In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots

As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization

Practical implementation of nonlinear time series methods: The TISEAN package

Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena despite the fact that very few natural systems have actually been found to be low dimensional deterministic in the sense of the theory. In order to evaluate the long term usefulness of the nonlinear time series approach as inspired by chaos theory, it will be important that the corresponding methods become more widely accessible. This paper, while not a proper review on nonlinear time series analysis, tries to make a contribution to this process by describing the actual implementation of the algorithms, and their proper usage. Most of the methods require the choice of certain parameters for each specific time series application. We will try to give guidance in this respect. The scope and selection of topics in this article, as well as the implementational choices that have been made, correspond to the contents of the software package TISEAN which is publicly available from http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as an extended manual for the TISEAN programs. It fills the gap between the technical documentation and the existing literature, providing the necessary entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at http://www.mpipks-dresden.mpg.de/~tisea

Time Series Analysis using Embedding Dimension on Heart Rate Variability

Heart Rate Variability (HRV) is the measurement sequence with one or more visible variables of an underlying dynamic system, whose state changes with time. In practice, it is difficult to know what variables determine the actual dynamic system. In this research, Embedding Dimension (ED) is used to find out the nature of the underlying dynamical system. False Nearest Neighbour (FNN) method of estimating ED has been adapted for analysing and predicting variables responsible for HRV time series. It shows that the ED can provide the evidence of dynamic variables which contribute to the HRV time series. Also, the embedding of the HRV time series into a four-dimensional space produced the smallest number of FNN. This result strongly suggests that the Autonomic Nervous System that drives the heart is a two features dynamic system: sympathetic and parasympathetic nervous system.Peer reviewedFinal Published versio

Trends in recurrence analysis of dynamical systems

The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research

Signal Modality Characterization: from Phase Space Reconstruction to Real Applications

