Recurrence Quantification Analysis: A Promising Method for Data Evaluation in Medicine

The methods of recurrence plots (RPs) and recurrence quantification analysis (RQA) have been used to investigate the tribosystem. The morphology of RPs and RQA measures are strongly dependent on the embedding parameters of the recursive matrix and the segment sizes of the time-series. To improve the calculation accuracy of recursive characteristics analysis, the influences of the embedding parameters and segment sizes on the morphology of RPs and RQA measures have been studied in this letter. Three kinds of theoretical chaotic time-series and measured coefficient of friction (COF) signals during the running-in process were chosen as research objects, and the morphology of RPs and RQA measures were obtained using CRP toolbox afterward. The results indicate that no embedding was actually needed if the data sets are to be qualitatively analyzed using RPs and RQA. Additionally, the morphology of RPs and RQA measures are sensitive to the segment sizes for theoretical chaotic time-series, while the RQA measures of COF signal in the steady-state period are rather stable due to its self-similarity. Finally, according to the guidelines of the parameter settings, the dynamical evolution of measured COF signals during the running-in process have been investigated. It is indicated that recursive characteristics of COF signals could reveal the tribological behaviors’ evolution and conduct the running-in status identification. The results in this paper are significant for improving the calculation accuracy and saving computational time when using the method of recursive characteristics analysis on the tribological behaviors.

In this study, we present results of the application of nonlinear time series analysis on traffic data for incident detection. More specifically, we analyze daily volume records of Attica Tollway (Greece) collected from sensors located at various locations. The analysis was performed using the Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) method of the volume data of the lane closest to the median. The results show that it is possible to identify, through the abrupt change of the dynamics of the system revealed by RPs and RQA, the occurrence of incidents on the freeway and differentiate from recurrent traffic congestion. The proposed methodology could be of interest for big data traffic analysis.

Recurrence quantification analysis (RQA) was developed in order to quantify differently appearing recurrence plots (RPs) based on their small-scale structures, which generally indicate the number and duration of recurrences in a dynamical system. Although RQA measures are traditionally employed in analyzing complex systems and identifying transitions, recent work has shown that they can also be used for pairwise dissimilarity comparisons of time series. We explain why RQA is not only a modern method for nonlinear data analysis but also is a very promising technique for various time series mining tasks.

The purpose of this study was to apply recurrence plots and recurrence quantification analysis (RQA) on event related potentials (ERPs) recorded during memory recognition tests. Data recorded during memory retrieval in four scalp region was used. Tow most important ERP's components corresponding to memory retrieval, FN400 and LPC, were detected in recurrence plots computed for single-trial EEGs. In addition, the RQA was used to quantify changes in signal dynamic structure during memory retrieval, and measures of complexity as RQA variables were computed. Given the stimulus, amplitude of the RQA variables increases around 400ms, corresponding to dimension reduction of system. Furthermore, after 800ms these amplitudes decreased which can be as a consequence of an increase in system dimension and back to its basic state. The mean amplitude of Old items was more than New one. Using this method, we found its ability to detect memory components of EEG signals and do a distinction between Old/ New items. In contrast with linear techniques recurrence plots and RQA do not need large number of recorded trials, and they can indicate changes in even single-trial EEGs. RQA can also show differences between old and new events in a memory process.

The movement of lifting heavy objects with upper limb exoskeleton is a dynamic process of multi-muscle coordination. Muscle fatigue occurs after repetitive lifting heavy objects with exoskeleton robot for a long time. Due to the dynamic characteristics of the moving process, the traditional linear analysis methods can not fully characterize the muscle fatigue problem of upper limb. In this paper, a novel approach base on ross recurrence plot (CRP)and recurrence quantification analysis (RQA)is proposed to analyze the progression of muscle fatigue of upper limb. Firstly, distance threshold and date length of the recurrence plot is chosen according to the RP dynamical structures of the electromyography (EMG)signals. Then the phase space reconstruction techniques and recurrence plot theory are utilized to analyze the nonstationarity characteristics of the multichannel and single-channel surface EMG signals during the fatigue process. Finally, the RQA indices of the overall and local muscles are calculated. The experiments show that the CRP can qualitatively reflect the change of muscle fatigue state. Meanwhile, the RQA indices of multi-channel and single-channel EMG signals can quantitatively reveal the changes of muscle fatigue from the overall and local perspectives. This method provides a theoretical basis for evaluating muscle fatigue during repeated moving in the way of nonlinear dynamics.

