This work studies a mechanical system composed of two‐spring coupled masses arrangement without damping using fractional derivatives under the Caputo sense. We determine and implement an explicit ...model based on the Caputo‐Fabrizio operator. To achieve this model, we detail a systematic methodology that avoids dimensional inconsistencies. Then, we use the proposed model to explain the system dynamic acquired from an experimental (quite rudimentary) setup. We also compare our results to those achieved from the ordinary model and the numerical implementation using the Caputo derivative definition. Results prove that the proposed model describes the dynamic of this mechanical system better than the ordinary and numerical models. We also show that the fractional order allows the model (obtained from an idealized undamped system) to describe dynamics from fully dissipative to wholly oscillatory. Moreover, we discuss other exciting characteristics of the obtained responses.
•An alternative Active Contour Model solution for medical images is introduced.•A multi-population Cuckoo Search Strategy (MCSS) is implemented to boost ACM.•Proposed method was applied on Magnetic ...Resonance Imaging (MRI) data.•MCSS outperforms traditional ACM and ACM driven by multi-population PSO.
In this paper, an alternative Active Contour Model (ACM) driven by Multi-population Cuckoo Search (CS) algorithm is introduced. This strategy assists the converging of control points towards the global minimum of the energy function, unlike the traditional ACM version which is often trapped in a local minimum. In the proposed methodology, each control point is constrained in a local search window, and its energy minimisation is performed through a Cuckoo Search via Lévy flights paradigm. With respect to local search window, two shape approaches have been considered: rectangular shape and polar coordinates. Results showed that the CS method using polar coordinates is generally preferable to CS performed in rectangular shapes. Real medical and synthetic images were used to validate the proposed strategy, through three performance metrics as the Jaccard index, the Dice index and the Hausdorff distance. Applied specifically to Magnetic Resonance Imaging (MRI) images, the proposed method enables to reach better accuracy performance than the traditional ACM formulation, also known as Snakes and the use of Multi-population Particle Swarm Optimisation (PSO) algorithm.
Fractional solution of the catenary curve Martínez–Jiménez, Leonardo; Cruz–Duarte, Jorge Mario; Rosales–García, J. Juan
Mathematical methods in the applied sciences,
15 July 2021, Letnik:
44, Številka:
10
Journal Article
Recenzirano
The catenary curve has been used in a vast number of practical applications, and several mathematical models have been studied to approximate its behavior. This work, motivated by the success of ...fractional calculus, proposes a fractional model for the catenary curve, using the Caputo‐Fabrizio (CF) definition. It was analyzed how the fractional derivative order and the fractional initial condition directly affect the hanging cable shape. It was noticed that the proposed model provides the possibility of describing new scenarios and revealing new information about the system. Therefore, this work gives rise to a new family of curves that can be used in any practical problem involving catenaries, varying at most two parameters.
Asphaltenes removal from heavy and extra-heavy crudes is paramount within the oil industry. This work describes several electrodeposition studies by considering the simultaneous presence of external ...magnetic fields and ferromagnetic nanoparticles, i.e., composite carbon-nano magnetite nanoparticles (CMG). To do so, we used a Colombian extra-heavy crude oil. With the conventional electrodeposition technique, it is possible to separate up to 46% of the asphaltenes present in the original oil. In contrast, after the proposed electrodeposition process, results show asphaltene removals between 45% and 55%. The highest percentages relate to the process where an external with both, magnetic field and nanoparticles with magnetic properties. The asphaltene fractions were characterized by spectroscopic (FTIR) and thermogravimetric (TGA) techniques. We also carried out a compositional analysis. The nanoparticles were characterized by X-ray powder detraction (XRD) utilizing a Bruker D8 Advance equipment with DaVinci geometry. Its morphology was analyzed using the Quanta FEG 650 Scanning Electron Microscope (SEM), with a FEG electron source, and a scattered electron image detector type SSD, with an EDS detector type EDAX APOLLO X and a resolution of 126.1 eV. The percentages of carbon, nitrogen, sulfur, and hydrogen were also determined using the Vario CUBE equipment. The CMG thermal behavior was analyzed under the same operating conditions as the asphaltenes and utilizing the Netzsch 449 F1 equipment. Likewise, the electrode deposits were characterized physicochemically to corroborate that, in all cases, they corresponded to asphaltene fractions.
It is common to find multiple metaheuristics to solve continuous optimization problems. However, choosing what optimizer may obtain the best results for a given task requires exhaustive evaluations ...that are highly application-dependent. Besides, it is necessary to find sufficiently good tuning parameters to achieve satisfactory performance with the selected approach. In this context, the automatic design of algorithms, particularly those based on heuristics, has been increasing in popularity in the previous years due to its undoubted relevance nowadays. This paper explores a novel approach based on hyper-heuristics to carefully select population-based search operators and their tuning parameters to generate metaheuristics capable of dealing with a given practical engineering problem. The proposed strategy is assessed using three highly relevant and illustrative problems: training Artificial Neural Networks, designing PID controllers, and modeling a calorimetric phenomenon based on fractional calculus. In addition, we implement three well-known optimization metaheuristics to compare achieved solutions via the proposed hyper-heuristic strategy, namely Particle Swarm Optimization, Genetic Algorithm, and Cuckoo Search. Results from extensive numerical tests prove that the customized metaheuristics are generally superior to the three well-known algorithms, taking only a few iterations to converge to an optimal solution. This is an excellent indicator of alleviating the effort and expertise required to choose the proper methodology when dealing with real-valued optimization problems.
