{"id":281,"date":"2025-12-18T00:24:29","date_gmt":"2025-12-17T16:24:29","guid":{"rendered":"http:\/\/114.55.133.236\/?p=281"},"modified":"2026-03-13T20:35:44","modified_gmt":"2026-03-13T12:35:44","slug":"%e5%8f%91%e5%b0%84%e6%9c%ba%e6%9e%84%e4%ba%91%e5%8f%b0%e7%9a%84pitch%e7%94%b5%e6%9c%ba%e7%9a%84%e8%bd%af%e4%bb%b6%e9%87%8d%e5%8a%9b%e8%a1%a5%e5%81%bf","status":"publish","type":"post","link":"http:\/\/qianmo.icu\/index.php\/2025\/12\/18\/%e5%8f%91%e5%b0%84%e6%9c%ba%e6%9e%84%e4%ba%91%e5%8f%b0%e7%9a%84pitch%e7%94%b5%e6%9c%ba%e7%9a%84%e8%bd%af%e4%bb%b6%e9%87%8d%e5%8a%9b%e8%a1%a5%e5%81%bf\/","title":{"rendered":"\u53d1\u5c04\u673a\u6784\u4e91\u53f0\u7684pitch\u7535\u673a\u7684\u8f6f\u4ef6\u91cd\u529b\u8865\u507f"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p 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class=\"wp-block-paragraph\"><strong>\u7535\u673a\u524d\u9988\u529b\u77e9\u8865\u507f<\/strong>\u662f\u4e00\u79cd<strong>\u4e3b\u52a8\u8865\u507f\u63a7\u5236\u7b56\u7565<\/strong>\uff0c\u6838\u5fc3\u662f\u5728<strong>\u53cd\u9988\u63a7\u5236<\/strong>\u7684\u57fa\u7840\u4e0a\uff0c\u63d0\u524d\u6839\u636e\u7cfb\u7edf\u6a21\u578b\u6216\u5df2\u77e5\u6270\u52a8\uff0c\u8ba1\u7b97\u51fa\u62b5\u6d88\u5e72\u6270\u3001\u8ddf\u8e2a\u6307\u4ee4\u6240\u9700\u7684\u529b\u77e9\uff0c\u5e76\u76f4\u63a5\u53e0\u52a0\u5230\u63a7\u5236\u5668\u8f93\u51fa\u4e2d\uff0c\u4ece\u800c\u63d0\u5347\u7535\u673a\u7684\u52a8\u6001\u54cd\u5e94\u901f\u5ea6\u548c\u63a7\u5236\u7cbe\u5ea6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b80\u5355\u6765\u8bf4\uff0c\u4f20\u7edf\u7684<strong>\u53cd\u9988\u63a7\u5236<\/strong>\uff08\u5982 PID\uff09\u662f \u201c\u4e8b\u540e\u8865\u6551\u201d\u2014\u2014 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class=\"wp-block-list\">\n<li><strong>\u63d0\u5347\u52a8\u6001\u54cd\u5e94\u901f\u5ea6<\/strong>\uff1a\u524d\u9988\u529b\u77e9\u63d0\u524d\u63d0\u4f9b\u4e86\u8ddf\u8e2a\u6307\u4ee4\u6240\u9700\u7684\u529b\u77e9\uff0c\u65e0\u9700\u7b49\u5f85\u53cd\u9988\u504f\u5dee\u79ef\u7d2f\uff0c\u7535\u673a\u80fd\u66f4\u5feb\u5730\u8ddf\u968f\u6307\u4ee4\u53d8\u5316\uff0c\u51cf\u5c11\u52a8\u6001\u6ede\u540e\u3002<\/li>\n\n\n\n<li><strong>\u63d0\u9ad8\u63a7\u5236\u7cbe\u5ea6<\/strong>\uff1a\u4e3b\u52a8\u62b5\u6d88\u5df2\u77e5\u6270\u52a8\uff08\u5982\u6469\u64e6\u3001\u91cd\u529b\u3001\u60ef\u6027\uff09\uff0c\u5927\u5e45\u964d\u4f4e\u7a33\u6001\u8bef\u5dee\uff0c\u5c24\u5176\u9002\u5408\u9ad8\u7cbe\u5ea6\u5b9a\u4f4d\u3001\u901f\u5ea6\u8ddf\u8e2a\u573a\u666f\uff08\u5982\u6570\u63a7\u673a\u5e8a\u3001\u4f3a\u670d\u673a\u68b0\u81c2\uff09\u3002<\/li>\n\n\n\n<li><strong>\u964d\u4f4e\u53cd\u9988\u63a7\u5236\u5668\u8d1f\u62c5<\/strong>\uff1a\u524d\u9988\u627f\u62c5\u4e86\u5927\u90e8\u5206 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src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"287\" class=\"wp-image-286\" style=\"width: 800px;\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/a3d2dc69-c5fa-4eb1-89c9-65c8de6e9281.