Nonlinear Time Series Analysis Methods Research Articles

Mathematical modeling and seasonal solar radiation variability in Nigeria’s geo-political zones: A recurrence and multifractal analysis

This article delves into the seasonal variation of solar radiation patterns across Nigeria’s four geo-political zones, exploring their complex, scale-dependent behaviors. By employing chaotic quantifiers, the study characterizes irregular and self-similar patterns, enhancing our understanding of solar radiation variability and heterogeneity. The research uniquely fits meteorological parameters onto a global solar radiation model and focuses on the underexplored nonlinear aspects within tropical regions, specifically in the Nigerian context. Utilizing daily data from ERA INTERIM satellite archives for representative stations, the study employs nonlinear time series analysis methods like recurrence plots, recurrence qualitative analysis, and multifractal spectral analysis to comprehensively explore the unpredictable behaviors observed. The quantifier spectrums play a key role in revealing intricate scaling behaviors and correlation structures among environmental variables, shedding light on patterns often concealed by conventional statistical methods. For instance, we found that solar radiation variability in the northern region increases more significantly during the dry season compared to the wet season, unlike in the southern region. Additionally, the multifractal spectral analysis revealed a higher degree of complexity in solar radiation patterns during transition periods between seasons. The findings reveal a low recurrence quantitative analysis, long right tail, and truncations at both ends of the spectrum. This suggests instability in solar radiation across different seasons and locations. Nonetheless, the results also demonstrate that solar radiation is consistently available throughout the year, which is typical of tropical regions.

Characterization of homogeneous nucleation of superheated liquid droplets by nonlinear analysis

The homogeneous bubble nucleation in superheated liquid droplets can be initiated by energetic particles or radiation. The nonlinearity in the heat transfer introduces chaos in the temperature time series of a boiling system. In the present study, the acoustical pulses from the homogeneous nucleation of superheated liquid droplets by neutrons and gamma-rays have been collected. Nonlinear time series analysis methods like 3D attractor reconstruction and Fast Fourier transformation (FFT) have been performed on the collected pulses. The analysis predicts the possibility of the existence of chaos, and the positive value of the largest Lyapunov exponent confirms it. The nonlinearity in the energy deposition by both the recoil nuclei and electrons from the neutrons and gamma-rays respectively, introduce chaos. A qualitative difference has been observed in the 3D attractor and Rescaled Range (R/S) plots between the neutron and gamma-ray-induced pulses, and the present differences are useful for the identification of these pulses.

Research on Recurrence Plot Feature Quantization Method Based on Image Texture Analysis.

The nonlinear time-series analysis method, based on the recurrence plot theory, has received great attention from researchers and has been successfully used in multiple fields. However, traditional recurrence plots that use Heaviside step functions to determine the recursive behavior of a point in the phase space have two problems: (1) Heaviside step functions produce a rigid boundary, resulting in information loss; and (2) the selection of the critical distance, ε, is crucial; if the selection is inappropriate, it will result in a low-dimensional dynamics error, and as of now, there exists no unified method for selecting this parameter. With regard to the problems described above, the novelty of this article lies in the following: (1) when determining the state-phase point recursiveness, a Gaussian function is used to replace the Heaviside function, thereby solving the rigidity and binary value problems of the recursive analysis results caused by the Heaviside step function; and (2) texture analysis is performed on a recurrence plot, new ways of studying complex system dynamics features are proposed, and a system of complex system dynamic-like measurement methods is built.

Experimental Diagnosis on Combustion Characteristic of Shock Wave Focusing Initiation Engine.

A shock wave focusing initiation engine was assembled and tested in an experimental program. The effective pyrolysis rate of the pre-combustor was evaluated over a range of supplementary fuel ratio in this paper. Results highlight two operational modes of the resonant cavity: (1) pulsating combustion mode, (2) stable combustion mode. The appearance of the two combustion modes is jointly affected by the flow and the structural characteristic value of the combustion chamber. This paper uses images, time-frequency analysis, and nonlinear time series analysis methods to identify and distinguish these two combustion modes. It is believed that the interaction between the combustion chamber and the supply plenum is the probable reason for different combustion modes. The experiment has found that structural parameters and import flow parameters have an impact on the initiation of the combustion chamber. Increasing the injection pressure can appropriately broaden the fuel-rich boundary of initiation. Low equivalence ratio and high injection pressure can also appropriately increase the combustion working frequency in a small range. From the perspective of pressure utilization, under the premise of ensuring successful initiation, injection pressure should not be too high.

