{"id":103328,"date":"2026-09-10T09:25:28","date_gmt":"2026-09-10T01:25:28","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/103328.html"},"modified":"2026-09-10T09:25:28","modified_gmt":"2026-09-10T01:25:28","slug":"%e3%80%90%e9%9b%b6%e5%9f%ba%e7%a1%80%e5%ad%a6%e6%99%ba%e8%83%bd%e4%bb%bf%e7%9c%9f-14%e3%80%91%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%9f%ba%e7%a1%80-%e4%bb%8e%e9%9b%86%e6%88%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/103328.html","title":{"rendered":"\u3010\u96f6\u57fa\u7840\u5b66\u667a\u80fd\u4eff\u771f-14\u3011\u795e\u7ecf\u7f51\u7edc\u57fa\u7840\u2014\u2014\u4ece\u96c6\u6210\u5b66\u4e60\u8d70\u5411\u6df1\u5ea6\u5b66\u4e60"},"content":{"rendered":"<h3>\u8bfe\u7a0b\u6458\u8981<\/h3>\n<p>\u4e0a\u4e00\u8282\u901a\u8fc7Stacking\u7ec4\u5408\u591a\u4e2a\u673a\u5668\u5b66\u4e60\u6a21\u578b&#xff0c;\u672c\u8282\u8fdb\u4e00\u6b65\u5b66\u4e60\u80fd\u591f\u81ea\u52a8\u6784\u9020\u975e\u7ebf\u6027\u7279\u5f81\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u8bfe\u7a0b\u4ee5\u60ac\u81c2\u6881\u6700\u5927\u5f2f\u66f2\u5e94\u529b\u9884\u6d4b\u4e3a\u6848\u4f8b&#xff0c;\u8bb2\u89e3\u795e\u7ecf\u5143\u3001\u6743\u91cd\u3001\u504f\u7f6e\u3001\u6fc0\u6d3b\u51fd\u6570\u3001\u7f51\u7edc\u5c42\u3001\u524d\u5411\u4f20\u64ad\u3001\u635f\u5931\u51fd\u6570\u548c\u53cd\u5411\u4f20\u64ad&#xff0c;\u5e76\u5b8c\u6210\u6570\u636e\u6807\u51c6\u5316\u3001MLP\u8bad\u7ec3\u3001\u9a8c\u8bc1\u96c6\u65e9\u505c\u548c\u72ec\u7acb\u6d4b\u8bd5\u3002\u5b66\u4e60\u8005\u5c06\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u201c\u5982\u4f55\u9884\u6d4b\u3001\u600e\u6837\u5b66\u4e60\u3001\u5982\u4f55\u5224\u65ad\u53ef\u9760\u201d&#xff0c;\u4e3a\u540e\u7eedCNN\u3001LSTM\u3001Transformer\u548cPINN\u8bfe\u7a0b\u5efa\u7acb\u57fa\u7840\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"1600\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260910012520-6aa2070072488.png\" width=\"2848\" \/><\/p>\n<hr \/>\n<h3>\u4e00\u3001\u627f\u63a5\u7b2c\u5341\u4e09\u8282&#xff1a;\u4e3a\u4ec0\u4e48\u7ee7\u7eed\u5b66\u4e60\u795e\u7ecf\u7f51\u7edc&#xff1f;<\/h3>\n<p>\u7b2c\u5341\u4e09\u8282\u4f7f\u7528Ridge\u3001\u968f\u673a\u68ee\u6797\u3001\u68af\u5ea6\u63d0\u5347\u548cRBF-SVR\u6784\u5efa\u4e86Stacking\u6a21\u578b&#xff0c;\u5176\u57fa\u672c\u601d\u60f3\u662f&#xff1a;<\/p>\n<p>\\\\[ \\\\text{\u591a\u4e2a\u57fa\u6a21\u578b\u7684\u9884\u6d4b} \\\\longrightarrow \\\\text{\u5143\u5b66\u4e60\u5668} \\\\longrightarrow \\\\text{\u6700\u7ec8\u9884\u6d4b} \\\\]<\/p>\n<p>Stacking\u7684\u4f18\u52bf\u662f\u7efc\u5408\u5df2\u6709\u6a21\u578b&#xff0c;\u4f46\u6bcf\u4e2a\u57fa\u6a21\u578b\u4ecd\u9700\u4eba\u5de5\u9009\u62e9\u3002\u9762\u5bf9\u5e94\u529b\u573a\u3001\u4f4d\u79fb\u573a\u3001\u88c2\u7eb9\u56fe\u50cf\u548c\u77ac\u6001\u54cd\u5e94\u7b49\u9ad8\u7ef4\u95ee\u9898&#xff0c;\u4f20\u7edf\u6a21\u578b\u4f1a\u9047\u5230\u4e09\u4e2a\u56f0\u96be&#xff1a;<\/p>\n<li>\u8f93\u5165\u53ef\u80fd\u5305\u542b\u6210\u5343\u4e0a\u4e07\u4e2a\u7f51\u683c\u8282\u70b9\u6216\u50cf\u7d20&#xff1b;<\/li>\n<li>\u51e0\u4f55\u3001\u8f7d\u8377\u548c\u6750\u6599\u4e4b\u95f4\u5b58\u5728\u590d\u6742\u975e\u7ebf\u6027\u8026\u5408&#xff1b;<\/li>\n<li>\u5f88\u96be\u5b8c\u5168\u4f9d\u9760\u4eba\u5de5\u8bbe\u8ba1\u7279\u5f81\u3002<\/li>\n<p>\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u81ea\u52a8\u6784\u9020\u4e2d\u95f4\u7279\u5f81&#xff1a;<\/p>\n<p>\\\\[ \\\\text{\u539f\u59cb\u8f93\u5165} \\\\longrightarrow \\\\text{\u591a\u5c42\u7279\u5f81\u53d8\u6362} \\\\longrightarrow \\\\text{\u529b\u5b66\u54cd\u5e94} \\\\]<\/p>\n<p>\u672c\u8282\u5148\u4ece\u6700\u57fa\u672c\u7684\u591a\u5c42\u611f\u77e5\u673a\u5f00\u59cb\u3002\u540e\u7eed\u7684CNN\u3001LSTM\u3001Transformer\u548cPINN&#xff0c;\u672c\u8d28\u4e0a\u90fd\u5efa\u7acb\u5728\u795e\u7ecf\u5143\u3001\u6fc0\u6d3b\u51fd\u6570\u3001\u524d\u5411\u4f20\u64ad\u4e0e\u53cd\u5411\u4f20\u64ad\u4e4b\u4e0a\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u3001\u672c\u8282\u5b66\u4e60\u76ee\u6807<\/h3>\n<p>\u5b8c\u6210\u672c\u8282\u540e&#xff0c;\u5b66\u4e60\u8005\u5e94\u80fd\u591f&#xff1a;<\/p>\n<ul>\n<li>\u89e3\u91ca\u795e\u7ecf\u5143\u4e2d\u6743\u91cd\u548c\u504f\u7f6e\u7684\u4f5c\u7528&#xff1b;<\/li>\n<li>\u7406\u89e3\u6fc0\u6d3b\u51fd\u6570\u4e3a\u4ec0\u4e48\u80fd\u591f\u5f15\u5165\u975e\u7ebf\u6027&#xff1b;<\/li>\n<li>\u533a\u5206\u8f93\u5165\u5c42\u3001\u9690\u85cf\u5c42\u548c\u8f93\u51fa\u5c42&#xff1b;<\/li>\n<li>\u8bf4\u6e05\u695a\u524d\u5411\u4f20\u64ad\u3001\u635f\u5931\u8ba1\u7b97\u548c\u53cd\u5411\u4f20\u64ad\u7684\u5173\u7cfb&#xff1b;<\/li>\n<li>\u4f7f\u7528MLP\u9884\u6d4b\u60ac\u81c2\u6881\u6700\u5927\u5f2f\u66f2\u5e94\u529b&#xff1b;<\/li>\n<li>\u6b63\u786e\u5212\u5206\u8bad\u7ec3\u96c6\u3001\u9a8c\u8bc1\u96c6\u548c\u6d4b\u8bd5\u96c6&#xff1b;<\/li>\n<li>\u67e5\u770b\u8bad\u7ec3\u66f2\u7ebf\u3001\u9884\u6d4b\u6563\u70b9\u56fe\u548c\u6b8b\u5dee\u56fe&#xff1b;<\/li>\n<li>\u8ba4\u8bc6\u795e\u7ecf\u7f51\u7edc\u5728\u529b\u5b66\u9884\u6d4b\u4e2d\u7684\u80fd\u529b\u8fb9\u754c\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u4e09\u3001\u4ece\u4e00\u4e2a\u795e\u7ecf\u5143\u5f00\u59cb<\/h3>\n<h4>3.1 \u795e\u7ecf\u5143\u7684\u8ba1\u7b97\u8fc7\u7a0b<\/h4>\n<p>\u8bbe\u795e\u7ecf\u5143\u63a5\u6536\u56db\u4e2a\u6807\u51c6\u5316\u540e\u7684\u529b\u5b66\u53c2\u6570&#xff1a;<\/p>\n<p>\\\\[ \\\\tilde{\\\\boldsymbol{x}} &#061; \\\\begin{bmatrix} \\\\tilde{F}\\\\\\\\ \\\\tilde{L}\\\\\\\\ \\\\tilde{b}\\\\\\\\ \\\\tilde{h} \\\\end{bmatrix} \\\\]<\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>\\\\(F\\\\)&#xff1a;\u8f7d\u8377&#xff1b;<\/li>\n<li>\\\\(L\\\\)&#xff1a;\u6881\u957f&#xff1b;<\/li>\n<li>\\\\(b\\\\)&#xff1a;\u622a\u9762\u5bbd\u5ea6&#xff1b;<\/li>\n<li>\\\\(h\\\\)&#xff1a;\u622a\u9762\u9ad8\u5ea6\u3002<\/li>\n<\/ul>\n<p>\u795e\u7ecf\u5143\u9996\u5148\u8fdb\u884c\u52a0\u6743\u6c42\u548c&#xff1a;<\/p>\n<p>\\\\[ z&#061; w_1\\\\tilde{F} &#043;w_2\\\\tilde{L} &#043;w_3\\\\tilde{b} &#043;w_4\\\\tilde{h} &#043;c \\\\]<\/p>\n<p>\u5f0f\u4e2d&#xff1a;<\/p>\n<ul>\n<li>\\\\(w_1,w_2,w_3,w_4\\\\) \u4e3a\u6743\u91cd&#xff1b;<\/li>\n<li>\\\\(c\\\\) \u4e3a\u504f\u7f6e&#xff1b;<\/li>\n<li>\\\\(z\\\\) \u4e3a\u795e\u7ecf\u5143\u7684\u7ebf\u6027\u8f93\u5165\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u91cc\u7528 \\\\(c\\\\) \u8868\u793a\u504f\u7f6e&#xff0c;\u907f\u514d\u4e0e\u622a\u9762\u5bbd\u5ea6 \\\\(b\\\\) \u6df7\u6dc6\u3002<\/p>\n<p>\u968f\u540e&#xff0c;\u795e\u7ecf\u5143\u901a\u8fc7\u6fc0\u6d3b\u51fd\u6570\u5f97\u5230\u8f93\u51fa&#xff1a;<\/p>\n<p>\\\\[ a&#061;\\\\phi(z) \\\\]<\/p>\n<p>\u56e0\u6b64&#xff0c;\u4e00\u4e2a\u795e\u7ecf\u5143\u5305\u542b\u4e24\u4e2a\u6b65\u9aa4&#xff1a;<\/p>\n<p>\\\\[ \\\\boxed{ \\\\text{\u52a0\u6743\u6c42\u548c} \\\\longrightarrow \\\\text{\u6fc0\u6d3b\u51fd\u6570} } \\\\]<\/p>\n<hr \/>\n<h4>3.2 \u4e00\u4e2a\u53ef\u4ee5\u624b\u7b97\u7684\u4f8b\u5b50<\/h4>\n<p>\u5047\u8bbe\u8f93\u5165\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\tilde{\\\\boldsymbol{x}} &#061; \\\\begin{bmatrix} 1&amp;0&amp;-1&amp;0.5 \\\\end{bmatrix}^{\\\\mathrm T} \\\\]<\/p>\n<p>\u6743\u91cd\u548c\u504f\u7f6e\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{w} &#061; \\\\begin{bmatrix} 0.4&amp;0.2&amp;-0.3&amp;-0.6 \\\\end{bmatrix}^{\\\\mathrm T} \\\\]\\\\[ c&#061;0.1 \\\\]<\/p>\n<p>\u5219\u52a0\u6743\u6c42\u548c\u7ed3\u679c\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\begin{aligned} z &amp;&#061;0.4\\\\times1 &#043;0.2\\\\times0 &#043;(-0.3)\\\\times(-1)\\\\\\\\ &amp;\\\\quad&#043;(-0.6)\\\\times0.5 &#043;0.1\\\\\\\\ &amp;&#061;0.5 \\\\end{aligned} \\\\]<\/p>\n<p>\u5982\u679c\u4f7f\u7528Tanh\u6fc0\u6d3b\u51fd\u6570&#xff1a;<\/p>\n<p>\\\\[ a&#061;\\\\tanh(0.5)\\\\approx0.4621 \\\\]<\/p>\n<p>\u8fd9\u91cc\u7684 \\\\(0.4621\\\\) \u662f\u795e\u7ecf\u5143\u4ea7\u751f\u7684\u4e2d\u95f4\u7279\u5f81\u503c&#xff0c;\u4e0d\u76f4\u63a5\u4ee3\u8868\u5e94\u529b\u6216\u4f4d\u79fb\u3002<\/p>\n<hr \/>\n<h3>\u56db\u3001\u4e3a\u4ec0\u4e48\u5fc5\u987b\u4f7f\u7528\u6fc0\u6d3b\u51fd\u6570&#xff1f;<\/h3>\n<p>\u5047\u8bbe\u4e00\u4e2a\u4e24\u5c42\u7f51\u7edc\u6ca1\u6709\u6fc0\u6d3b\u51fd\u6570&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{a}^{(1)} &#061; \\\\boldsymbol{W}^{(1)}\\\\boldsymbol{x} &#043;\\\\boldsymbol{c}^{(1)} \\\\]\\\\[ \\\\hat{\\\\boldsymbol{y}} &#061; \\\\boldsymbol{W}^{(2)}\\\\boldsymbol{a}^{(1)} &#043;\\\\boldsymbol{c}^{(2)} \\\\]<\/p>\n<p>\u5c06\u7b2c\u4e00\u5f0f\u4ee3\u5165\u7b2c\u4e8c\u5f0f&#xff1a;<\/p>\n<p>\\\\[ \\\\hat{\\\\boldsymbol{y}} &#061; \\\\boldsymbol{W}^{(2)} \\\\boldsymbol{W}^{(1)} \\\\boldsymbol{x} &#043; \\\\boldsymbol{W}^{(2)} \\\\boldsymbol{c}^{(1)} &#043; \\\\boldsymbol{c}^{(2)} \\\\]<\/p>\n<p>\u65e0\u8bba\u53e0\u52a0\u591a\u5c11\u5c42&#xff0c;\u6700\u7ec8\u4ecd\u7136\u662f\u5173\u4e8e\u8f93\u5165\u7684\u7ebf\u6027\u51fd\u6570\u3002<\/p>\n<p>\u6fc0\u6d3b\u51fd\u6570\u53ef\u4ee5\u6253\u7834\u8fd9\u79cd\u7ebf\u6027\u5173\u7cfb&#xff0c;\u4f7f\u7f51\u7edc\u80fd\u591f\u5b66\u4e60&#xff1a;<\/p>\n<ul>\n<li>\u5e94\u529b\u4e0e\u6881\u9ad8\u4e4b\u95f4\u7684\u5e73\u65b9\u53cd\u6bd4\u5173\u7cfb&#xff1b;<\/li>\n<li>\u6750\u6599\u8fdb\u5165\u5851\u6027\u540e\u7684\u975e\u7ebf\u6027\u54cd\u5e94&#xff1b;<\/li>\n<li>\u88c2\u7eb9\u6269\u5c55\u7684\u7a81\u53d8\u8d8b\u52bf&#xff1b;<\/li>\n<li>\u63a5\u89e6\u72b6\u6001\u6539\u53d8\u4ea7\u751f\u7684\u5206\u6bb5\u54cd\u5e94&#xff1b;<\/li>\n<li>\u591a\u79cd\u6750\u6599\u53c2\u6570\u548c\u8fb9\u754c\u6761\u4ef6\u7684\u8026\u5408\u5173\u7cfb\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u4e94\u3001\u5e38\u7528\u6fc0\u6d3b\u51fd\u6570<\/h3>\n<h4>5.1 ReLU\u51fd\u6570<\/h4>\n<p>\\\\[ \\\\operatorname{ReLU}(z)&#061;\\\\max(0,z) \\\\]<\/p>\n<p>\u5f53 \\\\(z&lt;0\\\\) \u65f6&#xff1a;<\/p>\n<p>\\\\[ \\\\operatorname{ReLU}(z)&#061;0 \\\\]<\/p>\n<p>\u5f53 \\\\(z\\\\geq0\\\\) \u65f6&#xff1a;<\/p>\n<p>\\\\[ \\\\operatorname{ReLU}(z)&#061;z \\\\]<\/p>\n<p>ReLU\u8ba1\u7b97\u7b80\u5355&#xff0c;\u5728\u6df1\u5c42\u7f51\u7edc\u548cCNN\u4e2d\u4f7f\u7528\u975e\u5e38\u5e7f\u6cdb\u3002<\/p>\n<hr \/>\n<h4>5.2 Tanh\u51fd\u6570<\/h4>\n<p>\\\\[ \\\\tanh(z) &#061; \\\\frac{e^z-e^{-z}}{e^z&#043;e^{-z}} \\\\]<\/p>\n<p>\u8f93\u51fa\u8303\u56f4\u4e3a&#xff1a;<\/p>\n<p>\\\\[ -1&lt;\\\\tanh(z)&lt;1 \\\\]<\/p>\n<p>Tanh\u8fde\u7eed\u3001\u5e73\u6ed1&#xff0c;\u5728\u67d0\u4e9b\u5e73\u6ed1\u529b\u5b66\u54cd\u5e94\u548c\u7269\u7406\u4fe1\u606f\u795e\u7ecf\u7f51\u7edc\u4e2d\u8f83\u5e38\u89c1\u3002<\/p>\n<p