This work presents a new two-step iterative technique for solving absolute value equations. The developed technique is valuable and effective for solving the absolute value equation. Various examples are given to demonstrate the accuracy and efficacy of the suggested technique.
Design/methodology/approach
In this paper, we present a new two-step iterative technique for solving absolute value equations. This technique is very straightforward, and due to the simplicity of this approach, it can be used to solve large systems with great effectiveness. Moreover, under certain assumptions, we examine the convergence of the proposed method using various theorems. Numerical outcomes are conducted to present the feasibility of the proposed technique.
Findings
This paper gives numerical experiments on how to solve a system of absolute value equations.
Originality/value
Nowadays, two-step approaches are very popular for solving equations (1). For solving AVEs, Liu in Shams (2021), Ning and Zhou (2015) demonstrated two-step iterative approaches. Moosaei et al. (2015) introduced a novel approach that utilizes a generalized Newton’s approach and Simpson’s rule to solve AVEs. Zainali and Lotfi (2018) presented a two-step Newton technique for AVEs that converges linearly. Feng and Liu (2016) have proposed minimization approaches for AVEs and presented their convergence under specific circumstances. Khan et al. (2023), suggested a nonlinear CSCS-like technique and a Picard-CSCS approach. Based on the benefits and drawbacks of the previously mentioned methods, we will provide a two-step iterative approach to efficiently solve equation (1). The numerical results show that our proposed technique converges rapidly and provides a more accurate solution.
{"title":"A new two-step iterative technique for efficiently solving absolute value equations","authors":"Nisar Gul, Haibo Chen, Javed Iqbal, Rasool Shah","doi":"10.1108/ec-11-2023-0754","DOIUrl":"https://doi.org/10.1108/ec-11-2023-0754","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>This work presents a new two-step iterative technique for solving absolute value equations. The developed technique is valuable and effective for solving the absolute value equation. Various examples are given to demonstrate the accuracy and efficacy of the suggested technique.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>In this paper, we present a new two-step iterative technique for solving absolute value equations. This technique is very straightforward, and due to the simplicity of this approach, it can be used to solve large systems with great effectiveness. Moreover, under certain assumptions, we examine the convergence of the proposed method using various theorems. Numerical outcomes are conducted to present the feasibility of the proposed technique.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>This paper gives numerical experiments on how to solve a system of absolute value equations.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>Nowadays, two-step approaches are very popular for solving equations (1). For solving AVEs, Liu in Shams (2021), Ning and Zhou (2015) demonstrated two-step iterative approaches. Moosaei <em>et al</em>. (2015) introduced a novel approach that utilizes a generalized Newton’s approach and Simpson’s rule to solve AVEs. Zainali and Lotfi (2018) presented a two-step Newton technique for AVEs that converges linearly. Feng and Liu (2016) have proposed minimization approaches for AVEs and presented their convergence under specific circumstances. Khan <em>et al</em>. (2023), suggested a nonlinear CSCS-like technique and a Picard-CSCS approach. Based on the benefits and drawbacks of the previously mentioned methods, we will provide a two-step iterative approach to efficiently solve equation (1). The numerical results show that our proposed technique converges rapidly and provides a more accurate solution.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xian Zhang, Changming Zhang, Peng Wang, Fan Yang, Chunlei Peng
Purpose
The purpose of this paper is to analyze the stiffness reliability of harmonic drive (HD) considering contact pairs wear.
Design/methodology/approach
In terms of theoretical calculation, the contact pairs wear of HD are calculated based on Archard wear formula and the relative motion characteristics of contact pairs. According to the motion trajectory of flexspline teeth, the teeth backlash and the number of meshing teeth, the meshing stiffness and overall stiffness of HD are analyzed considering the wear and its randomness of contact pairs. Combined with Monte Carlo Simulation, the stiffness reliability evaluation method considering contact pairs wear is proposed, and the result of this method is verified by the stiffness reliability result deduced from the stiffness degradation measurement data.