Data-based modeling and identification for general nonlinear dynamical systems by the multidimensional Taylor network

PurposeThe present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).Design/methodology/approachThe authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.FindingsCompared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.Research limitations/implicationsOnce models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.Practical implicationsMTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.Social implicationsThe operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.Originality/valueNonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

A Nonlinear Time-Series Analysis to Identify the Thresholds in Relationships Between Antimicrobial Consumption and Resistance in a Chinese Tertiary Hospital.

IntroductionBalancing the benefits and risks of antimicrobials in health care requires an understanding of their effects on antimicrobial resistance at the population scale. Therefore, we aimed to investigate the association between the population antibiotics use and resistance rates and further identify their critical thresholds.MethodsData for monthly consumption of six antibiotics (daily defined doses [DDDs]/1000 inpatient-days) and the number of cases caused by five common drug-resistant bacteria (occupied bed days [OBDs]/10,000 inpatient-days) from inpatients during 2009–2020 were retrieved from the electronic prescription system at Nanjing Drum Tower Hospital, a tertiary hospital in Jiangsu Province, China. Then, a nonlinear time series analysis method, named generalized additive models (GAM), was applied to analyze the pairwise relationships and thresholds of these antibiotic consumption and resistance.ResultsThe incidence densities of carbapenem-resistant Acinetobacter baumannii (CRAB), carbapenem-resistant Klebsiella pneumoniae (CRKP), and aminoglycoside-resistant Pseudomonas aeruginosa were all strongly synchronized with recent hospital use of carbapenems and glycopeptides. Besides, the prevalence of carbapenem-resistant Escherichia coli was also highly connected the consumption of carbapenems and fluoroquinolones. To lessen resistance, we determined a threshold for carbapenem and glycopeptide usage, where the maximum consumption should not exceed 31.042 and 25.152 DDDs per 1000 OBDs, respectively; however, the thresholds of fluoroquinolones, third-generation cephalosporin, aminoglycosides, and β-lactams have not been identified.ConclusionsThe inappropriate usage of carbapenems and glycopeptides was proved to drive the incidence of common drug-resistant bacteria in hospitals. Nonlinear time series analysis provided an efficient and simple way to determine the thresholds of these antibiotics, which could provide population-specific quantitative targets for antibiotic stewardship.

Fault Diagnosis of Bearings Using Recurrences and Artificial Intelligence Techniques

Abstract Rolling element bearings are one of the most common mechanical components used in a wide variety of rotating systems. The performance of these systems is closely associated with the health of bearings. In this study, a nonlinear time series analysis method, i.e., recurrence analysis is utilized to assess the health of bearings using time domain data. The recurrence analysis acquires the quantitative measures from the recurrence plots and provides an insight to the system under investigations. Experiments are performed to generate the vibration data from the healthy and faulty bearing. Eight recurrence quantitative analysis measures and five time-domain measures are used for the investigations. Three artificial intelligence techniques: rotation forest, artificial neural network, and support vector machine are employed to quantify the diagnosis performance. Results highlight the ability of recurrence analysis to identify the health state of the bearing at the early stage and superior diagnosis accuracy of the proposed methodology.

Performance Evaluation of New Feature based on Ordinal Pattern Analysis for Iris Biometric Recognition

The Iris recognition technique is currently the most efficient biometric identification system and is a common system on the practical front. Though most of the commercial systems use the patented Daugman’s algorithm, which mainly uses wavelet-based features, research is still active in identifying novel features that can provide personal identification. Here the first novel proposal of using ordinal pattern measure based on nonlinear time series analysis is put forth to characterize the unique pattern of the iris of individuals and thereby perform personal identification. Dispersion Entropy is a nonlinear time-series analysis method highly efficient in the characterization of the complexity of any data series with proven effectiveness in the characterization of model system dynamics as well as real-world data series. The results show that dispersion entropy can be used to identify iris images of specific individuals. The efficiency of this method is evaluated by computing correlation and RMSE between dispersion entropy values of normalized iris image rubber sheet data. The experimental results on the popular IRIS database- CASIA v1- demonstrate that the proposed method can effectively perform differential identification of iris images from different individuals. The results specifically indicate that the density of information along the angular direction of iris images which falls along the rows of rubber sheet data. This can be efficiently utilized with the method or ordinal pattern characterization and proves to be having promising potential for being incorporated into biometrics personal identification systems.