style=\"text-align:center\">\u3010\u6b63\u6587\u63d2\u56fe1&#xff1a;ReLU\u4e0eTanh\u6fc0\u6d3b\u51fd\u6570\u3011<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"660\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260910012526-6aa20706599e6.png\" width=\"1754\" \/><\/p>\n<p>\u9700\u8981\u6ce8\u610f&#xff0c;\u9690\u85cf\u5c42\u4f7f\u7528Tanh&#xff0c;\u5e76\u4e0d\u610f\u5473\u7740\u6700\u7ec8\u9884\u6d4b\u5e94\u529b\u53ea\u80fd\u5728 \\\\(-1\\\\) \u5230 \\\\(1\\\\) MPa\u4e4b\u95f4\u3002\u56de\u5f52\u7f51\u7edc\u7684\u8f93\u51fa\u5c42\u901a\u5e38\u4f7f\u7528\u7ebf\u6027\u51fd\u6570&#xff0c;\u6807\u51c6\u5316\u540e\u7684\u7ed3\u679c\u8fd8\u4f1a\u88ab\u6062\u590d\u4e3a\u539f\u6765\u7684\u5e94\u529b\u5355\u4f4d\u3002<\/p>\n<hr \/>\n<h3>\u516d\u3001\u4ece\u795e\u7ecf\u5143\u7ec4\u6210\u591a\u5c42\u611f\u77e5\u673a<\/h3>\n<p>\u591a\u4e2a\u795e\u7ecf\u5143\u53ef\u4ee5\u7ec4\u6210\u4e00\u5c42&#xff0c;\u591a\u5c42\u795e\u7ecf\u5143\u8fde\u63a5\u540e\u5f62\u6210\u591a\u5c42\u611f\u77e5\u673a&#xff0c;\u5373MLP\u3002<\/p>\n<p>\u672c\u8282\u91c7\u7528\u7684\u7f51\u7edc\u7ed3\u6784\u4e3a&#xff1a;<\/p>\n<p>\\\\[ 4 \\\\longrightarrow 32 \\\\longrightarrow 32 \\\\longrightarrow 1 \\\\]<\/p>\n<p>\u5b83\u8868\u793a&#xff1a;<\/p>\n<table>\n<tr>\u7f51\u7edc\u5c42\u795e\u7ecf\u5143\u6570\u91cf\u4f5c\u7528<\/tr>\n<tbody>\n<tr>\n<td>\u8f93\u5165\u5c42<\/td>\n<td>4<\/td>\n<td>\u63a5\u6536 \\\\(F,L,b,h\\\\)<\/td>\n<\/tr>\n<tr>\n<td>\u7b2c\u4e00\u9690\u85cf\u5c42<\/td>\n<td>32<\/td>\n<td>\u63d0\u53d6\u521d\u7ea7\u975e\u7ebf\u6027\u7279\u5f81<\/td>\n<\/tr>\n<tr>\n<td>\u7b2c\u4e8c\u9690\u85cf\u5c42<\/td>\n<td>32<\/td>\n<td>\u7ec4\u5408\u66f4\u590d\u6742\u7684\u7279\u5f81<\/td>\n<\/tr>\n<tr>\n<td>\u8f93\u51fa\u5c42<\/td>\n<td>1<\/td>\n<td>\u9884\u6d4b\u6700\u5927\u5f2f\u66f2\u5e94\u529b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u9700\u8981\u5f3a\u8c03\u7684\u662f&#xff0c;\u666e\u901a\u795e\u7ecf\u7f51\u7edc\u7684\u9690\u85cf\u795e\u7ecf\u5143\u901a\u5e38\u6ca1\u6709\u660e\u786e\u7684\u7269\u7406\u540d\u79f0\u3002\u4e0d\u80fd\u76f4\u63a5\u65ad\u8a00\u67d0\u4e2a\u795e\u7ecf\u5143\u4ee3\u8868\u5f2f\u77e9&#xff0c;\u53e6\u4e00\u4e2a\u795e\u7ecf\u5143\u4ee3\u8868\u60ef\u6027\u77e9\u3002<\/p>\n<hr \/>\n<h4>6.1 \u7f51\u7edc\u53c2\u6570\u91cf<\/h4>\n<p>\u8f93\u5165\u5c42\u5230\u7b2c\u4e00\u9690\u85cf\u5c42&#xff1a;<\/p>\n<p>\\\\[ 4\\\\times32&#043;32&#061;160 \\\\]<\/p>\n<p>\u7b2c\u4e00\u9690\u85cf\u5c42\u5230\u7b2c\u4e8c\u9690\u85cf\u5c42&#xff1a;<\/p>\n<p>\\\\[ 32\\\\times32&#043;32&#061;1056 \\\\]<\/p>\n<p>\u7b2c\u4e8c\u9690\u85cf\u5c42\u5230\u8f93\u51fa\u5c42&#xff1a;<\/p>\n<p>\\\\[ 32\\\\times1&#043;1&#061;33 \\\\]<\/p>\n<p>\u603b\u53c2\u6570\u91cf\u4e3a&#xff1a;<\/p>\n<p>\\\\[ 160&#043;1056&#043;33&#061;1249 \\\\]<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u8fd9\u4e2a\u770b\u8d77\u6765\u5e76\u4e0d\u5927\u7684\u7f51\u7edc&#xff0c;\u5df2\u7ecf\u5305\u542b1249\u4e2a\u9700\u8981\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u7684\u53c2\u6570\u3002<\/p>\n<hr \/>\n<h3>\u4e03\u3001\u795e\u7ecf\u7f51\u7edc\u5982\u4f55\u5b8c\u6210\u9884\u6d4b&#xff1f;<\/h3>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u6837\u672c&#xff0c;\u7b2c\u4e00\u9690\u85cf\u5c42\u8ba1\u7b97&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{a}^{(1)} &#061; \\\\tanh \\\\left( \\\\boldsymbol{W}^{(1)} \\\\tilde{\\\\boldsymbol{x}} &#043; \\\\boldsymbol{c}^{(1)} \\\\right) \\\\]<\/p>\n<p>\u7b2c\u4e8c\u9690\u85cf\u5c42\u8ba1\u7b97&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{a}^{(2)} &#061; \\\\tanh \\\\left( \\\\boldsymbol{W}^{(2)} \\\\boldsymbol{a}^{(1)} &#043; \\\\boldsymbol{c}^{(2)} \\\\right) \\\\]<\/p>\n<p>\u8f93\u51fa\u5c42\u8ba1\u7b97&#xff1a;<\/p>\n<p>\\\\[ \\\\hat{\\\\tilde{\\\\sigma}} &#061; \\\\boldsymbol{W}^{(3)} \\\\boldsymbol{a}^{(2)} &#043;c^{(3)} \\\\]<\/p>\n<p>\u8fd9\u4e00\u8fc7\u7a0b\u79f0\u4e3a\u524d\u5411\u4f20\u64ad&#xff1a;<\/p>\n<p>\\\\[ \\\\boxed{ \\\\text{\u8f93\u5165} \\\\longrightarrow \\\\text{\u9690\u85cf\u5c421} \\\\longrightarrow \\\\text{\u9690\u85cf\u5c422} \\\\longrightarrow \\\\text{\u9884\u6d4b\u7ed3\u679c} } \\\\]<\/p>\n<p>\u524d\u5411\u4f20\u64ad\u53ea\u8d1f\u8d23\u4f7f\u7528\u5f53\u524d\u53c2\u6570\u5b8c\u6210\u9884\u6d4b&#xff0c;\u8fd8\u6ca1\u6709\u4fee\u6539\u7f51\u7edc\u53c2\u6570\u3002<\/p>\n<hr \/>\n<h3>\u516b\u3001\u795e\u7ecf\u7f51\u7edc\u5982\u4f55\u5b66\u4e60&#xff1f;<\/h3>\n<h4>8.1 \u8ba1\u7b97\u635f\u5931<\/h4>\n<p>\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898&#xff0c;\u53ef\u4ee5\u4f7f\u7528\u5747\u65b9\u8bef\u5dee&#xff1a;<\/p>\n<p>\\\\[ \\\\mathcal{L}_{\\\\mathrm{data}} &#061; \\\\frac{1}{N} \\\\sum_{i&#061;1}^{N} \\\\left( \\\\hat{\\\\tilde{\\\\sigma}}_i &#8211; \\\\tilde{\\\\sigma}_i \\\\right)^2 \\\\]<\/p>\n<p>\u635f\u5931\u8d8a\u5c0f&#xff0c;\u8bf4\u660e\u9884\u6d4b\u503c\u6574\u4f53\u8d8a\u63a5\u8fd1\u76ee\u6807\u503c\u3002<\/p>\n<p>\u4e3a\u4e86\u6291\u5236\u8fc7\u5927\u7684\u6743\u91cd&#xff0c;\u8fd8\u53ef\u4ee5\u52a0\u5165L2\u6b63\u5219\u5316&#xff1a;<\/p>\n<p>\\\\[ \\\\mathcal{L} &#061; \\\\mathcal{L}_{\\\\mathrm{data}} &#043; \\\\alpha \\\\sum_l \\\\left\\\\| \\\\boldsymbol{W}^{(l)} \\\\right\\\\|_2^2 \\\\]<\/p>\n<p>\u5176\u4e2d \\\\(\\\\alpha\\\\) \u63a7\u5236\u6b63\u5219\u5316\u5f3a\u5ea6\u3002<\/p>\n<hr \/>\n<h4>8.2 \u53cd\u5411\u4f20\u64ad<\/h4>\n<p>\u53cd\u5411\u4f20\u64ad\u5229\u7528\u94fe\u5f0f\u6cd5\u5219\u8ba1\u7b97&#xff1a;<\/p>\n<p>\\\\[ \\\\frac{\\\\partial\\\\mathcal{L}} {\\\\partial\\\\boldsymbol{W}^{(l)}} \\\\]<\/p>\n<p>\u4ee5\u53ca&#xff1a;<\/p>\n<p>\\\\[ \\\\frac{\\\\partial\\\\mathcal{L}} {\\\\partial\\\\boldsymbol{c}^{(l)}} \\\\]<\/p>\n<p>\u5b83\u56de\u7b54\u7684\u95ee\u9898\u662f&#xff1a;<\/p>\n<p>\u67d0\u4e2a\u6743\u91cd\u53d1\u751f\u5fae\u5c0f\u53d8\u5316\u65f6&#xff0c;\u9884\u6d4b\u8bef\u5dee\u5c06\u600e\u6837\u53d8\u5316&#xff1f;<\/p>\n<hr \/>\n<h4>8.3 \u53c2\u6570\u66f4\u65b0<\/h4>\n<p>\u5f97\u5230\u68af\u5ea6\u540e&#xff0c;\u4f18\u5316\u5668\u66f4\u65b0\u53c2\u6570&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{W}_{t&#043;1} &#061; \\\\boldsymbol{W}_t &#8211; \\\\eta \\\\frac{\\\\partial\\\\mathcal{L}} {\\\\partial\\\\boldsymbol{W}_t} \\\\]<\/p>\n<p>\u5176\u4e2d \\\\(\\\\eta\\\\) \u662f\u5b66\u4e60\u7387\u3002<\/p>\n<p>\u5b8c\u6574\u8bad\u7ec3\u5faa\u73af\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\boxed{ \\\\text{\u524d\u5411\u9884\u6d4b} \\\\rightarrow \\\\text{\u8ba1\u7b97\u635f\u5931} \\\\rightarrow \\\\text{\u53cd\u5411\u4f20\u64ad} \\\\rightarrow \\\\text{\u66f4\u65b0\u53c2\u6570} } \\\\]<\/p>\n<p>\u53cd\u5411\u4f20\u64ad\u8d1f\u8d23\u8ba1\u7b97\u68af\u5ea6&#xff0c;Adam\u7b49\u4f18\u5316\u5668\u8d1f\u8d23\u6839\u636e\u68af\u5ea6\u66f4\u65b0\u53c2\u6570&#xff0c;\u4e24\u8005\u4e0d\u662f\u540c\u4e00\u4e2a\u6982\u5ff5\u3002<\/p>\n<hr \/>\n<h3>\u4e5d\u3001\u5b9e\u6218\u9879\u76ee&#xff1a;\u60ac\u81c2\u6881\u6700\u5927\u5e94\u529b\u9884\u6d4b<\/h3>\n<h4>9.1 \u529b\u5b66\u6a21\u578b<\/h4>\n<p>\u77e9\u5f62\u622a\u9762\u60ac\u81c2\u6881\u81ea\u7531\u7aef\u627f\u53d7\u96c6\u4e2d\u8f7d\u8377 \\\\(F\\\\)\u3002<\/p>\n<p>\u56fa\u5b9a\u7aef\u5f2f\u77e9\u4e3a&#xff1a;<\/p>\n<p>\\\\[ M&#061;FL \\\\]<\/p>\n<p>\u622a\u9762\u60ef\u6027\u77e9\u4e3a&#xff1a;<\/p>\n<p>\\\\[ I&#061;\\\\frac{bh^3}{12} \\\\]<\/p>\n<p>\u622a\u9762\u6700\u5916\u7f18\u8ddd\u79bb\u4e2d\u6027\u8f74&#xff1a;<\/p>\n<p>\\\\[ c&#061;\\\\frac{h}{2} \\\\]<\/p>\n<p>\u6700\u5927\u5f2f\u66f2\u6b63\u5e94\u529b\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\sigma_{\\\\max} &#061; \\\\frac{Mc}{I} &#061; \\\\frac{6FL}{bh^2} \\\\]<\/p>\n<p>\u5f53\u8f7d\u8377\u4f7f\u7528N\u3001\u5c3a\u5bf8\u4f7f\u7528mm\u65f6&#xff1a;<\/p>\n<p>\\\\[ 1\\\\ \\\\mathrm{N\/mm^2}&#061;1\\\\ \\\\mathrm{MPa} \\\\]<\/p>\n<hr \/>\n<h4>9.2 \u6570\u636e\u8303\u56f4<\/h4>\n<p>\u751f\u62101000\u7ec4\u6559\u5b66\u6570\u636e&#xff1a;<\/p>\n<table>\n<tr>\u53c2\u6570\u8303\u56f4<\/tr>\n<tbody>\n<tr>\n<td>\u8f7d\u8377 \\\\(F\\\\)<\/td>\n<td>10&#xff5e;50 N<\/td>\n<\/tr>\n<tr>\n<td>\u6881\u957f \\\\(L\\\\)<\/td>\n<td>300&#xff5e;600 mm<\/td>\n<\/tr>\n<tr>\n<td>\u6881\u5bbd \\\\(b\\\\)<\/td>\n<td>15&#xff5e;30 mm<\/td>\n<\/tr>\n<tr>\n<td>\u6881\u9ad8 \\\\(h\\\\)<\/td>\n<td>10&#xff5e;20 mm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u76ee\u6807\u6570\u636e\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\sigma_{\\\\mathrm{target}} &#061; \\\\frac{6FL}{bh^2} &#043;\\\\varepsilon \\\\]<\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<p>\\\\[ \\\\varepsilon \\\\sim \\\\mathcal{N}(0,0.40^2) \\\\]<\/p>\n<p>\u8fd9\u91cc\u52a0\u5165\u5c0f\u5e45\u53ef\u91cd\u590d\u6270\u52a8&#xff0c;\u7528\u4e8e\u6a21\u62df\u542b\u566a\u58f0\u6570\u636e\u7684\u8bad\u7ec3\u8fc7\u7a0b\u3002\u672c\u8282\u6570\u636e\u6765\u81ea\u89e3\u6790\u516c\u5f0f&#xff0c;\u5e76\u975e\u771f\u5b9e\u6709\u9650\u5143\u8ba1\u7b97\u7ed3\u679c\u3002<\/p>\n<hr \/>\n<h3>\u5341\u3001\u51c6\u5907\u6570\u636e<\/h3>\n<p>from copy import deepcopy<\/p>\n<p>import numpy as np<br \/>\nimport pandas as pd<\/p>\n<p>from sklearn.model_selection import train_test_split<br \/>\nfrom sklearn.preprocessing import StandardScaler<br \/>\nfrom sklearn.neural_network import MLPRegressor<br \/>\nfrom sklearn.linear_model import Ridge<br \/>\nfrom sklearn.metrics import (<br \/>\n    mean_squared_error,<br \/>\n    mean_absolute_error,<br \/>\n    r2_score<br \/>\n)<\/p>\n<p>def rmse(y_true, y_pred):<br \/>\n    return float(<br \/>\n        np.sqrt(mean_squared_error(y_true, y_pred))<br \/>\n    )<\/p>\n<p>rng &#061; np.random.default_rng(42)<br \/>\nn_samples &#061; 1000<\/p>\n<p>F &#061; rng.uniform(10.0, 50.0, n_samples)<br \/>\nL &#061; rng.uniform(300.0, 600.0, n_samples)<br \/>\nb &#061; rng.uniform(15.0, 30.0, n_samples)<br \/>\nh &#061; rng.uniform(10.0, 20.0, n_samples)<\/p>\n<p>sigma_theory &#061; 6.0 * F * L \/ (b * h**2)<\/p>\n<p>sigma_target &#061; (<br \/>\n    sigma_theory<br \/>\n    &#043; rng.normal(0.0, 0.40, n_samples)<br \/>\n)<\/p>\n<p>features &#061; [<br \/>\n    &#034;load_N&#034;,<br \/>\n    &#034;length_mm&#034;,<br \/>\n    &#034;width_mm&#034;,<br \/>\n    &#034;height_mm&#034;<br \/>\n]<\/p>\n<p>X &#061; pd.DataFrame({<br \/>\n    &#034;load_N&#034;: F,<br \/>\n    &#034;length_mm&#034;: L,<br \/>\n    &#034;width_mm&#034;: b,<br \/>\n    &#034;height_mm&#034;: h<br \/>\n}) <\/p>\n<hr \/>\n<h3>\u5341\u4e00\u3001\u5212\u5206\u8bad\u7ec3\u96c6\u3001\u9a8c\u8bc1\u96c6\u548c\u6d4b\u8bd5\u96c6<\/h3>\n<p>X_dev, X_test, y_dev, y_test &#061; train_test_split(<br \/>\n    X,<br \/>\n    sigma_target,<br \/>\n    test_size&#061;0.20,<br \/>\n    random_state&#061;42<br \/>\n)<\/p>\n<p>X_train, X_val, y_train, y_val &#061; train_test_split(<br \/>\n    X_dev,<br \/>\n    y_dev,<br \/>\n    test_size&#061;0.20,<br \/>\n    