Kushal Mukherjee

Wavelet-based feature extraction using probabilistic finite state automata for pattern classification

Real-time data-driven pattern classification requires extraction of relevant features from the observed time series as low-dimensional and yet information-rich representations of the underlying dynamics. These low-dimensional features facilitate in situ decision-making in diverse applications, such as computer vision, structural health monitoring, and robotics. Wavelet transforms of time series have been widely used for feature extraction owing to their time-frequency localization properties. In this regard, this paper presents a symbolic dynamics-based method to model surface images, generated by wavelet coefficients in the scale-shift space. These symbolic dynamics-based models (e.g., probabilistic finite state automata (PFSA)) capture the relevant information, embedded in the sensor data, from the associated Perron-Frobenius operators (i.e., the state-transition probability matrices). The proposed method of pattern classification has been experimentally validated on laboratory apparatuses for two different applications: (i) early detection of evolving damage in polycrystalline alloy structures, and (ii) classification of mobile robots and their motion profiles.

State splitting and merging in probabilistic finite state automata for signal representation and analysis

Probabilistic finite state automata (PFSA) are often constructed from symbol strings that, in turn, are generated by partitioning time series of sensor signals. This paper focuses on a special class of PFSA, which captures finite history of the symbol strings; these PFSA, called D-Markov machines, have a simple algebraic structure and are computationally efficient to construct and implement. The procedure of PFSA construction is based on (i) state splitting that generates symbol blocks of different lengths based on their information contents; and (ii) state merging that assimilates histories by combining two or more symbol blocks without any significant loss of the embedded information. A metric on the probability distribution of symbol blocks is introduced for trade-off between loss of information (e.g., entropy rate) and the number of PFSA states. The underlying algorithms have been validated with three test examples. While the first and second examples elucidate the key concepts and the pertinent numerical steps, the third example presents the results of analysis of time series data, generated from laboratory experimentation, for detection of fatigue crack damage in a polycrystalline alloy.

Fast communication: Generalization of Hilbert transform for symbolic analysis of noisy signals

A recent publication has reported a Hilbert-transform-based partitioning method, called analytic signal space partitioning (ASSP), which essentially replaces wavelet space partitioning (WSP) for symbolic analysis of time series data in dynamical systems. When used in conjunction with D-Markov machines, also reported in the recent literature, ASSP provides a fast method of pattern recognition. However, wavelet transform facilitates denoising, which allows D-Markov machines to have a small depth D even if the time series data have a low signal-to-noise ratio. Since Hilbert transform does not specifically address the issue of noise reduction, usage of D-Markov machines with a small D could potentially lead to information loss for noisy signals. On the other hand, a large D tends to make execution of pattern recognition computationally less efficient due to an increased number of machine states. This paper explores generalization of Hilbert transform that addresses symbolic analysis of noise-corrupted dynamical systems. In this context, theoretical results are derived based on the concepts of information theory. These results are validated on time series data, generated from a laboratory apparatus of nonlinear electronic systems.

Symbolic Dynamic Analysis of Transient Time Series for Fault Detection in Gas Turbine Engines

This brief paper presents a symbolic dynamics-based method for detection of incipient faults in gas turbine engines. The underlying algorithms for fault detection and classification are built upon the recently reported work on symbolic dynamic filtering. In particular, Markov model-based analysis of quasi-stationary steady-state time series is extended to analysis of transient time series during takeoff. The algorithms have been validated by simulation on the NASA Commercial Modular Aero Propulsion System Simulation (C-MAPSS) transient test-case generator.

Optimization of symbolic feature extraction for pattern classification

The concept of symbolic dynamics has been used in recent literature for feature extraction from time series data for pattern classification. The two primary steps of this technique are partitioning of time series to optimally generate symbol sequences and subsequently modeling of state machines from such symbol sequences. The latter step has been widely investigated and reported in the literature. However, for optimal feature extraction, the first step needs to be further explored. The paper addresses this issue and proposes a data partitioning procedure to extract low-dimensional features from time series while optimizing the class separability. The proposed procedure has been validated on two examples: (i) parameter identification in a Duffing system and (ii) classification of fatigue damage in mechanical structures, made of polycrystalline alloys. In each case, the classification performance of the proposed data partitioning method is compared with those of two other classical data partitioning methods, namely uniform partitioning (UP) and maximum entropy partitioning (MEP).

