Chaotic dynamical systems are essentially nonlinear and are highly sensitive to variations in initial conditions and process parameters. Chaos may appear both in natural (e.g., heartbeat rhythms and weather fluctuations) and human-engineered (e.g., thermo-fluid, urban traffic, and stock market) systems. For prediction and control of such systems, it is often necessary to be able to distinguish between non-chaotic and chaotic behavior; several methods exist to detect the presence (or absence) of chaos, specially in noisy signals. A dynamical system may exhibit multiple chaotic regimes, and apparently, there exist no methods, reported in open literature, to classify these regimes individually. This paper demonstrates an application of standard hidden Markov modeling (HMM), which is a commonly used supervised method, as a technique to classify multiple regimes from a time series of dynamical systems, where classified regimes could be chaotic or non-chaotic. The proposed HMM-based method of regime classification has been tested using numerical data obtained from several well-known chaotic dynamical systems (e.g., Hénon, forced Duffing, Rössler, and Lorenz attractor). It is apparently well-suited to serve as a bench mark for the development of alternative data-driven methods to enhance the performance (e.g., accuracy and computational speed) of regime classification in chaotic dynamical systems.

The paper presents a coupled machine learning and pattern recognition algorithm to enable early-stage fatigue damage detection in aerospace-grade aluminum alloys. U- and V-notched Al7075-T6 specimens are instrumented with a pair of ultrasonic sensors and, thereafter, tested on an MTS apparatus integrated with a confocal microscope and a digital microscope. The confocal microscope is focused on the notch root of the specimens, whereas the digital microscope is focused on the side of the notch. Two features, viz., the crack opening displacement (COD) and the crack length, are extracted during the tests in addition to the ultrasonic signal data. These signal data are analyzed using a machine learning framework that is built upon a symbolic time-series algorithm. This framework is interrogated for crack detection in the crack coalescence (CC) regime defined by COD of ~3 μm and detected through the confocal microscope. Additionally, the framework is probed in the crack propagation (CP) regime characterized by a crack length of ~0.2 mm and detected via the digital microscope. For the CC regime, training accuracies of 79.82% and 81.94% are achieved, whereas testing accuracies of 68.18% and 74.12% are observed for the U- and V-notched specimens, respectively. For the CP regime, overall training accuracies of 88.3% and 91.85% are observed, and accordingly, testing accuracies of 81.94% and 85.62% are obtained for the U- and V-notched specimens, respectively. The results show that a combined machine learning and pattern recognition algorithm enables robust and reliable fatigue damage detection in aerospace structural components.

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 analyze 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 TL, 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 TL have been validated by comparison with those of two shallow neural networks (NNs)-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.

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.