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Numerical approximations of CNLS equations via UAH tension B-spline DQM 基于UAH张力b样条DQM的CNLS方程数值逼近
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0283
Mamta Kapoor, V. Joshi
Abstract Via UAH tension B-spline DQM in the present research, numerical approximation of coupled Schrödinger equations in one and two dimensions is fetched. In the present research, a novel regime is generated as a fusion of a UAH tension B-spline of fourth-order and DQM to fetch the requisite weighting coefficients. To ensure the adaptability and effectiveness of the proposed regime, different numerical examples are elaborated. Present results are matched with previous results, and the elastic property is also validated for solitons. The fetched ordinary differential equations system is handled via the SSP-RK43 regime. The stability of the present method is verified via the matrix method. The robustness of the proposed regime is affirmed via error norms. The fetched results are acceptable and validated. Elasticity property via wave interaction is also covered in the present research. The present study also focuses on one very important property of physics, like elasticity, which is rarely discussed in the literature. The developed numerical regime will undoubtedly be useful in addressing various fractional partial differential equations of complex nature as well.
摘要本研究通过UAH张力b样条DQM,得到了一维和二维耦合Schrödinger方程的数值逼近。在本研究中,将四阶UAH张力b样条与DQM融合生成一个新的区域,以获得所需的加权系数。为了保证所提机制的适应性和有效性,给出了不同的数值算例。本文的结果与以往的结果相吻合,并验证了孤子的弹性性质。所得到的常微分方程组通过SSP-RK43域进行处理。通过矩阵法验证了该方法的稳定性。该方法的鲁棒性通过误差范数得到了验证。获取的结果是可接受的,并且经过验证。本文还研究了波浪相互作用下的弹性特性。目前的研究还集中在一个非常重要的物理性质,如弹性,这在文献中很少讨论。所发展的数值体系无疑也将有助于解决各种复杂性质的分数阶偏微分方程。
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引用次数: 0
Nonlinear numerical simulation of bond performance between recycled concrete and corroded steel bars 再生混凝土与腐蚀钢筋粘结性能的非线性数值模拟
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0275
Zhenfang Li, Dongshao Gao, Chuanji Wu, Guoqing Lv, Xin Liu, Haoran Zhai, Zhan-Fang Huang
Abstract In this article, the bond performance between recycled concrete and corroded steel bars is analyzed by the nonlinear numerical simulation. The result shows that the maximum bond strength between recycled concrete and steel bar decreases with the increase in steel bar corrosion rate; when the recycled concrete strength is large, the simulated maximum bond strength is in good agreement with the experimental maximum bond strength; when the recycled concrete strength is small, the simulated maximum bond strength is in relatively poor agreement with the experimental maximum bond strength, but there is still an error within the allowable range; the slip between recycled concrete and steel bar increases with the increase in steel bar corrosion rate; when the steel bar corrosion rate exceeded 5%, the bond strength decreases more rapidly; the maximum bond strength increases with the increase in specimen sizes under the same steel bar corrosion rate; the maximum bond strength decreases with the increase in steel bar diameter under the same steel bar corrosion rate.