La caracterización de la modalidad de la señal es un nuevo concepto objeto de recientes trabajos de investigación cuyo principal propósito es identificar cambios en la naturaleza de señales reales. Con el término naturaleza de las señales se hace referencia al modelo subyacente que genera una señal desde el punto de vista de dos características principales: determinismo y linealidad. En esta tesis se emplea la modalidad de la señal para el procesado avanzado de señales acústicas, y en particular, en ensayos no destructivos de materiales no homogéneos como el hormigón. El problema de la caracterización de la modalidad comienza con la correcta reconstrucción del espacio de fases (Capítulo 2). Este nuevo dominio permite identificar los diferentes estados de una señal, recurrentes o no en función de su naturaleza determinista o aleatoria, respectivamente. En el ámbito de los ensayos no destructivos basados en ultrasonidos, el material se excita con una señal puramente determinista, sin embargo, la naturaleza de la señal recibida depende y es proporcional a la estructura interna del material. Esta hipótesis de trabajo permite plantear la medida del grado de determinismo como una alternativa complementaria a parámetros habituales de ultrasonidos como la atenuación y la velocidad. El nivel de determinismo ha resultado ser proporcional al nivel de porosidad en materiales cementantes (Capítulo 3). También permite la caracterización del nivel de daño de probetas de mortero sometidas a diferentes procesos de daño: ataque externo de sulfato y procesos de carga (Capítulo 4). El estudio de la no linealidad/ complejidad de una serie temporal se plantea inicialmente de forma ciega (sin tener información de la señal de entrada) mediante tests de hipótesis: generando datos surrogados y aplicando un test estadístico. Importantes avances se han logrado adaptando este enfoque a datos no estacionarios, característica habitual de señales no lineales reales. Los principales resultados en este sentido se han conseguido en la caracterización de la complejidad de señales oscilatorias de duración limitada (Capítulo 5). El concepto de la modalidad de la señal también se ha empleado para realizar un detallado estudio del fenómeno no lineal de espectroscopía acústica por impacto. Este análisis ha permitido entender las variables involucradas y plantear así un modelo matemático que caracterice el fenómeno. La comprensión del fenómeno y el modelo han permitido plantear un nuevo algoritmo de procesado equivalente a la técnica habitual NIRAS, pero óptimo en su aplicación. Esta alternativa de procesado puede suponer significativos avances sobre todo en aplicaciones industriales donde el tiempo y el esfuerzo son variables óptimas (Capítulo 6). Esta tesis demuestra que la caracterización de la modalidad de la señal no solo supone una alternativa a la caracterización de complejos fenómenos reales, sino que abre una nueva perspectiva de trabajo dentro del ámbito del procesado de señal. La medida del determinismo y el algoritmo FANSIRAS han demostrado que la modalidad de la señal es una interesante herramienta para futuros trabajos de caracterización de materiales cementantes.The characterization of the modality of a signal is a new concept, which has been the subject of recent research. Its main purpose is to identify any changes in the nature of a real signal. The term `nature of a signal' refers to the underlying model that generates the signal from the point of view of two main characteristics: determinism and linearity. In this thesis, the modality of a signal is used for the advanced processing of acoustic signals, and in particular, in non-destructive tests of non-homogeneous materials, such as concrete. The problem of the characterization of the modality begins with the correct reconstruction of the phase space (Chapter 2). This new domain allows identifying the different states of a signal, as to whether they are recurrent or not, depending on whether they are deterministic, respectively, random. In the field of non-destructive testing based on ultrasound, the material is excited with a purely deterministic signal. However, the nature of the received signal depends on the internal structure of the material. This working hypothesis allows us to propose measuring the degree of determinism as a complementary alternative to the usual ultrasound parameters such, as attenuation and speed. The level of determinism has been found to be proportional to the level of porosity in cementitious materials (Chapter 3). It also allows characterizing the level of damage of mortar test pieces subjected to different kinds of damaging processes: external attack by sulphates, and loading processes (Chapter 4). The study of the non-linearity or complexity of a time series is initially presented blindly (without having information about the input signal) through hypothesis tests: generating surrogate data and applying a statistical test. Significant progress has been made in adapting this approach to nonstationary data, a common feature of real non-linear signals. The main results in this regard have been achieved in the characterization of the complexity of oscillatory signals of limited duration (Chapter 5). The concept of signal modality has also been used to perform a detailed study of the non-linear phenomenon of acoustic impact spectroscopy. This analysis has allowed understanding the variables involved, and thus, proposing a mathematical model that characterizes the phenomenon. The understanding of the phenomenon and the model have allowed proposing a new processing algorithm equivalent to the usual NIRAS technique, but optimal in its application. This processing alternative may mean significant advances, especially in industrial applications where time and e ort are variables to be optimized (Chapter 6). This thesis demonstrates that the characterization of the modality of a signal not only presents an alternative to the characterization of complicated real phenomena, but it also opens a new research perspective within the field of signal processing. The measure of determinism and the FANSIRAS algorithm have shown that the modality of a signal is an interesting tool for future research into the characterization of cementitious materials.La caracterització de la modalitat del senyal és un nou concepte, objecte de recents treballs de recerca amb el propòsit d'identificar canvis en la natura de senyals reals. Amb el terme natura dels senyals es fa referència al model subjacent que genera un senyal des del punt de vista de dues característiques principals: determinisme i linealitat. En aquesta tesi es fa servir la modalitat del senyal per al processament avançat de senyals acústics i, en particular, en assajos no destructius de materials no homogenis com ara el formigó. El problema de la caracterització de la modalitat comença amb la correcta reconstrucció de l'espai de fase (Capítol 2). Aquest nou domini permet identificar els diferents estats d'un senyal, recurrents o no en funció de la seva natura determinista o aleatòria, respectivament. Dins l'àmbit dels assajos no destructius basats en ultrasons, el material s'excita amb un senyal purament determinista, tanmateix, la natura del senyal rebut depèn i és proporcional a l'estructura interna del material. Aquesta hipòtesi de treball permet plantejar la mesura del grau de determinisme com una alternativa complementària a paràmetres habituals dels ultrasons com ara l'atenuació i la velocitat. El nivell de determinisme ha resultat ésser proporcional al nivell de porositat en materials cementants (Capítol 3). També permet la caracterització del nivell de dany de provetes de morter sotmeses a diferents processos de dany: atac extern de sulfat i processos de càrrega (Capítol 4). L'estudi de la no linealitat/ complexitat d'una sèrie temporal es planteja inicialment de forma cega (sense tindre cap informació del senyal d'entrada) mitjançant tests d'hipòtesi: generant dades subrogades i aplicant un test estadístic. Avanços importants s'han aconseguit adaptant aquest enfoc a dades no estacionàries, característica habitual de senyals no lineals reals. Els principals resultats en aquest sentit s'han aconseguit en la caracterització de la complexitat de senyals oscil·latoris de durada limitada (Capítol 5). El concepte de modalitat del senyal també s'ha emprat per realitzar un detallat estudi del fenomen no lineal d'espectroscòpia acústica per impacte. Aquesta anàlisi ha permet entendre les variables involucrades i plantejar llavors un nou algoritme de processament equivalent a la tècnica habitual NIRAS, però òptim en la seva aplicació. Aquesta alternativa de processament pot suposar significatius avanços sobretot en aplicacions industrials, on el temps i l'esforç són variables òptimes (Capítol 6). Aquesta tesi demostra que la caracterització de la modalitat del senyal no solament suposa una alternativa a la caracterització de complexes fenòmens reals, sinó que obri una nova perspectiva de treball dins l'àmbit del processament de senyal. La mesura del determinisme i l'algoritme FANSIRAS han demostrat que la modalitat del senyal és una ferramenta interessant per a futurs treballs de caracterització de materials cementants.Carrión García, A. (2018). Signal Modality Characterization: from Phase Space Reconstruction to Real Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/106366TESI