random_state&#061;42<br \/>\n)<\/p>\n<p>print(&#034;\u8bad\u7ec3\u96c6&#xff1a;&#034;, len(X_train))<br \/>\nprint(&#034;\u9a8c\u8bc1\u96c6&#xff1a;&#034;, len(X_val))<br \/>\nprint(&#034;\u6d4b\u8bd5\u96c6&#xff1a;&#034;, len(X_test)) <\/p>\n<p>\u5b9e\u9645\u8f93\u51fa&#xff1a;<\/p>\n<p>\u8bad\u7ec3\u96c6&#xff1a; 640<br \/>\n\u9a8c\u8bc1\u96c6&#xff1a; 160<br \/>\n\u6d4b\u8bd5\u96c6&#xff1a; 200 <\/p>\n<p>\u4e09\u7c7b\u6570\u636e\u7684\u804c\u8d23\u4e0d\u540c&#xff1a;<\/p>\n<ul>\n<li>\u8bad\u7ec3\u96c6\u7528\u4e8e\u66f4\u65b0\u7f51\u7edc\u53c2\u6570&#xff1b;<\/li>\n<li>\u9a8c\u8bc1\u96c6\u7528\u4e8e\u9009\u62e9\u6700\u4f73\u8bad\u7ec3\u8f6e\u6b21&#xff1b;<\/li>\n<li>\u6d4b\u8bd5\u96c6\u53ea\u7528\u4e8e\u6700\u7ec8\u8bc4\u4ef7\u3002<\/li>\n<\/ul>\n<p>\u6d4b\u8bd5\u96c6\u4e0d\u80fd\u53c2\u4e0e\u6807\u51c6\u5316\u5668\u62df\u5408\u3001\u8bad\u7ec3\u8f6e\u6570\u9009\u62e9\u548c\u6a21\u578b\u53c2\u6570\u8c03\u6574\u3002<\/p>\n<hr \/>\n<h3>\u5341\u4e8c\u3001\u4e3a\u4ec0\u4e48\u795e\u7ecf\u7f51\u7edc\u9700\u8981\u6807\u51c6\u5316&#xff1f;<\/h3>\n<p>\u56db\u4e2a\u8f93\u5165\u7279\u5f81\u7684\u6570\u503c\u5c3a\u5ea6\u660e\u663e\u4e0d\u540c&#xff1a;<\/p>\n<p>\\\\[ F\\\\approx10\\\\sim50 \\\\]\\\\[ L\\\\approx300\\\\sim600 \\\\]\\\\[ h\\\\approx10\\\\sim20 \\\\]<\/p>\n<p>\u5982\u679c\u76f4\u63a5\u8f93\u5165\u7f51\u7edc&#xff0c;\u6881\u957f\u7684\u6570\u503c\u53ef\u80fd\u5728\u68af\u5ea6\u8ba1\u7b97\u4e2d\u5360\u636e\u8fc7\u5927\u5f71\u54cd\u3002<\/p>\n<p>\u6807\u51c6\u5316\u516c\u5f0f\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\tilde{x}_j &#061; \\\\frac{x_j-\\\\mu_{j,\\\\mathrm{train}}} {s_{j,\\\\mathrm{train}}} \\\\]<\/p>\n<p>\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/p>\n<p>input_scaler &#061; StandardScaler()<br \/>\ntarget_scaler &#061; StandardScaler()<\/p>\n<p>X_train_scaled &#061; input_scaler.fit_transform(X_train)<br \/>\nX_val_scaled &#061; input_scaler.transform(X_val)<br \/>\nX_test_scaled &#061; input_scaler.transform(X_test)<\/p>\n<p>y_train_scaled &#061; target_scaler.fit_transform(<br \/>\n    y_train.reshape(-1, 1)<br \/>\n).ravel()<\/p>\n<p>print(X_train_scaled.shape)<br \/>\nprint(y_train_scaled.shape) <\/p>\n<p>\u5b9e\u9645\u8f93\u51fa&#xff1a;<\/p>\n<p>(640, 4)<br \/>\n(640,) <\/p>\n<p>\u6807\u51c6\u5316\u5668\u53ea\u80fd\u5728\u8bad\u7ec3\u96c6\u4e0a\u8c03\u7528fit\u3002\u9a8c\u8bc1\u96c6\u3001\u6d4b\u8bd5\u96c6\u548c\u540e\u7eed\u65b0\u5de5\u51b5\u53ea\u80fd\u8c03\u7528transform\u3002<\/p>\n<hr \/>\n<h3>\u5341\u4e09\u3001\u5efa\u7acbMLP\u7f51\u7edc<\/h3>\n<p>model &#061; MLPRegressor(<br \/>\n    hidden_layer_sizes&#061;(32, 32),<br \/>\n    activation&#061;&#034;tanh&#034;,<br \/>\n    solver&#061;&#034;adam&#034;,<br \/>\n    learning_rate_init&#061;0.001,<br \/>\n    alpha&#061;0.0001,<br \/>\n    batch_size&#061;64,<br \/>\n    random_state&#061;42,<br \/>\n    early_stopping&#061;False<br \/>\n) <\/p>\n<p>\u4e3b\u8981\u53c2\u6570\u542b\u4e49&#xff1a;<\/p>\n<table>\n<tr>\u53c2\u6570\u672c\u8282\u8bbe\u7f6e\u4f5c\u7528<\/tr>\n<tbody>\n<tr>\n<td>hidden_layer_sizes<\/td>\n<td>(32, 32)<\/td>\n<td>\u4e24\u4e2a\u9690\u85cf\u5c42&#xff0c;\u6bcf\u5c4232\u4e2a\u795e\u7ecf\u5143<\/td>\n<\/tr>\n<tr>\n<td>activation<\/td>\n<td>tanh<\/td>\n<td>\u9690\u85cf\u5c42\u6fc0\u6d3b\u51fd\u6570<\/td>\n<\/tr>\n<tr>\n<td>solver<\/td>\n<td>adam<\/td>\n<td>\u53c2\u6570\u4f18\u5316\u65b9\u6cd5<\/td>\n<\/tr>\n<tr>\n<td>learning_rate_init<\/td>\n<td>0.001<\/td>\n<td>\u521d\u59cb\u5b66\u4e60\u7387<\/td>\n<\/tr>\n<tr>\n<td>alpha<\/td>\n<td>0.0001<\/td>\n<td>L2\u6b63\u5219\u5316\u5f3a\u5ea6<\/td>\n<\/tr>\n<tr>\n<td>batch_size<\/td>\n<td>64<\/td>\n<td>\u6bcf\u6279\u8bad\u7ec3\u6837\u672c\u6570<\/td>\n<\/tr>\n<tr>\n<td>random_state<\/td>\n<td>42<\/td>\n<td>\u4fdd\u8bc1\u7ed3\u679c\u53ef\u91cd\u590d<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5b9a\u4e49\u9884\u6d4b\u51fd\u6570&#xff0c;\u5c06\u6807\u51c6\u5316\u7ed3\u679c\u6062\u590d\u4e3aMPa&#xff1a;<\/p>\n<p>def predict_mpa(network, X_scaled):<br \/>\n    pred_scaled &#061; network.predict(X_scaled)<\/p>\n<p>    return target_scaler.inverse_transform(<br \/>\n        pred_scaled.reshape(-1, 1)<br \/>\n    ).ravel() <\/p>\n<hr \/>\n<h3>\u5341\u56db\u3001\u9010\u8f6e\u8bad\u7ec3\u5e76\u4fdd\u5b58\u6700\u4f73\u6a21\u578b<\/h3>\n<p>history &#061; []<\/p>\n<p>best_val_rmse &#061; np.inf<br \/>\nbest_epoch &#061; 0<br \/>\nbest_model &#061; None<\/p>\n<p>max_epochs &#061; 1500<br \/>\npatience &#061; 120<\/p>\n<p>for epoch in range(1, max_epochs &#043; 1):<br \/>\n    model.partial_fit(<br \/>\n        X_train_scaled,<br \/>\n        y_train_scaled<br \/>\n    )<\/p>\n<p>    train_pred &#061; predict_mpa(<br \/>\n        model,<br \/>\n        X_train_scaled<br \/>\n    )<\/p>\n<p>    val_pred &#061; predict_mpa(<br \/>\n        model,<br \/>\n        X_val_scaled<br \/>\n    )<\/p>\n<p>    train_error &#061; rmse(<br \/>\n        y_train,<br \/>\n        train_pred<br \/>\n    )<\/p>\n<p>    val_error &#061; rmse(<br \/>\n        y_val,<br \/>\n        val_pred<br \/>\n    )<\/p>\n<p>    history.append([<br \/>\n        epoch,<br \/>\n        train_error,<br \/>\n        val_error<br \/>\n    ])<\/p>\n<p>    if val_error &lt; best_val_rmse:<br \/>\n        best_val_rmse &#061; val_error<br \/>\n        