The conception of 'main direction' of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investiga...The conception of 'main direction' of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis (MRA) of L2(R2). Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods are given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.展开更多
为了提取被强噪声淹没的机械设备振动信号中蕴含的微弱故障特征,依据有用信号和噪声在空间分布特性的不同,将流形学习的方法引入到信号降噪中,提出一种将双树复小波包(DTCWPT)和t分布随机近邻嵌入(t-SNE)结合的去噪方法,充分利用了DTCWP...为了提取被强噪声淹没的机械设备振动信号中蕴含的微弱故障特征,依据有用信号和噪声在空间分布特性的不同,将流形学习的方法引入到信号降噪中,提出一种将双树复小波包(DTCWPT)和t分布随机近邻嵌入(t-SNE)结合的去噪方法,充分利用了DTCWPT分解的多尺度特性以及t-SNE的非线性降维能力。将振动信号进行双树复小波包分解,依据各尺度小波包系数Shannon熵值搜索最佳小波包基,利用提出的新的阈值函数,对最佳小波包基的小波包系数进行去噪并单支重构组成高维信号空间,然后,采用t-SNE提取高维空间的低维流形,对低维信号序列进一步采用阈值去噪,利用谱回归分析重构回一维信号序列。最后,通过对仿真信号与滚动轴承振动信号进行去噪,结果证实了方法具有良好的非线性去噪性能,将仿真信号的信噪比从-1提高到8.6 d B,并且能更有效的提取强噪声干扰下滚动轴承的故障特征频率。展开更多
基金Supported by National Natural Science Foundation of P.R.China (10171109)the Special Research Fund for Doctoral Program of Higher Education of P. R. China (20049998006)
文摘The conception of 'main direction' of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis (MRA) of L2(R2). Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods are given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.
文摘为了提取被强噪声淹没的机械设备振动信号中蕴含的微弱故障特征,依据有用信号和噪声在空间分布特性的不同,将流形学习的方法引入到信号降噪中,提出一种将双树复小波包(DTCWPT)和t分布随机近邻嵌入(t-SNE)结合的去噪方法,充分利用了DTCWPT分解的多尺度特性以及t-SNE的非线性降维能力。将振动信号进行双树复小波包分解,依据各尺度小波包系数Shannon熵值搜索最佳小波包基,利用提出的新的阈值函数,对最佳小波包基的小波包系数进行去噪并单支重构组成高维信号空间,然后,采用t-SNE提取高维空间的低维流形,对低维信号序列进一步采用阈值去噪,利用谱回归分析重构回一维信号序列。最后,通过对仿真信号与滚动轴承振动信号进行去噪,结果证实了方法具有良好的非线性去噪性能,将仿真信号的信噪比从-1提高到8.6 d B,并且能更有效的提取强噪声干扰下滚动轴承的故障特征频率。
