Search Results (295)

Analyzing the fluctuations of particulate matter (PM) concentrations and their scaling correlation structures are useful for air quality management. Multifractal characterization of PM2.5 and PM10 of three cities in India wase considered using the detrended fluctuation procedure from 2018 to 2021. The cross-correlation of PM concentration in a multifractal viewpoint using the multifractal cross-correlation analysis (MFCCA) framework is proposed in this study. It was observed that PM2.5 was more multifractal and complex than PM10 at all the locations. The PM–gaseous pollutant (GP) and PM–meteorological variable (MV) correlations across the scales were found to be weak to moderate in different cities. There was no definite pattern in the correlation of PM with different meteorological and gaseous pollutants variables. The nature of correlation in the pairwise associations was found to be of diverse and mixed nature across the time scales and locations. All the time series exhibited multifractality when analyzed pairwise using multifractal cross-correlation analysis. However, there was a reduction in multifractality in individual cases during PM–GP and PM–MV paired analyses. The insights gained into the scaling behavior and cross-correlation structure from this study are valuable for developing prediction models for PMs by integrating them with machine learning techniques. Full article

A better understanding of climate change impact on dry/wet conditions is crucial for agricultural planning and the use of renewable energy, in terms of sustainable development and preservation of natural resources for future generations. The objective of this study was to investigate the impact of climate change on temporal fluctuations of dry/wet conditions in Serbia on multiple temporal scales through multifractal analysis of the standardized precipitation evapotranspiration index (SPEI). We used the well-known method of multifractal detrended fluctuation analysis (MFDFA), which is suitable for the analysis of scaling properties of nonstationary temporal series. The complexity of the underlying stochastic process was evaluated through the parameters of the multifractal spectrum: position of maximum ${\alpha }_0$ (persistence), spectrum width $W$ (degree of multifractality) and skew parameter $r$ dominance of large/small fluctuations). MFDFA was applied on SPEI time series for the accumulation time scale of 1, 3, 6 and 12 months that were calculated using the high-resolution meteorological gridded dataset E-OBS for the period from 1961 to 2020. The impact of climate change was investigated by comparing two standard climatic periods (1961–1990 and 1991–2020). We found that all the SPEI series show multifractal properties with the dominant contribution of small fluctuations. The short and medium dry/wet conditions described by SPEI-1, SPEI-3, and SPEI-6 are persistent ($0.5<{\alpha }_0<1$); stronger persistence is found at higher accumulation time scales, while the SPEI-12 time series is antipersistent ($0<{\alpha }_0-1<0.5$). The degree of multifractality increases from SPEI-1 to SPEI-6 and decreases for SPEI-12. In the second period, the SPEI-1, SPEI-3, and SPEI-6 series become more persistent with weaker multifractality, indicating that short and medium dry/wet conditions (which are related to soil moisture and crop stress) become easier to predict, while SPEI-12 changed toward a more random regime and stronger multifractality in the eastern and central parts of the country, indicating that long-term dry/wet conditions (related to streamflow, reservoir levels, and groundwater levels) become more difficult for modeling and prediction. These results indicate that the complexity of dry/wet conditions, in this case described by the multifractal properties of the SPEI temporal series, is affected by climate change. Full article

Multifractality is a concept that helps compactly grasp the most essential features of financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from 6 June 2023 to 30 June 2024, the present study using multifractal detrended fluctuation analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges, convincing traces of multifractality are already emerging in this new trading as well. The resulting multifractal spectra are, however, strongly left-side asymmetric, which indicates that this multifractality comes primarily from large fluctuations, and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events, a trace of multifractal cross-correlations between the two characteristics is also observed. Full article

The Rank-Ordered Multifractal Analysis (ROMA) is a tool designed to characterize scale (in)variance and multifractality based on rank ordering the fluctuations in “groups” characterized by the same mono-fractal behavior (Hurst exponent). A range-limited structure-function analysis provides the mono-fractal index for each rank-ordered range of fluctuations. We discuss here two examples of multi-scale solar wind turbulence and complexity where ROMA is applied on the following: (a) data collected by Ulysses spacecraft in the fast solar wind, outside the ecliptic, between 25 and 31 January 2007, at roughly 2.5 Astronomical Units (AU) from the Sun, in the Southern heliosphere, at latitudes between −76.5 and −77.3 degrees, and (b) slow solar wind data collected in the ecliptic plane by Venus Express spacecraft, at 0.72 AU, on 28 January 2007. The ROMA spectrum of fast solar wind derived from ULYSSES data shows a scale-dependent structure of fluctuations: (1) at the smallest/kinetic range of scales (800 to 3200 km), persistent fluctuations are dominant, and (2) at the inertial range of scales (10⁴ to 2 × 10⁵ km), anti-persistent fluctuations are dominant, but less clearly developed and possibly indicative for the development of instabilities with cross-over behavior. The ROMA spectrum of the slow solar wind derived from Venus Express data, suggests a different structure of turbulence: (1) fully developed multifractal turbulence across scales between 5 × 10⁴ and 4 × 10⁵ km, with the Hurst index changing from anti-persistent to persistent values for the larger amplitude magnetic fluctuations; (2) at the smallest scales (400 to 6400 km), fluctuations are mainly anti-persistent, and the ROMA spectrum indicates a tendency towards mono-fractal behavior. Full article