摘要本文采用非线性数值模拟方法分析了再生混凝土与腐蚀钢筋之间的粘结性能。结果表明:随着钢筋腐蚀速率的增大,再生混凝土与钢筋的最大粘结强度减小;当再生混凝土强度较大时,模拟最大粘结强度与试验最大粘结强度吻合较好;再生混凝土强度较小时,模拟最大粘结强度与实验最大粘结强度吻合较差,但仍在允许范围内存在误差;随着钢筋腐蚀速率的增加,再生混凝土与钢筋之间的滑移量增大;当钢筋腐蚀速率超过5%时,粘结强度下降较快;在相同钢筋腐蚀速率下,最大粘结强度随试样尺寸的增大而增大;在相同钢筋腐蚀速率下,最大粘结强度随钢筋直径的增大而减小。
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引用次数: 0
Dynamical aspects of transient electro-osmotic flow of Burgers' fluid with zeta potential in cylindrical tube 具有zeta势的Burgers流体在圆柱管内瞬态电渗透流动的动力学方面
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0256
N. Raza, Ahmad Kamal Khan, A. Awan, K. A. Abro
Abstract In this article, we consider the flow of a Burgers’ fluid of transient electro-osmotic type in a small tube with a circular cross-section. Analytical results are found for the transient velocity and, electric potential profile by solving the Navier–Stokes and the linearized Poisson–Boltzmann equations. Moreover, these equations are solved with the help of the integral transform method. We consider cases in which the velocity of the fluid changes with time and those in which the velocity of the fluid does not change with time. Furthermore, special results for classical fluids such as Newtonian, second grade, Maxwell, and Oldroyd-B fluids are obtained as the particular cases of the outcomes of this work and that these results actually strengthen the results of the solution. This study of the nonlinear problem of Burgers’ fluid in a specified physical model will help us to understand the behavior of blood clotting and the block of any kind of problem in which this type of fluid is used. The solution of the complex velocity profile of Burgers’ fluid will help us in the future to solve the problems in which this transient electro-osmotic type of small tube is involved. At the end, numerical results are shown graphically that can help us to understand the complex behavior of the Burgers’ fluid, and also the analysis of the Burgers’ fluid shows dissimilarity with other fluids that are considered in this work.
摘要本文考虑瞬态电渗透型Burgers流体在圆截面小管内的流动。通过求解Navier-Stokes方程和线性化泊松-玻尔兹曼方程,得到了瞬态速度和电势分布的解析结果。并利用积分变换法对这些方程进行了求解。我们考虑流体速度随时间变化的情况和流体速度不随时间变化的情况。此外,对于经典流体,如牛顿流体、二级流体、麦克斯韦流体和奥尔德罗伊德- b流体,得到了特殊的结果,作为本工作结果的特殊情况,这些结果实际上加强了解的结果。在一个特定的物理模型中研究伯格流体的非线性问题,将有助于我们理解血液凝固的行为,以及使用这种流体的任何一种问题的阻塞。伯格流体的复速度分布的求解将有助于我们将来解决这种瞬态电渗透型小管所涉及的问题。最后,数值结果以图形形式显示,可以帮助我们理解Burgers流体的复杂行为,并且对Burgers流体的分析显示了与本工作中考虑的其他流体的不同之处。
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引用次数: 2
Research on optimization of crane fault predictive control system based on data mining 基于数据挖掘的起重机故障预测控制系统优化研究
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0202
Xu Yanbin, Zhang Jianhua, Xiongwei Wang, Mohammad Shabaz, Mohd Wazih Ahmad, Samrat Ray
Abstract To ensure the safe functioning of lifting equipment, a data mining-based optimization study of a crane failure predictive control system is provided. To diagnose lifting machinery faults, the system employs decision tree categorization. Using association rules, a correlation study of hoisting machinery defect and failure was performed. When the minimal confidence and support degree are entered, a total of 244 instances of 18 frequent itemset A9 (safety protection device) may be obtained, indicating that lifting machinery does not perform well in this category. A6 (main parts) and A9 appeared a total of 98 times, with support and confidence of 29.4 and 35.6, respectively, indicating that the main parts can detect that the safety protection device is also having problems. A7 (electrical control system) and A9 appeared a total of 67 times, with support and confidence of 20.1 and 27.3, respectively, indicating that the electrical control system can detect that the safety protection device is also having problems; the correlation between them was also quite large. The system’s feasibility and efficacy shows that it has some application value.
摘要为了保证起重设备的安全运行,对起重机故障预测控制系统进行了基于数据挖掘的优化研究。该系统采用决策树分类方法对起重机械进行故障诊断。利用关联规则对起重机械缺陷与故障进行了相关性研究。当输入最小置信度和支持度时,可以得到18个频繁项目集A9(安全保护装置)的总共244个实例,表明起重机械在这一类别中表现不佳。A6(主要部件)和A9共出现98次,支持度和置信度分别为29.4和35.6,说明主要部件可以检测到安全保护装置也存在问题。A7(电气控制系统)和A9共出现67次,支持度和置信度分别为20.1和27.3,说明电气控制系统可以检测到安全保护装置也存在问题;它们之间的相关性也很大。系统的可行性和有效性表明,该系统具有一定的应用价值。
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引用次数: 3
Pricing weather derivatives in an uncertain environment 在不确定环境下为天气衍生品定价
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0291
Zulfiqar Ali, J. Hussain, Z. Bano
Abstract This article deals with the problem of finding a pricing formula for weather derivatives based on temperature dynamics through an uncertain differential equation. Weather-related derivatives are being employed more frequently in alternative risk portfolios with multiple asset classes. We first propose an uncertain process that uses data from the past to describe how the temperature has changed. Despite this, pricing these assets is difficult since it necessitates an incomplete market framework. The volatility is described by a truncated Fourier series, and we provide a novel technique for calculating this constant using Monte Carlo simulations. With this approach, the risk is assumed to have a fixed market price.
