An Auto-Framing Method for Stochastic Process Signal by using a Hidden Markov Model based Approach

Abstract

In this paper, an "auto-framing" method, an algorithmic method to divide stochastic time-series process data into appropriate intervals, is developed based on the approach of hidden Markov model (HMM). While enormous amounts of process time-series data are being measured and collected today, their use is limited by the high costs to gather, store, and analyze them. "Data-framing" refers to the task of dividing stochastic signal data into time frames of distinct patterns so that the data can be stored and analyzed in an efficient manner. Data-framing is typically carried out manually, but doing so can be both laborious and ineffective. For the purpose of automating the data-framing task, stochastic signals of switching patterns are modeled using a hidden Markov model (HMM) based jump linear system (JLS), which switches the stochastic model probabilistically in accordance with the underlying Markov chain. Based on the model, an estimator is constructed to estimate from the collected signal data the state sequence of the underlying Markov chain, which is subsequently used to decide on the framing points. An Expectation Maximization (EM) algorithm, which is composed of two optimal estimators, fixed interval Kalman smoother and Viterbi algorithm, is used to estimate for the state estimation. We demonstrate the effectiveness of the HMM-based approach for auto-framing using simulated data constructed based on real industrial data.