In the paper, application of the Recurrence Plots (RP) method to damage detection and localization in the beam structure is proposed. The RP is a well-established method of nonlinear data analysis dedicated to investigation into changes in dynamic behaviour of mechanical systems during their normal work. Interpretation of information provided by the recurrence plots can be supported by the estimation of the measures of Recurrence Quantification Analysis (RQA).

The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.

The analysis of financial markets has significantly developed throughout the last few decades shifting towards models of complexity, volatility clustering and unpredictability. One of the most significant components in this evolution is the use of nonlinear dynamics and chaos theory in financial market models which give an understanding of what appears to be random price changes and of the underlying deterministic patterns. The study examines the application of nonlinear dynamical systems and chaotic behavior in the modeling of financial markets, that is, foreign exchange, equity returns and commodity prices. The study is conducted using a combination of econometric tests, phase space reconstruction, the Lyapunov exponent estimation and the recurrence quantification analysis, to determine how much market time series are nonlinearly dependent and sensitive to initial conditions which are characteristic of chaotic systems. Prices of leading stock indices, forex pairs, and energy commodities of both major stock indices were compiled on a daily basis over 20 years. In addition to quantitative testing, the study combines a literature review of theoretical principles and simulation studies of simple nonlinear maps ( e.g. logistic map and Hénon map ) to demonstrate how simple nonlinear systems can produce complex behaviour similar to financial time series.

Grasslands in the Iberian Peninsula are some of the most valuable ecosystems in Europe and are vulnerable because of their location in arid-semiarid regions. Remote sensing techniques have the potential for monitoring grasslands using vegetation indices (VIs), which can reveal bare soil and non-photosynthetic vegetation reflectance in these regions. The temporal variability of the VI time-series is commonly measured as the standard deviation of the records, insufficient to study the system dynamics. Recurrence plots (RP) and recurrence quantification analysis (RQA) allow us to visualize and quantify system dynamics based on topology. These advanced analyses calculate stochasticity through determinism (DET) and predictability degree based on the average length of diagonal structures (LT). This study aims to evaluate RPs, Cross Recurrence Plots (CRP), and RQA to visualize and quantify VIs and climatic series and their anomalies responses dynamics.The approach was tested at two sites with different agro-climatic characteristics in Central Spain: Guadalix de la Sierra (ZGU) and Soto del Real (ZSO). The Normalized Difference Vegetation Index (NDVI) and the Modified Soil Adjusted Vegetation Index (MSAVI), which includes a soil factor, were calculated from MODIS images. Temperature (TEMP) and precipitation (PCP) series were acquired from two meteorological stations close to each site. All the anomalies series were obtained seasonally adjusted to the original ones.RPs showed the different VIs responses in both areas. The MSAVI patterns showed a clear structure, while NDVI presented a noisy pattern showing a higher random behaviour. To quantify these visual differences with RQA, four parameters were calculated, including DET and LT. The MSAVI series and the corresponding anomaly series presented higher DET and LT than the NDVI in both sites. CRPs of VIs with TMIN shows a higher DET in ZGU, suggesting that time synchronization is higher than in ZSO. When CRPs were applied over anomalies series, we could observe that precipitation is more synchronized with VIs anomalies, most likely because of the influence of soil moisture. LT of CRPs in all the cases was low and close to 2, indicating low predictability. Overall, our results suggest that VI time series show a more evident pattern and differentiate both sites better when a variable soil adjustment factor is included. Therefore, in arid-semiarid grasslands, a soil factor should be considered in VI calculations.

Dual fuel combustion is a promising solution to lowering engine emissions and enabling higher fuel flexibility. High cyclic variability is one of the main challenges of dual fuel combustion which can compromise emissions, operational stability, and drivability. Recurrence quantification analysis (RQA) is a potent tool for the quantification of cyclic variability, however the application of RQA to engine cylinder pressure data represents methodological challenges. In this work, a systematic RQA approach for cyclic pressure variations is proposed with two main contributions: (1) a methodology to determine RQA parameters to capture inter-cycle recurrences, and (2) a sliding window technique to enable real-time crank-angle-resolved analysis. This methodology was demonstrated using four firing conditions with increased cyclic variability from the most stable neat diesel case to highly unstable dual fuel cases with increasing percentage of natural gas substitution. Phase-space reconstruction enabled qualitative investigation using recurrence plots. The results showed that RQA can capture nuances in the cyclic dynamics not readily captured using averaged integrated quantities such as the indicated mean effective pressure, cumulative heat release, or combustion phasing. The median recurrence rate (RR) was shown to consistently decrease with increased cyclic variability. Determinism (DET) decreases then increases with higher cyclic variability. This finding reveals the paradox that lower repeatability (or RR) does not necessarily lead to lower predictability (or DET) as is sometimes the case with partially misfiring cycles being followed by more robust recovery cycles. These results can have significant implications for real-time cycle-by-cycle engine control.