Combining Snow Depth From FY-3C and In Situ Data Over the Tibetan Plateau Using a Nonlinear Analysis Method

Snow cover over the Tibetan Plateau plays a vital role in the regional and global climate system because it affects not only the climate but also the hydrological cycle and ecosystem. However, high-quality snow data are hindered due to the sparsity of observation networks and complex terrain in the region. In this study, a nonlinear time series analysis method called phase space reconstruction was used to obtain the Tibetan Plateau snow depth by combining the FY-3C satellite data andin situdata for the period 2014–2017. This method features making a time delay reconstruction of a phase space to view the dynamics. Both of the grids and their nearbyin situsnow depth time series were reconstructed with two appropriate parameters called time delay and embedding dimension. The values of the snow depth for grids were averaged over thein situobservations and retrieval of the satellite if their two parameters were the same. That implies that the two trajectories of the time series had the same evolution trend. Otherwise, the snow depth values for grids were averaged over thein situobservation. If there were noin situsites within the grids, the retrieval of the satellite remained. The results show that the integrated Tibetan Plateau snow depth (ITPSD) had an average bias of –1.35 cm and 1.14 cm, standard deviation of the bias of 3.96 cm and 5.67 cm, and root mean square error of 4.18 cm and 5.79 cm compared with thein situdata and FY-3C satellite data, respectively. ITPSD expressed the issue that snow depth is usually overestimated in mountain regions by satellites. This is due to the introduction of more station observations using a dynamical statistical method to correct the biases in the satellite data.

Searching for signatures of chaos in γ-ray light curves of selected Fermi-LAT blazars

ABSTRACT Blazar variability appears to be stochastic in nature. However, a possibility of low-dimensional chaos was considered in the past, but with no unambiguous detection so far. If present, it would constrain the emission mechanism by suggesting an underlying dynamical system. We rigorously searched for signatures of chaos in Fermi-Large Area Telescope light curves of 11 blazars. The data were comprehensively investigated using the methods of nonlinear time-series analysis: phase-space reconstruction, fractal dimension, and maximal Lyapunov exponent (mLE). We tested several possible parameters affecting the outcomes, in particular the mLE, in order to verify the spuriousness of the outcomes. We found no signs of chaos in any of the analysed blazars. Blazar variability is either truly stochastic in nature or governed by high-dimensional chaos that can often resemble randomness.

Maximum envelope-based Autogram and symplectic geometry mode decomposition based gear fault diagnosis method

Autogram is an effective optimal frequency band selection method, in which the signal spectrum is divided by the maximum overlapping discrete wavelet packet transform (MODWPT) and the position of maximum kurtosis value is used as the optimal frequency band. However, Autogram follows a binary tree structure in segmenting frequency domain and its segmentation position is fixed, this causes that its position cannot be adaptively determined according to the signal characteristics. To solve this issue, in this paper an improved frequency band selection method called maximum envelope based-Autogram (MEAutogram) is proposed. In MEAutogram method, the maximum value envelope method is used to process the signal spectrum and then the minimum value point closest to the middle position of adjacent maximum value points in envelope signal is used as the segmentation position. However, the segmentation accuracy of MEAutogram will decrease when the signal contains lots of irrelevant components. The recently proposed nonlinear time series analysis method termed symplectic geometry mode decomposition (SGMD) founded on the symplectic matrix similar transformation is used to remove irrelevant components. Based on this, a new SGMD and MEAutogram based fault diagnosis method for gear is proposed. The proposed fault diagnosis method of gear can reduce the calculation amount through overcoming the influence of irrelevant components on the segmentation position, which can be adaptively determined according to the characteristics of the raw signal. Finally, the analysis results of simulation and gear test data was used to verify that the appropriate demodulation frequency band can be accurately detected by the proposed method and the fault characteristics obtained by the proposed method are more obvious than that of the comparative methods.

Investigation of rotating detonation fueled by a methane–hydrogen–carbon dioxide mixture under lean fuel conditions

Rotating detonation combustor (RDC) operation is investigated under the main composition of the coal and supercritical water gasification process (a methane–hydrogen–carbon dioxide mixture), and air is selected as an oxidizer. Experiments are performed under four flow rates (79.1, 101.2, 125.8, and 158.2 g/s), and the equivalence ratio (ER) ranges from 0.23 to 0.87. The detonation delay time and propagation characteristics of the rotating detonation wave (RDW) are investigated, and the nonlinear time series analysis method is applied to the pressure signal using the wavelet entropy algorithm and phase space reconstruction. It is demonstrated that a decrease in the flow rate can increase the detonation delay time near the lean fuel boundary; however, the detonation delay time is affected only slightly when the ER is greater than 0.4. The ER significantly affects the wave velocity but is affected only slightly by the flow rate. Contrary to the wave velocity performance, the pressure of the RDW increases with the flow rate. The lean fuel boundary becomes wider when the flow rate increases. Five combustion modes are investigated: failure, fast deflagration, sawtooth wave, single-wave, and two-counter rotating wave modes. The fast deflagration and sawtooth wave modes may occur near the detonation operating boundary, and a higher flow rate tends to increase the occurrence probability of a multiwave mode. The phase space pattern and distribution of wavelet entropy can be used to distinguish the combustion modes intuitively.