Findings
Considering contact pairs wear, during operation, the teeth backlash increases, the number of meshing teeth decreases, the meshing stiffness decreases, ultimately leading to a gradual decrease in the overall stiffness of HD. When only one type of contact pair wear is considered, the influence of flexspline and circular spline contact pair wear on HD stiffness reliability is greater. Compared with the stiffness reliability evaluation results obtained from the stiffness degradation data in the literature, the mathematic expectation of stiffness degradation failure life distribution obtained from the proposed method is relatively bigger.
Originality/value
The stiffness reliability evaluation method of HD considering contact pairs wear is firstly proposed. The stiffness reliability evaluation result from theoretical calculation is verified by the stiffness reliability results deduced from HD stiffness degradation measurement.
设计/方法/步骤在理论计算方面，根据 Archard 磨损公式和接触对的相对运动特性计算谐波传动（HD）的接触对磨损。根据挠性齿的运动轨迹、齿间隙和啮合齿数，考虑接触对的磨损及其随机性，分析了 HD 的啮合刚度和整体刚度。结合蒙特卡罗模拟，提出了考虑接触对磨损的刚度可靠性评估方法，并通过刚度退化测量数据推导出的刚度可靠性结果对该方法的结果进行了验证。研究结果考虑到接触对磨损，在运行过程中，齿背间隙增加，啮合齿数减少，啮合刚度降低，最终导致 HD 整体刚度逐渐降低。如果只考虑一种接触对磨损，则挠性花键和圆花键接触对磨损对 HD 刚度可靠性的影响更大。与文献中根据刚度退化数据得到的刚度可靠性评价结果相比，本文提出的方法得到的刚度退化失效寿命分布的数学期望值相对较大。 原创性/价值 首次提出了考虑接触对磨损的 HD 刚度可靠性评价方法。理论计算得出的刚度可靠性评估结果通过 HD 刚度退化测量推导出的刚度可靠性结果得到了验证。
{"title":"Stiffness reliability analysis of harmonic drive considering contact pairs wear","authors":"Xian Zhang, Changming Zhang, Peng Wang, Fan Yang, Chunlei Peng","doi":"10.1108/ec-11-2023-0897","DOIUrl":"https://doi.org/10.1108/ec-11-2023-0897","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>The purpose of this paper is to analyze the stiffness reliability of harmonic drive (HD) considering contact pairs wear.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>In terms of theoretical calculation, the contact pairs wear of HD are calculated based on Archard wear formula and the relative motion characteristics of contact pairs. According to the motion trajectory of flexspline teeth, the teeth backlash and the number of meshing teeth, the meshing stiffness and overall stiffness of HD are analyzed considering the wear and its randomness of contact pairs. Combined with Monte Carlo Simulation, the stiffness reliability evaluation method considering contact pairs wear is proposed, and the result of this method is verified by the stiffness reliability result deduced from the stiffness degradation measurement data.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>Considering contact pairs wear, during operation, the teeth backlash increases, the number of meshing teeth decreases, the meshing stiffness decreases, ultimately leading to a gradual decrease in the overall stiffness of HD. When only one type of contact pair wear is considered, the influence of flexspline and circular spline contact pair wear on HD stiffness reliability is greater. Compared with the stiffness reliability evaluation results obtained from the stiffness degradation data in the literature, the mathematic expectation of stiffness degradation failure life distribution obtained from the proposed method is relatively bigger.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The stiffness reliability evaluation method of HD considering contact pairs wear is firstly proposed. The stiffness reliability evaluation result from theoretical calculation is verified by the stiffness reliability results deduced from HD stiffness degradation measurement.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Singular perturbation turning point problems (SP-TPPs) involving parabolic convection–diffusion Partial Differential Equations (PDEs) with large spatial delay are studied in this paper. These type of equations are important in various fields of mathematics and sciences such as computational neuroscience and require specialized techniques for their numerical analysis.
