Time Series Analysis Methods Research Articles

A New Grey Prediction Model and Its Application in Renewable Energy Consumption

Renewable energy is an energy resource that can be used continuously. At present, international oil prices continue to rise, the problem of global climate change is becoming increasingly prominent, and renewable energy and clean energy have ushered in a new round of development opportunities. Based on the new gray prediction model, this paper forecasts the consumption of renewable energy and further analyzes the sustainable development of renewable energy. In this paper, the combinatorial optimization method of cumulative order, background value coefficient, and initial conditions, parameter optimization combination, parameter combinatorial optimization process of the gray prediction model, and parameter optimization mechanism based on the PSO algorithm are proposed, and the reduction error analysis is carried out. The consumption of wind power and photovoltaic renewable energy is forecasted, and three different forecasting methods as exponential smoothing method, time series analysis method, and new gray forecasting method are compared, and the wind speed, irradiation intensity, and load are forecasted by these three different forecasting methods. Compared with the time series analysis method and the exponential smoothing method, the RMSE of the new grey prediction method is reduced by 127.12% and 160.59%, and the error rate is reduced by 3.16% and 4%, respectively. Based on the consumption forecast of renewable energy, this paper analyzes its sustainability from three directions economy, resource supply, and environment, and finally gives energy policy recommendations.

Early Fault Detection and Operator-Based MIMO Fault-Tolerant Temperature Control of Microreactor

A microreactor is a chemical reaction device that mixes liquids in a very narrow channel and continuously generates reactions. They are attracting attention as next-generation chemical reaction devices because of their ability to achieve small-scale and highly efficient reactions compared to the conventional badge method. However, the challenge is to design a control system that is tolerant of faults in some of the enormous number of sensors in order to achieve parallel production by numbering up. In a previous study, a simultaneous control system for two different temperatures was proposed in an experimental system that imitated the microreactor cooled by Peltier devices. In addition, a fault-tolerant control system for one area has also been proposed. However, the fault-tolerant control system could not be applied to the control system of two temperatures in the previous study. In this paper, we extend it to a two-input, two-output fault-tolerant control system. We also use a fault detection system that combines ChangeFinder, a time-series data analysis method, and One-Class SVM, an unsupervised learning method. Finally, the effectiveness of the proposed method is confirmed by experiments.

Ridge estimation for uncertain autoregressive moving average model with imprecise observations

An uncertain time series is a sequence of imprecisely observed values arranged in chronological order, whose main purpose is to predict future values based on previously observed values. It is significant to select an appropriate parameter estimation method in uncertain time series analysis. Firstly, the paper transforms a one-order uncertain autoregressive moving average model into an uncertain autoregressive model by the iterative method. Secondly, the ridge method is used to estimate the unknown parameters in the uncertain autoregressive moving average model, in which the shrinkage parameter is determined by ridge trace analysis. Thirdly, the forecast value and confidence interval are acquired by the residual analysis of the fitted model. Finally, two examples are provided to verify the validity and feasibility of the method. The result shows that the ridge method can effectually cut down the affection of outliers and improve the prediction accuracy compared with the least square estimation.

Machine Learning Clustering Techniques to Support Structural Monitoring of the Valgadena Bridge Viaduct (Italy)

