Search Results (18)

The ongoing exploration of brain–computer interfaces (BCIs) provides deeper insights into the workings of the human brain. Motor imagery (MI) tasks, such as imagining movements of the tongue, left and right hands, or feet, can be identified through the analysis of electroencephalography (EEG) signals. The development of BCI systems opens up opportunities for their application in assistive devices, neurorehabilitation, and brain stimulation and brain feedback technologies, potentially helping patients to regain the ability to eat and drink without external help, move, or even speak. In this context, the accurate recognition and deciphering of a patient’s imagined intentions is critical for the development of effective BCI systems. Therefore, to distinguish motor tasks in a manner differing from the commonly used methods in this context, we propose a fractal dimension (FD)-based approach, which effectively captures the self-similarity and complexity of EEG signals. For this purpose, all four classes provided in the BCI Competition IV 2a dataset are utilized with nine different combinations of seven FD methods: Katz, Petrosian, Higuchi, box-counting, MFDFA, DFA, and correlation dimension. The resulting features are then used to train five machine learning models: linear, Gaussian, polynomial support vector machine, regression tree, and stochastic gradient descent. As a result, the proposed method obtained top-tier results, achieving 79.2% accuracy when using the Katz vs. box-counting vs. correlation dimension FD combination (KFD vs. BCFD vs. CDFD) classified by LinearSVM, thus outperforming the state-of-the-art TWSB method (achieving 79.1% accuracy). These results demonstrate that fractal dimension features can be applied to achieve higher classification accuracy for online/offline MI-BCIs, when compared to traditional methods. The application of these findings is expected to facilitate the enhancement of motor imagery brain–computer interface systems, which is a key issue faced by neuroscientists. Full article

Research on brain–computer interfaces (BCIs) advances the way scientists understand how the human brain functions. The BCI system, which is based on the use of electroencephalography (EEG) signals to detect motor imagery (MI) tasks, enables opportunities for various applications in stroke rehabilitation, neuroprosthetic devices, and communication tools. BCIs can also be used in emotion recognition (ER) research to depict the sophistication of human emotions by improving mental health monitoring, human–computer interactions, and neuromarketing. To address the low accuracy of MI-BCI, which is a key issue faced by researchers, this study employs a new approach that has been proven to have the potential to enhance motor imagery classification accuracy. The basic idea behind the approach is to apply feature extraction methods from the field of emotion recognition to the field of motor imagery. Six feature sets and four classifiers were explored using four MI classes (left and right hands, both feet, and tongue) from the BCI Competition IV 2a dataset. Statistical, wavelet analysis, Hjorth parameters, higher-order spectra, fractal dimensions (Katz, Higuchi, and Petrosian), and a five-dimensional combination of all five feature sets were implemented. GSVM, CART, LinearSVM, and SVM with polynomial kernel classifiers were considered. Our findings show that 3D fractal dimensions predominantly outperform all other feature sets, specifically during LinearSVM classification, accomplishing nearly 79.1% mean accuracy, superior to the state-of-the-art results obtained from the referenced MI paper, where CSP reached 73.7% and Riemannian methods reached 75.5%. It even performs as well as the latest TWSB method, which also reached approximately 79.1%. These outcomes emphasize that the new hybrid approach in the motor imagery/emotion recognition field improves classification accuracy when applied to motor imagery EEG signals, thus enhancing MI-BCI performance. Full article

Corrosion negatively impacts the functionality of civil structures. This paper introduces a new methodology that combines the fractality of vibration signals with a data processing stage utilizing autoencoders to detect corrosion damage in a truss-type bridge. Firstly, the acquired vibration signals are analyzed using six fractal dimension (FD) algorithms (Katz, Higuchi, Petrosian, Sevcik, Castiglioni, and Box dimension). The obtained FD values are then used to generate a gray-scale image. Then, autoencoders analyze these images to generate a damage indicator based on the reconstruction error between input and output images. These indicators estimate the damage probability in specific locations within the structure. The methodology was tested on a truss-type bridge model placed at the Vibrations Laboratory from the Autonomous University of Queretaro, Mexico, where three damage corrosion levels were evaluated, namely incipient, moderate, and severe, as well as healthy conditions. The results demonstrate that the proposal is a reliable tool to evaluate the condition of truss-type bridges, achieving an accuracy of 99.8% in detecting various levels of corrosion, including incipient stages, within the elements of truss-type structures regardless of their location. Full article

