Application Of Recurrence Quantification Analysis Research Articles

Coating failure detection in scratch testing: A cross-sectional SEM/FIB microscopic study coupled with nonlinear analysis methods in a model titanium nitride/stainless steel system

In modern scratch testing, efforts are made to improve the quality of quantitative measurement of the coating adhesion. This paper proposes a new method for analyzing data collected in scratch tests. The nonlinear analysis methods of both penetration depth and tangential force time series were combined with SEM/FIB cross-sectional studies to monitor the progression of coating failure in a model titanium nitride coated stainless steel system. The applicability of recurrence quantification analysis and diagonal cross-recurrence analysis in scratch testing were discussed.

Application of Recurrence Quantification Analysis in the Detection of Osteoarthritis of the Knee with the Use of Vibroarthrography

Application of Recurrence Quantification Analysis in the Detection of Osteoarthritis of the Knee with the Use of Vibroarthrography

Application of recurrence quantification analysis of acoustic emission time series to analysis of a plastic flow of metals.

As a result of the application of recurrence quantification analysis to acoustic emission time series obtained in uniaxial tensile testing of copper and silver, we detected the existence of a characteristic interval in which the Shannon information entropy (as a parameter of the quantitative analysis of recurrence plots) increased rapidly. Using statistical analysis of the behavior of the dislocation ensemble, we established a relation between the physical parameters of the given interval and the global stability loss parameters of the plastic flow of metals, indicating the predictability of the distinctive point determined long before the critical state was attained.

Nonlinear dynamics in Divisia monetary aggregates: an application of recurrence quantification analysis

We construct recurrence plots (RPs) and conduct recurrence quantification analysis (RQA) to investigate the dynamic properties of the new Center for Financial Stability (CFS) Divisia monetary aggregates for the United States. In this study, we use the latest vintage of Divisia aggregates, maintained within CFS. We use monthly data, from January 1967 to December 2020, which is a sample period that includes the extreme economic events of the 2007–2009 global financial crisis. We then make comparisons between narrow and broad Divisia money measures and find evidence of a nonlinear but reserved possible chaotic explanation of their origin. The application of RPs to broad Divisia monetary aggregates encompasses an additional drift structure around the global financial crisis in 2008. Applying the moving window RQA to the growth rates of narrow and broad Divisia monetary aggregates, we identify periods of changes in data-generating processes and associate such changes to monetary policy regimes and financial innovations that occurred during those times.

Detection of cybersecurity spoofing attacks in vehicular networks with recurrence quantification analysis

Cybersecurity aspects in modern automotive vehicles are becoming increasingly important due to the recent demonstration of successful cybersecurity attacks. Intrusion Detection System (IDS) is one of the approaches proposed in the research literature to detect such attacks. This paper proposes a novel IDS approach based on the application of Recurrence Quantification Analysis (RQA), in combination with a sliding window, to the information of the CAN-bus message arrival time, which has the benefit of not requiring the processing of the arbitration field or the payload data of the CAN-bus message. The rationale for the application of RQA to this problem is to consider the in-vehicle network as a dynamic system where the CAN-bus message time is used as an observable. This approach is evaluated with various machine learning algorithms on two public data sets recently published by the research community with a focus on spoofing attacks since they are the most difficult to detect. The proposed approach is compared with the application of entropy measures for attack detection, which are commonly adopted in the literature and with the results from the literature on the same data sets. The results show that the RQA based approach provides a better detection accuracy than entropy measures in a consistent way across different sliding window sizes in both data sets and it is competitive against other approaches in the literature. This paper provides also an extensive evaluation of the impact on detection accuracy of the sliding window size and the hyper-parameters present in the definition of RQA and the machine learning algorithms.

Recurrence Quantification Analysis of Ankle Kinematics During Gait in Individuals With Chronic Ankle Instability.

