A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Wavelets: theory and applications
Wavelets: theory and applications
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Singularity detection and processing with wavelets
IEEE Transactions on Information Theory - Part 2
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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This paper presents a statistical chatter detection method. The methodology is based on the study of discrete wavelet transform (DWT) scheme and statistical analysis of wavelet transform modulus maxima (WTMM). Wavelet transform modulus maxima is used to describe any point where wavelet transform of a signal is locally maximal at corresponding time location. Meanwhile, due to the noisy machining environment, a wavelet-based de-noising method including a hybrid thresholding function and a level-dependent universal threshold rule is proposed. A non-dimensional chatter index varying between 0 and 1 is designed based on the statistical analysis of the WTMM. The main advantages of the proposed chatter index include that: (a) its variation range is independent of process parameters and machining systems, and (b) its threshold value is much less susceptible to cutting condition changes since its value is in relative term. As a result, the chatter index could be used for different machining processes without the time-consuming recalibration process.