Recurrence quantification analysis of sustained sub-maximal grip contractions in patients with various metabolic muscle disorders

<p>Clouds are the source of the biggest uncertainty in weather and climate models. One cannot fully understand clouds without understanding turbulence and microphysical processes in clouds. EUREC4A [1] experiment conducted during January and February focused on studying stratocumulus clouds (the most common marine clouds on earth) in atmoshperic boundary layer near Barbados. One of many measurements conducted during the campaign, was one using Twin-Otter aircraft, on which an Ultra Fast Thermometer 2b [2] was mounted. This thermometer, developed at Institute of Geophysics at the University of Warsaw is able to measure temperature at a 20 kHz frequency. After averaging to a frequency of 2 kHz, and assuming that the plane is moving at an average speed of 60 m/s, the spatial resolution of the thermometer is of the order of centimeters. The aircraft performed cloud penetrations together with measurements of temperature and other parameters such as the three components of wind velocity, pressure and humidity. The proposed method to study temperature time series is the time-dependent Recurrence Quantification Analysis (RQA) [3].</p><p>Recurrence Plots (RPs) are a visualization of a square matrix, which elements correspond to the moments when the system recurs, or when phase space trajectory of a system visits the same area in the phase space. RQA is a technique of data analysis based on the analysis of structures present in RPs. This method is used to study non-linear behaviors in the system, and to study determinism and chaos of the system, and transitions between them. In this study, portions of temperature records corresponding to cloud penetration were analyzed.</p><p>The analyzed clouds were divided into groups based on the angle of the penetration (windward, leeward, or from the side), as well as the variability of the wind during the penetration. Preliminary results suggest that the sharp edges of either the windward side of a dissipative cloud or both sides of a developing cloud are the places where the behavior of temperature is the most stochastic. Some clouds exhibited a behavior where the temperature behavior shifted from more stochastic near the windward side to more deterministic near the leeward side of the cloud. There are also side penetrations that, based on the RQA, contain information about the structure of the cloud and its dynamical properties.</p><p>We acknowledge funding by Poland’s National Science Centre grant no. UMO-2018/30/M/ST10/00674.</p><p>[1] Stevens B. et. al. 2021: EUREC4A, Earth System Science Data, vol. 13(8), pp. 4067-4119, 10.5194/essd-13-4067-2021<br>[2] Kumala, W. et. al. 2013: Modified ultrafast thermometer UFT-M and temperature measurements during Physics of Stratocumulus Top (POST), Atmos. Meas. Tech., vol. 6, pp. 2043–2054, 10.5194/amt-6-2043-2013<br>[3] N. Marwan, et. al. 2007: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, vol. 438(5–6), pp. 237–329, 10.1016/j.physrep.2006.11.001</p>

The estimation of the time difference of arrival (TDOA) consists of the determination of the travel-time of a wavefront between two spatially separated receivers, and it is the first step of processing systems dedicated to the identification, localization and tracking of radiating sources. This article presents a TDOA estimator based on cross recurrence plots and on recurrence quantification analysis. Six recurrence quantification analyses measures are considered for this purpose, including two new ones that we propose in this article. Simulated signals are used to study the influence of the parameters of the cross recurrence plot, such as the embedding dimension, the similarity function, and the recurrence threshold, on the reliability and effectiveness of the estimator. Finally, the proposed method is validated on real underwater acoustic data, for which the cross recurrence plot estimates correctly 77.6 % of the TDOAs, whereas the classical cross-correlation estimates correctly only 70.2 % of the TDOAs.

Non-stationary assessment of structural operational measurements using recurrence quantification analysis

In this paper, the spectroscopy signals have been analyzed in recurrence plots (RP), and extract recurrence quantification analysis (RQA) parameters from the RP in order to classify the tissues into normal and different precancerous grades. Three RQA parameters have been quantified in order to extract the important features in the spectroscopy data. These features have been fed to different classifiers for classification. Simulation results validate the efficacy of the recurrence quantification as potential bio-markers for diagnosis of pre-cancer.