PurposeAn investigation of the ankle dynamics in a motor task may generate insights into the etiology of chronic ankle instability (CAI). This study presents a novel application of recurrence quantification analysis (RQA) to examine the ankle dynamics during walking. We hypothesized that CAI is associated with changes in the ankle dynamics as assessed by measures of determinism and laminarity using RQA.MethodsWe recorded and analyzed the ankle position trajectories in the frontal and sagittal planes from 12 participants with CAI and 12 healthy controls during treadmill walking. We used time-delay embedding to reconstruct the position trajectories to a phase space that represents the states of the ankle dynamics. Based on the phase space trajectory, a recurrence plot was constructed and two RQA variables, the percent determinism (%DET) and the percent laminarity (%LAM), were derived from the recurrence plot to quantify the ankle dynamics.ResultsIn the frontal plane, the %LAM in the CAI group was significantly lower than that in the control group (p < 0.05. effect size = 0.86). This indicated that the ankle dynamics in individuals with CAI is less likely to remain in the same state. No significant results were found in the %DET or in the sagittal plane.ConclusionA lower frontal-plane %LAM may reflect more frequent switching between different patterns of neuromuscular control states due to the instabilities associated with CAI. With further study and development, %LAM may have the potential to become a useful biomarker for CAI.

Testing for Non-Linear Structures in Artificial and Real-World Financial Data with Recurrence Quantification Analysis

Early applications of empirical methods from chaos theory suggested the existence of low dimensional chaotic motion in empirical financial data. However, such results were questioned, and it is then believed that the search for low dimensional chaos in financial data was not successful. On the other hand, at the same time that the hypotheses that raw returns are independent and identically distributed (IID) is often rejected, they indeed present a quite small degree of autocorrelation. These facts suggest that prices in financial markets do not behave completely at random, although their hidden structures seem more complex than those observed in low dimensional chaotic systems. Previous work tested for non-linearity or the presence of low dimensional chaos in artificial financial data generated from the Lux-Marchesi model by means of the BDS and Kaplan tests. Addressing the same model, researchers extended those results by applying Hinich’s bi-spectral and White’s tests and introducing the application of Recurrence Quantification Analysis (RQA) on artificial financial data based on Recurrence Rate, Determinism, Entropy, and Maximal Diagonal Length. Contributing to this research, the present paper has two main goals: (i) to contrast previous findings with an RQA application on data generated by a more evolved of microscopic model of financial markets – the Structural Stochastic Volatility (SSV ) model; and (ii) to extend the RQA investigation above with additional recurrence measures (namely, Divergence, Laminarity, and Maximal Vertical Length) being applied to distinct real-world financial data. The objective is to assess if RQA results could help to distinguish between artificial and real-world data, even if linearity is rejected in both cases. It is shown evidence, in agreement previous findings, to support the rejection of linearity or low dimensional chaotic motion in an artificial financial time series generated from the SSV microscopic model. In addition, it is also shown that that RQA measures can help to discriminate artificial from real-world financial data, at least when specific RQA measures are considered.

Application of RQA and SOM for identification of two-phase flow patterns during boiling in horizontal minichannel

In the paper, numerical methods of data analysis recurrence quantification analysis (RQA) and self-organizing map (SOM) have been used to analyse pressure drop oscillations during the flow boiling in minichannel. The performed analysis allows us to identify flow patterns based on the character of the pressure drop oscillations. The following two-phase flow patterns have been identified: liquid flow, liquid flow with small vapour bubble, slug flow, long slug flow and confined bubble flow. In the experiment, the open-loop boiling system in a circular horizontal minichannel with an inner diameter of 1 mm was investigated. The two-phase flow patterns at the outlet of the heated section were observed through the glass tube (with an inner diameter of 1 mm) and recorded by a high-speed camera Phantom v1610.

Study of tribological behaviour of surface modified stainless-steel using recurrence quantification analysis and principal component analysis

In tribological studies, one of the main challenges is the proper identification of the prevalent wear phenomena that affect the mating pair of materials. In surface-modified materials, it is particularly difficult to identify the onset of wear-induced damage of the protective film. In this paper, an example of successful application of Recurrence Quantification Analysis (RQA) and Principal Component Analysis (PCA) on two tribological signals: coefficient of friction (COF) and electrical contact resistance (ECR), is presented. Based on the results provided, with the use of RQA and PCA, it is possible to identify the prevalent wear modes of a tribological pair, as well as to spot the transition between chaotic and periodic friction.

