Search Results (14)

We introduce hyperbolic oscillation spaces and mixed fractional lifting oscillation spaces expressed in terms of hyperbolic wavelet leaders of multivariate signals on ${\mathbb{R}}^d$, with $d\ge 2$. Contrary to Besov spaces and fractional Sobolev spaces with dominating mixed smoothness, the new spaces take into account the geometric disposition of the hyperbolic wavelet coefficients at each scale $(j_1,\cdots ,j_d)$, and are therefore suitable for a multifractal analysis of rectangular regularity. We prove that hyperbolic oscillation spaces are closely related to hyperbolic variation spaces, and consequently do not almost depend on the chosen hyperbolic wavelet basis. Therefore, the so-called rectangular multifractal analysis, related to hyperbolic oscillation spaces, is somehow ‘robust’, i.e., does not change if the analyzing wavelets were changed. We also study optimal relationships between hyperbolic and mixed fractional lifting oscillation spaces and Besov spaces with dominating mixed smoothness. In particular, we show that, for some indices, hyperbolic and mixed fractional lifting oscillation spaces are not always sharply imbedded between Besov spaces or fractional Sobolev spaces with dominating mixed smoothness, and thus are new spaces of a really different nature. Full article

The article presents a method for diagnosing cycloidal gear damage on a laboratory stand. The damage was simulated by removing the sliding sleeves from two adjacent external pins of the cycloidal gearbox. Damage to the sliding sleeves may occur under operating conditions and can lead to the destruction of the gear unit. Hence, early detection is essential. Signals from torque sensors, rotational speed sensors and vibration acceleration sensors of input and output shafts for various rotational speeds and transmission loads were recorded. The frequency analysis of these signals was carried out. Due to the fluctuation of the rotational speed, the frequency spectrum gives an approximate picture and is not useful in detecting this type of damage. The statistical characteristics of the signal were determined. However, only statistical moments of higher orders, such as kurtosis, are sensitive to the tested damage. Therefore, the use of multifractal analysis of the vibration signal using the wavelet leader method (WLMF) was considered. Then log-cumulants of the multifractal spectrum were selected as the new signal features. Full article

Congestive heart failure (CHF) is a chronic heart condition associated with debilitating symptoms that can lead to mortality. The electrocardiogram (ECG) is a noninvasive and simple diagnostic method that can show detectable changes in CHF. However, manual diagnosis of ECG signals is often erroneous due to the small amplitude and duration of the ECG signals. This paper presents a CHF diagnosis method based on generalized multiscale entropy (MSE)-wavelet leaders (WL) and extreme learning machine (ELM). Firstly, ECG signals from normal sinus rhythm (NSR) and congestive heart failure (CHF) patients are pre-processed. Then, parameters such as segmentation time and scale factor are chosen, and the multifractal spectrum features and number of ELM hidden layer nodes are determined. Two different data sets (A, B) were used for training and testing. In both sets, the balanced data set (B) had the highest accuracy of 99.72%, precision, sensitivity, specificity, and F1 score of 99.46%, 100%, 99.44%, and 99.73%, respectively. The unbalanced data set (A) attained an accuracy of 99.56%, precision of 99.44%, sensitivity of 99.81%, specificity of 99.17%, and F1 score of 99.62%. Finally, increasing the number of ECG segments and different algorithms validated the probability of detection of the unbalanced data set. The results indicate that our proposed method requires a lower number of ECG segments and does not require the detection of R waves. Moreover, the method can improve the probability of detection of unbalanced data sets and provide diagnostic assistance to cardiologists by providing a more objective and faster interpretation of ECG signals. Full article

The fine particulate matter (PM2.5) concentration has been a vital source of info and an essential indicator for measuring and studying the concentration of other air pollutants. It is crucial to realize more accurate predictions of PM2.5 and establish a high-accuracy PM2.5 prediction model due to their social impacts and cross-field applications in geospatial engineering. To further boost the accuracy of PM2.5 prediction results, this paper proposes a new wavelet PM2.5 prediction system (called WD-OSMSSA-KELM model) based on a new, improved variant of the salp swarm algorithm (OSMSSA), kernel extreme learning machine (KELM), wavelet decomposition, and Boruta-XGBoost (B-XGB) feature selection. First, we applied the B-XGB feature selection to realize the best features for predicting hourly PM2.5 concentrations. Then, we applied the wavelet decomposition (WD) algorithm to reach the multi-scale decomposition results and single-branch reconstruction of PM2.5 concentrations to mitigate the prediction error produced by time series data. In the next stage, we optimized the parameters of the KELM model under each reconstructed component. An improved version of the SSA is proposed to reach higher performance for the basic SSA optimizer and avoid local stagnation problems. In this work, we propose new operators based on oppositional-based learning and simplex-based search to mitigate the core problems of the conventional SSA. In addition, we utilized a time-varying parameter instead of the main parameter of the SSA. To further boost the exploration trends of SSA, we propose using the random leaders to guide the swarm towards new regions of the feature space based on a conditional structure. After optimizing the model, the optimized model was utilized to predict the PM2.5 concentrations, and different error metrics were applied to evaluate the model’s performance and accuracy. The proposed model was evaluated based on an hourly database, six air pollutants, and six meteorological features collected from the Beijing Municipal Environmental Monitoring Center. The experimental results show that the proposed WD-OLMSSA-KELM model can predict the PM2.5 concentration with superior performance (R: 0.995, RMSE: 11.906, MdAE: 2.424, MAPE: 9.768, KGE: 0.963, $R^2$: 0.990) compared to the WD-CatBoost, WD-LightGBM, WD-Xgboost, and WD-Ridge methods. Full article