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"  sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/div><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">3.\u8f6f\u4ef6\u91cd\u529b\u8865\u507f\u5e94\u7528<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u7535\u673a\u63a7\u5236\uff08\u5c24\u5176\u662f\u673a\u5668\u4eba\u5173\u8282\u3001\u673a\u68b0\u81c2\u8fd9\u7c7b\u9700\u8981\u529b\u63a7\u6216\u4f4d\u7f6e\u7cbe\u51c6\u4fdd\u6301\u7684\u573a\u666f\uff09\u4e2d\uff0c\u91cd\u529b\u8865\u507f\u662f\u4e00\u79cd\u62b5\u6d88\u8d1f\u8f7d\u81ea\u8eab\u91cd\u529b\u5bf9\u7535\u673a\u8f93\u51fa\u529b\u77e9\u5f71\u54cd\u7684\u63a7\u5236\u7b56\u7565\uff0c\u6838\u5fc3\u76ee\u7684\u662f\u8ba9\u7535\u673a\u53ea\u9700\u8f93\u51fa \u201c\u6709\u6548\u63a7\u5236\u529b\u77e9\u201d\uff0c\u800c\u975e\u989d\u5916\u627f\u62c5\u514b\u670d\u91cd\u529b\u7684\u529b\u77e9\uff0c\u4ece\u800c\u63d0\u5347\u63a7\u5236\u7cbe\u5ea6\u3001\u54cd\u5e94\u901f\u5ea6\u548c\u80fd\u6548\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6838\u5fc3\u539f\u7406\uff1a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u673a\u5668\u4eba\u5173\u8282\u4e3a\u4f8b\uff0c\u5173\u8282\u7535\u673a\u9a71\u52a8\u7684\u8fde\u6746 \/ \u8d1f\u8f7d\u4f1a\u56e0\u81ea\u8eab\u91cd\u91cf\u4ea7\u751f\u4e00\u4e2a<strong>\u91cd\u529b\u77e9<\/strong>\uff0c\u8fd9\u4e2a\u529b\u77e9\u7684\u5927\u5c0f\u548c\u65b9\u5411\u4f1a\u968f\u5173\u8282\u89d2\u5ea6\u53d8\u5316\u800c\u6539\u53d8\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u82e5\u6ca1\u6709\u91cd\u529b\u8865\u507f\uff1a\u7535\u673a\u9700\u8981\u540c\u65f6\u8f93\u51fa&nbsp;<strong>\u514b\u670d\u91cd\u529b\u7684\u529b\u77e9<\/strong>&nbsp;+&nbsp;<strong>\u5b9e\u73b0\u8fd0\u52a8 \/ \u4fdd\u6301\u4f4d\u7f6e\u7684\u63a7\u5236\u529b\u77e9<\/strong>\u3002<\/li>\n\n\n\n<li>\u82e5\u52a0\u5165\u91cd\u529b\u8865\u507f\uff1a\u9884\u5148\u8ba1\u7b97\u51fa\u5f53\u524d\u89d2\u5ea6\u4e0b\u7684\u91cd\u529b\u77e9\uff0c\u8ba9\u7535\u673a\u8f93\u51fa\u4e00\u4e2a\u5927\u5c0f\u76f8\u7b49\u3001\u65b9\u5411\u76f8\u53cd\u7684<strong>\u8865\u507f\u529b\u77e9<\/strong>\uff0c\u62b5\u6d88\u91cd\u529b\u7684\u5f71\u54cd\uff0c\u6b64\u65f6\u7535\u673a\u53ea\u9700\u8f93\u51fa \u201c\u63a7\u5236\u529b\u77e9\u201d \u5373\u53ef\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6570\u5b66\u8868\u8fbe\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u5355\u5173\u8282\u7535\u673a\uff0c\u91cd\u529b\u8865\u507f\u7684\u6838\u5fc3\u662f\u8ba1\u7b97<strong>\u91cd\u529b\u77e9<\/strong>&nbsp;<em>\u03c4g<\/em>\u200b\uff0c\u516c\u5f0f\u4e3a\uff1a<div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/3ad79713-db1b-4252-9311-6243bb89870d.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"87\" class=\"wp-image-287\" style=\"width: 600px;\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/3ad79713-db1b-4252-9311-6243bb89870d.