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style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由于采集到信号可能含有各种噪声和干扰信号</span> <span style="font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">比如突变和尖峰信号</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以在对信号进一步分析之前</span> <span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">必须对监测得到的信号进行降噪</span><span lang="EN-US">[1]</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">等预处理</span> <span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">提取有效信号</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">图</span><span lang="EN-US"> 1 </span><span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">是数控机床主轴振动信号预处理后的主轴振动信号</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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">相空间重构</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">相空间重构</span><span lang="EN-US">[2]</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">是混沌时间序列判定和预测的基础</span> <span style="font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">作为分析时间序列混沌特性的一种重要方法</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">它通过单一的系统输出时间序列来构造一组表征原系统动力学特性的坐标分量</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">从而近似地恢复系统的混沌吸引子</span> <span style="font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">在数值计算过程中</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">首先必须根据获得的单变量时间序列计算相空间重构的时间延迟和嵌入维数</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">并进行相空间重构</span> <span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">即通过单一系统输出时间序列来构造一组表征原系统动力学特性的坐标分量</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">从而近似恢复系统的混沌吸引子</span> <span style="font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">相空间重构建立了时间序列波动和动力系统空间特征之间的桥梁</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">根据</span><span lang="EN-US">Takes</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">等提出的相空间重构</span></p> <p class="MsoNormal"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">理论</span> <span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">将传感器采集到的</span><span lang="EN-US"> 3000 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">个正常工况下数控机床主轴振动数据记为一个单变量时间序列</span><span lang="EN-US"> X1,X2,…X3000</span><span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">将其嵌入到</span><span lang="EN-US">m</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">维相空间</span> <span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">时间延迟为</span><span lang="EN-US">T</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">为了重构一个合适的相空间</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">必须选取恰当的时间延迟</span><span lang="EN-US">T</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入维数</span><span lang="EN-US">m</span><span style="font-family: 宋体;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:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">法进行时间延迟</span><span lang="EN-US">T</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入维数</span><span lang="EN-US">m</span><span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">的计算</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:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">用互信息法求时间延迟</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">是估计重构相空间延迟时间的一种有效方法</span> <span style="font-family:宋体; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">取互信息函数的第一个极小值点为延迟时间</span><span lang="EN-US">T</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">计算求得互信息时间函数如图</span><span lang="EN-US"> 2 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">所示</span> <span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">从图中可看出</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">互信息第一次取极小值的时间为</span><span lang="EN-US"> 4 </span><span style="font-family:宋体;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: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">为数控机床主轴相空间重构的时间延迟</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:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">法估计嵌入维数</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:宋体;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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">即改进的虚假邻近点法</span> <span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">通过</span><span lang="EN-US"> Cao </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">方法可以画出</span><span lang="EN-US">E1 (m )</span><span style="font-family:宋体;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: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">随嵌入维数增加的曲线图如图</span><span lang="EN-US"> 3 </span><span style="font-family:宋体;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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">从图</span><span lang="EN-US"> 3 </span><span style="font-family: 宋体;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:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">不是恒为</span><span lang="EN-US"> 1 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">所以该序列不是随机序列当</span><span lang="EN-US">m>4 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">时</span><span lang="EN-US">E1 (m)</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">逐渐停止变化或变化很小</span> <span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">所以取相空间嵌入维数去</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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">数控机床主轴振动数据最大</span><span lang="EN-US">Lyapunov</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">指数估计</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">由计算出的时间延迟</span><span lang="EN-US">T=4 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入维数</span><span lang="EN-US">m=5 </span><span style="font-family:宋体;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: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">定理对数控机床主轴正常工况下振动时间序列进行相空间重构后</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">即可采用小数据量法</span><span lang="EN-US">[5]</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">对其最大</span><span lang="EN-US"> Lyapunov </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">指数进行计算</span> <span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">计算得到最大</span><span lang="EN-US"> Lyapunov </span><span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">指数值为</span><span lang="EN-US"> 0.2111 </span><span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">说明主轴振动信号具有混沌特性</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">数控机床是个混沌系统</span></p> <p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">结论</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:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">通过对数控机床主轴的振动信号进行向空间重构选取恰当的时间延迟</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">和嵌入维数</span><span lang="EN-US">m</span><span style="font-family: 宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">计算得到振动信号的最大</span><span lang="EN-US">Lyapunov </span><span style="font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">指数大于</span><span lang="EN-US"> 0 </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman"">验证了数控机床运行状态的混沌特性</span> <span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">这为后续应用混沌理论对对数控机床进行状态监测和趋势预测奠定了基础具有较强的使用价值</span><span lang="EN-US"> </span></p> <h1 align="center" style="margin-top:4.5pt;margin-right:0cm;margin-bottom:7.5pt; margin-left:0cm;text-align:center;line-height:13.5pt"><span style="font-size: 10.5pt;color:#666666;mso-font-kerning:0pt">本文由<span lang="EN-US"> <a href="http://www.bethel-cnc.com/"><span lang="EN-US" style="color:#333333"><span lang="EN-US">伯特利数控</span></span></a></span>文章<span lang="EN-US"> </span>整理发表，文章来自网络仅参考学习，本站不承担任何法律责任。</span><span lang="EN-US" style="font-size: 15pt; font-family: 微软雅黑; font-weight: normal;"><o:p></o:p></span></h1> <p class="MsoNormal" align="center" style="text-align:center;text-indent:21.0pt; mso-char-indent-count:2.0"><span lang="EN-US" style="mso-bidi-font-size:10.5pt; font-family:宋体;mso-bidi-font-family:宋体;color:#666666;mso-font-kerning:0pt"><a 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