Multifractal behavior in the cepstrum representation of healthy and unhealthy infant cry signals is examined by means of wavelet leaders and compared using the Student t-test. The empirical results show that both expiration and inspiration signals exhibit clear evidence of multifractal properties under healthy and unhealthy conditions. In addition, expiration and inspiration signals exhibit more complexity under healthy conditions than under unhealthy conditions. Furthermore, distributions of multifractal characteristics are different across healthy and unhealthy conditions. Hence, this study improves the understanding of infant crying by providing a complete description of its intrinsic dynamics to better evaluate its health status. Full article

In this paper, to realize a better adaptive method for the lightning electric field signal denoising, we firstly compared the decomposition results of three methods called the EMD (empirical mode decomposition), the CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise), and the EWT (empirical wavelet transform) by artificial signals, respectively, and found that the EWT was better than the other two methods. Then, a MEWT (modified empirical wavelet transform) method based on the EWT was presented for processing the natural lightning signals data. By using our MEWT method, we processed three types of electric field signal data with different frequency bands radiated by the lightning step leader, the cloud pulse and the return stroke, respectively, and the VLF (very low frequency) lightning signals propagating different distances from 500 km to 3500 km, by using the data of the fast electric field change sensors from Nanjing Lightning Location Network (NLLN) in 2018 and the data of the fast electric field change sensors and the VLF electric antennas from the NUIST Wide-range Lightning Location System (NWLLS) in 2021. The results showed that our presented MEWT method could adaptively process different lightning signal data with different frequencies from the step leader, the cloud pulse, and the return stroke; for the lightning VLF signal data from 500 km to 3500 km, the MEWT also achieved a better noise reduction effect. After denoising the signal by using our MEWT, the detection ability of the fast electric field change sensor was improved, and more weak lightning signals could be identified. Full article

The rapid development of Internet of Things (IoT) technology, together with mobile network technology, has created a never-before-seen world of interconnection, evoking research on how to make it vaster, faster, and safer. To support the ongoing fight against the malicious misuse of networks, in this paper we propose a novel algorithm called AMDES (unmanned aerial system multifractal analysis intrusion detection system) for spoofing attack detection. This novel algorithm is based on both wavelet leader multifractal analysis (WLM) and machine learning (ML) principles. In earlier research on unmanned aerial systems (UAS), intrusion detection systems (IDS) based on multifractal (MF) spectral analysis have been used to provide accurate MF spectrum estimations of network traffic. Such an estimation is then used to detect and characterize flooding anomalies that can be observed in an unmanned aerial vehicle (UAV) network. However, the previous contributions have lacked the consideration of other types of network intrusions commonly observed in UAS networks, such as the man in the middle attack (MITM). In this work, this promising methodology has been accommodated to detect a spoofing attack within a UAS. This methodology highlights a robust approach in terms of false positive performance in detecting intrusions in a UAS location reporting system. Full article

Diagnosing the condition of rotating machines by non-invasive methods is based on the analysis of dynamic signals from sensors mounted on the machine—such as vibration, velocity, or acceleration sensors; torque meters; force sensors; pressure sensors; etc. The article presents a new method combining the empirical mode decomposition algorithm with wavelet leader multifractal formalism applied to diagnosing damages of rotating machines in non-stationary conditions. The development of damage causes an increase in the level of multifractality of the signal. The multifractal spectrum obtained as a result of the algorithm changes its shape. Diagnosis is based on the classification of the features of this spectrum. The method is effective in relation to faults causing impulse responses in the dynamic signal registered by the sensors. The method has been illustrated with examples of vibration signals of rotating machines recorded on a laboratory stand, as well as on real objects. Full article

The article represents results of a physical simulation of incomplete upward leader discharges induced on air transmission lines’ elements, using charged artificial thunderstorm cells of negative polarity. The influence of such discharges on closely located model sensors (both of rod and elongated types) of digital monitoring systems, as well as on the models of receiver-transmission systems of local data collection (antennas), was determined. Effect of heterogeneity of electromagnetic field caused by incomplete upward discharges on frequency specter of signals generated on sensors and antennas was estimated. Wavelet analysis was carried out to determine the basic frequency diapasons of such signals. Based on experimental data obtained, suppositions about the extent of influence of nearby incomplete leader discharges on the functioning of currently used systems of transmission lines’ monitoring were made. Full article

