Search Results (39)

Financial crises are usually identified through drawdowns, volatility, and changes in returns, but these indicators do not directly describe whether the recurrence structure of market behaviour changes during a shock. This study tests Laminarity, a Recurrence Quantification Analysis measure derived from vertical structures in recurrence plots, as a nonlinear diagnostic of persistence and market-regime structure during the COVID-19 market shock. Daily data for the Dow Jones Industrial Average, S&P 500, and NASDAQ Composite from 2018 to 2022 are analysed using adjusted prices and log returns. Rolling-window Recurrence Quantification Analysis is applied across alternative window lengths and recurrence thresholds, testing crisis-responsive and longer robustness windows, as well as sparse, intermediate, and denser recurrence definitions. Drawdown and rolling volatility are used as descriptive benchmarks for cumulative loss and fluctuation intensity over the same stress episode. The results show that conventional indicators identify the COVID-19 shock clearly. Price-based Laminarity generally increases during the stress period, consistent with a more persistent crisis trajectory in price levels. Return-based Laminarity is more heterogeneous, with some specifications showing Laminarity loss and others increases. The findings do not support Laminarity as a universal crisis-warning signal, but as a parameter-sensitive diagnostic of recurrence structure, especially when interpreted alongside related RQA metrics. Full article

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. Full article

Accurate anomaly detection in rotating machinery under noisy conditions remains challenging in Prognostics and Health Management (PHM). Existing deep learning autoencoders and attention mechanisms rely primarily on data-driven similarity measures and fail to explicitly incorporate nonlinear dynamical characteristics of degradation. In this study, we propose a Recurrence Quantification Analysis-Aware Attention (RQAA) framework that systematically injects chaos-theoretic descriptors into the attention mechanism of LSTM-based autoencoders for unsupervised anomaly detection. Specifically, RQA metrics including recurrence rate, determinism, laminarity, entropy, and trapping time are computed at the window level and embedded into the query-key-value attention scoring to guide the model toward dynamically informative temporal patterns. Three attention variants are developed to investigate different fusion strategies between learned representations and RQA-driven structural cues. The proposed framework is evaluated on three widely used bearing vibration datasets, which are IMS, CWRU, and HUST. Experimental results demonstrate that RQAA consistently outperforms conventional LSTM autoencoders and classical attention-based models, achieving up to 99.85% F1-score and 99.00% AUC while exhibiting superior robustness in low signal-to-noise scenarios. Further analysis reveals that explicit dynamical guidance enhances anomaly separability and reduces false alarms, particularly in early-stage fault detection. These findings indicate that integrating nonlinear dynamical information directly into attention scoring offers a principled and effective pathway for advancing unsupervised anomaly detection in rotating machinery and safety-critical industrial systems. Full article

This paper presents a comprehensive analysis of the flute grinding process in end cutters, focusing on the influence of machining parameters on recurrence indicators. Recurrence quantification analysis (RQA) was employed to assess the dynamic behavior, regularity, and predictability of the process. Based on experimental data, a grinding force model was developed, along with mathematical formulations of the recurrence indicators. Leveraging these models, a novel parameter, the dominant index was proposed to identify which cutting parameters have the greatest impact on the RQA measures. The results reveal that cutting speed exerts a dominant influence on both the grinding force and recurrence metrics. However, for specific indicators, the feed rate emerges as the prevailing factor. The study also demonstrates a strong correlation between cutting parameters and the harmonic content of the grinding force signal. Furthermore, increasing cutting speed was found to generally stabilize the process, whereas variations in feed rate may either enhance or deteriorate machining stability. Full article