Across many resting-state electroencephalography (EEG) studies, dementia is associated with changes to the power spectrum and fractal dimension. Here, we describe a novel method to examine changes in the fractal dimension over time and within frequency bands. This method, which we call fractal dimension distributions (FDD), combines spectral and complexity information. In this study, we illustrate this new method by applying it to resting-state EEG data recorded from patients with subjective cognitive impairment (SCI) or dementia. We compared the performance of FDD with the performance of standard fractal dimension metrics (Higuchi and Katz FD). FDD revealed larger group differences detectable at greater numbers of EEG recording sites. Moreover, linear models using FDD features had lower AIC and higher R² than models using standard full time-course measures of the fractal dimension. FDD metrics also outperformed the full time-course metrics when comparing SCI with a subset of dementia patients diagnosed with Alzheimer’s disease. FDD offers unique information beyond traditional full time-course fractal analyses and may help to identify dementia caused by Alzheimer’s disease and dementia from other causes. Full article

This paper discusses the problem of detecting cancer using such biomarkers as blood protein markers. The purpose of this research is to propose an approach for making decisions in the diagnosis of cancer through the creation of cost-sensitive SVM classifiers on the basis of datasets with a variety of features of different nature. Such datasets may include compositions of known features corresponding to blood protein markers and new features constructed using methods for calculating entropy and fractal dimensions, as well as using the UMAP algorithm. Based on these datasets, multiclass SVM classifiers were developed. They use cost-sensitive learning principles to overcome the class imbalance problem, which is typical for medical datasets. When implementing the UMAP algorithm, various variants of the loss function were considered. This was performed in order to select those that provide the formation of such new features that ultimately allow us to develop the best cost-sensitive SVM classifiers in terms of maximizing the mean value of the metric $Macro{F}_1-score$. The experimental results proved the possibility of applying the UMAP algorithm, approximate entropy and, in addition, Higuchi and Katz fractal dimensions to construct new features using blood protein markers. It turned out that when working with the UMAP algorithm, the most promising is the application of a loss function on the basis of fuzzy cross-entropy, and the least promising is the application of a loss function on the basis of intuitionistic fuzzy cross-entropy. Augmentation of the original dataset with either features on the basis of the UMAP algorithm, features on the basis of the UMAP algorithm and approximate entropy, or features on the basis of approximate entropy provided the creation of the three best cost-sensitive SVM classifiers with mean values of the metric $Macro{F}_1-score$ increased by 5.359%, 5.245% and 4.675%, respectively, compared to the mean values of this metric in the case when only the original dataset was utilized for creating the base SVM classifier (without performing any manipulations to overcome the class imbalance problem, and also without introducing new features). Full article

The Katz fractal dimension (KFD) is an effective nonlinear dynamic metric that characterizes the complexity of time series by calculating the distance between two consecutive points and has seen widespread applications across numerous fields. However, KFD is limited to depicting the complexity of information from a single scale and ignores the information buried under different scales. To tackle this limitation, we proposed the variable-step multiscale KFD (VSMKFD) by introducing a variable-step multiscale process in KFD. The proposed VSMKFD overcomes the disadvantage that the traditional coarse-grained process will shorten the length of the time series by varying the step size to obtain more sub-series, thus fully reflecting the complexity of information. Three simulated experimental results show that the VSMKFD is the most sensitive to the frequency changes of a chirp signal and has the best classification effect on noise signals and chaotic signals. Moreover, the VSMKFD outperforms five other commonly used nonlinear dynamic metrics for ship-radiated noise classification from two different databases: the National Park Service and DeepShip. Full article

This study reports a fractal analysis of one-year radon in groundwater disturbances from five stations in China amidst the catastrophic Wenchuan ($M_w$ = 7.9) earthquake of 12 May 2008 (day 133). Five techniques are used (DFA, fractal dimensions with Higuchi, Katz, Sevcik methods, power-law analysis) in segmented portions glided throughout each signal. Noteworthy fractal areas are outlined in the KDS, GS, MSS data, whilst the portions were non-significant for PZHS and SPS. Up to day 133, critical epoch DFA-exponents are $1.5\le \alpha <2.0$, with several above 1.8. The fractal dimensions exhibit Katz’s D around 1.0–1.2, Higuchi’s D between 1.5 and 2.0, and Sevcik’s D between 1.0 and 1.5. Several power-law exponents are above 1.7, and numerous are above 2.0. All fractal results of the KDS-GS-MSS are further analysed using a novel computerised methodology that locates the exact out-of-threshold fractal areas and combines the outcomes of different methods per five, four, three, and two (maximum 13 combinations) versus nineteen $M_w\ge$ 5.5 earthquakes of the greater area. Most coincidences using different techniques are before the great Wenchuan earthquake and after the earthquake. This is not only with one method but with 13 different methods. Other interpretations are also discussed. Full article

