{"id":23301,"date":"2024-03-15T10:21:44","date_gmt":"2024-03-15T02:21:44","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=23301"},"modified":"2024-03-19T18:33:11","modified_gmt":"2024-03-19T10:33:11","slug":"%e9%9a%8f%e6%9c%ba%e6%8c%af%e5%8a%a8-%e9%9a%8f%e6%9c%ba%e8%bf%87%e7%a8%8b%e4%b8%ad%e7%9a%84%e7%a8%b3%e6%80%81%e4%b8%8e%e5%90%84%e6%80%81%e5%8e%86%e7%bb%8f-stationarity-and-ergodicity-in-random-proc","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=23301","title":{"rendered":"[\u6570\u5b66][\u7b14\u8bb0] \u968f\u673a\u8fc7\u7a0b\u4e2d\u7684\u5e73\u7a33\u4e0e\u5404\u6001\u5386\u7ecf (Stationarity and ergodicity in random processes)"},"content":{"rendered":"<p><span style=\"color: #ff00ff; background-color: #ccffcc;\"><strong>\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002<\/strong><\/span><\/p>\n<hr \/>\n<p>\u5b66\u4e60\u968f\u673a\u632f\u52a8\u5206\u6790\u9700\u8981\u641e\u6e05\u695a \u4e24\u4e2a\u6700\u91cd\u8981\u7684\u968f\u673a\u8fc7\u7a0b\u7279\u6027\uff1a<strong>\u5e73\u7a33\u6027\uff08Stationarity \uff09<\/strong>\u53ca<strong>\u5404\u6001\u5386\u7ecf\uff08ergodicity \uff09<\/strong>\u3002<\/p>\n<p><strong>[\u5e73\u7a33\u6027] <\/strong>\u6307\u7684\u662f\u968f\u673a\u8fc7\u7a0b\u7684\u6982\u7387\u7279\u6027\uff08\u5982\u671f\u671b\u503c\u3001\u81ea\u76f8\u5173\u51fd\u6570\u7b49\uff09\u4e0e\u65f6\u95f4\u65e0\u5173\u3002<\/p>\n<p><strong>[\u5404\u6001\u5386\u7ecf] \u5404\u6001\u5386\u7ecf\u4e5f\u79f0\u4e3a\u904d\u5386\u6027\uff0c<\/strong>\u6307\u7684\u662f\u4e00\u4e2a\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\u4efb\u610f\u6837\u672c\u51fd\u6570\u7684\u65f6\u95f4\u5e73\u5747\u90fd\u76f8\u7b49\uff0c\u4e14\u7b49\u4e8e\u96c6\u5408\u7684\u5e73\u5747\u3002\u5176\u6700\u5927\u4f5c\u7528\u662f\uff0c\u6709\u4e86\u5404\u6001\u5386\u7ecf\u5047\u5b9a\uff0c\u610f\u5473\u7740\u53ef\u4ee5\u901a\u8fc7\u5bf9\u4e00\u4e2a\u5177\u4f53\u7684\u6837\u672c\u8fdb\u884c\u5206\u6790\uff0c\u83b7\u5f97\u603b\u4f53\u96c6\u5408\u7684\u6982\u7387\u7279\u6027\u3002<\/p>\n<p>\u4e00\u4e2a\u968f\u673a\u8fc7\u7a0b\u5177\u6709\u5e73\u7a33\u6027\uff0c\u5219\u63cf\u8ff0\u8d77\u6765\u5927\u5927\u7b80\u5316\uff0c\u6bd4\u5982\uff0c\u53ea\u9700\u8981\u7528\u4e00\u4e2a\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u63cf\u8ff0\u5404\u4e2a\u65f6\u95f4\u70b9\u7684\u6982\u7387\u5206\u5e03\u7279\u6027\uff0c\u56e0\u4e3a\u968f\u673a\u8fc7\u7a0b\u7684\u6982\u7387\u7279\u6027\u4e0d\u968f\u65f6\u95f4\u6539\u53d8\u3002\u5f88\u591a\u975e\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\u7684\u7814\u7a76\uff0c\u4e5f\u91c7\u7528\u4ee5\u5e73\u7a33\u8fc7\u7a0b\u4e3a\u7814\u7a76\u5165\u624b\uff0c\u7136\u540e\u901a\u8fc7\u67d0\u79cd\u65b9\u5f0f\u8fdb\u884c\u975e\u5e73\u7a33\u968f\u673a\u4fee\u6b63\u3002<\/p>\n<p>\u5982\u679c\u4e00\u4e2a\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