best_epoch &#061; epoch<br \/>\n        best_model &#061; deepcopy(model)<\/p>\n<p>    if epoch &#8211; best_epoch &gt;&#061; patience:<br \/>\n        break<\/p>\n<p>model &#061; best_model<\/p>\n<p>print(&#034;\u5b9e\u9645\u8bad\u7ec3\u8f6e\u6570&#xff1a;&#034;, len(history))<br \/>\nprint(&#034;\u6700\u4f73\u6a21\u578b\u8f6e\u6570&#xff1a;&#034;, best_epoch)<br \/>\nprint(<br \/>\n    f&#034;\u6700\u4f73\u9a8c\u8bc1RMSE&#xff1a;&#034;<br \/>\n    f&#034;{best_val_rmse:.6f} MPa&#034;<br \/>\n) <\/p>\n<p>\u5b9e\u9645\u8fd0\u884c\u8f93\u51fa&#xff1a;<\/p>\n<p>\u5b9e\u9645\u8bad\u7ec3\u8f6e\u6570&#xff1a; 1374<br \/>\n\u6700\u4f73\u6a21\u578b\u8f6e\u6570&#xff1a; 1254<br \/>\n\u6700\u4f73\u9a8c\u8bc1RMSE&#xff1a;0.427851 MPa <\/p>\n<p>deepcopy\u7528\u4e8e\u4fdd\u5b58\u5f53\u65f6\u7684\u6a21\u578b\u53c2\u6570\u526f\u672c\u3002\u5982\u679c\u53ea\u5199&#xff1a;<\/p>\n<p>best_model &#061; model <\/p>\n<p>\u4e24\u4e2a\u53d8\u91cf\u4f1a\u6307\u5411\u540c\u4e00\u4e2a\u6301\u7eed\u66f4\u65b0\u7684\u5bf9\u8c61&#xff0c;\u65e0\u6cd5\u771f\u6b63\u4fdd\u7559\u6700\u4f73\u8f6e\u6b21\u3002<\/p>\n<hr \/>\n<h3>\u5341\u4e94\u3001\u5206\u6790\u8bad\u7ec3\u66f2\u7ebf<\/h3>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>plt.rcParams[&#034;font.sans-serif&#034;] &#061; [<br \/>\n    &#034;Microsoft YaHei&#034;,<br \/>\n    &#034;SimHei&#034;,<br \/>\n    &#034;DejaVu Sans&#034;<br \/>\n]<br \/>\nplt.rcParams[&#034;axes.unicode_minus&#034;] &#061; False<\/p>\n<p>history_array &#061; np.asarray(history)<\/p>\n<p>plt.figure(figsize&#061;(9, 4.5))<\/p>\n<p>plt.plot(<br \/>\n    history_array[:, 0],<br \/>\n    history_array[:, 1],<br \/>\n    label&#061;&#034;\u8bad\u7ec3\u96c6&#034;<br \/>\n)<\/p>\n<p>plt.plot(<br \/>\n    history_array[:, 0],<br \/>\n    history_array[:, 2],<br \/>\n    label&#061;&#034;\u9a8c\u8bc1\u96c6&#034;<br \/>\n)<\/p>\n<p>plt.axvline(<br \/>\n    best_epoch,<br \/>\n    linestyle&#061;&#034;&#8211;&#034;,<br \/>\n    color&#061;&#034;gray&#034;,<br \/>\n    label&#061;f&#034;\u4fdd\u7559\u7b2c{best_epoch}\u8f6e&#034;<br \/>\n)<\/p>\n<p>plt.yscale(&#034;log&#034;)<br \/>\nplt.xlabel(&#034;\u8bad\u7ec3\u8f6e\u6570 Epoch&#034;)<br \/>\nplt.ylabel(&#034;RMSE&#xff08;MPa&#xff0c;\u5bf9\u6570\u523b\u5ea6&#xff09;&#034;)<br \/>\nplt.legend()<br \/>\nplt.grid(alpha&#061;0.2)<br \/>\nplt.tight_layout()<br \/>\nplt.show() <\/p>\n<p style=\"text-align:center\">\u3010\u6b63\u6587\u63d2\u56fe2&#xff1a;\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u66f2\u7ebf\u3011<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"786\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260910012526-6aa20706c8559.png\" width=\"1597\" \/><\/p>\n<p>\u4ece\u66f2\u7ebf\u53ef\u4ee5\u770b\u5230&#xff1a;<\/p>\n<li>\u8bad\u7ec3\u521d\u671f&#xff0c;\u8bef\u5dee\u8fc5\u901f\u4e0b\u964d&#xff1b;<\/li>\n<li>\u7ea6200\u8f6e\u540e&#xff0c;\u7f51\u7edc\u5df2\u7ecf\u5b66\u5230\u4e3b\u8981\u975e\u7ebf\u6027\u8d8b\u52bf&#xff1b;<\/li>\n<li>\u540e\u671f\u8bef\u5dee\u4ecd\u5728\u7f13\u6162\u4e0b\u964d&#xff1b;<\/li>\n<li>\u7b2c1254\u8f6e\u53d6\u5f97\u6700\u4f4e\u9a8c\u8bc1\u8bef\u5dee&#xff1b;<\/li>\n<li>\u6b64\u540e\u8fde\u7eed120\u8f6e\u6ca1\u6709\u5237\u65b0\u6700\u4f73\u503c&#xff0c;\u8bad\u7ec3\u505c\u6b62\u3002<\/li>\n<p>\u672c\u4f8b\u540e\u671f\u9a8c\u8bc1\u66f2\u7ebf\u57fa\u672c\u8d8b\u4e8e\u5e73\u7a33&#xff0c;\u5e76\u672a\u51fa\u73b0\u660e\u663e\u7684\u5927\u5e45\u4e0a\u5347\u3002\u56e0\u6b64&#xff0c;\u66f4\u51c6\u786e\u7684\u5224\u65ad\u662f\u6a21\u578b\u5df2\u7ecf\u63a5\u8fd1\u6536\u655b&#xff0c;\u800c\u4e0d\u662f\u4e25\u91cd\u8fc7\u62df\u5408\u3002<\/p>\n<hr \/>\n<h3>\u5341\u516d\u3001\u72ec\u7acb\u6d4b\u8bd5\u4e0e\u7ebf\u6027\u57fa\u7ebf\u6bd4\u8f83<\/h3>\n<p>\u4e3a\u4e86\u5224\u65ad\u795e\u7ecf\u7f51\u7edc\u662f\u5426\u771f\u6b63\u5b66\u5230\u4e86\u975e\u7ebf\u6027\u5173\u7cfb&#xff0c;\u4f7f\u7528\u76f8\u540c\u8bad\u7ec3\u6570\u636e\u5efa\u7acbRidge\u57fa\u7ebf\u3002<\/p>\n<p>mlp_pred &#061; predict_mpa(<br \/>\n    model,<br \/>\n    X_test_scaled<br \/>\n)<\/p>\n<p>ridge &#061; Ridge(alpha&#061;1.0)<br \/>\nridge.fit(<br \/>\n    X_train_scaled,<br \/>\n    y_train<br \/>\n)<\/p>\n<p>ridge_pred &#061; ridge.predict(<br \/>\n    X_test_scaled<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;Ridge\u6d4b\u8bd5RMSE&#xff1a;&#034;<br \/>\n    f&#034;{rmse(y_test, ridge_pred):.6f} MPa&#034;<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;MLP\u6d4b\u8bd5RMSE&#xff1a;&#034;<br \/>\n    f&#034;{rmse(y_test, mlp_pred):.6f} MPa&#034;<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;MLP\u6d4b\u8bd5MAE&#xff1a;&#034;<br \/>\n    f&#034;{mean_absolute_error(y_test, mlp_pred):.6f} MPa&#034;<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;MLP\u6d4b\u8bd5R\u00b2&#xff1a;&#034;<br \/>\n    f&#034;{r2_score(y_test, mlp_pred):.6f}&#034;<br \/>\n) <\/p>\n<p>\u5b9e\u9645\u8fd0\u884c\u8f93\u51fa&#xff1a;<\/p>\n<p>Ridge\u6d4b\u8bd5RMSE&#xff1a;4.696376 MPa<br \/>\nMLP\u6d4b\u8bd5RMSE&#xff1a;0.470548 MPa<br \/>\nMLP\u6d4b\u8bd5MAE&#xff1a;0.367447 MPa<br \/>\nMLP\u6d4b\u8bd5R\u00b2&#xff1a;0.998709 <\/p>\n<p>\u7ed3\u679c\u8bf4\u660e&#xff0c;\u5728\u53ea\u8f93\u5165 \\\\(F,L,b,h\\\\) \u56db\u4e2a\u539f\u59cb\u7279\u5f81\u7684\u6761\u4ef6\u4e0b&#xff0c;MLP\u6bd4\u7ebf\u6027\u6a21\u578b\u66f4\u597d\u5730\u5b66\u4e60\u4e86&#xff1a;<\/p>\n<p>\\\\[ \\\\sigma_{\\\\max} &#061; \\\\frac{6FL}{bh^2} \\\\]<\/p>\n<p>\u4e2d\u7684\u4e58\u6cd5\u3001\u9664\u6cd5\u548c\u5e73\u65b9\u5173\u7cfb\u3002<\/p>\n<p>\u8fd9\u4e2a\u5b9e\u9a8c\u4e0d\u8868\u793a\u795e\u7ecf\u7f51\u7edc\u6bd4\u89e3\u6790\u516c\u5f0f\u66f4\u5408\u9002\u3002\u5df2\u77e5\u51c6\u786e\u516c\u5f0f\u65f6&#xff0c;\u76f4\u63a5\u8ba1\u7b97\u66f4\u5feb\u901f\u3001\u66f4\u900f\u660e\u3002\u672c\u4f8b\u4f7f\u7528\u89e3\u6790\u95ee\u9898&#xff0c;\u662f\u4e3a\u4e86\u6838\u9a8c\u795e\u7ecf\u7f51\u7edc\u662f\u5426\u5b66\u5230\u4e86\u6b63\u786e\u7684\u8f93\u5165\u8f93\u51fa\u5173\u7cfb\u3002<\/p>\n<hr \/>\n<h3>\u5341\u4e03\u3001\u67e5\u770b\u9884\u6d4b\u7ed3\u679c\u4e0e\u6b8b\u5dee<\/h3>\n<p style=\"text-align:center\">\u3010\u6b63\u6587\u63d2\u56fe3&#xff1a;\u6d4b\u8bd5\u96c6\u9884\u6d4b\u548c\u6b8b\u5dee\u3011<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"787\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260910012527-6aa2070756b92.png\" width=\"1955\" \/><\/p>\n<p>\u5de6\u56fe\u4e2d&#xff0c;\u6563\u70b9\u6574\u4f53\u63a5\u8fd1\u7406\u60f3\u9884\u6d4b\u7ebf&#xff1a;<\/p>\n<p>\\\\[ \\\\hat{\\\\sigma}&#061;\\\\sigma \\\\]<\/p>\n<p>\u53f3\u56fe\u5c55\u793a\u6b8b\u5dee&#xff1a;<\/p>\n<p>\\\\[ e_i&#061; \\\\hat{\\\\sigma}_i-\\\\sigma_i \\\\]<\/p>\n<p>\u6b8b\u5dee\u56fe\u53ef\u4ee5\u5e2e\u52a9\u53d1\u73b0&#xff1a;<\/p>\n<ul>\n<li>\u6a21\u578b\u662f\u5426\u6574\u4f53\u504f\u9ad8\u6216\u504f\u4f4e&#xff1b;<\/li>\n<li>\u9ad8\u5e94\u529b\u533a\u57df\u662f\u5426\u8bef\u5dee\u66f4\u5927&#xff1b;<\/li>\n<li>\u662f\u5426\u5b58\u5728\u5c11\u91cf\u5f02\u5e38\u5de5\u51b5&#xff1b;<\/li>\n<li>\u8bef\u5dee\u662f\u5426\u968f\u76ee\u6807\u503c\u53d1\u751f\u7cfb\u7edf\u53d8\u5316\u3002<\/li>\n<\/ul>\n<p>\u867d\u7136\u6d4b\u8bd5\u96c6 \\\\(R^2\\\\) \u8fbe\u52300.9987&#xff0c;\u4f46\u9ad8\u5e94\u529b\u533a\u57df\u4ecd\u51fa\u73b0\u8f83\u5927\u7684\u4e2a\u522b\u6b8b\u5dee\u3002\u56e0\u6b64&#xff0c;\u4e0d\u80fd\u53ea\u770b\u4e00\u4e2a\u7efc\u5408\u6307\u6807\u3002<\/p>\n<p>\u5bf9\u4e8e\u5de5\u7a0b\u5e94\u7528&#xff0c;\u8fd8\u5e94\u68c0\u67e5&#xff1a;<\/p>\n<p>\\\\[ e_{\\\\max} &#061; \\\\max_i \\\\left| \\\\hat{\\\\sigma}_i-\\\\sigma_i \\\\right| \\\\]<\/p>\n<p>\u4ee5\u53ca\u76f8\u5bf9\u8bef\u5dee&#xff1a;<\/p>\n<p>\\\\[ e_{\\\\mathrm{relative},i} &#061; \\\\frac{ \\\\left| \\\\hat{\\\\sigma}_i-\\\\sigma_i \\\\right| }{ \\\\left| \\\\sigma_i \\\\right|&#043;\\\\epsilon } \\\\times100\\\\% \\\\]<\/p>\n<hr \/>\n<h3>\u5341\u516b\u3001\u9884\u6d4b\u4e00\u4e2a\u65b0\u5de5\u51b5<\/h3>\n<p>\u8bbe\u65b0\u5de5\u51b5\u4e3a&#xff1a;<\/p>\n<p>\\\\[ F&#061;30\\\\ \\\\mathrm{N} \\\\]\\\\[ L&#061;450\\\\ \\\\mathrm{mm} \\\\]\\\\[ b&#061;22\\\\ \\\\mathrm{mm} \\\\]\\\\[ h&#061;15\\\\ \\\\mathrm{mm} \\\\]<\/p>\n<p>\u7406\u8bba\u5e94\u529b\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\begin{aligned} \\\\sigma_{\\\\max} &amp;&#061; \\\\frac{6\\\\times30\\\\times450} {22\\\\times15^2}\\\\\\\\ &amp;&#061; 16.363636\\\\ \\\\mathrm{MPa} \\\\end{aligned} \\\\]<\/p>\n<p>\u7f51\u7edc\u9884\u6d4b\u4ee3\u7801&#xff1a;<\/p>\n<p>new_case &#061; pd.DataFrame(<br \/>\n    [[30.0, 450.0, 22.0, 15.0]],<br \/>\n    columns&#061;features<br \/>\n)<\/p>\n<p>new_case_scaled &#061; input_scaler.transform(<br \/>\n    new_case<br \/>\n)<\/p>\n<p>new_prediction &#061; predict_mpa(<br \/>\n    model,<br \/>\n    new_case_scaled<br \/>\n)[0]<\/p>\n<p>theory_value &#061; (<br \/>\n    6.0 * 30.0 * 450.0<br \/>\n    \/ (22.0 * 15.0**2)<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;\u7406\u8bba\u5e94\u529b&#xff1a;&#034;<br \/>\n    f&#034;{theory_value:.6f} MPa&#034;<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;\u7f51\u7edc\u9884\u6d4b&#xff1a;&#034;<br \/>\n    f&#034;{new_prediction:.6f} MPa&#034;<br \/>\n)<\/p>\n<p>print(<br \/>\n    f&#034;\u7edd\u5bf9\u8bef\u5dee&#xff1a;&#034;<br \/>\n    f&#034;{abs(new_prediction-theory_value):.6f} MPa&#034;<br \/>\n) <\/p>\n<p>\u5b9e\u9645\u8fd0\u884c\u8f93\u51fa&#xff1a;<\/p>\n<p>\u7406\u8bba\u5e94\u529b&#xff1a;16.363636 MPa<br \/>\n\u7f51\u7edc\u9884\u6d4b&#xff1a;16.391931 MPa<br \/>\n\u7edd\u5bf9\u8bef\u5dee&#xff1a;0.028295 MPa <\/p>\n<p>\u65b0\u5de5\u51b5\u4f4d\u4e8e\u8bad\u7ec3\u53c2\u6570\u8303\u56f4\u4e4b\u5185&#xff0c;\u56e0\u6b64\u5c5e\u4e8e\u63d2\u503c\u9884\u6d4b\u3002\u82e5\u8f93\u5165&#xff1a;<\/p>\n<p>\\\\[ F&#061;100\\\\ \\\\mathrm{N} \\\\]<\/p>\n<p>\u6216\u8005&#xff1a;<\/p>\n<p>\\\\[ h&#061;5\\\\ \\\\mathrm{mm} \\\\]<\/p>\n<p>\u5c31\u53ef\u80fd\u8fdb\u5165\u8bad\u7ec3\u8303\u56f4\u4e4b\u5916\u3002\u6b64\u65f6\u5373\u4f7f\u7a0b\u5e8f\u80fd\u591f\u7ed9\u51fa\u6570\u503c&#xff0c;\u4e5f\u4e0d\u80fd\u76f4\u63a5\u8ba4\u4e3a\u9884\u6d4b\u53ef\u9760\u3002<\/p>\n<hr \/>\n<h3>\u5341\u4e5d\u3001\u4e0e\u7b2c\u5341\u4e09\u8282\u7ed3\u679c\u5e94\u8be5\u600e\u6837\u6bd4\u8f83&#xff1f;<\/h3>\n<p>\u7b2c\u5341\u4e09\u8282\u4e2d&#xff0c;RBF-SVR\u548cStacking\u4e5f\u53d6\u5f97\u4e86\u5f88\u9ad8\u7cbe\u5ea6&#xff1b;\u672c\u8282MLP\u7684\u6d4b\u8bd5RMSE\u4e3a&#xff1a;<\/p>\n<p>\\\\[ 0.470548\\\\ \\\\mathrm{MPa} \\\\]<\/p>\n<p>\u5b83\u4e0e\u4e0a\u4e00\u8282\u7684\u4f18\u79c0\u6a21\u578b\u5904\u4e8e\u63a5\u8fd1\u6c34\u5e73\u3002\u4e0d\u8fc7\u4e24\u8282\u7684\u8bad\u7ec3\u65b9\u6848\u5b58\u5728\u5dee\u5f02&#xff1a;<\/p>\n<ul>\n<li>\u7b2c\u5341\u4e09\u8282\u4f7f\u7528800\u6761\u5f00\u53d1\u6570\u636e\u8fdb\u884c\u57fa\u6a21\u578b\u62df\u5408&#xff1b;<\/li>\n<li>\u7b2c\u5341\u56db\u8282\u4ece\u5f00\u53d1\u96c6\u4e2d\u5212\u51fa160\u6761\u9a8c\u8bc1\u6570\u636e&#xff1b;<\/li>\n<li>\u672c\u8282\u53ea\u6709640\u6761\u6837\u672c\u76f4\u63a5\u53c2\u4e0e\u7f51\u7edc\u53c2\u6570\u66f4\u65b0&#xff1b;<\/li>\n<li>\u6a21\u578b\u9009\u62e9\u548c\u8bad\u7ec3\u8fc7\u7a0b\u4e5f\u4e0d\u5b8c\u5168\u76f8\u540c\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64&#xff0c;\u8fd9\u4e9b\u7ed3\u679c\u9002\u5408\u5e2e\u52a9\u7406\u89e3\u7b97\u6cd5\u7279\u70b9&#xff0c;\u4e0d\u5e94\u4f5c\u4e3a\u4e25\u683c\u7684\u6392\u884c\u699c\u3002<\/p>\n<p>\u82e5\u8981\u6b63\u5f0f\u6bd4\u8f83&#xff0c;\u5e94\u4f7f\u7528\u76f8\u540c\u7684\u6570\u636e\u5212\u5206\u3001\u76f8\u540c\u7684\u8bc4\u4ef7\u6d41\u7a0b\u548c\u91cd\u590d\u4ea4\u53c9\u9a8c\u8bc1\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u5341\u3001\u5982\u4f55\u8fc1\u79fb\u5230\u771f\u5b9e\u6709\u9650\u5143\u9879\u76ee&#xff1f;<\/h3>\n<p>\u771f\u5b9e\u9879\u76ee\u53ef\u4ee5\u5c06\u8f93\u5165\u6269\u5c55\u4e3a&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{x} &#061; \\\\begin{bmatrix} \\\\text{\u51e0\u4f55\u53c2\u6570}\\\\\\\\ \\\\text{\u6750\u6599\u53c2\u6570}\\\\\\\\ \\\\text{\u8f7d\u8377\u53c2\u6570}\\\\\\\\ \\\\text{\u8fb9\u754c\u6761\u4ef6\u7f16\u7801}\\\\\\\\ \\\\text{\u7f51\u683c\u53c2\u6570} \\\\end{bmatrix} \\\\]<\/p>\n<p>\u8f93\u51fa\u53ef\u4ee5\u662f&#xff1a;<\/p>\n<p>\\\\[ \\\\boldsymbol{y} &#061; \\\\begin{bmatrix} U_{\\\\max}\\\\\\\\ \\\\sigma_{\\\\mathrm{Mises,max}}\\\\\\\\ J\\\\\\\\ K_I\\\\\\\\ N_f \\\\end{bmatrix} \\\\]<\/p>\n<p>\u4e00\u4e2a\u5b9e\u9645\u5de5\u4f5c\u6d41\u53ef\u4ee5\u5199\u6210&#xff1a;<\/p>\n<p>Abaqus\u53c2\u6570\u5316\u5efa\u6a21<br \/>\n        \u2193<br \/>\n\u591a\u5de5\u51b5\u6279\u91cf\u8ba1\u7b97<br \/>\n        \u2193<br \/>\nODB\u7ed3\u679c\u63d0\u53d6<br \/>\n        \u2193<br \/>\n\u5de5\u51b5\u7ea7\u6570\u636e\u5212\u5206<br \/>\n        \u2193<br \/>\n\u8f93\u5165\u4e0e\u76ee\u6807\u6807\u51c6\u5316<br \/>\n        \u2193<br \/>\n\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3<br \/>\n        \u2193<br \/>\n\u9a8c\u8bc1\u96c6\u9009\u62e9\u6a21\u578b<br \/>\n        \u2193<br \/>\n\u72ec\u7acb\u5de5\u51b5\u6d4b\u8bd5<br \/>\n        \u2193<br \/>\n\u7269\u7406\u5408\u7406\u6027\u68c0\u67e5 <\/p>\n<p>\u8fd9\u91cc\u6709\u4e09\u4e2a\u5fc5\u987b\u4fdd\u6301\u7684\u4e60\u60ef\u3002<\/p>\n<p>\u7b2c\u4e00&#xff0c;\u6a21\u578b\u4e0e\u6807\u51c6\u5316\u5668\u5e94\u540c\u65f6\u4fdd\u5b58\u3002\u53ea\u6709\u7f51\u7edc\u53c2\u6570\u800c\u6ca1\u6709\u8bad\u7ec3\u65f6\u7684\u5747\u503c\u3001\u6807\u51c6\u5dee\u548c\u7279\u5f81\u987a\u5e8f&#xff0c;\u6a21\u578b\u4e0d\u80fd\u53ef\u9760\u90e8\u7f72\u3002<\/p>\n<p>\u7b2c\u4e8c&#xff0c;\u8f93\u51fa\u91cf\u7684\u5b9a\u4e49\u5fc5\u987b\u7edf\u4e00\u3002\u4f8b\u5982\u201c\u56fa\u5b9a\u4f4d\u7f6e\u7684\u540d\u4e49\u5e94\u529b\u201d\u548c\u201c\u5168\u6a21\u578b\u6700\u5927\u79ef\u5206\u70b9\u5e94\u529b\u201d\u4e0d\u662f\u540c\u4e00\u4e2a\u76ee\u6807\u3002<\/p>\n<p>\u7b2c\u4e09&#xff0c;\u666e\u901aMLP\u53ea\u4ece\u6570\u636e\u8bef\u5dee\u4e2d\u5b66\u4e60\u3002\u672c\u8282\u635f\u5931\u51fd\u6570\u6ca1\u6709\u52a0\u5165\u5e73\u8861\u65b9\u7a0b\u3001\u672c\u6784\u65b9\u7a0b\u6216\u8fb9\u754c\u6761\u4ef6&#xff0c;\u56e0\u6b64\u5b83\u5c5e\u4e8e\u6570\u636e\u9a71\u52a8\u7f51\u7edc&#xff0c;\u4e0d\u5c5e\u4e8ePINN\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u5341\u4e00\u3001\u5e38\u89c1\u95ee\u9898<\/h3>\n<h4>1. \u9690\u85cf\u5c42\u8d8a\u591a\u8d8a\u597d\u5417&#xff1f;<\/h4>\n<p>\u4e0d\u4e00\u5b9a\u3002\u7f51\u7edc\u52a0\u6df1\u4f1a\u589e\u52a0\u53c2\u6570\u91cf\u548c\u8bad\u7ec3\u96be\u5ea6\u3002\u5bf9\u4e8e\u672c\u8282\u8fd9\u79cd\u56db\u8f93\u5165\u3001\u5355\u8f93\u51fa\u7684\u5c0f\u95ee\u9898&#xff0c;\u4e24\u5c42\u9690\u85cf\u5c42\u5df2\u7ecf\u5177\u6709\u8db3\u591f\u7684\u8868\u8fbe\u80fd\u529b\u3002<\/p>\n<h4>2. \u795e\u7ecf\u5143\u8d8a\u591a\u8d8a\u51c6\u786e\u5417&#xff1f;<\/h4>\n<p>\u4e0d\u4e00\u5b9a\u3002\u795e\u7ecf\u5143\u8fc7\u5c11\u53ef\u80fd\u6b20\u62df\u5408&#xff0c;\u8fc7\u591a\u5219\u53ef\u80fd\u589e\u52a0\u8fc7\u62df\u5408\u98ce\u9669\u548c\u8ba1\u7b97\u6210\u672c&#xff0c;\u5e94\u6839\u636e\u9a8c\u8bc1\u96c6\u7ed3\u679c\u9009\u62e9\u3002<\/p>\n<h4>3. \u635f\u5931\u4e0b\u964d\u5c31\u8868\u793a\u6a21\u578b\u53ef\u9760\u4e86\u5417&#xff1f;<\/h4>\n<p>\u53ea\u80fd\u8bf4\u660e\u4f18\u5316\u8fc7\u7a0b\u53d6\u5f97\u8fdb\u5c55\u3002\u6700\u7ec8\u8fd8\u9700\u8981\u72ec\u7acb\u6d4b\u8bd5\u3001\u6b8b\u5dee\u5206\u6790\u3001\u7269\u7406\u8d8b\u52bf\u68c0\u67e5\u548c\u9002\u7528\u8303\u56f4\u68c0\u67e5\u3002<\/p>\n<h4>4. \u4e3a\u4ec0\u4e48\u540c\u4e00\u4ee3\u7801\u53ef\u80fd\u5f97\u5230\u7565\u6709\u4e0d\u540c\u7684\u7ed3\u679c&#xff1f;<\/h4>\n<p>\u7f51\u7edc\u6743\u91cd\u521d\u59cb\u5316\u548c\u6279\u6b21\u8bad\u7ec3\u5305\u542b\u968f\u673a\u8fc7\u7a0b\u3002\u56fa\u5b9arandom_state\u53ef\u4ee5\u63d0\u9ad8\u53ef\u91cd\u590d\u6027&#xff0c;\u4f46\u4e0d\u540c\u8f6f\u4ef6\u7248\u672c\u6216\u8ba1\u7b97\u73af\u5883\u4ecd\u53ef\u80fd\u5bfc\u81f4\u6700\u540e\u51e0\u4f4d\u5b58\u5728\u5dee\u5f02\u3002<\/p>\n<h4>5. 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