Design/methodology/approach
We design a numerical method comprising a hybrid finite difference scheme on a layer-adapted mesh for the spatial discretization and an implicit-Euler scheme on a uniform mesh in the temporal variable. A combination of the central difference scheme and the simple upwind scheme is used as the hybrid scheme.
Findings
Consistency, stability and convergence are investigated for the proposed scheme. It is established that the present approach has parameter-uniform convergence of OΔτ+K−2(lnK)2, where Δτ and K denote the step size in the time direction and number of mesh-intervals in the space direction.
Originality/value
Parabolic SP-TPPs exhibiting twin boundary layers with large spatial delay have not been studied earlier in the literature. The presence of delay portrays an interior layer in the considered problem’s solution in addition to twin boundary layers. Numerical illustrations are provided to demonstrate the theoretical estimates.
目的本文研究了涉及具有大空间延迟的抛物对流扩散偏微分方程（PDEs）的星状扰动转折点问题（SP-TPPs）。这类方程在计算神经科学等数学和科学的各个领域都很重要，需要专门的数值分析技术。我们设计了一种数值方法，包括在层适应网格上进行空间离散化的混合有限差分方案，以及在时间变量均匀网格上的隐式欧拉方案。研究结果研究了拟议方案的一致性、稳定性和收敛性。结果表明，本方法的参数均匀收敛性为 OΔτ+K-2(lnK)2，其中 Δτ 和 K 分别表示时间方向的步长和空间方向的网格间隔数。除了孪生边界层之外，延迟的存在还在所考虑问题的解中描绘了一个内部层。本文提供了数值图解来证明理论估算。
{"title":"Numerical approximation of parabolic singularly perturbed problems with large spatial delay and turning point","authors":"Amit Sharma, Pratima Rai","doi":"10.1108/ec-09-2023-0534","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0534","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>Singular perturbation turning point problems (SP-TPPs) involving parabolic convection–diffusion Partial Differential Equations (PDEs) with large spatial delay are studied in this paper. These type of equations are important in various fields of mathematics and sciences such as computational neuroscience and require specialized techniques for their numerical analysis.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>We design a numerical method comprising a hybrid finite difference scheme on a layer-adapted mesh for the spatial discretization and an implicit-Euler scheme on a uniform mesh in the temporal variable. A combination of the central difference scheme and the simple upwind scheme is used as the hybrid scheme.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>Consistency, stability and convergence are investigated for the proposed scheme. It is established that the present approach has parameter-uniform convergence of <span><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mfenced close=\")\" open=\"(\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>τ</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">K</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>ln</mml:mi><mml:mi mathvariant=\"script\">K</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:math></span>, where <span><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Δ</mml:mi><mml:mi>τ</mml:mi></mml:math></span> and <span><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi mathvariant=\"script\">K</mml:mi></mml:mrow></mml:math></span> denote the step size in the time direction and number of mesh-intervals in the space direction.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>Parabolic SP-TPPs exhibiting twin boundary layers with large spatial delay have not been studied earlier in the literature. The presence of delay portrays an interior layer in the considered problem’s solution in addition to twin boundary layers. Numerical illustrations are provided to demonstrate the theoretical estimates.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aiming at solving the problems of low prediction accuracy and poor generalization caused by the difference in tool wear data distribution and the fixation of single global model parameters, a hybrid prediction modeling method for tool wear based on joint distribution adaptation (JDA) is proposed.
Design/methodology/approach
Firstly, JDA is exploited to adapt the data features with different data distributions. Then, the adapted data features are identified by the KNN classifier. Finally, according to the tool state classification results, different regression prediction models are assigned to different wear stages to complete the whole tool wear prediction task.
Findings
The results of milling experiments show that the maximum prediction accuracy of this method is 95.13%, and it has good recognition accuracy and generalization performance. Through the application of the tool wear hybrid prediction modeling method, the prediction accuracy and generalization performance of the model are improved and the tool monitoring is realized.
Originality/value
The research results can provide solutions and a theoretical basis for the application of tool wear monitoring technology in practical industrial applications.