\u5177\u6709\u5404\u6001\u5386\u7ecf\u6027\uff0c\u540c\u6837\u53ef\u4ee5\u5927\u5927\u7b80\u5316\u968f\u673a\u8fc7\u7a0b\u7684\u5206\u6790\u3002\u5982\u524d\u6240\u8ff0\uff0c\u6709\u4e86\u5404\u6001\u5386\u7ecf\u5047\u5b9a\uff0c\u610f\u5473\u7740\u53ef\u4ee5\u901a\u8fc7\u5206\u6790\u4e00\u4e2a\u5177\u4f53\u7684\u6837\u672c\u7684\u65b9\u5f0f\u83b7\u5f97\u603b\u4f53\u96c6\u5408\u7684\u6982\u7387\u7279\u6027\u3002\u5982\u679c\u6ca1\u6709\u5404\u6001\u5386\u7ecf\uff0c\u8981\u83b7\u5f97\u968f\u673a\u8fc7\u7a0b\u7684\u6982\u7387\u7279\u6027\uff0c\u5219\u9700\u8981\u8db3\u591f\u5927\u7684\u6837\u672c\uff0c\u8fdb\u884c\u6837\u672c\u95f4\u7edf\u8ba1\uff0c\u8fd9\u5728\u5927\u591a\u6570\u5b9e\u9645\u60c5\u51b5\u5747\u4e0d\u5177\u5907\u53ef\u884c\u6027\u3002<\/p>\n<p>\u7ec8\u4e0a\u6240\u8ff0\uff0c\u5e73\u7a33\u53ca\u5404\u6001\u5386\u7ecf\u7279\u6027\u662f\u6bd4\u8f83\u7406\u60f3\u7684\uff0c\u5e76\u4e0d\u662f\u6240\u6709\u968f\u673a\u8fc7\u7a0b\u90fd\u6ee1\u8db3\uff0c\u4f46\u4ece\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u8bb2\uff0c\u968f\u673a\u8fc7\u7a0b\u5177\u6709\u5e73\u7a33\u53ca\u5404\u6001\u5386\u7ecf\u7279\u6027\uff0c\u7814\u7a76\u624d\u5177\u6709\u53ef\u884c\u6027\u554a\u3002<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u76f8\u5173\u535a\u6587<span style=\"color: #0000ff;\">( Related Topics)<\/span><\/strong><\/li>\n<\/ul>\n<p><strong>[01] <a title=\"[\u7b14\u8bb0] \u968f\u673a\u8fc7\u7a0b\u4e2d\u7684\u5e73\u7a33\u4e0e\u5404\u6001\u5386\u7ecf (Stationarity and ergodicity in random processes)\" href=\"http:\/\/www.jdcui.com\/?p=23301\" target=\"_blank\" rel=\"noopener\">[\u7b14\u8bb0] \u968f\u673a\u8fc7\u7a0b\u4e2d\u7684\u5e73\u7a33\u4e0e\u5404\u6001\u5386\u7ecf (Stationarity and ergodicity in random processes)<\/a><\/strong><\/p>\n<p><strong>[02]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u632f\u52a8\u63a7\u5236] \u5e38\u89c1\u8d28\u91cf\u963b\u5c3c\u5668\u5206\u7c7b [Passive, semi-active, active and hybrid mass dampers]\" href=\"http:\/\/www.jdcui.com\/?p=22357\" target=\"_blank\" rel=\"noopener\">[\u632f\u52a8\u63a7\u5236] \u5e38\u89c1\u8d28\u91cf\u963b\u5c3c\u5668\u5206\u7c7b [Passive, semi-active, active and hybrid mass dampers]<\/a><\/span><\/strong><\/p>\n<p><strong>[03]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u8f6f\u4ef6] SDOF_FRE \u6848\u4f8b 2 \u2014\u2014 \u5730\u9707\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 2: Earthquake Time History Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20090\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u8f6f\u4ef6] SDOF_FRE \u6848\u4f8b 2 \u2014\u2014 \u5730\u9707\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 2: Earthquake Time History Analysis]<\/a><\/strong><\/p>\n<p><strong>[04]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE: Dynamic Response Analysis of SDOF System