The lack of precise and comprehensive information about the health of bridges, and in particular long span ones, can lead to incorrect decisions regarding maintenance, repair, modernization, and reinforcement of the structure itself. While the consequences of inadequate interventions are quite apparent, incorrect decisions can also result in unnecessary or misdirected actions. For example, an inadequate assessment of the structural health can lead to the modernization and replacement of some components that are still sound. Structural Health Monitoring (SHM) involves the use of time series derived from periodic measurements of the structure’s behavior, considered in its operational and load environment. The goal is to determine its response to various solicitations and, in particular, to highlight any critical issue in the structure’s behavior that may affect its reliability and safety due to anomalies and deterioration. This paper proposes an SHM method applied to the Valgadena bridge, one of the tallest viaducts in Italy and Europe (maximum height 160 m), located on the Altopiano dei Sette Comuni in the Province of Vicenza. Despite the fact that the viaduct itself had already been monitored during its construction using classical geometric leveling techniques, the methodology proposed here is based instead on the use of affordable dual-frequency GNSS (Global Navigation Satellite System) receivers to determine static and dynamic components of the bridge movements. Specifically, an effective combination of time series analysis methods and machine learning techniques is proposed in order to determine the vibration modes of the monitored viaduct. Monitoring is performed in regular operation conditions of the bridge (operational modal analysis (OMA)), and the use of certain machine learning methods aims at supporting the development of an effective automatic OMA procedure. To be more specific, the random decrements technique is used in order to make the vibration characteristics of the collected signals more apparent. Time-domain-based subspace identification is applied in order to determine a proper model of the collected measurements. Then, clustering methods, namely DBSCAN (Density-Based Spatial Clustering of Applications with Noise) and GMMs (Gaussian Mixture Models), are used in order to reliably estimate the system poles, and hence the corresponding vibration characteristics. The performance of the considered methods is compared on the Valgadena bridge case study, showing that the use of GMM clustering reduces, with respect to DBSCAN, the impact of the choice of certain parameter values in the considered case.

About Air Quality Assessment using Time Series Analysis Techniques on Air Particles Data

This study investigates the dynamics of air pollution caused by particulate matter (PM10 and PM2.5) in Omsk, Russia. Data collected from the Sensor.Community network between 2021 and 2023 were analyzed using time series analysis methods. The findings reveal a subtle weekly seasonality in the data, potentially attributed to fluctuations in industrial activity and traffic patterns throughout the week. Additionally, a concerning trend of deteriorating air quality was identified, characterized by increasing annual average concentrations of PM10 and PM2.5. The study employed various time series analysis techniques, including Empirical Cumulative Distribution Function (ECDF), Seasonal and Trend decomposition using Loess (STL), and autocorrelation function (ACF) analysis. These methods allowed for the visualization and examination of data distribution, trend identification, and seasonality detection. Furthermore, the Mann-Kendall test confirmed a statistically significant trend of increasing pollution levels over the three-year period. To enhance the accuracy of spatial analysis, data interpolation was performed using kriging with a Gaussian model. This method, compared to simple interpolation, provides a more precise assessment of the spatial distribution of pollutants. The study also implemented Long Short-Term Memory (LSTM) for forecasting hourly pollution values. LSTM exhibited promising results, demonstrating its potential for developing early warning systems, particularly when combined with meteorological data such as wind forecasts. The results highlight the need for effective measures to mitigate air pollution in Omsk and emphasize the importance of utilizing data from diverse sources, including official air quality monitoring stations, to ensure accuracy and reliability in air quality assessments.

Tornado Occurrence in the United States as Modulated by Multidecadal Oceanic Oscillations Using Empirical Model Decomposition

Studies have analyzed U.S. tornado variability and correlated F1–F5 tornado occurrence with various natural climate oscillations and anthropogenic factors. Using a relatively new empirical mode decommission (EMD) method that extracts time-frequency modes adaptively without priori assumptions like traditional time-series analysis methods, this study decomposes U.S. tornado variability during 1954–2022 into intrinsic modes on specific temporal scales. Correlating the intrinsic mode functions (IMFs) of EMD with climate indices found that 1. the U.S. overall tornado count is negatively (positively) correlated with the Atlantic Multidecadal Oscillation (AMO) index (the Southern Oscillation Index (SOI)); 2. the negative (positive) correlation tends to be more prevalent in the western (eastern) U.S.; 3. the increase in weak (F1–F2) and decrease in strong (F3–F5) tornadoes after around 2000, when both the AMO and the Pacific Decadal Oscillation (PDO) shifted phases, are likely related to their secular trends and low-frequency IMFs; and 4. the emerging Dixie Tornado Alley coincides with an amplifying intrinsic mode of the SOI that correlates positively with the eastern U.S. and Dixie Alley tornadoes. The long-term persistence of these climate indices can offer potential guidance for future planning for tornado hazards.

