Pub Date : 2024-06-14DOI: 10.3390/fractalfract8060354
Weidong Liu, Liwei Guo, Le Li, Jingming Xu, Guanghao Yang
In this paper, a fractional active disturbance rejection control (FADRC) scheme is proposed for remotely operated vehicles (ROVs) to enhance high-precision positioning and docking control in the presence of ocean current disturbances and model uncertainties. The scheme comprises a double closed-loop fractional-order PIλDμ controller (DFOPID) and a model-assisted finite-time sliding-mode extended state observer (MFSESO). Among them, DFOPID effectively compensates for non-matching disturbances, while its fractional-order term enhances the dynamic performance and steady-state accuracy of the system. MFSESO contributes to enhancing the estimation accuracy through the integration of sliding-mode technology and model information, ensuring the finite-time convergence of observation errors. Numerical simulations and pool experiments have shown that the proposed control scheme can effectively resist disturbances and successfully complete high-precision tasks in the absence of an accurate model. This underscores the independence of this control scheme on accurate model data of an operational ROV. Meanwhile, it also has the advantages of a simple structure and easy parameter tuning. The FADRC scheme presented in this paper holds practical significance and can serve as a valuable reference for applications involving ROVs.
{"title":"Fractional Active Disturbance Rejection Positioning and Docking Control of Remotely Operated Vehicles: Analysis and Experimental Validation","authors":"Weidong Liu, Liwei Guo, Le Li, Jingming Xu, Guanghao Yang","doi":"10.3390/fractalfract8060354","DOIUrl":"https://doi.org/10.3390/fractalfract8060354","url":null,"abstract":"In this paper, a fractional active disturbance rejection control (FADRC) scheme is proposed for remotely operated vehicles (ROVs) to enhance high-precision positioning and docking control in the presence of ocean current disturbances and model uncertainties. The scheme comprises a double closed-loop fractional-order PIλDμ controller (DFOPID) and a model-assisted finite-time sliding-mode extended state observer (MFSESO). Among them, DFOPID effectively compensates for non-matching disturbances, while its fractional-order term enhances the dynamic performance and steady-state accuracy of the system. MFSESO contributes to enhancing the estimation accuracy through the integration of sliding-mode technology and model information, ensuring the finite-time convergence of observation errors. Numerical simulations and pool experiments have shown that the proposed control scheme can effectively resist disturbances and successfully complete high-precision tasks in the absence of an accurate model. This underscores the independence of this control scheme on accurate model data of an operational ROV. Meanwhile, it also has the advantages of a simple structure and easy parameter tuning. The FADRC scheme presented in this paper holds practical significance and can serve as a valuable reference for applications involving ROVs.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141340254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The pore-throat structure is a critical factor in the study of unconventional oil and gas reservoirs, drawing particular attention from petroleum geologists, and it is of paramount significance to analyze to enhance oil and gas production. In tight sandstone, which serves as a significant hydrocarbon reservoir, the internal pore-throat structure plays a decisive role in the storage and migration of fluids such as water, gases, and hydrocarbons. This paper employs casting thin section (CTS), field emission scanning electron microscope (FE-SEM), high-pressure mercury injection (HPMI), and low-temperature nitrogen gas adsorption (LT−N2−GA) experimental tests to qualitatively and quantitatively analyze the characteristics of the pore-throat structure in tight sandstone. The results indicate that the pore types in tight sandstone include intergranular residual pores, dissolution pores, intercrystalline pores, and microfractures, while the throat types encompass sheet-shaped, curved-sheet-shaped, and tubular throats. Analysis of the physical and structural parameters from 13 HPMI and 5 LT−N2−GA samples reveals a bimodal distribution of pore-throat radii. The complexity of the pore-throat structure is identified as a primary controlling factor for reservoir permeability. The fractal dimension (D) exhibits an average value of 2.45, displaying a negative correlation with porosity (R2 = 0.22), permeability (R2 = 0.65), the pore-throat diameter (R2 = 0.58), and maximum mercury saturation (R2 = 0.86) and a positive correlation with threshold pressure (R2 = 0.56), median saturation pressure (R2 = 0.49), BET specific surface area (R2 = 0.51), and BJH total pore volume (R2 = 0.14). As D increases, reservoir pores tend to decrease in size, leading to reduced flow and deteriorated physical properties, indicative of a more complex pore-throat structure.