This study investigates the profitability of portfolios that integrate asymmetric fractality within the Black–Litterman (BL) framework. It predicts 10-day-ahead exchange-traded fund (ETF) prices using recurrent neural networks (RNNs) based on historical price information and technical indicators; these predictions are utilized as BL views. While constructing the BL portfolio, the Hurst exponent obtained from the asymmetric multifractal detrended fluctuation analysis is employed to determine the uncertainty associated with the views. The Hurst exponent describes the long-range persistence in time-series data, which can also be interpreted as the uncertainty in time-series predictions. Additionally, uncertainty is measured using asymmetric fractality to account for the financial time series’ asymmetric characteristics. Then, backtesting is conducted on portfolios comprising 10 countries’ ETFs, rebalanced on a 10-day basis. While benchmarking to a Markowitz portfolio and the MSCI world index, profitability is assessed using the Sharpe ratio, maximum drawdown, and sub-period analysis. The results reveal that the proposed model enhances the overall portfolio return and demonstrates particularly strong performance during negative trends. Moreover, it identifies ongoing investment opportunities, even in recent periods. These findings underscore the potential of fractality in adjusting uncertainty for diverse portfolio optimization applications. Full article

In order to quantitatively describe the influence of aggregate distribution on crack development and peak stress of recycled aggregate concrete, a multifractal spectrum theory was proposed to quantitatively characterize aggregate distribution in specimens. A mesomechanical model of reclaimed aggregate concrete mixed with natural aggregate and artificial aggregate was constructed. Numerical simulation tests were conducted on the uniaxial compression mechanical behavior of 25 groups of sample models with the same proportion and different aggregate distribution forms. Based on the box dimension theory, the multiple fractal spectrum method was used to quantitatively characterize the aggregate distribution form, and the key factors affecting cracks were explored based on the gray correlation degree. The research results show that the aggregate distribution in recycled aggregate concrete has multifractal characteristics. The multifractal spectrum was used to effectively characterize the aggregate distribution pattern, which can enlarge local details and provide new ideas for the quantitative analysis of the damage mode of recycled concrete. Secondly, by establishing a statistical model of the correlation between the multifractal spectrum width of the aggregate distribution pattern and the crack distribution box dimension, it was found that there was a positive correlation between the two, that is, the greater the multifractal spectrum width of the aggregate distribution pattern, the greater the crack box dimension, and the more complex the crack distribution. The complexity of aggregate distribution is closely related to the irregularity and complexity of mesoscopic failure crack propagation in recycled concrete specimens. In addition, gray correlation theory was applied to analyze the key factors affecting the formation of cracks in the specimens. The results showed that aggregate distribution had a first-order correlation with crack formation, and changes in aggregate distribution were an important factor affecting the performance of recycled concrete. Secondly, the poor mechanical properties of NAITZ led to obvious material damage, while NCA and MZ had a significant impact on the skeleton effect in the stress–strain process due to their large areas. This study deepens people’s understanding of the damage characteristics and cracking failure modes of recycled concrete. The study verifies the feasibility of the application of recycled aggregates and provides a valuable reference for engineering practice. Full article

The application of high-pressure fluid induces the closure of isolated pores inside the matrix and promotes the generation of new fractures, resulting in a compressive effect on the matrix. To examine the compressibility of coal-measure shale samples, the compression of the coal–shale matrix in the high-pressure stage was analyzed by a low-pressure nitrogen gas adsorption and mercury intrusion porosimetry experiment. The quantitative parameters describing the heterogeneity of the pore-size distribution of coal-measure shale are obtained using multifractal theory. The results indicate that the samples exhibit compressibility values ranging from 0.154 × 10⁻⁵ MPa⁻¹ to 4.74 × 10⁻⁵ MPa⁻¹ across a pressure range of 12–413 MPa. The presence of pliable clay minerals enhances the matrix compressibility, whereas inflexible brittle minerals exhibit resistance to matrix compression. There is a reduction in local fluctuations of pore volume across different pore sizes, an improvement in the autocorrelation of PSD, and a mitigation of nonuniformity after correction. Singular and dimension spectra have advantages in multifractal characterization. The left and right spectral width parameters of the singular spectrum emphasize the local differences between the high- and low-value pore volume areas, respectively, whereas the dimensional spectrum width is more suitable for reflecting the overall heterogeneity of the PSD. Full article