using Frequency Domain Analysis Method [\u5355\u81ea\u7531\u5ea6\u4f53\u7cfb\u52a8\u529b\u54cd\u5e94\u9891\u57df\u5206\u6790\u7a0b\u5e8f]\" href=\"http:\/\/www.jdcui.com\/?p=18955\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE: Dynamic Response Analysis of SDOF System using Frequency Domain Analysis Method [\u5355\u81ea\u7531\u5ea6\u4f53\u7cfb\u52a8\u529b\u54cd\u5e94\u9891\u57df\u5206\u6790\u7a0b\u5e8f]<\/a><\/strong><\/p>\n<p><strong>[05]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE \u6848\u4f8b1 \u2014\u2014 \u52a8\u529b\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 1: Dynamic Force Time History Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20087\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE \u6848\u4f8b1 \u2014\u2014 \u52a8\u529b\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 1: Dynamic Force Time History Analysis]<\/a><\/strong><\/p>\n<p><strong>[06]\u00a0<a title=\"[\u7b14\u8bb0][\u6570\u5b66] \u8109\u51b2\u51fd\u6570\u516c\u5f0f\u63a8\u5bfc [Derivation of Delta Function]\" href=\"http:\/\/www.jdcui.com\/?p=20957\" target=\"_blank\" rel=\"noopener\">[\u7b14\u8bb0][\u6570\u5b66] \u8109\u51b2\u51fd\u6570\u516c\u5f0f\u63a8\u5bfc [Derivation of Delta Function]<\/a><\/strong><\/p>\n<p><strong>[07]\u00a0<a title=\"[Dynamics][\u52a8\u529b\u5b66][SAP2000] \u6881\u7684\u632f\u52a8\u5f62\u6001\u53ca\u632f\u578b\u8d28\u91cf (Vibration Modes and Modal Mass of Beams)\" href=\"http:\/\/www.jdcui.com\/?p=15984\" target=\"_blank\" rel=\"noopener\">[Dynamics][\u52a8\u529b\u5b66][SAP2000] \u6881\u7684\u632f\u52a8\u5f62\u6001\u53ca\u632f\u578b\u8d28\u91cf (Vibration Modes and Modal Mass of Beams)<\/a><\/strong><\/p>\n<p><strong>[08]\u00a0<a title=\"[\u8f6f\u4ef6][\u5730\u9707\u6ce2][\u6297\u9707] GMS_RESEARCH: Ground Motion Selection Program for Research [\u57fa\u4e8e\u76ee\u6807\u8c31\u5339\u914d\u6cd5\u5730\u9707\u6ce2\u9009\u6ce2\u5de5\u5177 \u79d1\u7814\u7248]\" href=\"http:\/\/www.jdcui.com\/?p=23253\" target=\"_blank\" rel=\"noopener\">[\u8f6f\u4ef6][\u5730\u9707\u6ce2][\u6297\u9707] GMS_RESEARCH: Ground Motion Selection Program for Research [\u57fa\u4e8e\u76ee\u6807\u8c31\u5339\u914d\u6cd5\u5730\u9707\u6ce2\u9009\u6ce2\u5de5\u5177 \u79d1\u7814\u7248]<\/a><\/strong><\/p>\n<p><strong>[09]\u00a0<a title=\"[\u8f6f\u4ef6][\u8bd5\u9a8c][\u7f16\u7a0b] NoiseRemoval: A Program for De-Noising of Experimental Data [\u8bd5\u9a8c\u6570\u636e\u964d\u566a\u4fee\u6b63\u5de5\u5177]\" href=\"http:\/\/www.jdcui.com\/?p=15046\" target=\"_blank\" rel=\"noopener noreferrer\">[\u8f6f\u4ef6][\u8bd5\u9a8c][\u7f16\u7a0b] NoiseRemoval: A Program for De-Noising of Experimental Data [\u8bd5\u9a8c\u6570\u636e\u964d\u566a\u4fee\u6b63\u5de5\u5177]<\/a><\/strong><\/p>\n<p><strong>[10]\u00a0<a title=\"[\u5de5\u5177][\u8bd5\u9a8c][\u66f4\u65b0] DataSmoothing v2022: A Program for