002\u71b5\u8fd9\u4e2a\u6982\u5ff5\u6700\u521d\u7531\u7269\u7406\u5b66\u5bb6\u514b\u52b3\u5fb7\u00b7\u9999\u519c\u57281948\u5e74\u63d0\u51fa\uff0c\u7528\u4e8e\u91cf\u5316\u4fe1\u606f\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u91cf\u548c\u4e0d\u786e\u5b9a\u6027\u7a0b\u5ea6\u3002<\/p>\n<h2>\u71b5\u7684\u5b9a\u4e49<\/h2>\n<p>\u4fe1\u606f\u8bba\u4e2d\u7684\u71b5\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u4fe1\u606f\u6e90\uff0c\u5b83\u53ef\u4ee5\u8f93\u51fa\u4e00\u7ec4\u53ef\u80fd\u7684\u7b26\u53f7 <i>X<\/i> = {x<sub>1<\/sub>, x<sub>2<\/sub>, &#8230;, x<sub>n<\/sub>}\uff0c\u6bcf\u4e2a\u7b26\u53f7 <i>x<sub>i<\/sub><\/i> \u51fa\u73b0\u7684\u6982\u7387\u4e3a <i>p<sub>i<\/sub><\/i>\u3002\u90a3\u4e48\uff0c\u8be5\u4fe1\u606f\u6e90\u7684\u71b5\uff08<i>H(X)<\/i>\uff09\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n<pre>H(X) = -\u2211(p<sub>i<\/sub> log<sub>2<\/sub> p<sub>i<\/sub>)<\/pre>\n<p>\u5176\u4e2d\uff0c\u2211 \u8868\u793a\u5bf9\u6240\u6709\u53ef\u80fd\u7684\u7b26\u53f7\u6c42\u548c\uff0c<i>p<sub>i<\/sub><\/i> \u8868\u793a\u7b26\u53f7 <i>x<sub>i<\/sub><\/i> \u51fa\u73b0\u7684\u6982\u7387\u3002<\/p>\n<p>\u71b5\u8d8a\u5927\uff0c\u8868\u793a\u4fe1\u606f\u7684\u4e0d\u786e\u5b9a\u6027\u8d8a\u9ad8\uff1b\u71b5\u8d8a\u5c0f\uff0c\u4e0d\u786e\u5b9a\u6027\u8d8a\u4f4e\u3002<\/p>\n<h2>\u71b5\u5728\u7f16\u7801\u4e2d\u7684\u5e94\u7528<\/h2>\n<p>\u5728\u7f16\u7801\u7406\u8bba\u4e2d\uff0c\u71b5\u7528\u4e8e\u786e\u5b9a\u4fe1\u606f\u7684\u6700\u5c0f\u7f16\u7801\u957f\u5ea6\uff0c\u5373\u4fe1\u606f\u6e90\u4ea7\u751f\u7684\u7b26\u53f7\u5e8f\u5217\u6240\u9700\u7684\u6700\u5c0f\u6bd4\u7279\u6570\u3002\u8fd9\u4e5f\u5c31\u662f\u6240\u8c13\u7684\u6700\u4f18\u7f16\u7801\uff0c\u5b83\u80fd\u4fdd\u8bc1\u4f20\u8f93\u6548\u7387\u6700\u5927\u5316\u3002<\/p>\n<h3>\u970d\u592b\u66fc\u7f16\u7801<\/h3>\n<p>\u970d\u592b\u66fc\u7f16\u7801\u662f\u57fa\u4e8e\u71b5\u7684\u6700\u4f18\u7f16\u7801\u65b9\u6cd5\u4e4b\u4e00\u3002\u5b83\u901a\u8fc7\u7ed9\u9891\u7387\u9ad8\u7684\u7b26\u53f7\u8d4b\u4e88\u8f83\u77ed\u7684\u7f16\u7801\uff0c\u9891\u7387\u4f4e\u7684\u7b26\u53f7\u8d4b\u4e88\u8f83\u957f\u7684\u7f16\u7801\uff0c\u4ece\u800c\u6700\u5c0f\u5316\u6574\u4e2a\u7b26\u53f7\u5e8f\u5217\u7684\u5e73\u5747\u7f16\u7801\u957f\u5ea6\u3002\u970d\u592b\u66fc\u7f16\u7801\u5176\u5b9e\u8d28\u5c31\u662f\u6784\u5efa\u4e00\u68f5\u6700\u4f18\u524d\u7f00\u7801\u6811\uff0c\u4f7f\u5f97\u5b58\u50a8\u548c\u4f20\u8f93\u7684\u7f16\u7801\u957f\u5ea6\u6700\u5c0f\u3002<\/p>\n<h3>\u9999\u519c-\u8303\u8bfa\u7f16\u7801<\/h3>\n<p>\u9999\u519c-\u8303\u8bfa\u7f16\u7801\u662f\u53e6\u4e00\u79cd\u57fa\u4e8e\u71b5\u7684\u7f16\u7801\u6280\u672f\u3002\u5b83\u901a\u8fc7\u9012\u5f52\u5730\u5c06\u7b26\u53f7\u96c6\u5206\u6210\u4e24\u534a\uff0c\u4f7f\u5f97\u6bcf\u4e00\u90e8\u5206\u7684\u603b\u6982\u7387\u5c3d\u91cf\u63a5\u8fd1\