A Comparative Study of Feature Selection for Hidden Markov Model-Based Micro-Milling Tool Wear Monitoring

Abstract

& This paper presents a discriminant feature selection approach for hidden Markov model (HMM) modeling of micro-milling tool conditions. The approach is compared with other popular feature selection methods such as principal component analysis (PCA) and automatic relevance determination (ARD) according to their HMM classification rate. In tool condition monitoring (TCM), there are a lot of features that contain redundant information or less sensitive to tool state discrimination. These features are expected to be deleted for less computation and more robust modeling of tool conditions. Fisher's linear discriminant analysis (FDA) is modified for this purpose. The FDA is generally used for classification, and the features are mapped to another space and lose their physical meanings. In the modified discriminant feature selection, the features are selected in the original feature space by maximizing tool state separation and ranked by their separation ability between different tool states. Experimental results from both micro-milling of copper and steel under different working conditions indicate that the FDA is superior to both PCA and ARD for feature selection in HMM's classification. The reasons behind these differences are also discussed.

A Physically Segmented Hidden Markov Model Approach for Continuous Tool Condition Monitoring: Diagnostics and Prognostics

“…The average energy of these coefficients are used as the extracted [3] features. According to [29], the average energy can be written as (18) where is the scale, is the wavelet packet coefficient of the signal, is the number of coefficients at each scale and is the discrete time.…”

“…It is a ratio of scatter between and the scatter within . A modified version of FDR introduced in [29] is as follows: (19) where is the number of classes, is the th feature (element) in the observation vector is the mean value of in the th class and is the scatter within (variance) the th class measured for . In order to use the FDR criterion for feature selection in the continuous TCM, samples must be clustered based on their output values.…”

“…Hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs) are used [29]- [35] to distinguish various wearing stages or machinery fault types. In all the existing HMM and HSMM-based approaches, the wearing data is discretized into several stages and then multiple HMMs are used to distinguish between those stages.…”

Multimodal Hidden Markov Model-Based Approach for Tool Wear Monitoring

“…Estimating the tool wear as a continuous measure instead of setting thresholds and differentiating distinct health states would enable smoother condition-based maintenance systems that can incorporate various quality thresholds for different applications to guarantee different qualities in various products [3], [8]. As an example, in a milling machine, the extracted features are used as inputs to predict the continuous wearing metric of the cutter [3], [7]- [9]. In this work, TWM in a computer numerically controlled (CNC) milling machine is used as an illustrative example.…”

“…As a result, tool wear monitoring (TWM) helps to improve the quality and precision in the products [6], [7].…”