Background: Elite athletes are frequently subjected to high-intensity training regimens, which can result in cumulative physical stress, overtraining, and potential health risks. Monitoring autonomic responses to such load is essential for optimizing performance and preventing maladaptation. Objective: The present study aimed to assess changes in autonomic regulation immediately and two hours after training in athletes, using an integrated framework (combining time- and frequency-domain HRV indices with nonlinear and recurrence quantification analysis). It was investigated how repeated assessments over a 4-month period can reveal cumulative effects and identify athletes at risk. Special attention was paid to identifying signs of excessive fatigue, autonomic imbalance, and cardiovascular stress. Methods: Holter ECGs of 12 athletes (mean age 21 ± 2.22 years; males, athletes participating in competitions) over a 4-month period were recorded before, immediately after, and two hours after high-intensity training, with HRV calculated from 5-min segments. Metrics included HRV and recurrent quantitative analysis. Statistical comparisons were made between the pre-, post-, and recovery phases to quantify autonomic changes (repeated-measures ANOVA for comparisons across the three states, paired t-tests for direct two-state contrasts, post hoc analyses with Holm–Bonferroni corrections, and effect size estimates η²). Results: Immediately after training, significant decreases in SDNN (↓ 35%), RMSSD (↓ 40%), and pNN50 (↓ 55%), accompanied by increases in LF/HF (↑ 32%), were observed. DFA α1 and Recurrence Rate increased, indicating reduced complexity and more structured patterns of RR intervals. After two hours of recovery, partial normalization was observed; however, RMSSD (−18% vs. baseline) and HF (−21% vs. baseline) remained suppressed, suggesting incomplete recovery of parasympathetic activity. Indications of overtraining and cardiac risk were found in three athletes. Conclusion: High-intensity training in elite athletes induces pronounced acute autonomic changes and incomplete short-term recovery, potentially increasing fatigue and cardiovascular workload. Longitudinal repeated testing highlights differences between well-adapted, fatigued, and at-risk athletes. These findings highlight the need for individualized recovery strategies and ongoing monitoring to optimize adaptation and minimize the risk of overtraining and health complications. Full article

This study investigates the influence of cutting edge geometry (continuous, serrated, and wavy) and selected machining parameters (cutting speed v_c, feed per tooth f_z, and radial infeed a_e) on cutting-force components and dynamic behavior during the milling of an AlZn5.5MgCu aluminum alloy. The analysis was based on box plots and Recurrence Quantification Analysis (RQA) applied to the cutting-force signal. The results demonstrated that serrated and wavy-edge tools generated significantly lower values of the normal force component F_fN—up to −57% on average—compared to the continuous-edge tool, particularly at lower f_z and v_c, indicating enhanced process dynamics. At higher a_e values, however, these tools induced increased signal variability—up to 300% greater—suggesting potential resonance excitation. RQA indicators, such as DET, Lmax, and LAM, revealed a strong dependence of system dynamics on tool edge geometry. Linear Discriminant Analysis (LDA) confirmed that RQA measures effectively distinguish between cutting-edge types. The study concludes that tooldge geometry substantially affects milling process stability and can be purposefully selected to optimize performance under varying machining conditions. Full article

This study presents a comprehensive analysis of defect detection in the manufacturing process of solid carbide milling tools. The creep-feed flute grinding technique was used to fabricate a milling tool, with cutting force signals recorded and examined using recurrence analysis and conventional statistical methods. The analysis identified four distinct dynamic fluctuations (cutting force amplitude jumps), which showed a direct correlation with the formation of microcracks on the flute surface. These jumps exhibited varying levels of reduction, ranging from 5% to 22% in amplitude. A detailed investigation, including recurrence plots and recurrence quantification analysis (RQA) with a moving-window approach, revealed that several recurrence indicators, such as the recurrence rate (RR), determinism (DET), and maximum diagonal line length (L_MAX), were highly effective in detecting microcracks, as their values significantly deviated from the reference level. These results were compared with conventional statistical analysis, and interestingly, the recurrence methods demonstrated greater sensitivity, successfully detecting additional very small cutting force jumps that conventional statistical methods could not identify. Full article

This paper presents the mathematical framework of Recurrence Quantification Analysis (RQA) for dynamic video processing, exploring its applications in two primary tasks: scene change detection and adaptive foreground/background segmentation. Originally developed for time series analysis, Recurrence Quantification Analysis (RQA) examines the recurrence of states within a dynamic system. When applied to video streams, RQA detects recurrent patterns by leveraging the temporal dynamics of video frames. This approach offers a computationally efficient and robust alternative to traditional deep learning methods, which often demand extensive training data and high computational power. Our approach is evaluated on three annotated video datasets: Autoshot, RAI, and BBC Planet Earth, where it demonstrates effectiveness in detecting abrupt scene changes, achieving results comparable to state-of-the-art techniques. We also apply RQA to foreground/background segmentation using the UCF101 and DAVIS datasets, where it accurately distinguishes between foreground motion and static background regions. Through the examination of heatmaps based on the embedding dimension and Recurrence Plots (RPs), we show that RQA provides precise segmentation, with RPs offering clearer delineation of foreground objects. Our findings indicate that RQA is a promising, flexible, and computationally efficient approach to video analysis, with potential applications across various domains requiring dynamic video processing. Full article

