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面包屑導航結束 --> <!-- 頁面標題開始 --> <div id="n1l1njb9b" class="title"> <h3><a>如何識別CNC機床運作時的混沌特性<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="n1l1njb9b" class="container"> <!-- 正文 --> <div id="n1l1njb9b" class="lead" id="print"> <p> <span style="font-family: 宋體; text-indent: 21pt;">數據預處理</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由于采集到信號可能含有各種噪聲和干擾信號</span> <span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">比如突變和尖峰信號</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以在對信號進一步分析之前</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">必須對監測得到的信號進行降噪</span><span lang="EN-US">[1]</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">等預處理</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">提取有效信號</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">圖</span><span lang="EN-US"> 1 </span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">是數控機床主軸振動信號預處理后的主軸振動信號</span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14030196958414.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">相空間重構</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">相空間重構</span><span lang="EN-US">[2]</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">是混沌時間序列判定和預測的基礎</span> <span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">作為分析時間序列混沌特性的一種重要方法</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">它通過單一的系統輸出時間序列來構造一組表征原系統動力學特性的坐標分量</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">從而近似地恢復系統的混沌吸引子</span> <span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">在數值計算過程中</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">首先必須根據獲得的單變量時間序列計算相空間重構的時間延遲和嵌入維數</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">并進行相空間重構</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">即通過單一系統輸出時間序列來構造一組表征原系統動力學特性的坐標分量</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">從而近似恢復系統的混沌吸引子</span> <span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">相空間重構建立了時間序列波動和動力系統空間特征之間的橋梁</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">根據</span><span lang="EN-US">Takes</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">等提出的相空間重構</span></p> <p class="MsoNormal"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">理論</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">將傳感器采集到的</span><span lang="EN-US"> 3000 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">個正常工況下數控機床主軸振動數據記為一個單變量時間序列</span><span lang="EN-US"> X1,X2,…X3000</span><span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">將其嵌入到</span><span lang="EN-US">m</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">維相空間</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">時間延遲為</span><span lang="EN-US">T</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">為了重構一個合適的相空間</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">必須選取恰當的時間延遲</span><span lang="EN-US">T</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入維數</span><span lang="EN-US">m</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">采用互信息法和</span><span lang="EN-US"> Cao </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">法進行時間延遲</span><span lang="EN-US">T</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入維數</span><span lang="EN-US">m</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">的計算</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">2.1 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">用互信息法求時間延遲</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">互信息法</span><span lang="EN-US">[3]</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">是估計重構相空間延遲時間的一種有效方法</span> <span style="font-family:宋體; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">取互信息函數的第一個極小值點為延遲時間</span><span lang="EN-US">T</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">計算求得互信息時間函數如圖</span><span lang="EN-US"> 2 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">所示</span> <span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">從圖中可看出</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">互信息第一次取極小值的時間為</span><span lang="EN-US"> 4 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以</span><span lang="EN-US">T=4 </span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">為數控機床主軸相空間重構的時間延遲</span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14030197063017.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">2.2 Cao </span><span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">法估計嵌入維數</span><span lang="EN-US">m</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">Cao </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">方法</span><span lang="EN-US">[4]</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">即改進的虛假鄰近點法</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">通過</span><span lang="EN-US"> Cao </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">方法可以畫出</span><span lang="EN-US">E1 (m )</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和</span><span lang="EN-US">E2(m)</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">隨嵌入維數增加的曲線圖如圖</span><span lang="EN-US"> 3 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">所示</span></p> <p class="MsoNormal"><span lang="EN-US"><img src="/upload/images/201406/14030197293201.jpg" alt="" /><br /> <!--[endif]--></span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">從圖</span><span lang="EN-US"> 3 </span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">可以看出</span><span lang="EN-US">E2 (m)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">不是恒為</span><span lang="EN-US"> 1 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以該序列不是隨機序列當</span><span lang="EN-US">m>4 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">時</span><span lang="EN-US">E1 (m)</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">逐漸停止變化或變化很小</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">所以取相空間嵌入維數去</span><span lang="EN-US">m=5</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">數控機床主軸振動數據最大</span><span lang="EN-US">Lyapunov</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">指數估計</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由計算出的時間延遲</span><span lang="EN-US">T=4 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入維數</span><span lang="EN-US">m=5 </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由</span><span lang="EN-US">Takes</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">定理對數控機床主軸正常工況下振動時間序列進行相空間重構后</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">即可采用小數據量法</span><span lang="EN-US">[5]</span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">對其最大</span><span lang="EN-US"> Lyapunov </span><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">指數進行計算</span> <span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">計算得到最大</span><span lang="EN-US"> Lyapunov </span><span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">指數值為</span><span lang="EN-US"> 0.2111 </span><span style="font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">說明主軸振動信號具有混沌特性</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">數控機床是個混沌系統</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">結論</span><span lang="EN-US"> </span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">通過對數控機床主軸的振動信號進行向空間重構選取恰當的時間延遲</span> <span style="font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入維數</span><span lang="EN-US">m</span><span style="font-family: 宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">計算得到振動信號的最大</span><span lang="EN-US">Lyapunov </span><span 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