Robotic systems are a fundamental part of modern industrial development. In this regard, they are required for long periods, in repetitive processes that must comply with strict tolerance ranges. Hence, the positional accuracy of the robots is critical, since degradation of this can represent a considerable loss of resources. In recent years, prognosis and health management (PHM) methodologies, based on machine and deep learning, have been applied to robots, in order to diagnose and detect faults and identify the degradation of robot positional accuracy, using external measurement systems, such as lasers and cameras; however, their implementation is complex in industrial environments. In this respect, this paper proposes a method based on discrete wavelet transform, nonlinear indices, principal component analysis, and artificial neural networks, in order to detect a positional deviation in robot joints, by analyzing the currents of the actuators. The results show that the proposed methodology allows classification of the robot positional degradation with an accuracy of 100%, using its current signals. The early detection of robot positional degradation, allows the implementation of PHM strategies on time, and prevents losses in manufacturing processes. Full article

This paper deals with the problem of diagnosing oncological diseases based on blood protein markers. The goal of the study is to develop a novel approach in decision-making on diagnosing oncological diseases based on blood protein markers by generating datasets that include various combinations of features: both known features corresponding to blood protein markers and new features generated with the help of mathematical tools, particularly with the involvement of the non-linear dimensionality reduction algorithm UMAP, formulas for various entropies and fractal dimensions. These datasets were used to develop a group of multiclass kNN and SVM classifiers using oversampling algorithms to solve the problem of class imbalance in the dataset, which is typical for medical diagnostics problems. The results of the experimental studies confirmed the feasibility of using the UMAP algorithm and approximation entropy, as well as Katz and Higuchi fractal dimensions to generate new features based on blood protein markers. Various combinations of these features can be used to expand the set of features from the original dataset in order to improve the quality of the received classification solutions for diagnosing oncological diseases. The best kNN and SVM classifiers were developed based on the original dataset augmented respectively with a feature based on the approximation entropy and features based on the UMAP algorithm and the approximation entropy. At the same time, the average values of the metric ${\mathit{MacroF}}_1-\mathit{score}$ used to assess the quality of classifiers during cross-validation increased by 16.138% and 4.219%, respectively, compared to the average values of this metric in the case when the original dataset was used in the development of classifiers of the same name. Full article

Fractal dimension (FD) together with advances in imaging technologies has provided an increasing application of digital images to interpret biological phenomena. In ophthalmology, topography-based images are increasingly used in common practices of clinical settings. They provide detailed information about corneal surfaces. Few-micron alterations of the corneal geometry to the elevation and curvature cause a highly multifocal surface, change the corneal optical power up to several diopters, and therefore adversely affect the individual’s vision. Keratoconus (KCN) is a corneal disease characterized by a local alteration of the corneal anatomical and mechanical features. The formation of cone-shaped regions accompanied by thinning and weakening of the cornea are the major manifestations of KCN. The implantation of tiny arc-like polymeric sections, known as intracorneal implants, is considered to be effective in restoring the corneal curvature. This study investigated the FD nature of healthy corneas (n = 7) and compared it to the corresponding values before and after intracorneal implant surgery in KCN patients (n = 7). The generalized Hurst exponent, Higuchi, and Katz FDs were computed for topography-based parameters of corneal surfaces: front elevation (ELE-front), back elevation (ELE-back), and corneal curvature (CURV). The Katz FD showed better discriminating ability for the diseased group. It could reveal a significant difference between the healthy corneas and both pre- and post-implantation topographies (p < 0.001). Moreover, the Katz dimension varied between the topographic features of KCN patients before and after the treatment (p < 0.036). We propose to describe the curvature feature of corneal topography as a “strange attractor” with a self-similar (i.e., fractal) structure according to the Katz algorithm. Full article

This paper proposes a new method for epileptic seizure detection in electroencephalography (EEG) signals using nonlinear features based on fractal dimension (FD) and a deep learning (DL) model. Firstly, Bonn and Freiburg datasets were used to perform experiments. The Bonn dataset consists of binary and multi-class classification problems, and the Freiburg dataset consists of two-class EEG classification problems. In the preprocessing step, all datasets were prepossessed using a Butterworth band pass filter with 0.5–60 Hz cut-off frequency. Then, the EEG signals of the datasets were segmented into different time windows. In this section, dual-tree complex wavelet transform (DT-CWT) was used to decompose the EEG signals into the different sub-bands. In the following section, in order to feature extraction, various FD techniques were used, including Higuchi (HFD), Katz (KFD), Petrosian (PFD), Hurst exponent (HE), detrended fluctuation analysis (DFA), Sevcik, box counting (BC), multiresolution box-counting (MBC), Margaos-Sun (MSFD), multifractal DFA (MF-DFA), and recurrence quantification analysis (RQA). In the next step, the minimum redundancy maximum relevance (mRMR) technique was used for feature selection. Finally, the k-nearest neighbors (KNN), support vector machine (SVM), and convolutional autoencoder (CNN-AE) were used for the classification step. In the classification step, the K-fold cross-validation with k = 10 was employed to demonstrate the effectiveness of the classifier methods. The experiment results show that the proposed CNN-AE method achieved an accuracy of 99.736% and 99.176% for the Bonn and Freiburg datasets, respectively. Full article