Interdisciplinary application of nonlinear time series methods

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.Comment: 86 pages, 26 figure

Corrosion Monitoring Based on Recurrence Quantification Analysis of Electrochemical Noise and Machine Learning Methods

Although electrochemical noise (EN) has been studied for decades, the optimal approach for the analysis of EN data remains uncertain. This research innovatively combined the use of recurrence quantification analysis of electrochemical noise data and machine learning methods to develop models for corrosion monitoring and corrosion type identification. Case studies demonstrate that the proposed methodologies are potentially feasible for the development of online corrosion monitoring programs

Optimal state space reconstruction via Monte Carlo decision tree search

A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally, we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor

Paying attention to the evidence: a comparison of perception and decision making processes in novice and experienced scene of crime officers using eye tracking in simulated crime scene scenarios

Research on crime scene investigation has strongly focused on the technical aspects of the process, while cognitive aspects (searching, reasoning and perception) have often been overlooked. Textbooks on forensic sciences tend to focus on identifying and processing evidence, and the use of equipment while it can be argued that cognitive factors in processing such evidence and using equipment are equally important. This thesis studies the cognitive aspects of crime scene investigation by comparing eye movement patterns in experts and novices. Studies in various domains, including surgery, sports, and chess playing have shown that eye movements differ between experts and novices, providing a tool towards a more objective assessment of skill than is possible with peer assessment. In four experiments eye movements of experts and novices were examined during (1) inspection of photographs of crime scenes on a computer screen (2) a change blindness task on crime and non-crime scene images, (3) active exploration of a simulated crime scene and (4) the assessment of emotional crime and natural scenes. While some trends in eye movement differences, such as a tendency on longer fixation durations and a broader focus on the overall scene and less on the direct evidence could be found in experts compared to novices, differences between experts and novices were considerably smaller than in other domains, despite the broad range of measures extracted from the data. This lack of clear expertise effects may relate to the rather diverse range of perceptual layouts of crime scenes, reducing possible top-down effects of expertise on the deployment of attention. The results will be discussed with a view of possible directions of future research in this domain