How environmental data enables intelligent navigation: Factors assessment of affecting the navigation in the Northeast Arctic Route

Due to the more favorable navigational environment and higher safety along Northeast Arctic Route, this route is being used more and more frequently for international shipping. In this research, the factor analysis method is applied to assess the navigational environment of each sea area in the Northeast Arctic Route, revealing the effects of Arctic navigation influence factor on the navigational environment, and analyzing the change trend of the navigational environment of different sea areas in different seasons. Further, the effects of multiple factors on the number of voyages are discussed through multiple stepwise regression model, including the navigational environment score, geopolitical risk, export & import trade and the probability of pollution accidents, then the Interrupted time series analysis (ITSA) method combined with seasonal decomposition is explored the effect of emergencies on the number of voyages on the Northeast Arctic Route. The number of voyages on the Northeast Arctic Route has been altered to varying degrees by the occurrence of various emergencies. Further, the Yamal LNG project and the Russian-Ukrainian conflict have a significant effect on the number of voyages, while the Covid-19 epidemic has a lesser effect on the number of voyages.

Forecasting changes in the earth’s climate system by instrumental measurements and paleodata in the phase-time region, consistent with changes in the barycentric motions of the sun. Part 1

The relevance of the research is due to the need to establish the root cause of climate change on Earth and predict changes in heliocosmic, climatic variables, natural disasters by intramental measurements and paleodata, as time series, for long intervals of the time horizon in the phase domain, taking into account their cyclicity and interdependence of changes. Purpose of research: application of the time series analysis method of the time series to establish the strength of the influence of the barycentric movements of the Sun on the variability of heliocosmic, climatic variables, natural disasters and fires, high-precision prediction of variables in the phase-time domain for long horizons of hundreds and thousands of years by instrumental measurements and paleodata. Objects of research: time series of changes in heliocosmic and climatic variables, natural disasters and fires, curves of changes in climatic changes obtained by analysis of ice cores in Antarctica and bottom sediments in Antarctica. Methods of research: wavelet phase-frequency and phase-time analysis of images of heliocosmic and climatic variables, natural disasters and fires; calculation of the consistency of changes in selected groups on a set of phase-time characteristics of variables in a sliding mode. Main results of research: In the images of wavelet phase-time functions of many variables constructed from observations in 1600–2010, Jose periods of ~178 years were found, which are contained in changes in the characteristics of barycentric movements of the Sun, solar activity, solar constant, CO2,N2OEl Nino, solar wind, the level of the Caspian Sea, temperature in Greenland, the speed of rotation of the Earth, snow accumulation rates in the Indian Ocean sector of Antarctica, global temperature; cyclicity of changes in heliocosmic and climatic variables are consistent with changes in Baricentre; there is a significant difference in the consistency of changes in the phase-time characteristics of variables obtained at the southern hot and northern cold latitudes of the planet by about 2.1 times; in the northern part of the planet, changes in variables are more chaotic, due to the different influence of changes in the Baricentre variable, the magnetic fields of the Sun and the Earth on the variability of variables at different latitudes of the planet; significant variability and resonances of the phase characteristics of heliocosmic and climatic variables are observed by changes in Baricentre on the graphs of coordinated changes in groups of variables in the observed and predicted time intervals. The studies reveal multiple oscillatory responses of the Earth’s climate system to the impact of the Baricentre variable due to the heterogeneity of its components and the Earth’s magnetosphere in space. Changes in the set of phase-time characteristics of variables on the same graph in the observed and predicted time intervals in the interval ± π are displayed as changes in autowaves characteristic of self-organizing systems, characterizing climatic changes in environments in combination with the influence of the variable Baricentre.

Parameter inference from a non-stationary unknown process.

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet, most time-series analysis methods that are used in practice on important problems across science and industry make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as parameter inference from a non-stationary unknown process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here, we review and unify a diverse literature of algorithms for PINUP. We formulate the problem and categorize the various algorithmic contributions into those based on (1) dimension reduction, (2) statistical time-series features, (3) prediction error, (4) phase-space partitioning, (5) recurrence plots, and (6) Bayesian inference. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on-notably, the non-stationary Lorenz process and logistic map-are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing the non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