Application of recurrence quantification analysis for early detection of lean blowout in a swirl-stabilized dump combustor.

Lean blowout (LBO) is a serious issue in modern gas turbine engines that operate in a lean (premixed) mode to follow the stringent emission norms. When an engine operates with a lean fuel-air mixture, the flame becomes unstable and is at times carried out of the combustion chamber by the unburnt flow. Thus, the sudden loss of the flame, known as lean blowout, leads to fatal accidents in aircrafts and loss of production in power plants. Therefore, an in-depth analysis of lean blowout is necessary as the phenomenon involves complex interactions between flow dynamics and chemical kinetics. For understanding the complex dynamics of this phenomenon, recurrence analysis can be a very useful method. In the current study, we observe a transition to LBO as the global fuel-air ratio is reduced from stoichiometric condition and perform recurrence quantification analysis (RQA) with the CH∗ chemiluminescence data obtained experimentally. The extent of fuel-air mixing is varied with an objective of developing some robust early predictors of LBO that would work over a wide range of premixing. We find some RQA measures, such as determinism, laminarity, and trapping time, which show distinctive signature toward LBO and thereby can be used as early predictors of LBO for both premixed and partially premixed flames. Our analysis shows that the computational time for laminarity and trapping time is relatively less. However, computational time for those measures depends upon the dynamics of the combustor, size of the data taken, and choice of recurrence threshold.

Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

RQA correlations on real business cycles time series

Trade cycles are complex phenomena which oscillate because of economic downturns and expansions. Recurrence quantification analysis (RQA) detects state changes without necessitating any a priori mathematical assumption and highlights hidden features of the dynamics both at equilibrium and near transition phases. This paper aims to understand some potential application of recurrence quantification analysis in detecting recessions.

The Application of Recurrence Quantification Analysis in Detection of Abrupt Climate Change

This paper explores the possible application of recurrence quantification analysis in the detection of abrupt change of the dynamic structure of the climate system. It is discovered in the recurrence quantification analysis of the typical chaotic system-logistic model that the method may well distinguish the state of logistic model with different parameters, demonstrating its potential value in identifying the dynamic change of the system. When recurrence quantification analysis is later applied to the detection of abrupt change of average daily precipitation of all regions in China, the result indicates that the abrupt change of the dynamic structure corresponding to the precipitation of China in recent 50 years occurred in the late 1970s and the early 1980s. It is in agreement with the Chinese commonly recognized years of abruption; therefore the effectiveness is further demonstrated regarding the recognition of complexity of dynamical system.

Application of Recurrence Quantification Analysis to Power System Dynamic Studies

Recurrence quantification analysis (RQA) is a nonlinear data analysis technique that can quantify the number and duration of a dynamical system of being in nearly the same area in phase space trajectory. This paper proposes three applications of RQA to analyse power system dynamics. These are denoising of PMU data, localization of power system events, and transient stability contingency ranking of power system. All three applications have been demonstrated using a multimachine test system.

Characterizing Fluctuations of Arterial and Cerebral Tissue Oxygenation in Preterm Neonates by Means of Data Analysis Techniques for Nonlinear Dynamical Systems.

The cerebral autoregulatory state as well as fluctuations in arterial (SpO2) and cerebral tissue oxygen saturation (StO2) are potentially new relevant clinical parameters in preterm neonates. The aim of the present study was to test the investigative capabilities of data analysis techniques for nonlinear dynamical systems, looking at fluctuations and their interdependence. StO2, SpO2 and the heart rate (HR) were measured on four preterm neonates for several hours. The fractional tissue oxygenation extraction (FTOE) was calculated. To characterize the fluctuations in StO2, SpO2, FTOE and HR, two methods were employed: (1) phase-space modeling and application of the recurrence quantification analysis (RQA), and (2) maximum entropy spectral analysis (MESA). The correlation between StO2 and SpO2 as well as FTOE and HR was quantified by (1) nonparametric nonlinear regression based on the alternating conditional expectation (ACE) algorithm, and (2) the maximal information-based nonparametric exploration (MINE) technique. We found that (1) each neonate showed individual characteristics, (2) a ~60 min oscillation was observed in all of the signals, (3) the nonlinear correlation strength between StO2 and SpO2 as well as FTOE and HR was specific for each neonate and showed a high value for a neonate with a reduced health status, possibly indicating an impaired cerebral autoregulation. In conclusion, our data analysis framework enabled novel insights into the characteristics of hemodynamic and oxygenation changes in preterm infants. To the best of our knowledge, this is the first application of RQA, MESA, ACE and MINE to human StO2 data measured with near-infrared spectroscopy (NIRS).