{"title":"A hybrid tool wear prediction model based on JDA","authors":"Hua Huang, Weiwei Yu, Jiajing Yao, Peidong Yang","doi":"10.1108/ec-08-2023-0405","DOIUrl":"https://doi.org/10.1108/ec-08-2023-0405","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>Aiming at solving the problems of low prediction accuracy and poor generalization caused by the difference in tool wear data distribution and the fixation of single global model parameters, a hybrid prediction modeling method for tool wear based on joint distribution adaptation (JDA) is proposed.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>Firstly, JDA is exploited to adapt the data features with different data distributions. Then, the adapted data features are identified by the KNN classifier. Finally, according to the tool state classification results, different regression prediction models are assigned to different wear stages to complete the whole tool wear prediction task.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The results of milling experiments show that the maximum prediction accuracy of this method is 95.13%, and it has good recognition accuracy and generalization performance. Through the application of the tool wear hybrid prediction modeling method, the prediction accuracy and generalization performance of the model are improved and the tool monitoring is realized.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The research results can provide solutions and a theoretical basis for the application of tool wear monitoring technology in practical industrial applications.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.
Design/methodology/approach
The paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.
Findings
The computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.
Originality/value
This paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.
{"title":"Balanced task allocation and motion planning of a multi-robot system under fuzzy time windows","authors":"Elias Xidias, Paraskevi Zacharia","doi":"10.1108/ec-09-2023-0612","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0612","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>A fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>The paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>This paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PurposeAdaptive load-bearing structures pursue the approach of saving mass within a load-bearing structure by adding external energy, thus saving materials and resources. This paper provides an overview of current research developments and shows some examples of existing prototypes.Design/methodology/approachFirst, basic terms and definitions from the research field of adaptive structures are introduced. After a brief historical insight, the numerical methods and prototypes used are presented as examples. The paper concludes with a summary of the state-of-the-art and open questions.FindingsThe current state of the art shows that the idea of adaptive structures offers great potential for more sustainability and resource efficiency in the construction industry. However, it also shows that research is still at the basic stage and that there are still some gaps in research.Originality/valueThe implementation of adaptive load-bearing structures is just one of many different approaches to greater sustainability in the construction sector. The issue of adaptive structures is a highly interdisciplinary field of research. The following paper is a literature review intended to summarize and critically evaluate the state-of-the-art research in this field. In the final section, some open questions are addressed, indicating that this research topic is still evolving.
{"title":"Adaptive structures in civil engineering – state of the art","authors":"Lisa Schwegmann, Volkmar Zabel, Steffen Koch","doi":"10.1108/ec-12-2023-0952","DOIUrl":"https://doi.org/10.1108/ec-12-2023-0952","url":null,"abstract":"PurposeAdaptive load-bearing structures pursue the approach of saving mass within a load-bearing structure by adding external energy, thus saving materials and resources. This paper provides an overview of current research developments and shows some examples of existing prototypes.Design/methodology/approachFirst, basic terms and definitions from the research field of adaptive structures are introduced. After a brief historical insight, the numerical methods and prototypes used are presented as examples. The paper concludes with a summary of the state-of-the-art and open questions.FindingsThe current state of the art shows that the idea of adaptive structures offers great potential for more sustainability and resource efficiency in the construction industry. However, it also shows that research is still at the basic stage and that there are still some gaps in research.Originality/valueThe implementation of adaptive load-bearing structures is just one of many different approaches to greater sustainability in the construction sector. The issue of adaptive structures is a highly interdisciplinary field of research. The following paper is a literature review intended to summarize and critically evaluate the state-of-the-art research in this field. In the final section, some open questions are addressed, indicating that this research topic is still evolving.","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141334937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.
Design/methodology/approach
This article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.
Findings
The proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.
Originality/value
The fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.