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"  sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/div><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/cd9f5c0f-c868-47af-b0d3-4a1f36adc540.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"360\" class=\"wp-image-288\" style=\"width: 800px;\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/cd9f5c0f-c868-47af-b0d3-4a1f36adc540.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"  sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/div><\/li>\n\n\n\n<li>\u5728 MIT \u6a21\u5f0f\u7535\u673a\u63a7\u5236\u4e2d\uff0c\u91cd\u529b\u8865\u507f\u529b\u77e9\u901a\u5e38\u4f1a\u4f5c\u4e3a<strong>\u524d\u9988\u9879<\/strong>\uff08<em>cff<\/em>\u200b&nbsp;\u7684\u4e00\u90e8\u5206\uff09\u52a0\u5165\u63a7\u5236\u516c\u5f0f\uff1a<div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/01908962-9be1-487b-bead-29d59aad3196.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"84\" class=\"wp-image-282\" style=\"width: 800px;\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/01908962-9be1-487b-bead-29d59aad3196.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"  sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/div>\u6b64\u65f6\uff0c\u53c2\u8003\u7535\u6d41&nbsp;<em>cref<\/em>\u200b&nbsp;\u5df2\u7ecf\u5305\u542b\u4e86\u62b5\u6d88\u91cd\u529b\u7684\u5206\u91cf\uff0c\u7535\u673a\u8f93\u51fa\u7684\u529b\u77e9\u5c31\u80fd\u7cbe\u51c6\u8ddf\u8e2a\u6307\u4ee4\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u5173\u7cfb\u5f0f\u5b9e\u73b0\u65b9\u5f0f\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6a21\u578b\u6cd5\uff08\u5e38\u7528\uff09<\/strong>\uff1a\u57fa\u4e8e\u8d1f\u8f7d\u7684\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u901a\u8fc7\u7406\u8bba\u8ba1\u7b97\u5f97\u5230\u91cd\u529b\u77e9\u4e0e\u5173\u8282\u89d2\u5ea6\u7684\u5173\u7cfb\u3002\u9002\u5408\u5df2\u77e5\u8d1f\u8f7d\u53c2\u6570\uff08\u8d28\u91cf\u3001\u8d28\u5fc3\u4f4d\u7f6e\uff09\u7684\u573a\u666f\u3002<\/li>\n\n\n\n<li><strong>\u8fa8\u8bc6\u6cd5<\/strong>\uff1a\u82e5\u8d1f\u8f7d\u53c2\u6570\u672a\u77e5\uff0c\u53ef\u901a\u8fc7\u5b9e\u9a8c\u8fa8\u8bc6\uff1a\u63a7\u5236\u7535\u673a\u5728\u4e0d\u540c\u89d2\u5ea6\u4e0b\u4fdd\u6301\u9759\u6b62\uff0c\u8bb0\u5f55\u7535\u673a\u7684\u8f93\u51fa\u529b\u77e9\uff0c\u62df\u5408\u51fa\u91cd\u529b\u77e9\u4e0e\u89d2\u5ea6\u7684\u51fd\u6570\u5173\u7cfb\uff0c\u518d\u5c06\u5176\u4f5c\u4e3a\u8865\u507f\u9879\u3002<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">\u4e8c\u3001\u6f14\u793a<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6211\u5c06\u4ee5RM\u82f1\u96c4\u53d1\u5c04\u673a\u6784\u7684pitch\u7535\u673a\u4e3a\u4f8b\u5b50\uff0c\u4ee5\u8fa8\u8bc6\u6cd5\u7684\u65b9\u6cd5\u6765\u83b7\u5f97\u89d2\u5ea6\u548c\u91cd\u529b\u77e9\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u501f\u7528matlab\u8f6f\u4ef6\uff08\u7248\u672cR2024b\uff09\uff0c\u4f7f\u7528\u6b63\u5f26\u51fd\u6570\u4f5c\u4e3a\u62df\u5408\u51fd\u6570<\/strong>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b9e\u9a8c\u64cd\u4f5c\uff1a<\/h2>\n\n\n\n<details