{"title":"Fractal Characterization of the Pore-Throat Structure in Tight Sandstone Based on Low-Temperature Nitrogen Gas Adsorption and High-Pressure Mercury Injection","authors":"Taping He, Yaoqi Zhou, Zhaobing Chen, Zhenwei Zhang, Huanyu Xie, Yuehan Shang, Gaixia Cui","doi":"10.3390/fractalfract8060356","DOIUrl":"https://doi.org/10.3390/fractalfract8060356","url":null,"abstract":"The pore-throat structure is a critical factor in the study of unconventional oil and gas reservoirs, drawing particular attention from petroleum geologists, and it is of paramount significance to analyze to enhance oil and gas production. In tight sandstone, which serves as a significant hydrocarbon reservoir, the internal pore-throat structure plays a decisive role in the storage and migration of fluids such as water, gases, and hydrocarbons. This paper employs casting thin section (CTS), field emission scanning electron microscope (FE-SEM), high-pressure mercury injection (HPMI), and low-temperature nitrogen gas adsorption (LT−N2−GA) experimental tests to qualitatively and quantitatively analyze the characteristics of the pore-throat structure in tight sandstone. The results indicate that the pore types in tight sandstone include intergranular residual pores, dissolution pores, intercrystalline pores, and microfractures, while the throat types encompass sheet-shaped, curved-sheet-shaped, and tubular throats. Analysis of the physical and structural parameters from 13 HPMI and 5 LT−N2−GA samples reveals a bimodal distribution of pore-throat radii. The complexity of the pore-throat structure is identified as a primary controlling factor for reservoir permeability. The fractal dimension (D) exhibits an average value of 2.45, displaying a negative correlation with porosity (R2 = 0.22), permeability (R2 = 0.65), the pore-throat diameter (R2 = 0.58), and maximum mercury saturation (R2 = 0.86) and a positive correlation with threshold pressure (R2 = 0.56), median saturation pressure (R2 = 0.49), BET specific surface area (R2 = 0.51), and BJH total pore volume (R2 = 0.14). As D increases, reservoir pores tend to decrease in size, leading to reduced flow and deteriorated physical properties, indicative of a more complex pore-throat structure.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141341347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-14DOI: 10.3390/fractalfract8060355
Sheng Zhang, Xianghui Wang, Bo Xu
This article extends the celebrated Riemann–Hilbert (RH) method equipped with mixed spectrum to a new integrable system of three-component coupled time-varying coefficient complex mKdV equations (ccmKdVEs for short) generated by the mixed spectral equations (msEs). Firstly, the ccmKdVEs and the msEs for generating the ccmKdVEs are proposed. Then, based on the msEs, a solvable RH problem related to the ccmKdVEs is constructed. By using the constructed RH problem with mixed spectrum, scattering data for the recovery of potential formulae are further determined. In the case of reflectionless coefficients, explicit N-soliton solutions of the ccmKdVEs are ultimately obtained. Taking N equal to 1 and 2 as examples, this paper reveals that the spatiotemporal solution structures with time-varying nonlinear dynamic characteristics localized in the ccmKdVEs is attributed to the multiple selectivity of mixed spectrum and time-varying coefficients. In addition, to further highlight the application of our work in fractional calculus, by appropriately selecting these time-varying coefficients, the ccmKdVEs are transformed into a conformable time-fractional order system of three-component coupled complex mKdV equations. Based on the obtained one-soliton solutions, a set of initial values are assigned to the transformed fractional order system, and the N-th iteration formulae of approximate solutions for this fractional order system are derived through the variational iteration method (VIM).
