In this paper, a temporal probabilistic approach based on the hidden Markov model (HMM), named physically segmented HMM with continuous output, is introduced for continuous tool condition monitoring in machinery systems. The proposed approach has the advantage of providing an explicit relationship between the actual health states and the hidden state values. The provided relationship is further exploited for formulation and parameter estimation in the proposed approach. The introduced approach is tested for continuous tool wear prediction in a computer numerical control milling machine and compared with two well-established neural network (NN) approaches, namely, multilayer perceptron and Elman network. In the experimental study, the prediction results are provided and compared after adopting appropriate hyper-parameter values for all the approaches by cross-validation. Based on the experimental results, physically segmented HMM approach outperforms the NN approaches. Moreover, the prognosis ability of the proposed approach is studied.

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In this paper, a novel multimodal hidden Markov model (HMM)-based approach is proposed for tool wear monitoring (TWM). The proposed approach improves the performance of a pre-existing HMM-based approach named physically segmented HMM with continuous output (PSHMCO) by using multiple PSHMCOs in parallel. In this multimodal approach, each PSHMCO captures and emphasizes on a different tool wear regiment. In this paper, three weighting schemes, namely, bounded hindsight, discounted hindsight, and semi-nonparametric hindsight, are proposed, and two switching strategies named soft and hard switching are introduced to combine the outputs from multiple modes into one. As an illustrative example, the proposed approach is applied to TWM in a computer numerically controlled milling machine. The performance of the multimodal approach with various weighting schemes and switching strategies is reported and compared with PSHMCO.