Introduction: Aortic valve disease (AVD) is an inflammatory, lipid infiltration and calcification disease that has been associated with changes in the conventional linear heart rate variability (HRV) indices showing a marked shift towards sympathetic predominance and a deterioration of the autonomic control. Objective: To explore the HRV dynamics in AVD patients through nonlinear methods by recurrence quantification analysis (RQA). Methods: In total, 127 subjects participated in a cross-sectional study categorized into three groups: healthy valve (HV), aortic valve sclerosis (AVSc), and aortic valve stenosis (AVS), as determined by echocardiographic assessment. HRV data were collected from five-minute ECG recordings at both a supine position and active standing. RQA indices were calculated using the Cross Recurrence Plot Toolbox. Results: In the supine position, patients with AVS exhibited larger determinism and trapping time than those with AVSc and HV. The analysis of these differences revealed that determinism and laminarity increased progressively from HV to AVS. In the same way, the magnitude of change (Δ) between positions decreased and presented the lowest values in AVS in most of the nonlinear indices. Conclusion: RQA indices of HRV in AVD patients indicate a rigidizing dynamic characterized by larger determinism and extended trapping times in fewer system states in relation to the severity of AVD. These findings establish a precedent for future perspective assessments for the implementation of these methods in medical software or devices. Full article

One type of milling process is the face milling of flat surfaces using a toroidal face cutter. A key feature of this process is that changes in the depth of the cut alter the entering angle, impacting milling dynamics by shifting cutting force proportions. To investigate this phenomenon, an experimental study was conducted on the face milling process using different sets of cutting parameters. Cutting force components were recorded, as these signals provide essential information about the milling process. Statistical indicators were then calculated and analyzed based on the recorded data. Following this, a recursive force analysis was performed, and Recurrence Quantification Analysis (RQA) indicators were computed. Relationships between the RQA indicators and the cutting parameters, specifically the feed per tooth (f_z) and axial depth of the cut (a_p), were established using response surface methodology. Empirical relationships between these parameters were derived. The results indicate that the RQA indicators like the determinism DET, the entropy ENT, and the length of longest vertical line VMAX are correlated with the cutting parameters for both the feed force (F_f) and the component normal to the feed (F_fN). In the axial direction, the RQA indicators DET, ENT, and VMAX and also the percentage of recurrence points in a recurrence plot RR and the longest diagonal line length LMAX are shown to be relevant for analyzing the dynamics of the face milling process. Full article

Titanium alloys, particularly Ti-6Al-4V, are widely used in many industries due to their high strength, low density, and corrosion resistance. However, machining these materials is challenging due to high strength at elevated temperatures, low thermal conductivity, and high chemical reactivity. This study investigates Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) to analyze tool wear during the finish turning of Ti-6Al-4V. The tests were conducted under Minimum Quantity Lubrication (MQL). Three inserts (two coated, one uncoated) were tested, and tool life was evaluated based on material removal volume. The issue of tool exploitation and process reliability is crucial, as it directly impacts machining performance. Results show that the uncoated insert outperformed the coated ones. RQA parameters indicated a stable-to-unstable transition in coated inserts but not in the uncoated insert. This suggests that recurrence analysis can monitor cutting dynamics in coated insert machining, but further research is needed for uncoated tools. This paper’s novelty lies in applying RP and RQA to diagnose tool wear in titanium alloy machining under MQL conditions, a method not previously explored in this context. Full article

