Transfer Learning for Detection of Combustion Instability via Symbolic Time Series Analysis

Transfer learning (TL) is a machine learning (ML) tool where the knowledge, acquired from a source domain, is 'transferred' to perform a task in a target domain that has (to some extent) a similar setting. The underlying concept does not require the ML method to analyse a new problem from the beginning, and thereby both the learning time and the amount of required target-domain data are reduced for training. An example is the occurrence of thermoacoustic instability (TAI) in combustors, which may cause pressure oscillations, possibly leading to flame extinction as well as undesirable vibrations in the mechanical structures. In this situation, it is difficult to collect useful data from industrial combustion systems, due to the transient nature of TAI phenomena. A feasible solution is the usage of prototypes or emulators, like a Rijke tube, to produce largely similar phenomena. This paper proposes symbolic time series analysis (STSA)-based transfer learning, where the key idea is to develop a capability of discrimination between stable and unstable operations of a combustor, based on the time series of pressure oscillations from a data source that contains sufficient information, even if it is not the target regime, and then transfer the learnt models to the target regime. The proposed STSA-based pattern classifier is trained on a previously validated numerical model of a Rijke-tube apparatus. The knowledge of this trained classifier is 'transferred' to classify similar operational regimes in: (i) an experimental Rijke-tube apparatus and (ii) an experimental combustion system apparatus. Results of the proposed transfer learning have been validated by comparison with those of two shallow neural networks (NN)-based TL and another NN having an additional long-short-term-memory (LSTM) layer, which serve as benchmarks, in terms of classification accuracy and computational complexity.

Online Discovery and Classification of Operational Regimes From an Ensemble of Time Series Data

One of the pertinent problems in decision and control of dynamical systems is to identify the current operational regime of the physical process under consideration. To this end, there has been an upsurge in (data-driven) machine learning methods, such as symbolic time series analysis, hidden Markov modeling, and artificial neural networks, which often rely on some form of supervised learning based on preclassified data to construct the classifier. However, this approach may not be adequate for dynamical systems with a variety of operational regimes and possible anomalous/failure conditions. To address this issue, the technical brief proposes a methodology, built upon the concept of symbolic time series analysis, wherein the classifier learns to discover the patterns so that the algorithms can train themselves online while simultaneously functioning as a classifier. The efficacy of the methodology is demonstrated on time series of: (i) synthetic data from an unforced Van der Pol equation and (ii) pressure oscillation data from an experimental Rijke tube apparatus that emulates the thermoacoustics in real-life combustors where the process dynamics undergoes changes from the stable regime to an unstable regime and vice versa via transition to transient regimes. The underlying algorithms are capable of accurately learning and capturing the various regimes online in a (primarily) unsupervised manner.

Symbolic Time Series Analysis for Anomaly Detection in Measure-Invariant Ergodic Systems

This paper presents a novel framework of symbolic time series analysis (STSA) for anomaly detection in dynamical systems. The core concept is built upon a property of measure-preserving transformation (MPT) sequence, acting on a probability space with ergodic measure, that the eigenfunctions of these transformations would be time-invariant. As a result, unlike a standard STSA that is required to generate time-homogeneous Markov chains, the proposed MPT-based STSA is allowed to have time-inhomogeneous Markov chains, where the (possibly time-varying) state transition probability matrices have time-invariant eigenvectors. Such a time-invariance facilitates analysis of the dynamical system by using short-length time series of measurements. This is particularly important in applications, where the underlying dynamics and process anomalies need fast monitoring and control actions in order to mitigate any potential structural damage and/or to avoid catastrophic failures. The MPT-based STSA has been applied for low-delay detection of fatigue damage, which is a common source of failures in mechanical structures and which is known to have uncertain dynamical characteristics. The underlying algorithm has been validated with experimental data generated from a laboratory apparatus that uses ultrasonic sensors to detect fatigue damage in polycrystalline–alloy specimens. The performance of the proposed MPT-based STSA is evaluated by comparison with those of a standard STSA and a hidden Markov model (HMM) on the same experimental data. The results consistently show superior performance of the MPT-based STSA.

Using Entropy to Forecast Bitcoin’s Daily Conditional Value at Risk

Conditional value at risk (CVaR), or expected shortfall, is a risk measure for investments according to Rockafellar and Uryasev. Yamai and Yoshiba define CVaR as the conditional expectation of loss given that the loss is beyond the value at risk (VaR) level. The VaR is a risk measure that represents how much an investment might lose during usual market conditions with a given probability in a time interval. In particular, Rockafellar and Uryasev show that CVaR is superior to VaR in applications related to investment portfolio optimization. On the other hand, the Shannon entropy has been used as an uncertainty measure in investments and, in particular, to forecast the Bitcoin’s daily VaR. In this paper, we estimate the entropy of intraday distribution of Bitcoin’s logreturns through the symbolic time series analysis (STSA) and we forecast Bitcoin’s daily CVaR using the estimated entropy. We find that the entropy is positively correlated to the likelihood of extreme values of Bitcoin’s daily logreturns using a logistic regression model based on CVaR and the use of entropy to forecast the Bitcoin’s daily CVaR of the next day performs better than the naive use of the historical CVaR.

Using High-Frequency Entropy to Forecast Bitcoin’s Daily Value at Risk

In this paper we investigate the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using high frequency data for Bitcoin, we estimate the entropy of intraday distribution of logreturns through the symbolic time series analysis (STSA), producing low-resolution data from high-resolution data. Our results show that entropy has a strong explanatory power for the quantiles of the distribution of the daily returns. Based on Christoffersen’s tests for Value at Risk (VaR) backtesting, we can conclude that the VaR forecast build upon the entropy of intraday returns is the best, compared to the forecasts provided by the classical GARCH models.