class=\"wp-block-details has-pale-pink-color has-text-color has-link-color wp-elements-c033dbf9331a01be4772017096e7a914 is-layout-flow wp-block-details-is-layout-flow\"><summary><strong>matlab\u4ee3\u7801<\/strong>\uff08\u70b9\u6211\uff09<\/summary>\n<pre class=\"wp-block-code\"><code>\u03c4(\u03b8) \u6b63\u5f26\u62df\u5408\uff08\u591a\u521d\u59cb\u503c+\u5206\u533a\u62df\u5408\u7248\uff09\nclear; clc; close all;\n\n% ---------------------- 1. \u8f93\u5165\u5b9e\u9a8c\u6570\u636e ----------------------\n%\u6ce8\u610f\uff0c\u4e3a\u4e86\u786e\u4fdd\u7cbe\u5ea6\uff0c\u6700\u597d\u591a\u6d4b\u70b9\u6570\u636e\uff0c\u4ece\u4e0a\u5f80\u4e0b\u548c\u4ece\u4e0b\u5f80\u4e0a\u4e24\u4e2a\u65b9\u5411\u5404\u6d4b\u8bd5\u4e00\u904d\uff0c\u89d2\u5ea6\u4e00\u5b9a\u4e0d\u8981\u56de\u62e8\uff01\u4e0d\u7136\u6469\u64e6\u529b\u5f71\u54cd\u5927\uff01\u5e76\u4e14\u4e24\u4e2a\u65b9\u5411\u6570\u636e\u6570\u91cf\u548c\u89d2\u5ea6\u95f4\u9694\u6700\u597d\u76f8\u540c\uff0c\u5982\u679c\u8f93\u51fa\u7684\u56fe\u50cf\u770b\u5230\u6709\u4e9b\u70b9\u7684\u6570\u636e\u504f\u5dee\u5f88\u5927\uff0c\u53ef\u4ee5\u8003\u8651\u79fb\u9664\u8fd9\u4e2a\u6570\u636e\u3002\ntheta = &#91;-0.663959,-0.651751,-0.644503,-0.636492,-0.621614,-0.610933,-0.603304,-0.592240,-0.580796,-0.562486,-0.551423,-0.543412,-0.530441,-0.510223,-0.501450,-0.491531,-0.482758,-0.470169,-0.461013,-0.450713,-0.441176,-0.431640,-0.420959,-0.412566,-0.401503,-0.390821,-0.381285,-0.371748,-0.360685,-0.350386,-0.341992,-0.330548,-0.321393,-0.311093,-0.300031,-0.280575,-0.250439,-0.242046,-0.231365,-0.220684,-0.210383,-0.200847,-0.191310,-0.180629,-0.170711,-0.160029,-0.152781,-0.142099,-0.130655,-0.120737,-0.111200,-0.100519,-0.081445,-0.060845,-0.051309];%\u8bf7\u586b\u5165\u81ea\u5df1\u7684\u5b9e\u9a8c\u6570\u636e\uff08\u89d2\u5ea6\uff09\ntau   = &#91;-0.466422,-0.564102,-0.354091,-0.539682,-0.373627,-0.485958,-0.305250,-0.349206,-0.310134,-0.578754,-0.485958,-0.368742,-0.544566,-0.373627,-0.315019,-0.603174,-0.564102,-0.573871,-0.378510,-0.490843,-0.598290,-0.363858,-0.388278,-0.612943,-0.603174,-0.417583,-0.485958,-0.363858,-0.671551,-0.412699,-0.622710,-0.398046,-0.495727,-0.661782,-0.407814,-0.671551,-0.437119,-0.647131,-0.451771,-0.583638,-0.612943,-0.656898,-0.671551,-0.695971,-0.427350,-0.432235,-0.710623,-0.681318,-0.735043,-0.466422,-0.700854,-0.456655,-0.446886,-0.676435,-0.705739];%\u8bf7\u586b\u5165\u81ea\u5df1\u7684\u5b9e\u9a8c\u6570\u636e\uff08\u529b\u77e9\uff09\n\n% \u6570\u636e\u957f\u5ea6\u68c0\u67e5\nif length(theta) ~= length(tau)\n    error('\u03b8\u548c\u03c4\u6570\u636e\u957f\u5ea6\u5fc5\u987b\u4e00\u81f4\uff01');\nend\n\n% ---------------------- 2. \u5b9a\u4e49\u6b63\u5f26\u62df\u5408\u6a21\u578b ----------------------\nfit_fun = @(p, x) p(1)*sin(x - p(2)) + p(3);  % \u03c4 = (m\/L)*sin(\u03b8 - \u03b80) + C\n\n% ---------------------- 3. \u591a\u521d\u59cb\u503c\u751f\u6210\uff08\u5168\u5c40\u62df\u5408\uff09 ----------------------\nA_min = 0.3*max(tau); A_max = 1.7*max(tau);\ntheta0_min = -pi; theta0_max = pi; \nC_min = -0.2*mean(tau); C_max = 1.2*mean(tau);\n\nA_list = linspace(A_min, A_max, 4);\ntheta0_list = linspace(theta0_min, theta0_max, 4);\nC_list = linspace(C_min, C_max, 3);\n\ninit_guess = &#91;];\nfor i = 1:length(A_list)\n    for j = 1:length(theta0_list)\n        for k = 1:length(C_list)\n            init_guess = &#91;init_guess; A_list(i), theta0_list(j), C_list(k)];\n        end\n    end\nend\nfprintf('\u751f\u6210 %d \u7ec4\u521d\u59cb\u503c\uff08\u5168\u5c40\u62df\u5408\uff09\\n', size(init_guess,1));\n\n% ---------------------- 4. \u5168\u5c40\u62df\u5408\uff08\u539f\u84dd\u7ebf\uff09 ----------------------\noptions = optimoptions('lsqcurvefit','Display','off');\noptions.MaxFunctionEvaluations = 20000;\noptions.MaxIterations = 2000;\noptions.TolFun = 1e-12;\noptions.TolX = 1e-12;\n\nbest_res = inf;\nbest_p = &#91;];\nfor idx = 1:size(init_guess,1)\n    p0 = init_guess(idx,:);\n    try\n        &#91;p, res] = lsqcurvefit(fit_fun, p0, theta, tau, &#91;], &#91;], options);\n        if res &lt; best_res\n            best_res = res;\n            best_p = p;\n        end\n    catch\n        fprintf('\u7b2c%d\u7ec4\u521d\u59cb\u503c\uff08\u5168\u5c40\uff09\u62df\u5408\u5931\u8d25\uff0c\u8df3\u8fc7\\n',idx);\n        continue;\n    end\nend\n\n% \u5168\u5c40\u62df\u5408\u7ed3\u679c\nm_over_L = best_p(1);\ntheta0 = best_p(2);\nC = best_p(3);\ntau_fit = fit_fun(best_p, theta);  % \u5168\u5c40\u62df\u5408\u84dd\u7ebf\u7684\u6570\u503c\ntheta_smooth = linspace(min(theta),max(theta),500);\ntau_smooth_global = fit_fun(best_p, theta_smooth);\n\n% ---------------------- 5. \u6309\u84dd\u7ebf\u5212\u5206\u4e0a\u4e0b\u90e8\u5206\u6570\u636e ----------------------\nresidual = tau - tau_fit;  % \u6b8b\u5dee\uff1a\u539f\u59cb\u70b9 - \u84dd\u7ebf\u503c\n% \u4e0a\u90e8\u5206\uff1a\u6b8b\u5dee&gt;0\uff08\u70b9\u5728\u84dd\u7ebf\u4e0a\u65b9\uff09\uff1b\u4e0b\u90e8\u5206\uff1a\u6b8b\u5dee&lt;0\uff08\u70b9\u5728\u84dd\u7ebf\u4e0b\u65b9\uff09\nidx_upper = residual &gt; 0;  % \u4e0a\u90e8\u5206\u7d22\u5f15\nidx_lower = residual &lt; 0;  % \u4e0b\u90e8\u5206\u7d22\u5f15\n\n% \u63d0\u53d6\u4e0a\u4e0b\u90e8\u5206\u6570\u636e\ntheta_upper = theta(idx_upper);\ntau_upper   = tau(idx_upper);\ntheta_lower = theta(idx_lower);\ntau_lower   = tau(idx_lower);\n\nfprintf('\\n===== \u6570\u636e\u5212\u5206\u7ed3\u679c =====\\n');\nfprintf('\u4e0a\u90e8\u5206\u70b9\u6570\uff1a%d \u4e2a\\n', length(theta_upper));\nfprintf('\u4e0b\u90e8\u5206\u70b9\u6570\uff1a%d \u4e2a\\n', length(theta_lower));\n\n% ---------------------- 6. \u4e0a\u90e8\u5206\u6570\u636e\u5355\u72ec\u62df\u5408 ----------------------\nif ~isempty(theta_upper)\n    fprintf('\\n===== \u4e0a\u90e8\u5206\u62df\u5408 =====\\n');\n    best_res_upper = inf;\n    best_p_upper = &#91;];\n    for idx = 1:size(init_guess,1)\n        p0 = init_guess(idx,:);\n        