{"title":"New computational approaches to the fractional coupled nonlinear Helmholtz equation","authors":"KangLe Wang","doi":"10.1108/ec-08-2023-0501","DOIUrl":"https://doi.org/10.1108/ec-08-2023-0501","url":null,"abstract":"<h3>Purpose</h3>\u0000<p>The main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.</p><!--/ Abstract__block -->\u0000<h3>Design/methodology/approach</h3>\u0000<p>This article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.</p><!--/ Abstract__block -->\u0000<h3>Findings</h3>\u0000<p>The proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.</p><!--/ Abstract__block -->\u0000<h3>Originality/value</h3>\u0000<p>The fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nasiru Salihu, P. Kumam, Sulaiman Mohammed Ibrahim, Huzaifa Aliyu Babando
PurposePrevious RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.Design/methodology/approachThe conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.FindingsNumerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.Originality/valueThe strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.
{"title":"A sufficient descent hybrid conjugate gradient method without line search consideration and application","authors":"Nasiru Salihu, P. Kumam, Sulaiman Mohammed Ibrahim, Huzaifa Aliyu Babando","doi":"10.1108/ec-12-2023-0912","DOIUrl":"https://doi.org/10.1108/ec-12-2023-0912","url":null,"abstract":"PurposePrevious RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.Design/methodology/approachThe conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.FindingsNumerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.Originality/valueThe strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141335010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PurposeDynamic low adhesion (DLA) has become an urgent problem for the high-speed wheel-rail system because of continuous decrease of adhesion redundancy in the past decades. This article aims to provide a simulation method to reveal the mechanism of DLA under high-frequency vibrations.Design/methodology/approachA transient wheel-rail rolling contact model is developed for a typical Chinese high-speed railway system using the explicit finite element (FE) method. Instantaneous adhesion exploitation levels are studied in the time domain, for which driving cases over corrugated rails are taken as an example. A speed up to 500 km/h is considered together with different traction coefficients and corrugation dimensions. DLA is expected when the instantaneous adhesion exploitation level reaches 1.0, that is adhesion saturates and full sliding contact occurs.FindingsThe instantaneous adhesion exploitation level can be very high in the presence of corrugation, even at low traction coefficients. DLA is found to occur as great vertical unloading takes place and causes a significant increase of creepage. An approach is further developed to determine the critical depth of corrugation over which DLA occurs.Originality/valueThis study employs the transient wheel-rail rolling contact model to predict the instantaneous adhesion exploitation level under high-frequency vibrations. The presented results reveal a mechanism of DLA being beneficial to guidelines for future railway practice.
目的由于过去几十年来附着力冗余度不断降低，动态低附着力（DLA）已成为高速轮轨系统亟待解决的问题。本文旨在提供一种仿真方法，以揭示高频振动下的 DLA 机理。设计/方法/途径采用显式有限元（FE）方法为典型的中国高速铁路系统建立了瞬态轮轨滚动接触模型。在时域中研究了瞬时附着力利用水平，并以波纹钢轨上的行驶情况为例。考虑了最高 500 km/h 的速度以及不同的牵引系数和波纹尺寸。当瞬时附着力利用水平达到 1.0 时，即附着力达到饱和并发生完全滑动接触时，预计会出现 DLA。研究发现，当发生巨大的垂直卸载时会出现 DLA，并导致爬行量显著增加。本研究采用瞬态轮轨滚动接触模型来预测高频振动下的瞬时附着力利用水平。研究结果揭示了 DLA 的机理，有助于为未来的铁路实践提供指导。
{"title":"Explicit finite element simulations of dynamic low adhesion behavior between wheel and rail in the presence of high-frequency vibrations","authors":"Wen Liu, Shuangchao Huang, Hongfeng Qi, Xin Zhao, Shulin Liang, Xuesong Jin","doi":"10.1108/ec-01-2024-0028","DOIUrl":"https://doi.org/10.1108/ec-01-2024-0028","url":null,"abstract":"PurposeDynamic low adhesion (DLA) has become an urgent problem for the high-speed wheel-rail system because of continuous decrease of adhesion redundancy in the past decades. This article aims to provide a simulation method to reveal the mechanism of DLA under high-frequency vibrations.Design/methodology/approachA transient wheel-rail rolling contact model is developed for a typical Chinese high-speed railway system using the explicit finite element (FE) method. Instantaneous adhesion exploitation levels are studied in the time domain, for which driving cases over corrugated rails are taken as an example. A speed up to 500 km/h is considered together with different traction coefficients and corrugation dimensions. DLA is expected when the instantaneous adhesion exploitation level reaches 1.0, that is adhesion saturates and full sliding contact occurs.FindingsThe instantaneous adhesion exploitation level can be very high in the presence of corrugation, even at low traction coefficients. DLA is found to occur as great vertical unloading takes place and causes a significant increase of creepage. An approach is further developed to determine the critical depth of corrugation over which DLA occurs.Originality/valueThis study employs the transient wheel-rail rolling contact model to predict the instantaneous adhesion exploitation level under high-frequency vibrations. The presented results reveal a mechanism of DLA being beneficial to guidelines for future railway practice.","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141334852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Ai, Zheng Qing Lei, Danyang Li, Jingming Zeng, Dawei Liu