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates discrepancies between peak and off-peak hours, accounting for the daily cyclicity of the electricity market, and proposes a crossover point detection method based on the Chow test. Furthermore, the impacts of fuel cell introduction are evidenced through various methods that encompass multifractal spectra and market efficiency. The findings initially indicate a higher degree of multifractality during off-peak hours relative to peak hours. In particular, the crossover points emerged solely during off-peak hours, unveiling short- and long-term dynamics predicated on a near-annual cycle. Additionally, the average Hurst exponent for the short-term was 0.542, while the average for the long-term was 0.098, representing a notable discrepancy. The introduction of fuel cells attenuated the heterogeneity in the scaling behavior, which is potentially attributable to the decreased volatility in both the supply and demand spectra. Remarkably, after the introduction of fuel cells, there was a discernible decrease in the influence of long-range correlation within multifractality, and the market exhibited an increased propensity toward random-walk behavior. This phenomenon was also detected in the market deficiency measure, from an average of 0.536, prior to the introduction, to an average of 0.267, following the introduction, signifying an improvement in market efficiency. This implies that the introduction of fuel cells into the market engendered increased supply stability and a consistent increase in demand, mitigating volatility on both the supply and demand sides, thus increasing market efficiency. Full article

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability. Full article

Displacement prediction models based on measured data have been widely applied in structural health monitoring. However, most models neglect the particularity of displacement monitoring for arch dams with cracks, nor do they thoroughly analyze the non-stationarity and uncertainty of displacement. To address this issue, the influencing factors of displacement were first considered, with crack opening displacement being incorporated into them, leading to the construction of the HSCT model that accounts for the effects of cracks. Feature selection was performed on the factors of the HSCT model utilizing the max-relevance and min-redundancy (mRMR) algorithm, resulting in the screened subset of displacement influence factors. Next, displacement was decomposed into trend, seasonal, and remainder components applying the seasonal-trend decomposition using loess (STL) algorithm. The multifractal characteristics of these displacement components were then analyzed by multifractal detrended fluctuation analysis (MF-DFA). Subsequently, displacement components were predicted employing the convolutional neural network-long short-term memory (CNN-LSTM) model. Finally, the impact of uncertainty factors was quantified using prediction intervals based on the bootstrap method. The results indicate that the proposed methods and models are effective, yielding satisfactory prediction accuracy and providing scientific basis and technical support for the health diagnosis of hydraulic structures. Full article

Ensuring the safety of transmission line towers is vital for human safety, power supply, economic development, and environmental protection. This study specifically examines how temperature affects tower inclination. Multifractal detrended cross-correlation analysis (MF-DCCA) is a combination of multifractal detrended fluctuation analysis (MF-DFA) and DCCA that reveals the multifractal features of two cross-correlated non-stationary signals. This paper adopts the MF-DCCA tool to investigate the cross-correlations between the internal temperature of an inclination sensor device and the posture of a transmission line tower. The tilt angle data in the x- and y-axes are used to measure the posture of the transmission line tower. We start by using Pearson correlation to assess the relationship between temperature and two inclination angles, followed by verifying their correlation with a p-value below $0.05$ using first-order linear fitting. We initially assess the multifractal features of three time series using MF-DFA before MF-DCCA analysis. All exhibit multifractal traits with $H\left(2\right)<0.5$, indicating negative persistence, especially notable in the temperature series. Finally, we adopt the MF-DCCA approach to examine the multifractal cross-correlation between tilt-angle time series and temperature time series, and the results indicate the negative persistence of the cross-correlation between the time series. Furthermore, the multifractal cross-correlation of temperature and inclination data on the y-axis was also found to be stronger than on the x-axis based on features of the scaling exponent and symmetry exponent. Full article

As more and more transmission lines need to pass through areas with heavy icing, the problem of transmission line faults caused by ice and snow disasters frequently occurs. Existing ice coverage monitoring methods have defects such as the use of a single monitoring type, low accuracy of monitoring results, and an inability to obtain ice coverage data over time. Therefore, this study proposes a new algorithm for detecting the icing status of transmission lines. The algorithm uses two-dimensional multifractal detrended fluctuation analysis (2D MF-DFA) to determine the optimal sliding-window size and wave function and accurately segment and extract local feature areas. Based on the local Hurst exponent ($L_h\left(z\right)$) and the power-law relationship between the fluctuation function and the scale at multiple continuous scales, the ice-covered area of a transmission conductor was accurately detected. By analyzing and calculating the key target pixels, the icing thickness was accurately measured, achieving accurate detection of the icing status of the transmission lines. The experimental results show that this method can accurately detect ice-covered areas and the icing thickness of transmission lines under various working conditions, providing a strong guarantee for the safe and reliable operation of transmission lines under severe weather conditions. Full article