{"title":"Riemann–Hilbert Method Equipped with Mixed Spectrum for N-Soliton Solutions of New Three-Component Coupled Time-Varying Coefficient Complex mKdV Equations","authors":"Sheng Zhang, Xianghui Wang, Bo Xu","doi":"10.3390/fractalfract8060355","DOIUrl":"https://doi.org/10.3390/fractalfract8060355","url":null,"abstract":"This article extends the celebrated Riemann–Hilbert (RH) method equipped with mixed spectrum to a new integrable system of three-component coupled time-varying coefficient complex mKdV equations (ccmKdVEs for short) generated by the mixed spectral equations (msEs). Firstly, the ccmKdVEs and the msEs for generating the ccmKdVEs are proposed. Then, based on the msEs, a solvable RH problem related to the ccmKdVEs is constructed. By using the constructed RH problem with mixed spectrum, scattering data for the recovery of potential formulae are further determined. In the case of reflectionless coefficients, explicit N-soliton solutions of the ccmKdVEs are ultimately obtained. Taking N equal to 1 and 2 as examples, this paper reveals that the spatiotemporal solution structures with time-varying nonlinear dynamic characteristics localized in the ccmKdVEs is attributed to the multiple selectivity of mixed spectrum and time-varying coefficients. In addition, to further highlight the application of our work in fractional calculus, by appropriately selecting these time-varying coefficients, the ccmKdVEs are transformed into a conformable time-fractional order system of three-component coupled complex mKdV equations. Based on the obtained one-soliton solutions, a set of initial values are assigned to the transformed fractional order system, and the N-th iteration formulae of approximate solutions for this fractional order system are derived through the variational iteration method (VIM).","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141338555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-14DOI: 10.3390/fractalfract8060357
Haseeb Sultan, Nadeem Ullah, J. Hong, Seung Kim, Dong Lee, Seung Jung, Kang Park
The accurate recognition of a brain tumor (BT) is crucial for accurate diagnosis, intervention planning, and the evaluation of post-intervention outcomes. Conventional methods of manually identifying and delineating BTs are inefficient, prone to error, and time-consuming. Subjective methods for BT recognition are biased because of the diffuse and irregular nature of BTs, along with varying enhancement patterns and the coexistence of different tumor components. Hence, the development of an automated diagnostic system for BTs is vital for mitigating subjective bias and achieving speedy and effective BT segmentation. Recently developed deep learning (DL)-based methods have replaced subjective methods; however, these DL-based methods still have a low performance, showing room for improvement, and are limited to heterogeneous dataset analysis. Herein, we propose a DL-based parallel features aggregation network (PFA-Net) for the robust segmentation of three different regions in a BT scan, and we perform a heterogeneous dataset analysis to validate its generality. The parallel features aggregation (PFA) module exploits the local radiomic contextual spatial features of BTs at low, intermediate, and high levels for different types of tumors and aggregates them in a parallel fashion. To enhance the diagnostic capabilities of the proposed segmentation framework, we introduced the fractal dimension estimation into our system, seamlessly combined as an end-to-end task to gain insights into the complexity and irregularity of structures, thereby characterizing the intricate morphology of BTs. The proposed PFA-Net achieves the Dice scores (DSs) of 87.54%, 93.42%, and 91.02%, for the enhancing tumor region, whole tumor region, and tumor core region, respectively, with the multimodal brain tumor segmentation (BraTS)-2020 open database, surpassing the performance of existing state-of-the-art methods. Additionally, PFA-Net is validated with another open database of brain tumor progression and achieves a DS of 64.58% for heterogeneous dataset analysis, surpassing the performance of existing state-of-the-art methods.
