Construction of a symmetrical shifl-invariant fractional overcomplete wavelet and its application in bearing fault diagnosis
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摘要: 提出了一種分數階的對稱性近似平移不變過完備小波的構造方法.首先,給出一種構造具有對稱性且具有最小長度的低通濾波器方法.其次,通過拓普利茲矩陣分解法求出對應的具有近似平移不變性的高通濾波器,此方法比其他分解方法具有更低的計算復雜度.此外,利用此構造方法,也得到具有更高階消失矩的分數階過完備小波變換.最后,將構造出的分數階對稱平移不變過完備小波應用到軸承故障診斷中.實驗結果表明,提出的小波變換能有效地提取出軸承的故障特征.Abstract: This article introduces the design of symmetrical approximately shift-invariant fractional overcomplete wavelet transforms. First, a design scheme for the symmetrical low-pass filter with minimum-length was proposed, and then the corresponding highpass filters with approximately shift-invariant properties were constructed via Toeplitz matrix factorization, which has a lower computational complexity than other methods. In addition, fractional overcomplete wavelet transforms could he designed with higher vanishing moments through the method proposed. Subsequently, a bearing fault diagnosis scheme was proposed using the symmetrical shiftinvariant fractional overcomplete wavelet transforms. Experimental results show that the bearing faults can be detected effectively using the symmetrical shift-invariant fractional overcomplete wavelet transforms.
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Key words:
- wavelet transforms /
- symmetrical filters /
- bearings /
- fault diagnosis
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