This work introduces an alternative approach for developing a customized Metaheuristic (MH) tailored for tuning a Fractional-Order Proportional-Integral-Derivative (FOPID) controller within an ...Automatic Voltage Regulator (AVR) system. Leveraging an Automated Algorithm Design (AAD) methodology, our strategy generates MHs by utilizing a population-based Search Operator (SO) domain, thus minimizing human-induced bias. This approach eliminates the need for manual coding or the daunting task of selecting an optimal algorithm from a vast collection of the current literature. The devised MH consists of two distinct SOs: a dynamic swarm perturbator succeeded by a Metropolis-type selector and a genetic crossover perturbator, followed by another Metropolis-type selector. This MH fine-tunes the FOPID controller’s parameters, aiming to enhance control performance by reducing overshoot, rise time, and settling time. Our research includes a comparative analysis with similar studies, revealing that our tailored MH significantly improves the FOPID controller’s speed by 1.69 times while virtually eliminating overshoot. Plus, we assess the tuned FOPID controller’s resilience against internal disturbances within AVR subsystems. The study also explores two facets of control performance: the impact of fractional orders on conventional PID controller efficiency and the delineating of a confidence region for stable and satisfactory AVR operation. This work’s main contributions are introducing an innovative method for deriving efficient MHs in electrical engineering and control systems and demonstrating the substantial benefits of precise controller tuning, as evidenced by the superior performance of our customized MH compared to existing solutions.
This paper presents new solutions for twodimensional projectile motion in a free and resistive medium, obtained within the newly established conformable derivative. For free motion, we obtain ...analytical solutions and show that the trajectory, height, flight time, optimal angle, and maximum range depend on the order of the conformable derivative, 0 <
≤ 1. Likewise, we analyse and simulate the projectile motion in a resistive medium by assuming several scenarios. The obtained trajectories never exceed the ordinary ones, given by
= 1, unlike results reported in other studies.
Thermal design for electronic devices approached through the solution analysis of the Inverse Heat Transfer Problem (IHTP) has not been extensively explored. This article proposes an alternative ...strategy and a contrasting approach for the optimal inverse parameters' estimation of heat transfer systems, particularly in designing heat sinks. A framework to tackle a Rectangular Microchannel Heat Sink (RMCHS) design modeled by the Entropy Generation Minimization (EGM) criterion is developed. This framework comprises two strategies to be compared. The serial proposal works sequentially depending on the parameters' sensitivity into the RMCHS model, backpropagating estimated parameters to all processes. The parallel strategy processes all parameters simultaneously. Instead of focusing efforts on a typical optimization process, a sequential procedure takes advantage of the most influential parameters in the heat sink model and the excellent exploration-exploitation rate of Metaheuristic Optimization Algorithms (MOAs). The most sensitive design variables are prioritized in the serial strategy. The implemented estimation-optimization strategies are addressed through an IHTP's inverse analysis. Thereby, global MOAs are implemented to solve the specific application and become an alternative to the gradient-based methods when their efficiency and effectiveness are at stake. MOAs show overall relative errors related to minimal entropy generation rate inferior to 0.07% for data with 30 dB of SNR and less than 7.63% of error for data with 10 dB of SNR compared with the Levenberg-Marquardt method. Numerical results show that serial strategy provided a stable and reliable design solution even with contaminated data, obtaining better performances than the multiparametric strategy. Additionally, parametric and nonparametric statistical tests were used to validate the appropriate optimization algorithm and the most reliable strategy. The statistical tests confirmed the optimal-inverse problem estimation and optimization improvement by combining the serial strategy and analyzed MOAs to design the RMCHS based on the EGM criterion.
Motor Imagery Electroencephalogram (MI-EEG) signals are widely used in Brain-Computer Interfaces (BCI). MI-EEG signals of large limbs movements have been explored in recent researches because they ...deliver relevant classification rates for BCI systems. However, smaller and noisy signals corresponding to hand-finger imagined movements are less frequently used because they are difficult to classify. This study proposes a method for decoding finger imagined movements of the right hand. For this purpose, MI-EEG signals from C3, Cz, P3, and Pz sensors were carefully selected to be processed in the proposed framework. Therefore, a method based on Empirical Mode Decomposition (EMD) is used to tackle the problem of noisy signals. At the same time, the sequence classification is performed by a stacked Bidirectional Long Short-Term Memory (BiLSTM) network. The proposed method was evaluated using k-fold cross-validation on a public dataset, obtaining an accuracy of 82.26%.
Advances in the field of Brain-Computer Interfaces (BCIs) aim, among other applications, to improve the movement capacities of people suffering from the loss of motor skills. The main challenge in ...this area is to achieve real-time and accurate bio-signal processing for pattern recognition, especially in Motor Imagery (MI). The significant interaction between brain signals and controllable machines requires instantaneous brain data decoding. In this study, an embedded BCI system based on fist MI signals is developed. It uses an Emotiv EPOC+ Brainwear®, an Altera SoCKit® development board, and a hexapod robot for testing locomotion imagery commands. The system is tested to detect the imagined movements of closing and opening the left and right hand to control the robot locomotion. Electroencephalogram (EEG) signals associated with the motion tasks are sensed on the human sensorimotor cortex. Next, the SoCKit processes the data to identify the commands allowing the controlled robot locomotion. The classification of MI-EEG signals from the F3, F4, FC5, and FC6 sensors is performed using a hybrid architecture of Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks. This method takes advantage of the deep learning recognition model to develop a real-time embedded BCI system, where signal processing must be seamless and precise. The proposed method is evaluated using k-fold cross-validation on both created and public Scientific-Data datasets. Our dataset is comprised of 2400 trials obtained from four test subjects, lasting three seconds of closing and opening fist movement imagination. The recognition tasks reach 84.69% and 79.2% accuracy using our data and a state-of-the-art dataset, respectively. Numerical results support that the motor imagery EEG signals can be successfully applied in BCI systems to control mobile robots and related applications such as intelligent vehicles.
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