ACUTE PANCREATITIS IN AKMOLA REGION ACCORDING TO EMERGENCY SURGERY

Background: Acute pancreatitis is a major issue in surgical practice, with high complications and mortality rates. It severely affects patient quality of life and places a significant economic strain on healthcare systems, making its study crucial for public health. This study aims to analyze trends in acute pancreatitis incidence in the Akmola region from 2009 to 2022. Materials and methods: The study is based on a retrospective analysis of data from the Ministry of Health of the Republic of Kazakhstan according to the International Classification of Diseases-10 code: K85. Methods of health statistics and time series analysis were used to assess the dynamics of morbidity. Results: There was an increase in the total number of hospitalizations from 865 cases in 2009 to 1.061 in 2022. The percentage of surgical interventions decreased from 5.7% to 4.2%, while the share of conservative treatment increased to 95.8%. The mortality rate among operated patients was 20.4% in 2019 and increased to 33.3% in 2022. The incidence of hospitalization increased from 117.1 per 100000 population in 2009 to 144.6 per 100000 population in 2022, with a decrease in the rate of late visits from 42.6 to 36.1 per 100000 population, respectively. Conclusion: It has been established that for patients in the second group according to the Enhanced Recovery After Surgery strategy, hemodynamic support and effective pain management can contribute to early patient mobilization after surgery. Early mobilization, in turn, can expedite recovery and reduce the length of hospital stay, ultimately leading to potential cost savings. Conclusion. The study highlights the need to improve medical approaches to acute pancreatitis in the Akmola region. The results indicate the critical importance of early diagnosis and timely hospitalization to reduce complications and mortality. Additional research is needed to develop more effective clinical protocols.

SINGULAR SPECTRAL ANALYSIS OF TEMPERATURE MULTIDIMENSIONAL TIME SERIES

In the paper the algorithm of singular structural analysis and forecasting of a multidimensional series by the MSSA method is used. The program was developed, in which the steps of the method for the selection of singular decomposition components were implemented, the analysis and forecast of real time series was carried out. Singular spectrum analysis (SSA) is increasingly used in the study of time series. Unlike other methods of statistical research of time series, this method is used to study the structure, selection of individual components and forecast of both stationary and non-stationary time series. It does not require an analytical model of the series. In fact, this approach is based on the method of principal components. It is based on the transformation of a series into a matrix and its singular decomposition. After identifying the components of the singular decomposition, their grouping takes place, which leads to the decomposition of the original series into additive components, such as trend, oscillations (periodics), and noise. The SSA method allows you to continue the structure of the time series, thus building a forecast (continuation). An important direction of the development of the SSA method as a method of time series analysis is its generalization for the analysis of multidimensional time series. The method is known as MSSA (Multi-Channel SSA) or E-EOFs (Extended Empirical Orthogonal Functions). In this case, the expected result is the simultaneous decomposition of several series into interpreted components. However, a sufficiently complete theory for MSSA does not exist.

Impact of flexible working on traffic congestion in extreme weather conditions: Empirical evidence from a natural experiment

IntroductionClimate change increases the frequency and intensity of extreme weather events, which can lead to increased congestion on roadways as drivers slow down and navigate hazardous conditions. Flexible working can be a potential solution because it reduces the need for employees to commute to work. MethodsThis study investigates the traffic congestion spatiotemporal patterns of flexible working in extreme weather events (i.e., heavy snow) by using the public health emergency as a natural experiment. We collect real-time traffic data from Harbin, China, and provide a framework to quantify the reduction of traffic congestion under extreme weather conditions. During the epidemic lockdown period, only crucial workers were allowed to go to work in the study area; everybody else was working from home. This is the maximum level of flexible working that a system can allow. Hence, our findings provide an upper limit for traffic congestion reduction in extreme weather events. We constructed three scenarios, i.e., baseline, snow, and snow with work-from-home (WFH). We use time series analysis and Kaplan-Meier survival analysis methods to study the spatiotemporal patterns of traffic congestion during morning peak hours (6:30 a.m.–9:30 a.m.) at 10-min intervals. ResultsThe data analysis identified that significant traffic congestion reduction due to the WFH arrangement. For example, the longest travel duration is reduced from 120 min in the snow scenario to 50 min in the snow with WFH scenario. ConclusionsThis study reveals the geographical patterns of urban traffic congestion, providing support for guiding residents to optimize snowy travel methods in future interventions, policy changes, and research.

