Fractal and Fractional最新文献_第2页

FLRNN-FGA: Fractional-Order Lipschitz Recurrent Neural Network with Frequency-Domain Gated Attention Mechanism for Time Series Forecasting FLRNN-FGA：用于时间序列预测的具有频域门控注意机制的分数阶李普希兹循环神经网络

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070433

Chunna Zhao, Junjie Ye, Zelong Zhu, Yaqun Huang

{"title":"FLRNN-FGA: Fractional-Order Lipschitz Recurrent Neural Network with Frequency-Domain Gated Attention Mechanism for Time Series Forecasting","authors":"Chunna Zhao, Junjie Ye, Zelong Zhu, Yaqun Huang","doi":"10.3390/fractalfract8070433","DOIUrl":"https://doi.org/10.3390/fractalfract8070433","url":null,"abstract":"Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"13 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Predicting the Deformation of a Slope Using a Random Coefficient Panel Data Model 使用随机系数面板数据模型预测斜坡变形

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070429

Zhenxia Yuan, Yadong Bian, Weijian Liu, Fuzhou Qi, Haohao Ma, Sen Zheng, Zhenzhu Meng

{"title":"Predicting the Deformation of a Slope Using a Random Coefficient Panel Data Model","authors":"Zhenxia Yuan, Yadong Bian, Weijian Liu, Fuzhou Qi, Haohao Ma, Sen Zheng, Zhenzhu Meng","doi":"10.3390/fractalfract8070429","DOIUrl":"https://doi.org/10.3390/fractalfract8070429","url":null,"abstract":"Engineering constructions in coastal areas not only affect existing landslides, but also induce new landslides. Variation of the water level makes the coastal area a geological hazard-prone. Prediction of the slope displacement based on monitoring data plays an important role in early warning of potential landslide and slope failure, and supports the risk management of hazards. Given the complex characteristic of the slope deformation, we proposed a prediction model using random coefficient model under the frame of panel data analysis, so as to take the correlation among monitoring points into consideration. In addition, we classified the monitoring data using Gaussian mixture model, to take the temporal-spatial characteristics into consideration. Monitoring data of Guobu slope was used to validate the model. Results indicated that the proposed model have a better performance in prediction accuracy. We also compared the proposed model with the BP neural network model and temporal – temperature model, and found that the prediction accuracy of the proposed model is better than those of the two control models.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"11 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141815915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spectral Galerkin Methods for Riesz Space-Fractional Convection–Diffusion Equations 里兹空间-分数对流-扩散方程的谱伽勒金方法

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070431

Xinxia Zhang, Jihan Wang, Zhongshu Wu, Zheyi Tang, Xiaoyan Zeng

引用次数: 0

A Novel Semi-Analytical Scheme to Deal with Fractional Partial Differential Equations (PDEs) of Variable-Order 处理变阶分数偏微分方程 (PDE) 的新型半解析方案

Fractal and Fractional Pub Date : 2024-07-20 DOI: 10.3390/fractalfract8070425

S. Kheybari, Farzaneh Alizadeh, M.T. Darvishi, K. Hosseini, E. Hıncal

引用次数: 0

Novel Approach by Shifted Fibonacci Polynomials for Solving the Fractional Burgers Equation 利用移位斐波那契多项式求解分数布尔格斯方程的新方法

Fractal and Fractional Pub Date : 2024-07-20 DOI: 10.3390/fractalfract8070427

Mohammed H. Alharbi, Abdullah F. Abu Sunayh, A. G. Atta, W. Abd-Elhameed

引用次数: 0

Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities 涉及凹凸非线性的薛定谔-哈代型分数 p-拉普拉奇方程的多重解

Fractal and Fractional Pub Date : 2024-07-20 DOI: 10.3390/fractalfract8070426

Yun-Ho Kim

引用次数: 0

Fractional-Order Tabu Learning Neuron Models and Their Dynamics 分数阶 Tabu 学习神经元模型及其动力学