try\n            &#91;p, res] = lsqcurvefit(fit_fun, p0, theta_upper, tau_upper, &#91;], &#91;], options);\n            if res &lt; best_res_upper\n                best_res_upper = res;\n                best_p_upper = p;\n            end\n        catch\n            fprintf('\u7b2c%d\u7ec4\u521d\u59cb\u503c\uff08\u4e0a\u90e8\u5206\uff09\u62df\u5408\u5931\u8d25\uff0c\u8df3\u8fc7\\n',idx);\n            continue;\n        end\n    end\n    % \u4e0a\u90e8\u5206\u62df\u5408\u7ed3\u679c\n    m_over_L_upper = best_p_upper(1);\n    theta0_upper = best_p_upper(2);\n    C_upper = best_p_upper(3);\n    tau_smooth_upper = fit_fun(best_p_upper, theta_smooth);\n    % \u4e0a\u90e8\u5206R\u00b2\n    tau_fit_upper = fit_fun(best_p_upper, theta_upper);\n    SSE_upper = sum((tau_upper - tau_fit_upper).^2);\n    SST_upper = sum((tau_upper - mean(tau_upper)).^2);\n    R2_upper = 1 - SSE_upper\/SST_upper;\n    % \u6253\u5370\u4e0a\u90e8\u5206\u7ed3\u679c\n    fprintf('m\/L\uff08\u4e0a\uff09= %.8f\\n', m_over_L_upper);\n    fprintf('\u03b80\uff08\u4e0a\uff0c\u5f27\u5ea6\uff09= %.8f \uff08\u89d2\u5ea6=%.4f\u00b0\uff09\\n', theta0_upper, rad2deg(theta0_upper));\n    fprintf('\u504f\u7f6eC\uff08\u4e0a\uff09= %.8f\\n', C_upper);\n    fprintf('R\u00b2\uff08\u4e0a\uff09= %.8f\\n', R2_upper);\nelse\n    fprintf('\\n\u65e0\u4e0a\u90e8\u6570\u636e\u70b9\uff0c\u8df3\u8fc7\u4e0a\u90e8\u5206\u62df\u5408\\n');\n    tau_smooth_upper = nan(size(theta_smooth));\nend\n\n% ---------------------- 7. \u4e0b\u90e8\u5206\u6570\u636e\u5355\u72ec\u62df\u5408 ----------------------\nif ~isempty(theta_lower)\n    fprintf('\\n===== \u4e0b\u90e8\u5206\u62df\u5408 =====\\n');\n    best_res_lower = inf;\n    best_p_lower = &#91;];\n    for idx = 1:size(init_guess,1)\n        p0 = init_guess(idx,:);\n        try\n            &#91;p, res] = lsqcurvefit(fit_fun, p0, theta_lower, tau_lower, &#91;], &#91;], options);\n            if res &lt; best_res_lower\n                best_res_lower = res;\n                best_p_lower = p;\n            end\n        catch\n            fprintf('\u7b2c%d\u7ec4\u521d\u59cb\u503c\uff08\u4e0b\u90e8\u5206\uff09\u62df\u5408\u5931\u8d25\uff0c\u8df3\u8fc7\\n',idx);\n            continue;\n        end\n    end\n    % \u4e0b\u90e8\u5206\u62df\u5408\u7ed3\u679c\n    m_over_L_lower = best_p_lower(1);\n    theta0_lower = best_p_lower(2);\n    C_lower = best_p_lower(3);\n    tau_smooth_lower = fit_fun(best_p_lower, theta_smooth);\n    % \u4e0b\u90e8\u5206R\u00b2\n    tau_fit_lower = fit_fun(best_p_lower, theta_lower);\n    SSE_lower = sum((tau_lower - tau_fit_lower).^2);\n    SST_lower = sum((tau_lower - mean(tau_lower)).