A new method based on the Recurrence Quantification Analysis (RQA) of the heart rate (HR) offers an objective, efficient alternative to traditional methods for Aerobic Threshold (AerT) identification that have practical limitations due to the complexity of equipment and interpretation. This study aims to validate the RQA-based method’s applicability across varied demographics, exercise protocols, and health status. Data from 123 cardiopulmonary exercise tests were analyzed, and participants were categorized into four groups: athletes, young athletes, obese individuals, and cardiac patients. Each participant’s AerT was assessed using both traditional ventilatory equivalent methods and the automatic RQA-based method. Ordinary Least Products (OLP) regression analysis revealed strong correlations (r > 0.77) between the RQA-based and traditional methods in both oxygen consumption (VO₂) and HR at the AerT. Mean percentage differences in HR were below 2.5%, and the Technical Error for HR at AerT was under 8%. The study validates the RQA-based method, directly applied to HR time series, as a reliable tool for the automatic detection of the AerT, demonstrating its accuracy across diverse age groups and fitness levels. These findings suggest a versatile, cost-effective, non-invasive, and objective tool for personalized exercise prescription and health risk stratification, thereby fulfilling the study’s goal of broadening the method’s applicability. Full article

This study investigates the time-series behavior of vegetable prices in the Central Market of Thessaloniki, Greece, using Recurrence Plot (RP) analysis and Recurrence Quantification Analysis (RQA), which considers non-linearities and does not necessitate stationarity of time series. The period of study was 1999–2016 for practical and research reasons. In the present work, we focus on vegetables available throughout the year, exploring the dynamics and interrelationships between their prices to avoid missing data. The study applies RP visual inspection classification, a clustering based on RQA parameters, and a classification based on the RQA analysis graphs with epochs for the first time. The aim of the paper was to investigate the grouping of products based on their price dynamical behavior. The results show that the formed groups present similarities related to their use as dishes and their way of cultivation, which apparently affect the price dynamics. The results offer insights into market behaviors, helping to inform better management strategies and policymaking and offer a possibility to predict variability of prices. This information can interest government policies in various directions, such as what products to develop for greater stability, identity for fluctuating prices, etc. In future work, a larger dataset including missing data could be included, as well as a machine-learning algorithm to classify the products based on the RQA with epochs graphs. Full article

This paper addresses the problem of noncooperative spectrum sensing in very low signal-to-noise ratio (SNR) conditions. In our approach, detecting an unoccupied bandwidth consists of detecting the presence or absence of a communication signal on this bandwidth. Digital communication signals may contain hidden periodicities, so we use Recurrence Quantification Analysis (RQA) to reveal the hidden periodicities. RQA is very sensitive and offers reliable estimation of the phase space dimension m or the time delay $\tau$. In view of the limitations of the algorithms proposed in the literature, we have proposed a new algorithm to simultaneously estimate the optimal values of m and $\tau$. The new proposed optimal values allow the state reconstruction of the observed signal and then the estimation of the distance matrix. This distance matrix has particular properties that we have exploited to propose a Recurrence-Analysis-based Detector (RAD). The RAD can detect a communication signal in a very low SNR condition. Using Receiver Operating Characteristic curves, our experimental results corroborate the robustness of our proposed algorithm compared with classic widely used algorithms. Full article

Thermoacoustic oscillation is indeed a phenomenon characterized by the symmetric coupling of thermal and acoustic waves. This paper introduces a novel approach for monitoring and predicting thermoacoustic combustion instability using a combination of recurrence quantification analysis (RQA) and an optimized deep belief network (DBN). Six samples of combustion state data were collected using two distinct types of burners to facilitate the training and validation of GA-DBN. The proposed methodology leverages RQA to extract intricate patterns and dynamic features from time series data representing combustion behavior. By quantifying the recurrence plot of specific patterns, the analysis provides valuable insights into the underlying thermoacoustic dynamics. Among three different feature extraction methods, RQA stands out remarkably in performance. These RQA-derived features serve as input to a carefully tuned DBN, which is trained to learn the complex relationships within the combustion process. The classification accuracy of deep belief network optimized by genetic algorithm (GA-DBN) reached an impressive 99.8%. Subsequent multiple comparisons were conducted between GA-DBN, DBN, and support vector machine (SVM), revealing that GA-DBN consistently demonstrated satisfactory classification results. This method holds significant importance in monitoring intricate combustion states. Full article