Major depressive disorder (MDD) is a global healthcare issue and one of the leading causes of disability. Machine learning combined with non-invasive electroencephalography (EEG) has recently been shown to have the potential to diagnose MDD. However, most of these studies analyzed small samples of participants recruited from a single source, raising serious concerns about the generalizability of these results in clinical practice. Thus, it has become critical to re-evaluate the efficacy of various common EEG features for MDD detection across large and diverse datasets. To address this issue, we collected resting-state EEG data from 400 participants across four medical centers and tested classification performance of four common EEG features: band power (BP), coherence, Higuchi’s fractal dimension, and Katz’s fractal dimension. Then, a sequential backward selection (SBS) method was used to determine the optimal subset. To overcome the large data variability due to an increased data size and multi-site EEG recordings, we introduced the conformal kernel (CK) transformation to further improve the MDD as compared with the healthy control (HC) classification performance of support vector machine (SVM). The results show that (1) coherence features account for 98% of the optimal feature subset; (2) the CK-SVM outperforms other classifiers such as K-nearest neighbors (K-NN), linear discriminant analysis (LDA), and SVM; (3) the combination of the optimal feature subset and CK-SVM achieves a high five-fold cross-validation accuracy of 91.07% on the training set (140 MDD and 140 HC) and 84.16% on the independent test set (60 MDD and 60 HC). The current results suggest that the coherence-based connectivity is a more reliable feature for achieving high and generalizable MDD detection performance in real-life clinical practice. Full article

We are concerned with the time series resulting from the computed local horizontal geoelectric field, obtained with the aid of a 1-D layered Earth model based on local geomagnetic field measurements, for the full solar magnetic cycle of 1996–2019, covering the two consecutive solar activity cycles 23 and 24. To our best knowledge, for the first time, the roughness of severe geomagnetic storms is considered by using a monofractal time series analysis of the Earth electric field. We show that during severe geomagnetic storms the Katz fractal dimension of the geoelectric field grows rapidly. Full article

Electric motors have been widely used as fundamental elements for driving kinematic chains on mechatronic systems, which are very important components for the proper operation of several industrial applications. Although electric motors are very robust and efficient machines, they are prone to suffer from different faults. One of the most frequent causes of failure is due to a degradation on the bearings. This fault has commonly been diagnosed at advanced stages by means of vibration and current signals. Since low-amplitude fault-related signals are typically obtained, the diagnosis of faults at incipient stages turns out to be a challenging task. In this context, it is desired to develop non-invasive techniques able to diagnose bearing faults at early stages, enabling to achieve adequate maintenance actions. This paper presents a non-invasive gradual wear diagnosis method for bearing outer-race faults. The proposal relies on the application of a linear discriminant analysis (LDA) to statistical and Katz’s fractal dimension features obtained from stray flux signals, and then an automatic classification is performed by means of a feed-forward neural network (FFNN). The results obtained demonstrates the effectiveness of the proposed method, which is validated on a kinematic chain (composed by a 0.746 KW induction motor, a belt and pulleys transmission system and an alternator as a load) under several operation conditions: healthy condition, 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm hole diameter on the bearing outer race, and 60 Hz, 50 Hz, 15 Hz and 5 Hz power supply frequencies Full article

This paper reports one-month 3 kHz EM disturbances recorded at Kardamas, Ilia, Greece after a strong $M_L=6.6$ earthquake occurred on 2018/10/25 near Zakynthos and Ilia. During this period 17 earthquakes occurred with magnitudes $M_L=4.5$ and $M_L=5.5$ and depths between 3 km and 17 km, all near Zakynthos and Ilia. A two-stage, fully computational methodology was applied to the outcomes of five different time-evolving chaos analysis techniques (DFA, fractal dimension analysis through Higuchi, Katz and Sevcik methods and power-law analysis). Via literature-based thresholds, the out-of-threshold results of all chaos analysis methods were located and from these, the common time instances of 13 selected combinations per five, four, three and two methods. Numerous persistent segments were located with DFA exponents between $1.6\le \alpha \le 2.0$ , fractal dimensions between $1.4\le D\le 2.0$ and power-law exponents between $2.2\le \beta \le 3.0$ . Out of the 17 earthquakes, six earthquakes were jointly matched by 13 selected combinations of five, four, three and two chaos analysis methods, four earthquakes by all combinations of four, three and two, while the remaining seven earthquakes were matched by at least one combination of three methods. All meta-analysis matches are within typical forecast periods. Full article