The ultrasonic vibration rock-breaking method has been successfully applied to hard rock due to its high efficiency and controllable energy, providing a novel approach for the development of a more efficient, intelligent, safe, and environmentally friendly reconstruction method for coal and rock reservoirs. By subjecting the rock to ultra-high frequency (>15 kHz) vibration load, rapid fatigue damage can be induced within a short period of time, thereby enhancing the extent of cracking in hard rock. In order to investigate the impact of high-frequency vibration excitation on coal cracking, this study conducted exploratory tests using an independently designed ultrasonic vibration excitation system. These tests were combined with nuclear magnetic resonance (NMR) and permeability measurements to compare and analyze the pore fracture structure and permeability changes in coal samples under resonant and non-resonant conditions. Additionally, multifractal characteristics of the coal samples were investigated. The results demonstrate that high-frequency vibration excitation leads to significant expansion of micropores and mesopores in coal samples. Moreover, there is a strong exponential relationship between coal porosity/permeability and excitation time. After 40 s of stimulation, both porosity and permeability increase by 32.4% and over 8400%, respectively; these increases are five times higher for resonance-state compared to non-resonance-state conditions. Furthermore, water-saturated coal samples exhibit multifractal characteristics in their NMR T₂ spectrum distribution, and multifractal parameters ΔD(q)and Δα show positive correlations with the proportion of mesoporous/macropores but negative correlations with the proportion of micropores; conversely, Δf shows an opposite trend relative to pore proportions. The pore structure of coal exhibits intricate multi-scale characteristics, and the heterogeneity at various scales is quantified through multifractal analysis. This study confirms the feasibility of utilizing high-frequency vibration excitation for cracking coal rocks while also providing valuable insights for further expanding its application. Full article

The occurrence of landslide hazards significantly induces changes in slope surface displacement. This study conducts an in-depth analysis of the multifractal characteristics and displacement prediction of highway slope surface displacement sequences. Utilizing automated monitoring devices, data are collected to analyze the deformation patterns of the slope surface layer. Specifically, the multifractal detrended fluctuation analysis (MF-DFA) method is employed to examine the multifractal features of the monitoring data for slope surface displacement. Additionally, the Mann–Kendall (M-K) method is combined to construct the α indicator and $f\left(\alpha \right)$ indicator criteria, which provide early warnings for slope stability. Furthermore, the long short-term memory (LSTM) model is optimized using the particle swarm optimization (PSO) algorithm to enhance the prediction of slope surface displacement. The results indicate that the slope displacement monitoring data exhibit a distinct fractal sequence characterized by $h\left(q\right)$, with values decreasing as the fluctuation function q decreases. Through this study, the slope landslide warning classification has been determined to be Level III. Moreover, the PSO-LSTM model demonstrates superior prediction accuracy and stability in slope displacement forecasting, achieving a root mean square error (RMSE) of 0.72 and a coefficient of determination (R²) of 91%. Finally, a joint response synthesis of the slope landslide warning levels and slope displacement predictions resulted in conclusions. Subsequent surface displacements of the slope are likely to stabilize, indicating the need for routine monitoring and inspection of the site. Full article

Multifractal analysis offers a sophisticated method to examine the complex morphology of neurons, which traditionally have been analyzed using monofractal techniques. This study investigates the multifractal properties of two-dimensional neuron projections from the human dorsal striatum, focusing on potential morphological changes related to aging and differences based on spatial origin within the nucleus. Using multifractal spectra, we analyzed various parameters, including generalized dimensions and Hölder exponents, to characterize the neurons’ morphology. Despite the detailed analysis, no significant correlation was found between neuronal morphology and age. However, clear morphological differences were observed between neurons from the caudate nucleus and the putamen. Neurons from the putamen displayed higher morphological complexity and greater local homogeneity, while those from the caudate nucleus exhibited more scaling laws and higher local heterogeneity. These findings suggest that while age may not significantly impact neuronal morphology in the dorsal striatum, the spatial origin within this brain region plays a crucial role in determining neuronal structure. Further studies with larger samples are recommended to confirm these findings and to explore the full potential of multifractal analysis in neuronal morphology research. Full article