Application of recurrence quantification analysis to automatically estimate infant sleep states using a single channel of respiratory data

Previous work has identified that non-linear variables calculated from respiratory data vary between sleep states, and that variables derived from the non-linear analytical tool recurrence quantification analysis (RQA) are accurate infant sleep state discriminators. This study aims to apply these discriminators to automatically classify 30 s epochs of infant sleep as REM, non-REM and wake. Polysomnograms were obtained from 25 healthy infants at 2 weeks, 3, 6 and 12 months of age, and manually sleep staged as wake, REM and non-REM. Inter-breath interval data were extracted from the respiratory inductive plethysmograph, and RQA applied to calculate radius, determinism and laminarity. Time-series statistic and spectral analysis variables were also calculated. A nested cross-validation method was used to identify the optimal feature subset, and to train and evaluate a linear discriminant analysis-based classifier. The RQA features radius and laminarity and were reliably selected. Mean agreement was 79.7, 84.9, 84.0 and 79.2 % at 2 weeks, 3, 6 and 12 months, and the classifier performed better than a comparison classifier not including RQA variables. The performance of this sleep-staging tool compares favourably with inter-human agreement rates, and improves upon previous systems using only respiratory data. Applications include diagnostic screening and population-based sleep research.

Optimization of Euclidean distance threshold in the application of recurrence quantification analysis to heart rate variability studies

An integrated approach is proposed to solve the optimization problem of the Euclidean distance threshold ε in recurrence quantification analysis (RQA), which is increasingly applied in the study of heart rate variability (HRV). In this paper, ε is inversely computed from a given recurrence rate (REC), the percentage of recurrence points. From the inversely computed ε, two other RQA output variables: determinism (DET), the percentage of recurrence points forming diagonal line structures, and laminarity (LAM), the percentage of recurrence points forming vertical and horizontal structures, are computed out as well. The trend of DET, LAM values at different REC levels (DLR trend) is introduced to comprehensively represent the dynamic properties of a time series. Based on the DLR trend, the variation of discrimination power, represented by the average loss (or Bayes risk), of DET and LAM, at different REC values is analyzed. Surrogate techniques are used to generate reliable test data sets for the discrimination evaluation. In particular, the results show that (1) the optimal REC can be much higher than the widely used 1% REC, and (2) after the optimization, the average loss can be reduced compared to 1% REC. It is also demonstrated that the optimal ε depends on the dynamic source and RQA variables, and the DLR trend based ε optimization method can improve RQA discrimination analysis especially for the short term HRV analysis.

Recurrence quantification analysis and state space divergence reconstruction for financial time series analysis

The application of recurrence quantification analysis (RQA) and state space divergence reconstruction for the analysis of financial time series in terms of cross-correlation and forecasting is illustrated using high-frequency time series and random heavy-tailed data sets. The results indicate that these techniques, able to deal with non-stationarity in the time series, may contribute to the understanding of the complex dynamics hidden in financial markets. The results demonstrate that financial time series are highly correlated. Finally, an on-line trading strategy is illustrated and the results shown using high-frequency foreign exchange time series.

Combinatorics and synchronization in natural semiotics

In this study the derivation of an objective metrics to appreciate the degree of structuring of written and spoken texts is presented. The proposed metrics is based on the scoring of recurrences inside a text by means of the application of recurrence quantification analysis (RQA), a nonlinear technique widely used in other fields of sciences. The adopted approach allowed us to create a ranking of different poems strictly related to their prosodic structure and, more importantly, the possibility to recognize the same structure across different languages, to define a level of structuring typical of spoken texts and identifying the progressive synchronization of a dyadic relation between two speakers in terms of relative complexity of their speeches. These results suggest the possibility of introducing objective measurement methods into humanities studies.