Performance of Deep Learning Models on Imputed Time Series Data: A Simulation Study and Application to Leading Airline Companies' Stock Price

In this study, the validity of imputation techniques for deep learning methods in time series analysis is investigated using datasets based on daily closing data in the stock market. Datasets of daily closing stock prices for Turkish Airlines, Deutsche Lufthansa AG, and Delta Airlines, as well as a simulated dataset, are used. LSTM, GRU, RNN, and Transformer models, which are deep learning models, are employed. The original dataset and datasets with 5%, 15% and 25% missing data are analyzed imputing Linear, Spline, Stineman, Mean and Random imputation techniques. The results show that model performance varies depending on the imputation technique and the rate of missing data. GRU and Transformer models are favored for their robustness and excellent performance. For handling missing data, using spline and Stineman imputations is advisable to maintain high model accuracy. This study emphasizes the usability of various imputation techniques and deep learning models in time series analysis. It assesses model performance using both MAPE and RMSE to gain a comprehensive understanding of predictive accuracy and reliability, aiming to guide future research by comparing these methods.

Spray swirling flame dynamic under combined modulation of air and fuel

Combustion instability is still a main challenge in developing advanced gas turbine combustors. It is essential to conduct instability control once it occurs. In this paper, liquid fuel modulation by a high-speed on/off valve is used to control flame oscillation generated by loudspeakers. Spray swirling flame dynamic under the combined modulation of air and fuel is experimentally studied. Flame dynamical characteristics and coherent structures at different excitation phase delays are discussed with nonlinear time-series analysis and proper orthogonal decomposition method. Experimental results show flame heat release rate fluctuation is decreased by 86% at 40° while flame instability is intensively enhanced at 220°. Phase portraits and recurrence plots show the flame is in a chaotic oscillation with low amplitude aperiodic oscillations at 40° while it suffers from the largest fluctuation at 220°. Difference in flame dynamic is caused by the destructive (out of phase) and constructive (in phase) interference of heat release rate fluctuations induced by air excitation and fuel modulation. Flame returns back to its nature dynamical behavior under out-of-phase modulation. Longitudinal modes of the spray flame are enhanced while the spiral modes are inhibited under in-phase modulation.

Strain variation and anomalous climate synergistically influence cholera pandemics.

Explanations for the genesis and propagation of cholera pandemics since 1817 have remained elusive. Evolutionary pathogen change is presumed to have been a dominant factor behind the 7th "El Tor" pandemic, but little is known to support this hypothesis for preceding pandemics. The role of anomalous climate in facilitating strain replacements has never been assessed. The question is of relevance to guide the understanding of infectious disease emergence today and in the context of climate change. We investigate the roles of climate and putative strain variation for the 6th cholera pandemic (1899-1923) using newly assembled historical records for climate variables and cholera deaths in provinces of former British India. We compare this historical pandemic with the 7th (El Tor) one and with the temporary emergence of the O139 strain in Bangladesh and globally. With statistical methods for nonlinear time series analysis, we examine the regional synchrony of outbreaks and associations of the disease with regional temperature and rainfall, and with the El Niño Southern Oscillation (ENSO). To establish future expectations and evaluate climate anomalies accompanying historical strain replacements, climate projections are generated with multi-model climate simulations for different 50-year periods. The 6th cholera pandemic featured the striking synchronisation of cholera outbreaks over Bengal during the El Niño event of 1904-07, following the invasion of the Bombay Presidency with a delay of a few years. Accompanying anomalous weather conditions are similar to those related to ENSO during strain replacements and pandemic expansions into Africa and South America in the late 20th century. Rainfall anomalies of 1904-05 at the beginning of the large cholera anomaly fall in the 99th percentile of simulated changes for the regional climate. Evolutionary pathogen change can act synergistically with climatic conditions in the emergence and propagation of cholera strains. Increased climate variability and extremes under global warming provide windows of opportunity for emerging pathogens.