Symbolic Analysis of Sonar Data for Underwater Target Detection

This paper presents a symbolic pattern analysis method for robust feature extraction from sidescan sonar images that are generated from autonomous underwater vehicles (AUVs). The proposed data-driven algorithm, built upon the concepts of symbolic dynamics and automata theory, is used for detection of mines and mine-like objects in the undersea environment. This real-time algorithm is based on symbolization of the data space via coarse graining, i.e., partitioning of the two-dimensional sonar images. The statistical information, in terms of stochastic matrices that serve as features, is extracted from the symbolized images by construction of probabilistic finite state automata. A binary classifier is designed for discrimination of detected objects into mine-like and nonmine-like categories. The pattern analysis algorithm has been validated on sonar images generated in the exploration phase of a mine hunting operation; these data have been provided by the Naval Surface Warfare Center. The algorithm is formulated for real-time execution on limited-memory commercial-of-the-shelf platforms and is capable of detecting objects on the seabed-bottom.

Statistical-Mechanics-Inspired Optimization of Sensor Field Configuration for Detection of Mobile Targets

This paper presents a statistical-mechanics-inspired procedure for optimization of the sensor field configuration to detect mobile targets. The key idea is to capture the low-dimensional behavior of the sensor field configurations across the Pareto front in a multiobjective scenario for optimal sensor deployment, where the nondominated points are concentrated within a small region of the large-dimensional decision space. The sensor distribution is constructed using location-dependent energy-like functions and intensive temperature-like parameters in the sense of statistical mechanics. This low-dimensional representation is shown to permit rapid optimization of the sensor field distribution on a high-fidelity simulation test bed of distributed sensor networks.

State splitting and state merging in probabilistic finite state automata

Probabilistic finite state automata (PΓSA) are constructed from symbol sequences for modeling the behavior of dynamical systems. This paper presents construction of finite history automata from symbol sequences; such automata, called D-Markov machines, are structurally simple and computationally efficient. The construction procedure is based on: (i) state splitting that generates symbol blocks of different lengths according to their relative importance; and (ii) state merging that assimilates histories from symbol blocks leading to the same symbolic behavior. A metric on probability distribution of symbol blocks is introduced for trade-off between modeling performance and the number of PFSA states. These algorithms have been tested by two examples.

Underwater mine detection using symbolic pattern analysis of sidescan sonar images

This paper presents symbolic pattern analysis of sidescan sonar images for detection of mines and mine-like objects in the underwater environment. For robust feature extraction, sonar images are symbolized by partitioning the data sets based on the information generated from the ground truth. A binary classifier is constructed for identification of detected objects into mine-like and non-mine-like categories. The pattern analysis algorithm has been tested on sonar data sets in the form of images, which were provided by the Naval Surface Warfare Center. The algorithm is designed for real-time execution on limited-memory commercial-of-the-shelf platforms, and is capable of detecting seabed-bottom objects and vehicle-induced image artifacts.

Dynamic data driven sensor array fusion for target detection and classification

Target detection and classification using unattended ground sensors (UGS) has been addressed in literature. Various techniques have been proposed for target detection, but target classification is a challenging task to accomplish using the limited processing power on each sensor module. The major hindrance in using these sensors reliably is, that, the sensor observations are significantly affected by external conditions, which are referred to as context. When the context is slowly time-varying (e.g., day-night cycling and seasonal variations) the usage of the same classifier may not be a good way to perform target classification. In this paper, a new framework is proposed as a Dynamic Data Driven Application System (DDDAS) to dynamically extract and use the knowledge of context as feedback in order to adaptively choose the appropriate classifiers and thereby enhance the target classification performance. The features are extracted by symbolic dynamic filtering (SDF) from the time series of sensors in an array and spatio-temporal aggregation of these features represents the context. Then, a context evolution model is constructed as a deterministic finite state automata (DFSA) and, for every context state in this DFSA, an event classifier is trained to classify the targets. The proposed technique of detection and classification has been compared with a traditional method of training classifiers without using any contextual information.