Test Data Smoothing [\u8bd5\u9a8c\u6570\u636e\u66f2\u7ebf\u5e73\u6ed1+\u964d\u566a\u5de5\u5177]\" href=\"http:\/\/www.jdcui.com\/?p=18744\" target=\"_blank\" rel=\"noopener\">[\u5de5\u5177][\u8bd5\u9a8c][\u66f4\u65b0] DataSmoothing v2022: A Program for Test Data Smoothing [\u8bd5\u9a8c\u6570\u636e\u66f2\u7ebf\u5e73\u6ed1+\u964d\u566a\u5de5\u5177]<\/a><\/strong><\/p>\n<p><strong>[11]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b][\u6570\u5b66][\u4fe1\u53f7\u5904\u7406] \u4e09\u5206\u4e4b\u4e00\u500d\u9891\u7a0b\u8c31\u5206\u6790 [1\/3 Octave Spectra Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20164\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b][\u6570\u5b66][\u4fe1\u53f7\u5904\u7406] \u4e09\u5206\u4e4b\u4e00\u500d\u9891\u7a0b\u8c31\u5206\u6790 [1\/3 Octave Spectra Analysis]<\/a><\/span><\/strong><\/p>\n<p><strong>[12]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7f16\u7a0b] \u8499\u7279\u5361\u6d1b\u6a21\u62df\u6cd5\u6c42\u5706\u5468\u7387\u03c0 (Monte Carlo method to find PI)\" href=\"http:\/\/www.jdcui.com\/?p=17385\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7f16\u7a0b] \u8499\u7279\u5361\u6d1b\u6a21\u62df\u6cd5\u6c42\u5706\u5468\u7387\u03c0 (Monte Carlo method to find PI)<\/a><\/span><\/strong><\/p>\n<p><strong>[13] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7f16\u7a0b][\u6df7\u6c8c] \u866b\u53e3\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df [Numerical simulation of insect population model]\" href=\"http:\/\/www.jdcui.com\/?p=17603\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7f16\u7a0b][\u6df7\u6c8c] \u866b\u53e3\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df [Numerical simulation of insect population model]<\/a><\/span><\/strong><\/p>\n<p><strong>[14] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7b97\u6cd5][\u7f16\u7a0b\u8bad\u7ec3] \u6700\u5c0f\u4e8c\u4e58\u6cd5\u66f2\u7ebf\u62df\u5408( Least square curve fitting )\" href=\"http:\/\/www.jdcui.com\/?p=15600\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7b97\u6cd5][\u7f16\u7a0b\u8bad\u7ec3] \u6700\u5c0f\u4e8c\u4e58\u6cd5\u66f2\u7ebf\u62df\u5408( Least square curve fitting )<\/a><\/span><\/strong><\/p>\n<p><strong>[15] <span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b][\u6570\u5b66][\u51e0\u4f55] \u7f16\u7a0b\u8bad\u7ec3: \u62c9\u6885\u66f2\u7ebf |x|^n+|y|^n=1 \u53f7\u79f0200\u4e07\u7684\u5c0f\u7c73logo\u8f6e\u5ed3\u66f2\u7ebf (\u65b9\u4e0e\u5706\u7684\u8f6c\u53d8)\" href=\"http:\/\/www.jdcui.com\/?p=16029\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b][\u6570\u5b66][\u51e0\u4f55] \u7f16\u7a0b\u8bad\u7ec3: \u62c9\u6885\u66f2\u7ebf |x|^n+|y|^n=1 \u53f7\u79f0200\u4e07\u7684\u5c0f\u7c73logo\u8f6e\u5ed3\u66f2\u7ebf (\u65b9\u4e0e\u5706\u7684\u8f6c\u53d8)<\/a><\/span><\/strong><\/p>\n<p><strong>[16] <span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b\u8bad\u7ec3][\u6e38\u620f][\u6570\u5b66] \u7ea2\u9152\u676f\u4e0e\u767d\u9152\u676f\u91cc\u5230\u5e95\u6709\u591a\u5c11\u7ea2\u9152\u548c\u767d\u9152\uff1f\" href=\"http:\/\/www.jdcui.com\/?p=14118\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b\u8bad\u7ec3][\u6e38\u620f][\u6570\u5b66] \u7ea2\u9152\u676f\u4e0e\u767d\u9152\u676f\u91cc\u5230\u5e95\u6709\u591a\u5c11\u7ea2\u9152\u548c\u767d\u9152\uff1f<\/a><\/span><\/strong><\/p>\n<p><strong>[17] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u6982\u7387] Buffon\u2019s Needle problem [\u84b2\u4e30\u6295\u9488\u95ee\u9898]\" href=\"http:\/\/www.jdcui.com\/?p=1301\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u6982\u7387] Buffon\u2019s Needle problem [\u84b2\u4e30\u6295\u9488\u95ee\u9898]<\/a><\/span><\/strong><\/p>\n<p><strong>[18] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66] \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f (Several Forms of Fourier Transform Formulas)\" href=\"http:\/\/www.jdcui.com\/?p=23278\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66] \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f (Several Forms of Fourier Transform Formulas)<\/a><\/span><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: center;\"><strong>\u7ed3\u6784|\u8d85\u9650|\u8f6f\u4ef6\u5f00\u53d1|\u7f16\u7a0b|\u53c2\u6570\u5316|\u4f18\u5316|\u7b97\u6cd5|\u632f\u52a8\u63a7\u5236|\u51cf\u9694\u9707|\u6709\u9650\u5143|\u6280\u672f\u57f9\u8bad<\/strong><\/p>\n<p style=\"text-align: center;\">\u8ffd\u6c42\u5353\u8d8a \u811a\u8e0f\u5b9e\u5730 \u81f4\u529b\u4e8e\u63a2\u7d22\u548c\u62d3\u5c55\u884c\u4e1a\u8bbe\u8ba1\u524d\u6cbf<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3636 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\" alt=\"WeChat_QRCode\" width=\"250\" height=\"255\" \/><\/a><\/p>\n<p style=\"text-align: center;\">https:\/\/www.jdcui.com<\/p>\n<p style=\"text-align: center;\">\u5408\u4f5c\u53ca\u6280\u672f\u54a8\u8be2<\/p>\n<p style=\"text-align: center;\">COOPERATION &amp; CONTACT<\/p>\n<p style=\"text-align: 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&#8230;<\/p>\n","protected":false},"author":1,"featured_media":23311,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,3164],"tags":[4117,4124,4118,4119,4123,3664,4120,3168,4121,3304,3392,4122],"class_list":["post-23301","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-geometry","category--vibration-control","tag-ergodic-theorem","tag-ergodicity","tag-random-processes","tag-random-vibration","tag-stationarity","tag-3664","tag-4120","tag-3168","tag-4121","tag-3304","tag-3392","tag-4122"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"CJD\"\/>\n\t<meta name=\"keywords\" content=\"ergodic theorem,ergodicity,random processes,random 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