PurposeHighway traffic systems are complex and variable, and studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable bifurcation points can alleviate traffic congestion from a new perspective. Bifurcation analysis is used to explain the changes in system stability, identify the unstable bifurcation points of the system, and design feedback controllers to realize the control of the unstable bifurcation points of the traffic system. It helps to control the sudden changes in the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.Design/methodology/approachIn this paper, we improve the macroscopic traffic flow model by integrating severe weather factors such as rainfall, snowfall, and dust. We use traveling wave transform to convert it into a traffic flow stability model suitable for branching analysis, thus converting the traffic flow problem into a system stability analysis problem. First, this paper derives the existence conditions of the model Hopf bifurcation and saddle-node bifurcation for the improved macroscopic model, and finds the stability mutation point of the system. Secondly, the connection between the stability mutation points and bifurcation points of the traffic system is analyzed. Finally, for the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method.FindingsThe Hopf bifurcation is delayed and completely eliminated without changing the equilibrium point of the system, thus controlling the abrupt behavior of the traffic system.Originality/valueCurrently there are fewer studies to explain the changes in the stability of the transportation system through bifurcation analysis, in this paper; we design a feedback controller for the unstable bifurcation point of the system to realize the control of the transportation system. It is a new research method that helps to control the sudden change of the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.
{"title":"Bifurcation analysis and control of an improved continuous traffic model considering weather effect","authors":"W. Ai, Zheng Qing Lei, Danyang Li, Jingming Zeng, Dawei Liu","doi":"10.1108/ec-09-2023-0541","DOIUrl":"https://doi.org/10.1108/ec-09-2023-0541","url":null,"abstract":"PurposeHighway traffic systems are complex and variable, and studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable bifurcation points can alleviate traffic congestion from a new perspective. Bifurcation analysis is used to explain the changes in system stability, identify the unstable bifurcation points of the system, and design feedback controllers to realize the control of the unstable bifurcation points of the traffic system. It helps to control the sudden changes in the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.Design/methodology/approachIn this paper, we improve the macroscopic traffic flow model by integrating severe weather factors such as rainfall, snowfall, and dust. We use traveling wave transform to convert it into a traffic flow stability model suitable for branching analysis, thus converting the traffic flow problem into a system stability analysis problem. First, this paper derives the existence conditions of the model Hopf bifurcation and saddle-node bifurcation for the improved macroscopic model, and finds the stability mutation point of the system. Secondly, the connection between the stability mutation points and bifurcation points of the traffic system is analyzed. Finally, for the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method.FindingsThe Hopf bifurcation is delayed and completely eliminated without changing the equilibrium point of the system, thus controlling the abrupt behavior of the traffic system.Originality/valueCurrently there are fewer studies to explain the changes in the stability of the transportation system through bifurcation analysis, in this paper; we design a feedback controller for the unstable bifurcation point of the system to realize the control of the transportation system. It is a new research method that helps to control the sudden change of the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141334938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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