Hidden Markov Linear Regression Model and its Parameter Estimation

Liu, Hefei; Wang, Kunqjnu; Yong, Li

doi:10.1109/access.2020.3030776

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…It is developed on the basis of the Markov chain, which is a discrete memoryless random process responsible for describing the relationship between the sequence of states of the next moment with the current one [83][84][85]. An HMM is an evolution of a Markov chain that requires two stochastic processes, adding a random relationship between the sequence of states and the observation vector, and where the sequence of states cannot be directly observed [83,84,[86][87][88][89]. Then, an HMM is a probabilistic time series model, doubly stochastic, which includes the transition of hidden states and emitting observations [90].…”

Section: Hidden Markov Models (Hmms)mentioning

confidence: 99%

Predicting the Health Status of a Pulp Press Based on Deep Neural Networks and Hidden Markov Models

et al. 2023

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The maintenance paradigm has evolved over the last few years and companies that want to remain competitive in the market need to provide condition-based maintenance (CBM). The diagnosis and prognosis of the health status of equipment, predictive maintenance (PdM), are fundamental strategies to perform informed maintenance, increasing the company’s profit. This article aims to present a diagnosis and prognosis methodology using a hidden Markov model (HMM) classifier to recognise the equipment status in real time and a deep neural network (DNN), specifically a gated recurrent unit (GRU), to determine this same status in a future of one week. The data collected by the sensors go through several phases, starting by cleaning them. After that, temporal windows are created in order to generate statistical features of the time domain to better understand the equipment’s behaviour. These features go through a normalisation to produce inputs for a feature extraction process, via a principal component analysis (PCA). After the dimensional reduction and obtaining new features with more information, a clustering is performed by the K-means algorithm, in order to group similar data. These clusters enter the HMM classifier as observable states. After training using the Baum–Welch algorithm, the Viterbi algorithm is used to find the best path of hidden states that represent the diagnosis of the equipment, containing three states: state 1—“State of Good Operation”; state 2—“Warning State”; state 3—“Failure State”. Once the equipment diagnosis is complete, the GRU model is used to predict the future, both of the observable states as well as the hidden states coming out from the HMM. Thus, through this network, it is possible to directly obtain the health states 7 days ahead, without the necessity to run the whole methodology from scratch.

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Section: Hidden Markov Models (Hmms)mentioning

confidence: 99%

Predicting the Health Status of a Pulp Press Based on Deep Neural Networks and Hidden Markov Models

et al. 2023

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“…Xia et al analyzed the hidden Markov factor analysis model with the semi parametric Bayesian method [7]. Liu et al introduced linear regression model to hidden Markov model and used the maximum likelihood estimation method for inference analysis [8]. Wang et al proposed the hidden Markov structural equation model and estimated the corresponding parameters with Bayesian method [9].…”

Section: Introductionmentioning

confidence: 99%

Detection of Factors Affecting State Transition Based on Non-Homogeneous Markov Chain Model

Xiujuan

Liu

et al. 2021

IEEE Access

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The dependent and independent variables in traditional linear regression models are continuous numerical variables. When the dependent variable or independent variable is a discrete variable, the traditional linear regression model can no longer be used to analyze. To solve this problem, this article introduces the non-homogeneous Markov chain model. It introduces the mathematical definition of the non-homogeneous Markov chain model. And then this article uses Bayesian estimation method to derive posterior distribution of model parameters. Through the MCMC algorithm, we simulate an experiment, posterior means value of the parameters is estimated, and the estimation effect is found to be better. Finally, we analyze the impact of learning state transition about college students on the non-homogeneous Markov chain model. Influencing factors include whether to receive a scholarship and whether to serve as a class leader. In this paper, non-homogeneous Markov chain model is used to analyze and detect the impact of discrete variables on dependent variables. This is the major innovation in this article. INDEX TERMSNon-homogeneous Markov chain model, Bayesian estimation, MCMC algorithm, state transition.

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Hidden Markov Linear Regression Model and its Parameter Estimation

Cited by 2 publications

References 14 publications

Predicting the Health Status of a Pulp Press Based on Deep Neural Networks and Hidden Markov Models

Predicting the Health Status of a Pulp Press Based on Deep Neural Networks and Hidden Markov Models

Detection of Factors Affecting State Transition Based on Non-Homogeneous Markov Chain Model

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