{"title":"Estimation of Fractal Dimension and Segmentation of Brain Tumor with Parallel Features Aggregation Network","authors":"Haseeb Sultan, Nadeem Ullah, J. Hong, Seung Kim, Dong Lee, Seung Jung, Kang Park","doi":"10.3390/fractalfract8060357","DOIUrl":"https://doi.org/10.3390/fractalfract8060357","url":null,"abstract":"The accurate recognition of a brain tumor (BT) is crucial for accurate diagnosis, intervention planning, and the evaluation of post-intervention outcomes. Conventional methods of manually identifying and delineating BTs are inefficient, prone to error, and time-consuming. Subjective methods for BT recognition are biased because of the diffuse and irregular nature of BTs, along with varying enhancement patterns and the coexistence of different tumor components. Hence, the development of an automated diagnostic system for BTs is vital for mitigating subjective bias and achieving speedy and effective BT segmentation. Recently developed deep learning (DL)-based methods have replaced subjective methods; however, these DL-based methods still have a low performance, showing room for improvement, and are limited to heterogeneous dataset analysis. Herein, we propose a DL-based parallel features aggregation network (PFA-Net) for the robust segmentation of three different regions in a BT scan, and we perform a heterogeneous dataset analysis to validate its generality. The parallel features aggregation (PFA) module exploits the local radiomic contextual spatial features of BTs at low, intermediate, and high levels for different types of tumors and aggregates them in a parallel fashion. To enhance the diagnostic capabilities of the proposed segmentation framework, we introduced the fractal dimension estimation into our system, seamlessly combined as an end-to-end task to gain insights into the complexity and irregularity of structures, thereby characterizing the intricate morphology of BTs. The proposed PFA-Net achieves the Dice scores (DSs) of 87.54%, 93.42%, and 91.02%, for the enhancing tumor region, whole tumor region, and tumor core region, respectively, with the multimodal brain tumor segmentation (BraTS)-2020 open database, surpassing the performance of existing state-of-the-art methods. Additionally, PFA-Net is validated with another open database of brain tumor progression and achieves a DS of 64.58% for heterogeneous dataset analysis, surpassing the performance of existing state-of-the-art methods.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141342840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-13DOI: 10.3390/fractalfract8060352
Md Nur Hossain, M. M. Miah, Moataz Alosaimi, Faisal Alsharif, Mohammad Kanan
The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, which works with one variable, and the Ω′Ω, 1Ω method which utilizes two variables. These approaches supply significant improvements in efficiency, accuracy, and the ability to explore a broader spectrum of soliton solutions compared to traditional computational methods. By using these techniques, we construct a wide range of wave structures, including rational, trigonometric, and hyperbolic functions. Rigorous validation with Mathematica software 13.1 ensures precision, while dynamic visual representations illustrate soliton solutions with diverse patterns such as dark solitons, multiple dark solitons, singular solitons, multiple singular solitons, kink solitons, bright solitons, and bell-shaped patterns. These findings highlight the effectiveness of these methods in discovering new soliton solutions and supplying deeper insights into the DSW model’s behavior. The novel soliton solutions obtained in this study significantly enhance our understanding of the DSW equation’s underlying dynamics and offer potential applications across various scientific fields.
{"title":"Exploring Novel Soliton Solutions to the Time-Fractional Coupled Drinfel’d–Sokolov–Wilson Equation in Industrial Engineering Using Two Efficient Techniques","authors":"Md Nur Hossain, M. M. Miah, Moataz Alosaimi, Faisal Alsharif, Mohammad Kanan","doi":"10.3390/fractalfract8060352","DOIUrl":"https://doi.org/10.3390/fractalfract8060352","url":null,"abstract":"The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, which works with one variable, and the Ω′Ω, 1Ω method which utilizes two variables. These approaches supply significant improvements in efficiency, accuracy, and the ability to explore a broader spectrum of soliton solutions compared to traditional computational methods. By using these techniques, we construct a wide range of wave structures, including rational, trigonometric, and hyperbolic functions. Rigorous validation with Mathematica software 13.1 ensures precision, while dynamic visual representations illustrate soliton solutions with diverse patterns such as dark solitons, multiple dark solitons, singular solitons, multiple singular solitons, kink solitons, bright solitons, and bell-shaped patterns. These findings highlight the effectiveness of these methods in discovering new soliton solutions and supplying deeper insights into the DSW model’s behavior. The novel soliton solutions obtained in this study significantly enhance our understanding of the DSW equation’s underlying dynamics and offer potential applications across various scientific fields.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141348427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-13DOI: 10.3390/fractalfract8060353
Vytautė Pilipauskaitė, D. Surgailis
We consider fractional integral operators (I−T)d,d∈(−1,1) acting on functions g:Zν→R,ν≥1, where T is the transition operator of a random walk on Zν. We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels τ(s;d),s∈Zν of (I−T)d. The asymptotic behavior of τ(s;d) as |s|→∞ is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on Zν solving the difference equation (I−T)dX=ε with white noise on the right-hand side is discussed and their scaling limits. Several examples, including fractional lattice Laplace and heat operators, are studied in detail.
