發(fā)布時(shí)間：2018-06-26 03:58

  本文選題：線性時(shí)變結(jié)構(gòu) + 工作模態(tài)參數(shù)識別��； 參考：《華僑大學(xué)》2016年碩士論文

【摘要】：線性時(shí)變結(jié)構(gòu)的工作模態(tài)參數(shù)識別在振動(dòng)控制和故障診斷等領(lǐng)域具有重要的理論意義和工程應(yīng)用價(jià)值。本文基于線性時(shí)變結(jié)構(gòu)的“時(shí)間凍結(jié)”和“瞬態(tài)”表示,提出了自適應(yīng)主元分析的線性時(shí)變結(jié)構(gòu)工作模態(tài)參數(shù)在線識別方法,并進(jìn)行了理論推導(dǎo)和數(shù)值仿真驗(yàn)證。主要工作如下:(1)從基本主成分分析(PCA)算法出發(fā),建立其與線性時(shí)不變結(jié)構(gòu)位移響應(yīng)的模態(tài)坐標(biāo)表示之間的對應(yīng)關(guān)系,闡述了基于PCA工作模態(tài)參數(shù)識別方法各參數(shù)物理意義及適用條件,通過數(shù)值仿真驗(yàn)證了該方法在線性時(shí)不變結(jié)構(gòu)工作模態(tài)參數(shù)識別中的效果。(2)基于“短時(shí)時(shí)不變”思想,將基于PCA的線性時(shí)不變結(jié)構(gòu)工作模態(tài)參數(shù)識別方法與滑動(dòng)窗技術(shù)結(jié)合,提出了滑動(dòng)窗主元分析的線性時(shí)變結(jié)構(gòu)工作模態(tài)參數(shù)識別方法。在選取合適大小的數(shù)據(jù)窗后,該方法能有效識別線性時(shí)變結(jié)構(gòu)的瞬態(tài)模態(tài)頻率和模態(tài)振型。在此基礎(chǔ)上,將該方法與自相關(guān)矩陣遞推、特征值特征向量遞推技術(shù)相結(jié)合,分別提出滑動(dòng)窗自相關(guān)矩陣在線遞推和滑動(dòng)窗特征值特征向量在線遞推的主元分析算法。通過理論分析和數(shù)值仿真驗(yàn)證,基于滑動(dòng)窗特征值特征向量遞推的主元分析算法較滑動(dòng)窗自相關(guān)矩陣遞推的主元分析算法具有更低的時(shí)間復(fù)雜度、空間復(fù)雜度和數(shù)值穩(wěn)定性。(3)基于“遺忘因子加權(quán)”思想,將基于PCA的線性時(shí)不變結(jié)構(gòu)工作模態(tài)參數(shù)識別方法與“加權(quán)遺忘技術(shù)”結(jié)合,提出帶遺忘因子加權(quán)的主元分析的線性時(shí)變結(jié)構(gòu)工作模態(tài)參數(shù)識別方法。在選取合適大小的遺忘因子后,該方法能有效識別線性時(shí)變結(jié)構(gòu)的瞬態(tài)模態(tài)頻率和模態(tài)振型。在此基礎(chǔ)上,將該方法與自相關(guān)矩陣遞推、特征值特征向量遞推技術(shù)相結(jié)合,分別提出帶遺忘因子加權(quán)的自相關(guān)矩陣在線遞推和帶遺忘因子加權(quán)的特征值特征向量在線遞推主元分析算法。通過理論分析和數(shù)值仿真驗(yàn)證,基于帶遺忘因子加權(quán)的特征值特征向量遞推主元分析算法較帶遺忘因子加權(quán)的自相關(guān)矩陣遞推主元分析算法具有更低的時(shí)間復(fù)雜度、空間復(fù)雜度和數(shù)值穩(wěn)定性。
[Abstract]:The identification of working modal parameters of linear time-varying structures has important theoretical significance and engineering application value in the fields of vibration control and fault diagnosis. Based on the "time freeze" and "transient" representations of linear time-varying structures, an adaptive principal component analysis method for on-line identification of operating modal parameters of linear time-varying structures is proposed, and theoretical derivation and numerical simulation are carried out. The main work is as follows: (1) based on the basic principal component analysis (PCA) algorithm, the corresponding relationship between the principal component analysis (PCA) algorithm and the modal coordinate representation of the displacement response of the linear time-invariant structure is established. The physical meaning and applicable conditions of each parameter of the working modal parameter identification method based on PCA are expounded. The effectiveness of the method in identifying the operating modal parameters of linear time-invariant structures is verified by numerical simulation. (2) based on the idea of "short time invariance", Based on PCA and sliding window technique, a method for identifying the working modal parameters of linear time-invariant structures based on principal component analysis with sliding windows is proposed. The method can effectively identify the transient modal frequencies and modal modes of linear time-varying structures by selecting suitable data windows. On this basis, the method is combined with autocorrelation matrix recursion and eigenvalue eigenvector recursion technology, and the principal component analysis algorithm of sliding window autocorrelation matrix online recursion and sliding window eigenvalue eigenvector online recursion are presented respectively. Through theoretical analysis and numerical simulation, it is proved that the principal component analysis algorithm based on eigenvector recursion of sliding window has lower time complexity than that of sliding window autocorrelation matrix recursive principal component analysis algorithm. Space complexity and numerical stability. (3) based on the idea of "forgetting factor weighting", the paper combines the PCA based identification method of linear time-invariant structure working modal parameters with the "weighted forgetting technique". A method for identifying the working modal parameters of linear time-varying structures based on principal component analysis with forgetting factor weighted is presented. The method can effectively identify the transient modal frequencies and modal modes of linear time-varying structures by selecting appropriate forgetting factors. On this basis, the method is combined with the recursive technique of autocorrelation matrix and eigenvalue eigenvector. An online recursive principal component analysis algorithm with forgetting factor weighted autocorrelation matrix and eigenvalue eigenvector with forgetting factor weighting is proposed respectively. The theoretical analysis and numerical simulation show that the eigenvalue eigenvector recursive principal component analysis algorithm with forgetting factor weighting has lower time complexity than the autocorrelation matrix recursive principal component analysis algorithm with forgetting factor weighting. Space complexity and numerical stability.
【學(xué)位授予單位】：華僑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TB535
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本文編號：2068978