Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Damage identification in structural health monitoring: a brief review from its implementation to the Use of data-driven applications

The damage identification process provides relevant information about the current state of a structure under inspection, and it can be approached from two different points of view. The first approach uses data-driven algorithms, which are usually associated with the collection of data using sensors. Data are subsequently processed and analyzed. The second approach uses models to analyze information about the structure. In the latter case, the overall performance of the approach is associated with the accuracy of the model and the information that is used to define it. Although both approaches are widely used, data-driven algorithms are preferred in most cases because they afford the ability to analyze data acquired from sensors and to provide a real-time solution for decision making; however, these approaches involve high-performance processors due to the high computational cost. As a contribution to the researchers working with data-driven algorithms and applications, this work presents a brief review of data-driven algorithms for damage identification in structural health-monitoring applications. This review covers damage detection, localization, classification, extension, and prognosis, as well as the development of smart structures. The literature is systematically reviewed according to the natural steps of a structural health-monitoring system. This review also includes information on the types of sensors used as well as on the development of data-driven algorithms for damage identification.Peer ReviewedPostprint (published version

Unsupervised spectral learning of WCFG as low-rank matrix completion

We derive a spectral method for unsupervised learning ofWeighted Context Free Grammars. We frame WCFG induction as finding a Hankel matrix that has low rank and is linearly constrained to represent a function computed by inside-outside recursions. The proposed algorithm picks the grammar that agrees with a sample and is the simplest with respect to the nuclear norm of the Hankel matrix.Peer ReviewedPreprin

Smart monitoring of aeronautical composites plates based on electromechanical impedance measurements and artificial neural networks

This paper presents a structural health monitoring (SHM) method for in situ damage detection and localization in carbon fiber reinforced plates (CFRPs). The detection is achieved using the electromechanical impedance (EMI) technique employing piezoelectric transducers as high-frequency modal sensors. Numerical simulations based on the finite element method are carried out so as to simulate more than a hundred damage scenarios. Damage metrics are then used to quantify and detect changes between the electromechanical impedance spectrum of a pristine and damaged structure. The localization process relies on artificial neural networks (ANNs) whose inputs are derived from a principal component analysis of the damage metrics. It is shown that the resulting ANN can be used as a tool to predict the in-plane position of a single damage in a laminated composite plate

Brief Review of Vibration Based Machine Condition Monitoring

In the process of channeling energy into job to be performed all machines vibrate. Machines rarely break down without giving some previous warning. The signs of impeding failure are generally present long before a machine totally breaks down. When faults begin to develop in the machine, some of dynamic processes in the machine are changed as well, thereby influencing machine vibration level, temporal and spectral vibration properties. Such changes can act as an indicator for early detection and identification of developing faults. This paper briefly reviews the machine condition monitoring based on vibration data analysis. After the review of major, well established and mature approaches, new unsupervised approaches based on novelty detection are also briefly mentioned

Spectral learning with proper probabilities for finite state automation

International audienceProbabilistic Finite Automaton (PFA), Probabilistic Finite State Transducers (PFST) and Hidden Markov Models (HMM) are widely used in Automatic Speech Recognition (ASR), Text-to-Speech (TTS) systems and Part Of Speech (POS) tagging for language mod-eling. Traditionally, unsupervised learning of these latent variable models is done by Expectation-Maximization (EM)-like algorithms, as the Baum-Welch algorithm. In a recent alternative line of work, learning algorithms based on spectral properties of some low order moments matrices or tensors were proposed. In comparison to EM, they are orders of magnitude faster and come with theoretical convergence guarantees. However, returned models are not ensured to compute proper distributions. They often return negative values that do not sum to one, limiting their applicability and preventing them to serve as an initialization to EM-like algorithms. In this paper, we propose a new spectral algorithm able to learn a large range of models constrained to return proper distributions. We assess its performances on synthetic problems from the PAutomaC challenge and real datasets extracted from Wikipedia. Experiments show that it outperforms previous spectral approaches as well as the Baum-Welch algorithm with random restarts, in addition to serve as an efficient initialization step to EM-like algorithms

Local String Transduction as Sequence Labeling

[EN]We show that the general problem of string transduction can be reduced to the problem of sequence labeling. While character deletion and insertions are allowed in string transduction, they do not exist in sequence labeling. We show how to overcome this difference. Our approach can be used with any sequence labeling algorithm and it works best for problems in which string transduction imposes a strong notion of locality (no long range dependencies). We experiment with spelling correction for social media, OCR correction, and morphological inflection, and we see that it behaves better than seq2seq models and yields state-of-the-art results in several cases.Peer reviewe