本文通过不确定微分方程,研究了基于温度动力学的天气导数定价公式的求解问题。与天气相关的衍生品被更频繁地用于多种资产类别的另类风险投资组合。我们首先提出了一个不确定的过程,利用过去的数据来描述温度是如何变化的。尽管如此,这些资产的定价是困难的,因为它需要一个不完整的市场框架。波动性由截断的傅立叶级数描述,我们提供了一种使用蒙特卡罗模拟计算该常数的新技术。使用这种方法,假定风险具有固定的市场价格。
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引用次数: 0
Analytical and numerical study for the generalized q-deformed sinh-Gordon equation 广义q-变形sinh-Gordon方程的解析与数值研究
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0255
K. Ali
Abstract In this article, we study the generalized q q -deformed sinh-Gordon equation analytically using the new general form of Kudryashov’s approach and numerically using the finite difference method. We develop a general form of the Kudryashov method that contains more than one constant that is used to give more explanations for the solutions that are obtained. The numerical results are also presented using the finite difference approach. We also provide numerous figures to demonstrate the various solitons propagation patterns. The proposed equation has opened up new options for describing physical systems that have lost their symmetry. The equation under study has not been studied extensively, so we completed the lesson that started a short time ago on it.
本文采用Kudryashov方法的新一般形式对广义q q变形sinh-Gordon方程进行了解析研究,并采用有限差分法对其进行了数值研究。我们开发了一种一般形式的Kudryashov方法,它包含多个常数,用于对得到的解给出更多的解释。用有限差分方法给出了数值结果。我们还提供了许多图形来演示各种孤子的传播模式。提出的方程为描述失去对称性的物理系统提供了新的选择。我们正在学习的方程还没有被广泛地研究过,所以我们完成了刚刚开始的关于它的课程。
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引用次数: 2
Nonlinear adaptive sliding mode control with application to quadcopters 非线性自适应滑模控制及其在四轴飞行器中的应用
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0268
Ryan Mathewson, F. Fahimi
Abstract Nonlinear adaptive sliding mode control (NASMC) has the capability to adequately control a system whose parameters are unknown to the controller designer. Conventional model-based controllers require a mathematical dynamic model of the system with known parameters. These system parameters are normally determined by extensive system identification experiments, which are expensive and time-consuming to perform. A NASMC approach that does not require known system parameters is proposed. Using NASMC, a controller designer can skip the expensive and time-consuming system parameter identification and fast-forward to the control implementation. In addition, once a controller is derived for a quadcopter using NASMC, the same controller will work on any quadcopter with the same equations of motion but different dynamic parameters. The formulation of the NASMC is presented for general second-order and fourth-order systems. Then, as an implementation example, the application of the general NASMC approach is demonstrated by applying it to a quadcopter unmanned aerial vehicle in simulation.