我们考虑作用于函数 g:Zν→R,ν≥1 的分数积分算子 (I-T)d,d∈(-1,1)，其中 T 是 Zν 上随机行走的过渡算子。我们得到了 (I-T)d 的核τ(s;d),s∈Zν存在性、可逆性和平方可求和性的充分必要条件。τ(s;d)随着 |s|→∞ 的渐近行为是根据随机游走的局部极限定理确定的。讨论了 Zν 上一类求解右侧白噪声差分方程 (I-T)dX=ε 的分数积分随机场 X 及其缩放极限。详细研究了几个例子，包括分数格拉普拉斯算子和热算子。
{"title":"Fractional Operators and Fractionally Integrated Random Fields on Zν","authors":"Vytautė Pilipauskaitė, D. Surgailis","doi":"10.3390/fractalfract8060353","DOIUrl":"https://doi.org/10.3390/fractalfract8060353","url":null,"abstract":"We consider fractional integral operators (I−T)d,d∈(−1,1) acting on functions g:Zν→R,ν≥1, where T is the transition operator of a random walk on Zν. We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels τ(s;d),s∈Zν of (I−T)d. The asymptotic behavior of τ(s;d) as |s|→∞ is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on Zν solving the difference equation (I−T)dX=ε with white noise on the right-hand side is discussed and their scaling limits. Several examples, including fractional lattice Laplace and heat operators, are studied in detail.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141347804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-12DOI: 10.3390/fractalfract8060348
Jie Luo, Zhao Li
The main purpose of this article is to investigate the dynamic behavior and optical soliton for the M-truncated fractional paraxial wave equation arising in a liquid crystal model, which is usually used to design camera lenses for high-quality photography. The traveling wave transformation is applied to the M-truncated fractional paraxial wave equation. Moreover, a two-dimensional dynamical system and its disturbance system are obtained. The phase portraits of the two-dimensional dynamic system and Poincaré sections and a bifurcation portrait of its perturbation system are drawn. The obtained three-dimensional graphs of soliton solutions, two-dimensional graphs of soliton solutions, and contour graphs of the M-truncated fractional paraxial wave equation arising in a liquid crystal model are drawn.
本文的主要目的是研究液晶模型中产生的 M 截断分数副轴波方程的动态行为和光学孤子。行波变换被应用于 M 截断分数副轴波方程。此外，还得到了一个二维动力系统及其扰动系统。绘制了二维动力系统的相位肖像和波恩卡莱截面，以及扰动系统的分岔肖像。绘制了在液晶模型中产生的 M-截断分型旁轴波方程的孤子解三维图、孤子解二维图和等值线图。
{"title":"Dynamic Behavior and Optical Soliton for the M-Truncated Fractional Paraxial Wave Equation Arising in a Liquid Crystal Model","authors":"Jie Luo, Zhao Li","doi":"10.3390/fractalfract8060348","DOIUrl":"https://doi.org/10.3390/fractalfract8060348","url":null,"abstract":"The main purpose of this article is to investigate the dynamic behavior and optical soliton for the M-truncated fractional paraxial wave equation arising in a liquid crystal model, which is usually used to design camera lenses for high-quality photography. The traveling wave transformation is applied to the M-truncated fractional paraxial wave equation. Moreover, a two-dimensional dynamical system and its disturbance system are obtained. The phase portraits of the two-dimensional dynamic system and Poincaré sections and a bifurcation portrait of its perturbation system are drawn. The obtained three-dimensional graphs of soliton solutions, two-dimensional graphs of soliton solutions, and contour graphs of the M-truncated fractional paraxial wave equation arising in a liquid crystal model are drawn.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141350521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-12DOI: 10.3390/fractalfract8060351
Qi An, Yue Liu, Min Huang, Shuangfu Suo
A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.
