Search Results (16)

The paper oresents the analytical construction of approximate solutions to the generalized Fisher–Kolmogorov equation in the complex domain. The existence and uniqueness of such solutions are established within an analytic domanin of the complex plane. The study employs techniques from complex function theory and introduces a modified version of the Cauchy majorant method. The principal innovation of the proposed approach, as opposed to the classical method, lies in constructing the majorant for the solution of the equation rather than for its right-hand side. A formula for calculating the analyticity radius is derived, which guarantees the absence of a movable singular point of algebraic type for the solutions under consideration. Special exact periodic solutions are found in elementary functions. Theoretical results are verified by numerical study. Full article

The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system. Full article

In this paper, the Fibonacci sequence, renowned for its significance across various fields, its ability to illuminate numerical concepts, and its role in uncovering patterns in mathematics and nature, forms the foundation of this research. This study introduces innovative concepts of weighted density, weighted statistical summability, weighted statistical convergence, and weighted statistical Cauchy, uniquely defined via the Fibonacci sequence and modulus functions. Key theorems, relationships, examples, and properties substantiate these novel principles, advancing our comprehension of sequence behavior. Additionally, we extend the notion of statistical cluster points within a broader framework, surpassing traditional definitions and offering deeper insights into convergence in a statistical context. Our findings in this paper open avenues for new applications and further exploration in various mathematical fields. Full article

Feature selection (FS) constitutes a critical stage within the realms of machine learning and data mining, with the objective of eliminating irrelevant features while guaranteeing model accuracy. Nevertheless, in datasets featuring a multitude of features, choosing the optimal feature poses a significant challenge. This study presents an enhanced Sand Cat Swarm Optimization algorithm (MSCSO) to improve the feature selection process, augmenting the algorithm’s global search capacity and convergence rate via multiple innovative strategies. Specifically, this study devised logistic chaotic mapping and lens imaging reverse learning approaches for population initialization to enhance population diversity; balanced global exploration and local development capabilities through nonlinear parameter processing; and introduced a Weibull flight strategy and triangular parade strategy to optimize individual position updates. Additionally, the Gaussian–Cauchy mutation strategy was employed to improve the algorithm’s ability to overcome local optima. The experimental results demonstrate that MSCSO performs well on 65.2% of the test functions in the CEC2005 benchmark test; on the 15 datasets of UCI, MSCSO achieved the best average fitness in 93.3% of the datasets and achieved the fewest feature selections in 86.7% of the datasets while attaining the best average accuracy across 100% of the datasets, significantly outperforming other comparative algorithms. Full article

Gyros/star sensor integration provides a potential method to obtain high-accuracy spatial orientation for turntable structures. However, it is subjected to the problem of accuracy loss when the measurement noises become non-Gaussian due to the complex spatial environment. This paper presents an event-driven maximum correntropy filter based on Cauchy kernel to handle the above problem. In this method, a direct installation mode of gyros/star sensor integration is established and the associated mathematical model is derived to improve the turntable’s control stability. Based on this, a Cauchy kernel-based maximum correntropy filter is developed to curb the influence of non-Gaussian measurement noise for enhancing the gyros/star sensor integration’s robustness. Subsequently, an event-driven mechanism is constructed based on the filter’s innovation information for further reducing the unnecessary computational cost to optimize the real-time performance. The effectiveness of the proposed method has been validated by simulations of the gyros/star sensor integration for spatial orientation. This shows that the proposed filtering methodology not only has strong robustness to deal with the influence of non-Gaussian measurement noise but can also achieve superior real-time spatial applications with a small computational cost, leading to enhanced performance for the turntable’s spatial orientation using gyros/star sensor integration. Full article

In recent years, twin stacker crane units have been increasingly integrated into large automated storage and retrieval systems (AS/RSs) in shipyards to enhance operational efficiency. These common rail units often encounter conflicts, and the additional time costs incurred during collision avoidance significantly diminish AS/RS efficiency. Therefore, addressing the twin stacker cranes’ scheduling problem (TSSP) with a collision-free constraint is essential. This paper presents a novel approach to identifying and avoiding collisions by approximating the stacker crane’s trip trajectory as a triangular envelope. Utilizing the collision identification equation derived from this method, we express the collision-free constraint within the TSSP and formulate a mixed-integer programming model. Recognizing the multimodal characteristics of the TSSP objective function, we introduce the dung beetle optimizer (DBO), which excels in multimodal test functions, as the foundational framework for a heuristic optimizer aimed at large-scale TSSPs that are challenging for exact algorithms. To adapt the optimizer for bi-level programming problems like TSSPs, we propose a double-layer code mechanism and innovatively design a binary DBO for the binary layer. Additionally, we incorporate several components, including a hybrid initialization strategy, a Cauchy–Gaussian mixture distribution neighborhood search strategy, and a velocity revision strategy based on continuous space discretization, into the improved dung beetle optimizer (IDBO) to further enhance its performance. To validate the efficacy of the IDBO, we established a numerical experimental environment and generated a series of instances based on actual environmental parameters and operational conditions from an advanced AS/RS in southeastern China. Extensive comparative experiments on various scales and distributions demonstrate that the components of the IDBO significantly improve algorithm performance, yielding stable advantages over classical algorithms in solving TSSPs, with improvements exceeding 10%. Full article

This paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier series with the Laplace–Carson ($\mathcal{L}\text{-}C$) transform in the complex domain, utilizing complex time vectors to streamline the computation of the original function. The inverse transformation back into the time domain is achieved using the Cauchy-Heaviside ($C\text{-}\mathcal{H}$) method. The second approach applies the Fourier transform ($\mathcal{F}\text{-}{\rm T}$) for the transient analysis of a power converter circuit with both passive and active loads. The method of complex conjugate amplitudes is employed for steady-state analysis. Both contributions represent innovative approaches within this study. The process begins with Fourier series expansions and the computation of Fourier coefficients, followed by solving the system’s steady-state and transient responses. The transient states are then confirmed using the Fourier transform. To validate these findings, the analytical results are verified through simulations conducted in the Matlab/Simulink R2023b environment. Full article

In the realm of Ceph distributed storage systems, ensuring swift and symmetrical data recovery during severe data corruption scenarios is pivotal for data reliability and system stability. This paper introduces an innovative FPGA-based Multi-Dimensional Elastic Recovery Acceleration method, termed AMDER-Ceph. Utilizing FPGA technology, this method is a pioneer in accelerating erasure code data recovery within such systems symmetrically. By harnessing the parallel computing power of FPGAs and optimizing Cauchy matrix binary operations, AMDER-Ceph significantly enhances data recovery speed and efficiency symmetrically. Our evaluations in real-world Ceph environments show that AMDER-Ceph achieves up to 4.84 times faster performance compared with traditional methods, especially evident in the standard 4 MB block size configurations of Ceph systems. Full article

To enhance fault detection in slewing bearing vibration signals, an advanced noise-reduction model, HRCSA-VMD-WT, is designed for effective signal noise elimination. This model innovates by refining the Chameleon Swarm Algorithm (CSA) into a more potent Hybrid Reinforcement CSA (HRCSA), incorporating strategies from Chaotic Reverse Learning (CRL), the Whale Optimization Algorithm’s (WOA) bubble-net hunting, and the greedy strategy with the Cauchy mutation to diversify the initial population, accelerate convergence, and prevent local optimum entrapment. Furthermore, by optimizing Variate Mode Decomposition (VMD) input parameters with HRCSA, Intrinsic Mode Function (IMF) components are extracted and categorized into noisy and pure signals using cosine similarity. Subsequently, the Wavelet Threshold (WT) denoising targets the noisy IMFs before reconstructing the vibration signal from purified IMFs, achieving significant noise reduction. Comparative experiments demonstrate HRCSA’s superiority over Particle Swarm Optimization (PSO), WOA, and Gray Wolf Optimization (GWO) regarding convergence speed and precision. Notably, HRCSA-VMD-WT increases the Signal-to-Noise Ratio (SNR) by a minimum of 74.9% and reduces the Root Mean Square Error (RMSE) by at least 41.2% when compared to both CSA-VMD-WT and Empirical Mode Decomposition with Wavelet Transform (EMD-WT). This study improves fault detection accuracy and efficiency in vibration signals and offers a dependable and effective diagnostic solution for slewing bearing maintenance. Full article

Accurate structural analyses of continuous fiber-reinforced polymers (FRPs) are imperative for diverse engineering applications, demanding efficient material constitutive models. Nonetheless, the constitutive modeling of FRPs is complicated by the nonlinear behavior resulting from internal damages and the inherent plasticity. Consequently, this study presents an innovative anisotropic constitutive model for FRPs, designed to adeptly capture both the damage evolution and plasticity. All requisite parameters can be easily obtained through fundamental mechanical tests, rendering the model practical and user-friendly. The model utilizes the three-dimensional Puck criteria to determine damages, initiating the evolution process through a combination of continuum damage mechanics and linear stiffness attenuation methods. This evolution is coupled with a one-parameter plastic model. Subsequently, the numerical implementation method, integrated into ANSYS, is detailed. This emphasizes the Cauchy stress and consistent tangent stiffness solution strategy. Finally, the effectiveness of the developed model is demonstrated through comprehensive verification, encompassing existing biaxial tension and open-hole-tension tests conducted on carbon and glass FRP laminates. The simulation results exhibit a remarkable correspondence with the experimental data, validating the reliability and accuracy of the proposed model. Full article

