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id="tpnrxl7j" class="title"> <h3><a>頻域總體曲線擬合法<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="tpnrxl7j" class="container"> <!-- 正文 --> <div id="tpnrxl7j" class="lead" id="print"> <p> <span style="line-height: 21.85pt; text-align: justify; text-indent: 28pt; background-color: transparent;">以上的方法中，大多是用每個測點所得的頻響函數測試值，單獨進行曲線擬 合，而后，得到各階模態頻率、阻尼、留數的估值。不同測點同階模態參數理論 上應該是相同的。但是由于模型和測量都存在誤差，因此，不同測點所識別的模 態參數往往并不完全相同，特別是阻尼和留數的估值比固有頻率更難確定，并且 留數和阻尼估值又是相關的，阻尼有較大誤差，勢必導致留數估值有較大誤差。</span></p> <p class="150" style="text-align:justify;text-justify:inter-ideograph;text-indent: 28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><o:p></o:p></p> <p class="150" style="text-indent:28.0pt;line-height:21.85pt;mso-line-height-rule: exactly;background:transparent"><span id="tpnrxl7j" class="150pt">一般為了減小誤差，可以首先借助所有測點的測量值估計頻率和阻尼值，而 后進一步估計振型和留數，無疑這比單個測點的曲線擬合能得到更精確的參數， 這就是總體曲線擬合。</span><o:p></o:p></p> <p class="150" style="text-align:justify;text-justify:inter-ideograph;text-indent: 28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="150pt">從式</span><span id="tpnrxl7j" class="150pt">（</span><span id="tpnrxl7j" class="150pt"><span style="font-family: SimSun;">2-12)</span></span><span id="tpnrxl7j" class="150pt">可知由兩點間頻響函數表達式可以看出同一模態，不同測點的頻 響函數，其表達式的分母均一樣，因而可以把所有測點的頻響函數進行平均，然 后，以此平均的頻響函數求得總體頻率和阻尼。采用總體曲線擬合法，對模態耦 合緊密，有較大噪聲污染情況，仍能獲得較好的效果。</span><o:p></o:p></p> <p class="MsoNormal" style="text-indent:24.0pt;mso-char-indent-count:2.0">下面介紹正交多項式曲線擬合法，此法80年代初期開始應用研究，適用于單 點擬合，也適用于總體擬合方法。</p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:27.0pt; line-height:21.6pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">滿足上 述條件，使式</span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;">(2-45</span></span><span id="tpnrxl7j" class="2">；</span><span id="tpnrxl7j" class="2"><span style="font-family: SimSun;">)</span></span><span id="tpnrxl7j" class="2">系數矩陣對角線為單位矩陣，</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">C</span></span><span id="tpnrxl7j" class="2">，</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">D</span></span><span id="tpnrxl7j" class="2">可單獨求解，且方程階次 幾乎減小一半，因而運算速度明顯提高。</span></p> <p class="21" align="left" style="margin: 0cm 0cm 0.0001pt; text-indent: 27pt; line-height: 21.6pt; background: transparent;"><span id="tpnrxl7j" class="2">在已知分子、分母多項式系數后，令分母多項式為零，此時的</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">s</span></span><span id="tpnrxl7j" class="2">值即為極點， 由極點值可進一步求得固有頻率和阻尼比。</span></p> <p class="21" align="left" style="margin: 0cm 0cm 15.9pt; text-indent: 27pt; line-height: 21.6pt; background: transparent;"><span id="tpnrxl7j" class="2">總體曲線擬合的優點是借助所有測量數據，這比從單個測量的曲線擬合能得 到更精確的頻率和阻尼的估計。再因阻尼是作為第一步擬合的結果，是已知的， 所以，通常在第二步估計中能更精確地估計留數，總體頻率和阻尼的直接估計方 法可如下進行：因為同一模態，不同測點的頻響函數，其表達式的分母均一樣， 因而可以把所有測點的頻響函數進行平均，然后以此平均的頻響函數求得總體頻 率和阻尼，必須指出，平均頻響函數的分子項，已無明顯的物理意義，也許最簡 單方法是選擇具有很大響應的那些測量數據，然后從這些測量中進行頻率和阻尼 的估計，以此作為總體估計的近擬。該方法對模態藕合緊密，且有較大噪聲污染 的情況下，仍能獲得較好的效果。</span></p> <p class="21" align="left" style="margin: 0cm 0cm 15.9pt; text-indent: 27pt; line-height: 21.6pt; background: transparent;"> </p> <p class="21" align="left" style="margin: 0cm 0cm 15.9pt; text-indent: 27pt; line-height: 21.6pt; background: transparent;"><span style="font-size:9.0pt;font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language: ZH-CN;mso-bidi-language:AR-SA">本文采摘自“</span><span lang="EN-US" style="font-size: 9.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋體;mso-font-kerning: 1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language: AR-SA">VMC1060</span><span 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