^2);\n    R2_lower = 1 - SSE_lower\/SST_lower;\n    % \u6253\u5370\u4e0b\u90e8\u5206\u7ed3\u679c\n    fprintf('m\/L\uff08\u4e0b\uff09= %.8f\\n', m_over_L_lower);\n    fprintf('\u03b80\uff08\u4e0b\uff0c\u5f27\u5ea6\uff09= %.8f \uff08\u89d2\u5ea6=%.4f\u00b0\uff09\\n', theta0_lower, rad2deg(theta0_lower));\n    fprintf('\u504f\u7f6eC\uff08\u4e0b\uff09= %.8f\\n', C_lower);\n    fprintf('R\u00b2\uff08\u4e0b\uff09= %.8f\\n', R2_lower);\nelse\n    fprintf('\\n\u65e0\u4e0b\u90e8\u6570\u636e\u70b9\uff0c\u8df3\u8fc7\u4e0b\u90e8\u5206\u62df\u5408\\n');\n    tau_smooth_lower = nan(size(theta_smooth));\nend\n\n% ---------------------- 8. \u53ef\u89c6\u5316\uff1a\u5206\u533a\u62df\u5408\u7ed3\u679c ----------------------\nfigure('Color','white','Position',&#91;100,100,1200,600]);\n\n% \u5b50\u56fe1\uff1a\u5206\u533a\u6570\u636e+\u5168\u5c40\/\u5206\u533a\u62df\u5408\u66f2\u7ebf\nsubplot(1,2,1);\n% \u7ed8\u5236\u539f\u59cb\u70b9\uff08\u4e0a\u7ea2\uff0c\u4e0b\u7eff\uff09\nplot(theta_upper, tau_upper, 'ro', 'MarkerSize',6,'MarkerFaceColor','r','DisplayName','\u4e0a\u90e8\u5206\u70b9'); hold on;\nplot(theta_lower, tau_lower, 'go', 'MarkerSize',6,'MarkerFaceColor','g','DisplayName','\u4e0b\u90e8\u5206\u70b9');\n% \u7ed8\u5236\u62df\u5408\u66f2\u7ebf\uff08\u5168\u5c40\u84dd\uff0c\u4e0a\u6a59\uff0c\u4e0b\u7d2b\uff09\nplot(theta_smooth, tau_smooth_global, 'b-','LineWidth',2,'DisplayName','\u5168\u5c40\u62df\u5408\u7ebf');\nplot(theta_smooth, tau_smooth_upper, 'o-','Color',&#91;1 0.5 0],'LineWidth',2,'MarkerSize',1,'DisplayName','\u4e0a\u90e8\u5206\u62df\u5408\u7ebf');\nplot(theta_smooth, tau_smooth_lower, 'm-','LineWidth',2,'DisplayName','\u4e0b\u90e8\u5206\u62df\u5408\u7ebf');\nxlabel('\u03b8 (rad)'); ylabel('\u03c4(\u03b8)');\ntitle('\u5206\u533a\u6570\u636e\u4e0e\u62df\u5408\u66f2\u7ebf');\ngrid on; legend('Location','best');\nxlim(&#91;-0.67 0.00]);\nylim(&#91;-1.200 -0.800]);  % \u6309\u4f60\u7684\u9700\u6c42\u8c03\u6574y\u8f74\u8303\u56f4\n\n% \u5b50\u56fe2\uff1a\u5206\u533a\u6b8b\u5dee\nsubplot(1,2,2);\n% \u4e0a\u90e8\u5206\u6b8b\u5dee\uff08\u7ea2\uff09\nif ~isempty(theta_upper)\n    residual_upper = tau_upper - fit_fun(best_p_upper, theta_upper);\n    plot(theta_upper, residual_upper, 'ro', 'MarkerSize',6,'MarkerFaceColor','r','DisplayName','\u4e0a\u90e8\u5206\u6b8b\u5dee'); hold on;\nend\n% \u4e0b\u90e8\u5206\u6b8b\u5dee\uff08\u7eff\uff09\nif ~isempty(theta_lower)\n    residual_lower = tau_lower - fit_fun(best_p_lower, theta_lower);\n    plot(theta_lower, residual_lower, 'go', 'MarkerSize',6,'MarkerFaceColor','g','DisplayName','\u4e0b\u90e8\u5206\u6b8b\u5dee'); hold on;\nend\nyline(0,'r--');\nxlabel('\u03b8 (rad)'); ylabel('\u6b8b\u5dee');\ntitle('\u5206\u533a\u62df\u5408\u6b8b\u5dee\u5206\u5e03');\ngrid on; legend('Location','best');\nxlim(&#91;-0.67 0.00]);\n\n% ---------------------- 9. \u5168\u5c40\u62df\u5408\u7ed3\u679c\uff08\u8865\u5145\uff09 ----------------------\n% \u5168\u5c40R\u00b2\nSSE = sum((tau - tau_fit).^2);\nSST = sum((tau - mean(tau)).