OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 3 2024 where ωc is determined at the initial stage of wear and remains unchanged thereafter; S0(ω) is a spectrum at the initial processing stage, when w→0; Sw(ω,w) is a wear spectrum w. The secondly feature Π2(w) defines the emission at the contact of the auxiliary flank of the tool. It is convenient to consider it in the form 1 1 0 0 0 0 Ï ( ) ( , ) ( ) ( ) Ñ Ñ w S w d S d S d w - ω ∞ ∞ ω = ω ω ω - ω ω ω ∫ ∫ ∫ , (13) where ωc is determined at the initial stage of wear and subsequently remains unchanged; S0(ω) is a spectrum at the initial stage of processing, when wear w→0; Sw(ω,w) is a wear spectrum. Estimations Π1(w) and Π2(w) have a special feature: Πi(0) = 0,i = 1.2. The current spectrum Sw(ω,w) changes as the wear progresses. Its nonstationarity Sw(ω,t) in time t increases as w increases. For its estimation, let us introduce into consideration an increment of time Tw, during which it is estimated as a movingaverage.Then,attime t, estimatesofthetypeofexpectation [( ), ] 1 { ( , )} ( , ) w w t t t T t w t T M S t S t dt T ∈ - - ω = ω ∫ and dispersion 2 2 [( ), ] 1 { ( , )} { ( , ) [ ( , )]} w w t t t T t w t T S t S t M S t dt T ∈ - - s ω = ω - ω ∫ are valid. The following estimation is informative when monotonically increasing with the development of wear: [ ] { } [ ] { } 3 Ï ( ) , ( ) , ( ) w w w S w t M S w t = s ω ω . (14) The information attributes provided in the paper have the following features: – feature П1 characterizes a general property of the frequency response that consists in the shift of the dispersion-normalized spectrum of the VAE to the low-frequency region without revealing its peculiarities. For example, without revealing the shift of natural frequencies; – features П2 and П3 are oriented towards analyzing the high-frequency part of the spectrum. Shortened time sequences can be used for its estimation, as these estimates are in the high-frequency part of the spectrum. The information space is three-dimensional. The Bayesian rule [61] was used to determine the decisive rules for partitioning the wear into clusters. For this purpose, the clustering centers for each wear value and the dispersion of dispersion with respect to the centers were determined. Four clusters were chosen for the example: w ∈ (0–0.15) mm; w ∈ (0.15–0.30) mm; w ∈ (0.3–0.45) mm and w ∈ (0.45–0.60) mm. For each Fig. 8. Distribution of informative features in planes (П1, П2) and (П1, П3). Grouping centers are shown by shapes with a white background
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