Efficient navigation of multiple autonomous underwater vehicles (AUVs) plays an important role in monitoring underwater and off-shore environments. It has encountered challenges when AUVs work in complex underwater environments. Traditional swarm intelligence (SI) optimization algorithms have limitations such as insufficient path exploration ability, susceptibility to local optima, and difficulty in convergence. To address these issues, we propose an improved multi-objective manta ray foraging optimization (IMMRFO) method, which can improve the accuracy of trajectory planning through a comprehensive three-stage approach. Firstly, basic model sets are established, including a three-dimensional ocean terrain model, a threat source model, the physical constraints of AUV, path smoothing constraints, and spatiotemporal coordination constraints. Secondly, an innovative chaotic mapping technique is introduced to initialize the position of the manta ray population. Moreover, an adaptive rolling factor “S” is introduced from the manta rays’ rolling foraging. This allows the collaborative-vehicle population to jump out of local optima through “collaborative rolling." In the processes of manta ray chain feeding and manta ray spiral feeding, Cauchy reverse learning is integrated to broaden the search space and enhance the global optimization ability. The optimal Pareto front is then obtained using non-dominated sorting. Finally, the position of the manta ray population is mapped to the spatial positions of multi-AUVs, and cubic spline functions are used to optimize the trajectory of multi-AUVs. Through detailed analysis and comparison with five existing multi-objective optimization algorithms, it is found that the IMMRFO algorithm proposed in this paper can significantly reduce the average planned path length by 3.1~9.18 km in the path length target and reduce the average cost by 18.34~321.872 in the cost target. In an actual off-shore measurement process, IMMRFO enables AUVs to effectively bypass obstacles and threat sources, reduce risk costs, and improve mobile surveillance safety. Full article

The aim of this work is to investigate the influence of nonlinear multiplicative noise on the Cauchy problem of the nonlinear fractional Schrödinger equation in the non-radial case. Local well-posedness follows from estimates related to the stochastic convolution and deterministic non-radial Strichartz estimates. Furthermore, the blow-up criterion is presented. Then, with the help of Itô’s lemma and stopping time arguments, the global solution is constructed almost surely. The main innovation is that the non-radial global solution is given under fractional-order derivatives and a nonlinear noise term. Full article

The Gray Wolf Optimizer (GWO) is an established algorithm for addressing complex optimization tasks. Despite its effectiveness, enhancing its precision and circumventing premature convergence is crucial to extending its scope of application. In this context, our study presents the Cauchy Gray Wolf Optimizer (CGWO), a modified version of GWO that leverages Cauchy distributions for key algorithmic improvements. The innovation of CGWO lies in several areas: First, it adopts a Cauchy distribution-based strategy for initializing the population, thereby broadening the global search potential. Second, the algorithm integrates a dynamic inertia weight mechanism, modulated non-linearly in accordance with the Cauchy distribution, to ensure a balanced trade-off between exploration and exploitation throughout the search process. Third, it introduces a Cauchy mutation concept, using inertia weight as a probability determinant, to preserve diversity and bolster the capability for escaping local optima during later search phases. Furthermore, a greedy strategy is employed to incrementally enhance solution accuracy. The performance of CGWO was rigorously evaluated using 23 benchmark functions, demonstrating significant improvements in convergence rate, solution precision, and robustness when contrasted with conventional algorithms. The deployment of CGWO in solving the engineering challenge of pressure vessel design illustrated its superiority over traditional methods, highlighting its potential for widespread adoption in practical engineering contexts. Full article

In an emergency situation, fast and efficient logistics and distribution are essential for minimizing the impact of a disaster and for safeguarding property. When selecting a distribution center location, time satisfaction needs to be considered, in addition to the general cost factor. The improved jellyfish search algorithm (CIJS), which simulates the bionics of jellyfish foraging, is applied to solve the problem of an emergency logistics and distribution center site selection model considering time satisfaction. The innovation of the CIJS is mainly reflected in two aspects. First, when initializing the population, the two-level logistic map method is used instead of the original logistic map method to improve the diversity and uniform distribution of the population. Second, in the jellyfish search process, a Cauchy strategy is introduced to determine the moving distance of internal motions, which improves the global search capability and prevents the search from falling into local optimal solutions. The superiority of the improved algorithm was verified by testing 20 benchmark functions and applying them to site selection problems of different dimensions. The performance of the CIJS was compared to that of heuristic algorithms through the iterative convergence graph of the algorithm. The experimental results show that the CIJS has higher solution accuracy and faster solution speed than PSO, the WOA, and JS. Full article

An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si $5\%$ alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer. Full article