Fractal and Fractional Pub Date : 2024-07-20 DOI: 10.3390/fractalfract8070428

Yajuan Yu, Zhenhua Gu, Min Shi, Feng Wang

{"title":"Fractional-Order Tabu Learning Neuron Models and Their Dynamics","authors":"Yajuan Yu, Zhenhua Gu, Min Shi, Feng Wang","doi":"10.3390/fractalfract8070428","DOIUrl":"https://doi.org/10.3390/fractalfract8070428","url":null,"abstract":"In this paper, by replacing the exponential memory kernel function of a tabu learning single-neuron model with the power-law memory kernel function, a novel Caputo’s fractional-order tabu learning single-neuron model and a network of two interacting fractional-order tabu learning neurons are constructed firstly. Different from the integer-order tabu learning model, the order of the fractional-order derivative is used to measure the neuron’s memory decay rate and then the stabilities of the models are evaluated by the eigenvalues of the Jacobian matrix at the equilibrium point of the fractional-order models. By choosing the memory decay rate (or the order of the fractional-order derivative) as the bifurcation parameter, it is proved that Hopf bifurcation occurs in the fractional-order tabu learning single-neuron model where the value of bifurcation point in the fractional-order model is smaller than the integer-order model’s. By numerical simulations, it is shown that the fractional-order network with a lower memory decay rate is capable of producing tangent bifurcation as the learning rate increases from 0 to 0.4. When the learning rate is fixed and the memory decay increases, the fractional-order network enters into frequency synchronization firstly and then enters into amplitude synchronization. During the synchronization process, the oscillation frequency of the fractional-order tabu learning two-neuron network increases with an increase in the memory decay rate. This implies that the higher the memory decay rate of neurons, the higher the learning frequency will be.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"30 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141819490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-Point Seawall Settlement Prediction with Limited Data Volume Using an Improved Fractional-Order Grey Model 利用改进的分数阶灰色模型，在数据量有限的情况下进行多点海堤沉降预测

Fractal and Fractional Pub Date : 2024-07-19 DOI: 10.3390/fractalfract8070423

Peng Qin, Chunmei Cheng, Zhenzhu Meng, Chunmei Ding, Sen Zheng, Huaizhi Su

{"title":"Multi-Point Seawall Settlement Prediction with Limited Data Volume Using an Improved Fractional-Order Grey Model","authors":"Peng Qin, Chunmei Cheng, Zhenzhu Meng, Chunmei Ding, Sen Zheng, Huaizhi Su","doi":"10.3390/fractalfract8070423","DOIUrl":"https://doi.org/10.3390/fractalfract8070423","url":null,"abstract":"Settlement prediction based on monitoring data holds significant importance for engineering maintenance of seawalls. In practical engineering, the volume of the collected monitoring data is often limited due to the restrictions of devices and engineering budgets. Previous studies have applied the fractional-order grey model to time series prediction under the situation of limited data volume. However, the performance of the fractional-order grey model is easily affected by the inappropriate settings of fractional order. Also, the model cannot make dynamic predictions due to the characteristic of fixed step size. To solve the above problems, in this paper, the genetic algorithm with enhanced search capabilities was employed to solve the premature convergence problem. Additionally, to solve the problem of the fractional-order grey model associated with fixed step size, the real-time tracing algorithm was introduced to conduct equal-dimensionally recursive calculation. The proposed model was validated using monitoring data of four monitoring points at Haiyan seawall in Zhejiang province, China. The prediction performance of the proposed model was then compared with those of the fractional-order GM(1,1), integer-order GM(1,1), and fractal theory model. Results indicate that the proposed model significantly improves the prediction performance compared to other models.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"108 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mittag-Leffler Synchronization in Finite Time for Uncertain Fractional-Order Multi-Delayed Memristive Neural Networks with Time-Varying Perturbations via Information Feedback 通过信息反馈实现具有时变扰动的不确定分数阶多延迟膜神经网络的有限时间内 Mittag-Leffler 同步

Fractal and Fractional Pub Date : 2024-07-19 DOI: 10.3390/fractalfract8070422

Hongguang Fan, Xijie Chen, Kaibo Shi, Yaohua Liang, Yang Wang, Hui Wen

{"title":"Mittag-Leffler Synchronization in Finite Time for Uncertain Fractional-Order Multi-Delayed Memristive Neural Networks with Time-Varying Perturbations via Information Feedback","authors":"Hongguang Fan, Xijie Chen, Kaibo Shi, Yaohua Liang, Yang Wang, Hui Wen","doi":"10.3390/fractalfract8070422","DOIUrl":"https://doi.org/10.3390/fractalfract8070422","url":null,"abstract":"To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"120 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multifractal Analysis of 3D Correlated Nanoporous Networks 三维相关纳米多孔网络的多分形分析

Fractal and Fractional Pub Date : 2024-07-19 DOI: 10.3390/fractalfract8070424

C. Carrizales-Velazquez, Carlos Felipe, Ariel Guzmán-Vargas, Enrique Lima, L. Guzmán-Vargas

引用次数: 0