This paper explores the spatial variations of the statistical scaling features of low to high latitude geomagnetic field fluctuations at Swarm altitude. The data for this study comes from the vector field magnetometer onboard Swarm A satellite, measured at low resolution (1 Hz) for one year (from 9 March 2016, to 9 March 2017). We estimated the structure-function scaling exponents using the p-leaders discrete wavelet multifractal technique, from which we obtained the singularity spectrum related to the magnetic fluctuations in the North-East-Center (NEC) coordinate system. From this estimation, we retain just the maximal fractal subset, associated with the Hurst exponent H. Here we present thresholding for two levels of the Auroral Electrojet index and almost the whole northern and southern hemispheres, the Hurst exponent, the structure-function scaling exponent of order 2, and the multifractal p-exponent width for the geomagnetic fluctuations. The latter quantifies the relevance of the multifractal property. Sometimes, we found negative values of H, suggesting a behavior similar to wave breaking or shocklet-like propagating front. Furthermore, we found some asymmetries in the magnetic field turbulence between the northern and southern hemispheres. These estimations suggest that different turbulent regimes of the geomagnetic field fluctuations exist along the Swarm path. Full article

Research in football has been embracing the complex systems paradigm in order to identify different insights about key determinants of performance. The present study explored the multifractal properties of several football-related scenarios, as a candidate method to describe movement dynamics. The sample consisted of five footballers that were engaged in six different training situations (jogging, high intensity interval protocol, running circuit, 5 vs. 5, 8 vs. 8 and a 10 vs. 10 small-sided game). All kinematic measures were collected using a 100 Hz wireless and wearable inertial measurement unit (WIMUPRO©). Data were processed using a discrete wavelet leader transform in order to obtain a spectrum of singularities that could best describe the movement dynamics. The Holder exponent for each of all six conditions revealed mean values h < 0.5 indicating presence of long memory with anti-correlated behavior. A strong trend was found between the width of the multifractal spectrum and the type of task performed, with jogging showing the weakest multifractality ∆h = 0.215 ± 0.020, whereas, 10 vs. 10 small-sided game revealed the strongest ∆h = 0.992 ± 0.104. The Hausdorff dimension indicates that a maximal fluctuation rate occurs with a higher probability than that of the minimal fluctuation rate for all tasks, with the exception of the high intensity interval protocol. Moreover, the spectrum asymmetry values of jogging, running circuit, 5 vs. 5, 8 vs. 8 and 10 vs. 10 small-sided games reveal their multifractal structures are more sensitive to the local fluctuations with small magnitudes. The multifractal analysis has shown a potential to systematically elucidate the dynamics and variability structure over time for the training situations. Full article

Scale-free analysis of brain activity reveals a complexity of synchronous neuronal firing which is different from that assessed using classic rhythmic quantifications such as spectral analysis of the electroencephalogram (EEG). In humans, scale-free activity of the EEG depends on the behavioral state and reflects cognitive processes. We aimed to verify if fractal patterns of the mouse EEG also show variations with behavioral states and topography, and to identify molecular determinants of brain scale-free activity using the ‘multifractal formalism’ (Wavelet-Leaders). We found that scale-free activity was more anti-persistent (i.e., more different between time scales) during wakefulness, less anti-persistent (i.e., less different between time scales) during non-rapid eye movement sleep, and generally intermediate during rapid eye movement sleep. The scale-invariance of the frontal/motor cerebral cortex was generally more anti-persistent than that of the posterior cortex, and scale-invariance during wakefulness was strongly modulated by time of day and the absence of the synaptic protein Neuroligin-1. Our results expose that the complexity of the scale-free pattern of organized neuronal firing depends on behavioral state in mice, and that patterns expressed during wakefulness are modulated by one synaptic component. Full article

The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the statistical complexity evaluated with different sets of multiresolution wavelet coefficients are considered. Both methodologies are applied to the quantitative EEG time series analysis of a tonic-clonic epileptic seizure, and comparative results are presented. In particular, even when both methods describe the dynamical changes of the EEG time series, the one based on wavelet leaders presents a better time resolution. Full article

In this study, features of the financial returns of the PSI20index, related to market efficiency, are captured using wavelet- and entropy-based techniques. This characterization includes the following points. First, the detection of long memory, associated with low frequencies, and a global measure of the time series: the Hurst exponent estimated by several methods, including wavelets. Second, the degree of roughness, or regularity variation, associated with the H¨older exponent, fractal dimension and estimation based on the multifractal spectrum. Finally, the degree of the unpredictability of the series, estimated by approximate entropy. These aspects may also be studied through the concepts of non-extensive entropy and distribution using, for instance, the Tsallis q-triplet. They allow one to study the existence of efficiency in the financial market. On the other hand, the study of local roughness is performed by considering wavelet leader-based entropy. In fact, the wavelet coefficients are computed from a multiresolution analysis, and the wavelet leaders are defined by the local suprema of these coefficients, near the point that we are considering. The resulting entropy is more accurate in that detection than the H¨older exponent. These procedures enhance the capacity to identify the occurrence of financial crashes. Full article