Tag Archives: Semi-markov Processes

Semi-Markov HMMs for modelling time series in milling machines

Kai Li, Chaochao Qiu, Xinzhao Zhou, Mingsong Chen, Yongcheng Lin, Xianshi Jia, Bin Li, Modeling and tagging of time sequence signals in the milling process based on an improved hidden semi-Markov model, Expert Systems with Applications, Volume 205, 2022 DOI: 10.1016/j.eswa.2022.117758.

Vibration signals are widely used in the field of tool wear, tool residual life prediction and health monitoring of mechanical equipment. However, the current data-driven research methods mostly rely on high-value and high-density labeled data to establish relevant models and algorithms. Therefore, it is of great significance to solve the problem of automatic tagging of data, realize automatic signal interception, and enhance the value density of manufacturing process data. The Hidden semi-Markov model (HSMM) can describe the real spatial statistical characteristics of random models through observable data. As HSMM does not need the real labels of the signal, it can reduce tagging work to improve the marking efficiency. In this paper, an improved HSMM was proposed to model and tag the spindle vibration signals in the milling process. First, the Mel frequency cepstral coefficients (MFCCs) were extracted as observation sequences from the collected spindle vibration signals, and the dimension of the original features was reduced by linear discriminant analysis (LDA). Subsequently, a signal automatic tagging model based on HSMM was developed, in which the state duration can be explicitly modeled. Finally, the evaluation of the proposed methodology was carried out in the laboratory and real industry machining. The experimental results confirmed the effectiveness and robustness of the proposed model.

Modelling hierarchical stochastic signals (i.e., decomposable into sub-signals hierarchichally)

Truyen Tran, Dinh Phung, Hung Bui, Svetha Venkatesh, Hierarchical semi-Markov conditional random fields for deep recursive sequential data, Artificial Intelligence, Volume 246, May 2017, Pages 53-85, ISSN 0004-3702, DOI: 10.1016/j.artint.2017.02.003.

We present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of linear-chain conditional random fields to model deep nested Markov processes. It is parameterised as a conditional log-linear model and has polynomial time algorithms for learning and inference. We derive algorithms for partially-supervised learning and constrained inference. We develop numerical scaling procedures that handle the overflow problem. We show that when depth is two, the HSCRF can be reduced to the semi-Markov conditional random fields. Finally, we demonstrate the HSCRF on two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. The HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.