Regulatory pathways to green energy transition for sustainable environment: The fostering role of human rights, banking sector development, economic complexity, and economic freedom

Green energy transition directly contributes to Sustainable Development Goals 7 and 13, which are among the 17 development goals determined by the United Nations. However, what are the determinants of this green energy transition? Researchers' answers to this question will assist in formulating policy prescriptions that will enable concrete steps toward achieving these goals. This study investigates how the development of the banking sector, human rights, economic complexity, and economic freedom affect the green energy transition in China, which is the biggest emitter of greenhouse gases globally but is also one of the leading countries in renewable energy production. The study covers the years 1995–2022. Advanced time series analysis methods were employed, and robust results were reported. According to the findings, Economic Freedom, Human Rights, and Economic Complexity have increased the transition to green energy in China. No effect of banking sector development was found. The country should improve economic freedom and human rights and increase knowledge/innovation-based production to accelerate China's transition to green energy and contribute to environmental sustainability.

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.

Robust Methods for Assessing the Characteristics of Locomotor Activity Based on Markerless Video Capture Data

Introduction. Analysis of locomotor activity is essential in a number of biomedical and pharmacological research designs, as well as environmental monitoring. The movement trajectories of biological objects can be represented by time series exhibiting a complex multicomponent structure and non-stationary dynamics, thus limiting the effectiveness of conventional correlation and spectral time series analysis methods. Recordings obtained using markerless technologies are typically characterized by enhanced noise levels, including both instrumental noise and anomalous errors associated with false estimates of the location of the points of interest, as well as gaps in the trajectories, promoting an urgent need in the development of robust methods to assess the characteristics of locomotor activity.Aim. Development of robust methods for assessing the characteristics of locomotor activity capable of efficient processing of noisy recordings obtained by markerless video-based motion capture systems.Materials and methods. In order to assess the characteristics of locomotor activity, the relative movements of body parts of laboratory animals were analyzed using the stability metrics of the mutual dynamics of their trajectories, their relative delays, as well as the relative duration of the recording fragments when relatively stable mutual dynamics could be observed. The local maxima of the cross-correlation function of two body fragments, the minima of the standard deviation of the difference between their Hilbert phases, as well as their relative delays, were used as the metrics of mutual dynamics.Results. The considered phase metrics were shown to explicitly reflect changes in locomotor activity, while the assessment of time delays using phase metric was shown to be prone to periodic error. The above limitation could be largely overcome using the correlation metrics, assuming that phase and correlation metrics could be combined.Conclusion. The proposed robust methods provide stable estimates of the characteristics of locomotor activity based on markerless video capture recordings, altogether increasing the efficiency of diagnostic procedures and assessment of the therapeutic effect during rehabilitation.

Nonlinear Characteristics of Radio Variability in Quasar 3C 446

Quasars are characterized by violent and large amplitude variability in all the observation wavelengths, and the analysis of optical variability is useful for developing theoretical models. Long-term optical variability data of quasar 3C 446 were collected from the University of Michigan Radio Astronomy Observatory database in the 4.8, 8.0, and 14.5 GHz radio bands from 1976 to 2012. Due to the complexity of the variability data, it's hard to study by the linear time series analysis methods. For learning more about non-linear characteristics of the temporal evolution of quasar variability, the Ensemble Empirical Mode Decomposition and nonlinear analysis are used to analyse chaotic dynamics, fractal properties, and periodicity. This paper focuses on whether there is a significant difference between the periodic and non-linear properties of the quasar variability before and after the removal of the periodic or chaotic components. It turns out that the variability of quasar 3C 446 in the radio bands consists of periodic, trend, and chaotic components, and the periodic and trend components are dominant. The periods of the variability after removing the chaotic and trend components are exactly the same as the periods of the original variability data, but the chaotic and fractal characteristics of the two are significantly different. The saturated correlation dimension indicates that the reconstruction of the dynamical system requires more independent parameters than the original optical variables after the removal of the periodic and trend components. The Kolmogorov entropy indicates that the loss of information is greater for the former than the latter, and the system is more chaotic and more complex. The Hurst value indicates that the self-similarity and long-range correlation are slightly stronger for the latter than the former.

Power Peak Load Forecasting Based on Deep Time Series Analysis Method

Power Peak Load Forecasting Based on Deep Time Series Analysis Method