Effect of potassium channel noise on nerve discharge based on the Chay model.

BACKGROUND: The nervous system senses and transmits information through the firing behavior of neurons, and this process is affected by various noises. However, in the previous study of the influence of noise on nerve discharge, the channel of some noise effects is not clear, and the difference from other noises was not examined.OBJECTIVE: To construct ion channel noise which is more biologically significant, and to clarify the basic characteristics of the random firing rhythm of neurons generated by different types of noise acting on ion channels.Method: Based on the dynamics of the ion channel, we constructed ion channel noise. We simulated the nerve discharge based on the Chay model of potassium ion channel noise, and used the nonlinear time series analysis method to measure the certainty and randomness of nerve discharge.RESULTS: In the Chay model with potassium ion noise, the chaotic rhythm defined by the original model could be effectively unified with the random rhythm simulated by the previous random Chay model into a periodic bifurcation process.CONCLUSION: This method clarified the influence of ion channel noise on nerve discharge, better understood the randomness of nerve discharge and provided a more reasonable explanation for the mechanism of nerve discharge.

Research on network intrusion detection security based on improved extreme learning algorithms and neural network algorithms

In order to improve the ability of network fuzzy intrusion detection, a network intrusion detection method based on improved extreme learning algorithm and neural network algorithm is proposed to improve the security of the network. ARMA and other linear detection methods are used to construct the network intrusion signal model, and the nonlinear time series and chaos analysis methods are used to extract the feature of network intrusion and big data information analysis. The limit learning method is used for active detection of network intrusion; the adaptive learning method is used for iterative analysis of network intrusion detection, and the correlation characteristic decomposition method is used to improve the convergence of network intrusion detection. The fuzzy neural network algorithm is used to classify the network intrusion features to improve the intrusion detection performance. The simulation results show that this method has high accuracy and strong anti-jamming ability; it has good application value in network security.

Research on network intrusion detection security based on improved extreme learning algorithms and neural network algorithms

In order to improve the ability of network fuzzy intrusion detection, a network intrusion detection method based on improved extreme learning algorithm and neural network algorithm is proposed to improve the security of the network. ARMA and other linear detection methods are used to construct the network intrusion signal model, and the nonlinear time series and chaos analysis methods are used to extract the feature of network intrusion and big data information analysis. The limit learning method is used for active detection of network intrusion; the adaptive learning method is used for iterative analysis of network intrusion detection, and the correlation characteristic decomposition method is used to improve the convergence of network intrusion detection. The fuzzy neural network algorithm is used to classify the network intrusion features to improve the intrusion detection performance. The simulation results show that this method has high accuracy and strong anti-jamming ability; it has good application value in network security.

SVR-EEMD: An Improved EEMD Method Based on Support Vector Regression Extension in PPG Signal Denoising.

Photoplethysmography (PPG) has been widely used in noninvasive blood volume and blood flow detection since its first appearance. However, its noninvasiveness also makes the PPG signals vulnerable to noise interference and thus exhibits nonlinear and nonstationary characteristics, which have brought difficulties for the denoising of PPG signals. Ensemble empirical mode decomposition known as EEMD, which has made great progress in noise processing, is a noise-assisted nonlinear and nonstationary time series analysis method based on empirical mode decomposition (EMD). The EEMD method solves the “mode mixing” problem in EMD effectively, but it can do nothing about the “end effect,” another problem in the decomposition process. In response to this problem, an improved EEMD method based on support vector regression extension (SVR-EEMD) is proposed and verified by simulated data and real-world PPG data. Experiments show that the SVR-EEMD method can solve the “end effect” efficiently to get a better decomposition performance than the traditional EEMD method and bring more benefits to the noise processing of PPG signals.