本文提出了一种基于广义泛形 Sierpinski 地毯的新型分析模型，该模型可以更准确地获得磨削接头表面的法向接触刚度。首先，对磨削表面上的粗糙度轮廓和分布进行了表征。然后，基于广义泛形西尔品斯基地毯，实现磨削接头表面的接触表征。其次，对磨削表面上的微孔进行了接触力学分析。推导出不同变形阶段接触刚度的分析表达式，最终建立了磨削接头表面的综合分析模型。随后，对所提出模型的结果、KE 模型和实验数据进行了对比分析。研究结果表明，在相同的接触压力条件下，与 KE 模型相比，所提出的模型得出的结果与实验观察结果更接近。随着接触压力的增加，提出的模型的相对误差呈现先增大后减小的趋势，而 KE 模型则呈现增大的趋势。对于不同接触压力下四个表面的相对误差值，提出的模型的最大相对误差为 5.44%，而 KE 模型为 22.99%。该模型可为高精度机床的优化设计奠定坚实的理论基础，并为机床系统的性能分析提供科学的理论依据。
{"title":"A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory","authors":"Qi An, Yue Liu, Min Huang, Shuangfu Suo","doi":"10.3390/fractalfract8060351","DOIUrl":"https://doi.org/10.3390/fractalfract8060351","url":null,"abstract":"A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141355045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-12DOI: 10.3390/fractalfract8060350
Abdallah Aldosary
This work presents a model for solving the Economic-Environmental Dispatch (EED) challenge, which addresses the integration of thermal, renewable energy schemes, and natural gas (NG) units, that consider both toxin emission and fuel costs as its primary objectives. Three cases are examined using the IEEE 30-bus system, where thermal units (TUs) are replaced with NGs to minimize toxin emissions and fuel costs. The system constraints include equality and inequality conditions. A detailed modeling of NGs is performed, which also incorporates the pressure pipelines and the flow velocity of gas as procedure limitations. To obtain Pareto optimal solutions for fuel costs and emissions, three optimization algorithms, namely Fractional-Order Fish Migration Optimization (FOFMO), Coati Optimization Algorithm (COA), and Non-Dominated Sorting Genetic Algorithm (NSGA-II) are employed. Three cases are investigated to validate the effectiveness of the proposed model when applied to the IEEE 30-bus system with the integration of renewable energy sources (RESs) and natural gas units. The results from Case III, where NGs are installed in place of two thermal units (TUs), demonstrate that the economic dispatching approach presented in this study significantly reduces emission levels to 0.4232 t/h and achieves a lower fuel cost of 796.478 USD/MWh. Furthermore, the findings indicate that FOFMO outperforms COA and NSGA-II in effectively addressing the EED problem.