非线性自适应滑模控制(NASMC)具有对控制器设计者不知道参数的系统进行充分控制的能力。传统的基于模型的控制器要求系统具有已知参数的数学动态模型。这些系统参数通常是通过大量的系统识别实验来确定的,这些实验既昂贵又耗时。提出了一种不需要已知系统参数的NASMC方法。使用NASMC,控制器设计人员可以跳过昂贵且耗时的系统参数识别,并快速进入控制实现。此外,一旦使用NASMC为四轴飞行器导出了控制器,同一控制器将适用于具有相同运动方程但不同动态参数的任何四轴飞行器。给出了一般二阶和四阶系统的NASMC公式。然后,作为一个实现实例,将通用NASMC方法应用于四轴飞行器的仿真,验证了该方法的应用。
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引用次数: 1
The application of iterative hard threshold algorithm based on nonlinear optimal compression sensing and electronic information technology in the field of automatic control 基于非线性最优压缩感知和电子信息技术的迭代硬阈值算法在自动控制领域的应用
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0305
Kun-han jiang, M. Bradha
Abstract To improve the accuracy effect of the iterative hard threshold, an improved iterative hard threshold (IHT) method is proposed. The specific contents of this method include the principle of an IHT algorithm based on compression sensing (nonlinear optimization), weighted least squares improvement, the establishment of an IHT algorithm model based on weighted least squares improvement, and the experimental research of traditional algorithms and improved algorithms on one-dimensional signal reconstruction. The results show that the improved IRLSIHT algorithm takes 8.37, 29.63, and 30.86 s when the sampling rate is 0.2, 0.5, and 0.8, respectively, and the signal-to-noise ratio is 20.11, 27.47, and 31.82 dB, respectively. Compared with the traditional IHT algorithm, it takes a long time, which is a deficiency, but the signal-to-noise ratio is the largest, and the improved algorithm improves the accuracy. It has been proven that combining the method proposed in this article with automatic control can significantly save time and increase industrial output.
摘要为了提高迭代硬阈值的精度,提出了一种改进的迭代硬阈值(IHT)方法。该方法的具体内容包括基于压缩感知(非线性优化)的IHT算法原理、加权最小二乘改进、基于加权最小二乘改进的IHT算法模型的建立以及传统算法和改进算法在一维信号重构上的实验研究。结果表明,当采样率分别为0.2、0.5和0.8时,改进的IRLSIHT算法分别耗时8.37、29.63和30.86 s,信噪比分别为20.11、27.47和31.82 dB。与传统的IHT算法相比,耗时较长,这是不足之处,但信噪比最大,改进后的算法提高了精度。实践证明,将本文提出的方法与自动控制相结合,可以显著节省时间,提高工业产量。
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引用次数: 0
Numerical simulation of Burgers’ equations via quartic HB-spline DQM 基于四次hb样条DQM的Burgers方程数值模拟
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0264
Mamta Kapoor
Abstract Via modified quartic hyperbolic B-spline DQM, Burgers’ equation is numerically approximated in the current study. Ten numerical instances are discussed, and the findings are compared with those already in existence and with exact results. Error norms are assessed, and findings are shown in tabular as well as graphical formats, to validate the resilience and applicability portion of established numerical system. Matrix stability analysis approach is used to discuss proposed scheme’s stability. The current plan is robust, precise, and simple to put into action.
摘要本文利用改进的四次双曲b样条DQM,对Burgers方程进行了数值逼近。讨论了十个数值实例,并与已有的计算结果进行了比较,得到了准确的结果。评估误差规范,并以表格和图形格式显示结果,以验证已建立的数字系统的弹性和适用性部分。采用矩阵稳定性分析方法讨论了所提方案的稳定性。目前的计划是稳健、精确和易于实施的。
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引用次数: 0
A comparative study for the numerical approximation of 1D and 2D hyperbolic telegraph equations with UAT and UAH tension B-spline DQM 用UAT和UAH张力b样条DQM进行一维和二维双曲电报方程数值逼近的比较研究
IF 8.3 Q1 Mathematics Pub Date : 2023-01-01 DOI: 10.1515/nleng-2022-0280
Mamta Kapoor
Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.
摘要本文对比了一维和二维双曲电报方程的两种数值形式。第一种实现形式为均匀代数三角张力b样条DQM,第二种实现形式为均匀代数双曲张力b样条DQM。将上述方程进行空间离散化后,用SSP RK43方法求解得到的ode系统。为了评估所选战术的成功,给出了错误的比较。图中可以看到,并断言,精度和数值结果是一致的。并给出了收敛性和稳定性分析。应该强调的是,目前缺乏对一维和二维双曲电报方程的研究。这项研究的目的是有效地创造更少错误的结果。这些技术对于其他高阶非线性复杂性质的偏微分方程,包括分数阶方程、积分方程和部分积分方程,肯定是有用的。
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引用次数: 0
期刊
Nonlinear Engineering - Modeling and Application
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