Chaos prediction and control based on time series analysis

The nonlinear time-series analysis method is used to study the nonlinear large-scale measurement system and the discrete nonlinear system. For the instability of the linear steady-scale large-scale pulse system, a class of discrete Lipschitz nonlinear system dimensionality observer is used. The suboptimal control method for chaotic discrete systems with time-delay is obtained. The mathematical model of the large-scale pulsed system and the nonlinear discrete system is established. The instability of the large-scale steady-turbulence-type impulsive large-scale system is discussed by using the concept of the metric impulse system. The chaos of the nonlinear large-scale pulsating large-scale system with perturbation is proved by using the Lyapunov V function and the comparison principle. Bifurcation, using differential dynamic programming method to transform the suboptimal control problem of nonlinear discrete systems with time delay into the optimal control problem of nonlinear discrete systems without time delay, and realize the control of chaos.

Model-free time series analysis detected the contributions of middle-age spawner biomass and the environment on Pacific bluefin tuna recruitment

Abstract The relationship between the biomass of Pacific bluefin tuna (PBF) spawners and the amount of recruitment (stock–recruitment relationship, SRR) is unclear. It is likely that environmental effects have masked the SRR of PBF. As the basis of constructing an effective SRR for PBF, we examined the effect of spawning biomass at different ages and the spatiotemporal patterns of environmental effects on the amount of recruitment, using a recently developed model-free nonlinear time series analysis method (empirical dynamic modelling, EDM). EDM revealed where, when, and how the environment affected the amount of recruitment. EDM also found a significant contribution of ages 8–9 spawners on recruitment dynamics and that the amount of recruitment plateaus with increase in ages 8–9 spawners. Based on knowledge obtained from EDM, we formulated several example SRRs that incorporated environmental effects (sea surface temperature). The newly developed SRR with information from EDM outperformed the SRR without this information. Finally, we interpreted the results based on preceding observational and experimental studies and discussed the potential of applying the combination of EDM and mathematical modelling towards the sustainable use of other stocks.

ECG based human identification using Second Order Difference Plots

Background and objectiveECG is one of the biometric signals that has been studied in peer-reviewed over past years. The developments on the signal analysis methods show that the studies on the ECG would continue unabatedly. It has a common use on cardiac diseases with high rates of classification performances by integrating it with signal analysis methods. The aim of the study is to utilize the ECG for human identification. MethodsSecond Order Difference Plot (SODP) is a non-linear time-series analysis method that allows determining the features using the statistical analysis of the wave distributions. The SODP features were extracted using different quantification methods for ECG-based human identification. A new quantification approach has been proposed on the SODP for ECG-based human identification. The proposed method, Logarithmic Grid Analysis, was compared with the existing quantification methods on the SODP. The region of the SODP was divided into sub-regions with logarithmically increasing distances and the numbers of data points in each logarithmic sub regions were calculated in the proposed method. Three different databases were used to test the validity of the method. These records have been tested with the conventional feature extraction methods on the SODP. The long-term ECG signals were divided into 5-s short-term ECG signals. ResultsThe Logarithmic Grid Analysis features that were counted from short-time ECG signals were classified with k-Nearest Neighbor algorithm using 10-fold cross validation, and the identification performance of the proposed model was evaluated. Consequently, high accuracy rates of 91.96%, 99.86% and 95.12% were achieved on ECG-based human identification using the Logarithmic Grid Analysis method on the SODP. ConclusionsThe density score of data points at the center of the SODP is too high. This case increases the importance of the regions close the center in order to find the detailed and significant features from the SODP. The number of data points at the center has been extracted in more detail and the vertex areas of the major axes of the SODP can be interpreted in the aggregate sub-regions by using logarithmically increasing distances with a small number of feature size.

Efficient scheduling of power communication resources based on fuzzy weighted constraint equalisation

Resources in the power communication system are affected by crosstalk between power grid subnets during scheduling, resulting in a poor equalisation of resource allocation. In order to improve equalisation allocation of resources in the power communication system, an efficient scheduling method of power communication system resources based on fuzzy weighted constraint equalisation is proposed. In this method, the nonlinear time series analysis method is used to construct an information flow model of power communication system resource data and the channel equalisation control is carried out in transmission links of the power communication system; the fuzzy weighted constraint equalisation method is used to implement adaptive baud-spaced equalisation handling during resource scheduling and the fuzzy mesh-based clustering algorithm is used to carry out pairing of classification attribute weights of power resources, so as to achieve efficient clustering of resources and to improve the link equalisation in resource scheduling. Simulation results show that with this method, the average data recall rate during resource scheduling reaches about 90% and the equalisation curve changes very smoothly, which fully indicates that with this method, the data recall rate and scheduling efficiency are high and the equalisation capability of communication channels is strong.