本研究提出了一个解决经济-环境调度（EED）挑战的模型，该模型将热能、可再生能源方案和天然气（NG）机组整合在一起，并将毒素排放和燃料成本作为其主要目标。我们使用 IEEE 30 总线系统分析了三种情况，即用 NG 取代热机组 (TU)，以尽量减少毒素排放和燃料成本。系统约束条件包括相等和不相等条件。对 NGs 进行了详细建模，并将压力管道和气体流速作为程序限制。为了获得燃料成本和排放的帕累托最优解，采用了三种优化算法，即分数阶鱼类洄游优化算法（FOFMO）、Coati 优化算法（COA）和非支配排序遗传算法（NSGA-II）。研究了三个案例，以验证所提模型在应用于集成了可再生能源（RES）和天然气机组的 IEEE 30 总线系统时的有效性。在案例 III 中，天然气机组取代了两台热电机组（TU），该案例的结果表明，本研究提出的经济调度方法将排放水平大幅降低至 0.4232 吨/小时，并实现了 796.478 美元/兆瓦时的较低燃料成本。此外，研究结果表明，在有效解决 EED 问题方面，FOFMO 优于 COA 和 NSGA-II。
{"title":"Optimizing Economic Dispatch with Renewable Energy and Natural Gas Using Fractional-Order Fish Migration Algorithm","authors":"Abdallah Aldosary","doi":"10.3390/fractalfract8060350","DOIUrl":"https://doi.org/10.3390/fractalfract8060350","url":null,"abstract":"This work presents a model for solving the Economic-Environmental Dispatch (EED) challenge, which addresses the integration of thermal, renewable energy schemes, and natural gas (NG) units, that consider both toxin emission and fuel costs as its primary objectives. Three cases are examined using the IEEE 30-bus system, where thermal units (TUs) are replaced with NGs to minimize toxin emissions and fuel costs. The system constraints include equality and inequality conditions. A detailed modeling of NGs is performed, which also incorporates the pressure pipelines and the flow velocity of gas as procedure limitations. To obtain Pareto optimal solutions for fuel costs and emissions, three optimization algorithms, namely Fractional-Order Fish Migration Optimization (FOFMO), Coati Optimization Algorithm (COA), and Non-Dominated Sorting Genetic Algorithm (NSGA-II) are employed. Three cases are investigated to validate the effectiveness of the proposed model when applied to the IEEE 30-bus system with the integration of renewable energy sources (RESs) and natural gas units. The results from Case III, where NGs are installed in place of two thermal units (TUs), demonstrate that the economic dispatching approach presented in this study significantly reduces emission levels to 0.4232 t/h and achieves a lower fuel cost of 796.478 USD/MWh. Furthermore, the findings indicate that FOFMO outperforms COA and NSGA-II in effectively addressing the EED problem.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141352839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-12DOI: 10.3390/fractalfract8060349
Yuqin Song, Peijiang Liu, Anwarud Din
The epidemic norovirus causes vomiting and diarrhea and is a highly contagious infection. The disease is affecting human lives in terms of deaths and medical expenses. This study examines the governing dynamics of norovirus by incorporating Lévy noise into a stochastic SIRWF (susceptible, infected, recovered, water contamination, and food contamination) model. The existence of a non-negative solution and its uniqueness are proved after model formulation. Subsequently, the threshold parameter is calculated, and this number is used to explore the conditions under which disease tends to exist in the population. Likewise, additional conditions are derived that ensure the elimination of the disease from the community. It is proved that the norovirus is extinct whenever the threshold parameter is less than one and it persists for Rs>1. The work assumes two working examples to numerically explain the theoretical findings. Simulations of the study are visually presented, and comparisons are made. The results of this study suggest a robust approach for handling complex biological and epidemic phenomena.
{"title":"A Novel Stochastic Model for Human Norovirus Dynamics: Vaccination Impact with Lévy Noise","authors":"Yuqin Song, Peijiang Liu, Anwarud Din","doi":"10.3390/fractalfract8060349","DOIUrl":"https://doi.org/10.3390/fractalfract8060349","url":null,"abstract":"The epidemic norovirus causes vomiting and diarrhea and is a highly contagious infection. The disease is affecting human lives in terms of deaths and medical expenses. This study examines the governing dynamics of norovirus by incorporating Lévy noise into a stochastic SIRWF (susceptible, infected, recovered, water contamination, and food contamination) model. The existence of a non-negative solution and its uniqueness are proved after model formulation. Subsequently, the threshold parameter is calculated, and this number is used to explore the conditions under which disease tends to exist in the population. Likewise, additional conditions are derived that ensure the elimination of the disease from the community. It is proved that the norovirus is extinct whenever the threshold parameter is less than one and it persists for Rs>1. The work assumes two working examples to numerically explain the theoretical findings. Simulations of the study are visually presented, and comparisons are made. The results of this study suggest a robust approach for handling complex biological and epidemic phenomena.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141352978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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