uff0c\u4ece\u800c\u4e3a\u7b26\u53f7\u5206\u914d\u4ee3\u7801\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u4e0d\u5982\u970d\u592b\u66fc\u7f16\u7801\u7d27\u51d1\uff0c\u4f46\u5b9e\u73b0\u8d77\u6765\u76f8\u5bf9\u7b80\u5355\u3002<\/p>\n<h3>\u71b5\u7387<\/h3>\n<p>\u5728\u8ba8\u8bba\u4fe1\u606f\u6e90\u7684\u957f\u671f\u8868\u73b0\u65f6\uff0c\u6211\u4eec\u4f7f\u7528\u71b5\u7387\u8fd9\u4e2a\u6982\u5ff5\u3002\u71b5\u7387\u5b9a\u4e49\u4e3a\u6bcf\u4e2a\u7b26\u53f7\u7684\u5e73\u5747\u4fe1\u606f\u91cf\uff1a<\/p>\n<pre>H'(X) = lim (n\u2192\u221e) \\frac{H(X<sup>n<\/sup>)}{n}<\/pre>\n<p>\u5176\u4e2d\uff0cH(X<sup>n<\/sup>) \u4ee3\u8868\u524d n \u4e2a\u7b26\u53f7\u7684\u71b5\u3002\u71b5\u7387\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4fe1\u606f\u6e90\u5728\u65e0\u9650\u957f\u65f6\u95f4\u5185\u7684\u884c\u4e3a\u3002<\/p>\n<h2>\u5b9e\u9645\u5e94\u7528<\/h2>\n<p>\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u538b\u7f29\u3001\u52a0\u5bc6\u3001\u901a\u4fe1\u7cfb\u7edf\u548c\u7edf\u8ba1\u5b66\u4e60\u7b49\u9886\u57df\u3002\u901a\u8fc7\u7406\u89e3\u548c\u8fd0\u7528\u71b5\uff0c\u6211\u4eec\u80fd\u591f\u8bbe\u8ba1\u51fa\u66f4\u9ad8\u6548\u3001\u66f4\u5b89\u5168\u3001\u66f4\u53ef\u9760\u7684\u4fe1\u606f\u5904\u7406\u7cfb\u7edf\u3002<\/p>\n<h3>\u6570\u636e\u538b\u7f29<\/h3>\n<p>\u71b5\u5728\u6570\u636e\u538b\u7f29\u4e2d\u7684\u5e94\u7528\u5341\u5206\u5e7f\u6cdb\uff0c\u901a\u8fc7\u8ba1\u7b97\u6570\u636e\u7684\u71b5\uff0c\u53ef\u4ee5\u786e\u5b9a\u5176\u6700\u4f18\u538b\u7f29\u8def\u5f84\uff0c\u4ece\u800c\u5b9e\u73b0\u65e0\u635f\u6216\u6709\u635f\u7684\u6570\u636e\u538b\u7f29\u3002<\/p>\n<h3>\u901a\u4fe1\u7cfb\u7edf<\/h3>\n<p>\u5728\u901a\u4fe1\u7cfb\u7edf\u4e2d\uff0c\u71b5\u7528\u6765\u4f30\u8ba1\u4fe1\u9053\u5bb9\u91cf\uff0c\u5e2e\u52a9\u8bbe\u8ba1\u6709\u6548\u7684\u7f16\u7801\u65b9\u6848\uff0c\u4ece\u800c\u6700\u5927\u5316\u6570\u636e\u4f20\u8f93\u901f\u7387\u3002<\/p>\n<p>\u603b\u4e4b\uff0c\u4fe1\u606f\u8bba\u4e2d\u7684\u71b5\u6982\u5ff5\u4e0d\u4ec5\u63ed\u793a\u4e86\u4fe1\u606f\u4e0d\u786e\u5b9a\u6027\u7684\u672c\u8d28\uff0c\u8fd8\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u9ad8\u6548\u7f16\u7801\u548c\u6570\u636e\u5904\u7406\u7684\u65b9\u6cd5\uff0c\u662f\u73b0\u4ee3\u4fe1\u606f\u6280\u672f\u53d1\u5c55\u7684\u57fa\u77f3\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4fe1\u606f\u8bba\u4e0e\u7f16\u7801\u4e2d\u7684\u71b5\uff1a\u89e3\u91ca\u71b5\u5728\u4fe1\u606f\u4f20\u9012\u4e2d\u7684\u4f5c\u7528\uff0c\u5982\u4f55\u8861\u91cf\u4fe1\u606f\u7684\u4e0d\u786e\u5b9a\u6027\u4ee5\u53ca\u7f16\u7801\u6548\u7387\u4f18\u5316\u7684\u91cd\u8981\u6027\u3002\u9002\u5408\u521d\u5b66\u8005\u7684\u57fa\u7840\u4ecb\u7ecd\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[134],"tags":[],"yoast_head":"<!-- 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