Читать книгу Industry 4.1 - Группа авторов - Страница 54

Wavelet thresholding, or the so‐called wavelet de‐noising, mainly adopts the discrete wavelet transform (DWT) technique [8–10] to filter noises in signals. DWT provides a multi‐resolution representation using wavelets, which can discretely capture rich information both in time and frequency domains.

The discrete wavelet coefficient capability of spare distribution and auto‐zooming in the time and frequency domains provided by DWT can be applied to deal with the non‐stationary signals for enhancing the S/N ratios. Thus, critical information behind signals with noises can be accurately obtained. More details can be referred to Sections 2.3.3.2 and 2.3.3.3.

Suppose that M sets of machining signals related to machining precision are collected and each set has data length N, denoted as s[i], i = 1, …, N. Let r and c represent the raw and cleaned data, respectively. Based on DWT, data cleaning adopts the wavelet de‐noising algorithm to purify the discrete raw sensor data of precision item p, denoted as , to become the cleaned discrete sensor data, , by using the function:

(2.1)

where .

The general wavelet de‐noising process consists of three steps: decomposition, thresholding, and reconstruction. They are described as follows.