^2);\nR2 = 1 - SSE\/SST;\nfprintf('\\n===== \u5168\u5c40\u62df\u5408\u7ed3\u679c =====\\n');\nfprintf('m\/L = %.8f\\n', m_over_L);\nfprintf('\u03b80\uff08\u5f27\u5ea6\uff09= %.8f \uff08\u89d2\u5ea6=%.4f\u00b0\uff09\\n', theta0, rad2deg(theta0));\nfprintf('\u504f\u7f6eC = %.8f\\n', C);\nfprintf('\u62df\u5408\u4f18\u5ea6R\u00b2 = %.8f\\n', R2);\nfprintf('\u6b8b\u5dee\u5e73\u65b9\u548cSSE = %.8f\\n', best_res);\n<\/code><\/pre>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd0\u884c\u540e\u6211\u4eec\u80fd\u5f97\u5230\u4ee5\u4e0b\u56fe\u50cf\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/01a12e17-dc13-4d1d-a084-60dd20915ba2-1024x580.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"580\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/01a12e17-dc13-4d1d-a084-60dd20915ba2-1024x580.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-290\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/b711801d-41dd-46a2-a6c9-0ae09e6a0bc5-837x1024.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"837\" height=\"1024\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/b711801d-41dd-46a2-a6c9-0ae09e6a0bc5-837x1024.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-292\"  sizes=\"auto, (max-width: 837px) 100vw, 837px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/963e75ad-33e0-4a6b-91ef-ee22818f6a12.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"417\" height=\"238\" data-original=\"http:\/\/114.55.133.236\/wp-content\/uploads\/2025\/12\/963e75ad-33e0-4a6b-91ef-ee22818f6a12.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-291\"  sizes=\"auto, (max-width: 417px) 100vw, 417px\" \/><\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b9e\u9a8c\u5206\u6790\uff1a<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u770b\u56fe\u53d1\u73b0\uff0c\u8fd9\u91cc\u4f1a\u51fa\u73b0\u4e24\u6761\u62df\u51fd\u6570\u7ebf\uff0c\u5e76\u4e14\u5bf9\u4e8e\u6570\u636e\u70b9\u4f4d\uff0c\u76f8\u540c\u4f4d\u7f6e\uff0c\u4f46\u662f\u4e0d\u540c\u8fd0\u52a8\u65b9\u5411\u4e0b\uff0c\u7535\u673a\u529b\u77e9\u662f\u4e0d\u4e00\u6837\u7684\uff0c\u8fd9\u662f\u4e3a\u4ec0\u4e48\u5462\uff1f\u8fd9\u91cc\u6709\u4e00\u79cd\u731c\u6d4b\uff0cpitch\u7535\u673a\u7684\u5916\u90e8\u53d1\u5c04\u7ed3\u6784\u7684\u6709\u6469\u64e6\u529b\u7684\u5f71\u54cd\u3002\u5f53\u53d1\u5c04\u673a\u6784\u4e0a\u62ac\u7684\u65f6\u5019\uff0c\u6b64\u65f6\u8fdb\u884c\u53d7\u529b\u5206\u6790\uff0c\u7535\u673a\u8981\u4e0d\u4ec5\u8981\u514b\u670d\u91cd\u529b\u7684\u4f5c\u7528\uff0c\u8fd8\u8981\u514b\u670d\u6469\u64e6\u529b\uff0c\u6240\u4ee5\u7535\u673a\u9700\u8981\u66f4\u5927\u7684\u529b\u77e9\u6765\u62ac\u5347\u3002\u5f53\u53d1\u5c04\u673a\u6784\u4e0b\u964d\u7684\u65f6\u5019\uff0c\u6b64\u65f6\u8fdb\u884c\u53d7\u529b\u5206\u6790\uff0c\u91cd\u529b\u548c\u6469\u64e6\u529b\u53cd\u5411\uff0c\u6469\u64e6\u529b\u62b5\u6d88\u4e86\u4e00\u90e8\u5206\u91cd\u529b\uff0c\u6240\u4ee5\u7535\u673a\u9700\u8981\u7684\u529b\u77e9\u4f1a\u6bd4\u8f83\u5c0f\u3002\u7406\u8bba\u4e0a\uff0c\u4e24\u79cd\u60c5\u51b5\u5bf9\u5e94\u7684\u5c31\u662f\u8fd9\u4e0a\u4e0b\u4e24\u4e2a\u62df\u5408\u51fd\u6570\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u9a8c\u8bc1\u4e00\u4e0b\u3002<\/p>\n\n\n\n<figure 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