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Maximum likelihood LM identification based on particle filtering for scarce measurement-data MIMO Hammerstein Box-Jenkins systems 基于粒子滤波的最大似然 LM 识别,适用于稀缺测量数据 MIMO Hammerstein Box-Jenkins 系统
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-22 DOI: 10.1016/j.matcom.2024.11.012
Tiancheng Zong, Junhong Li, Guoping Lu
The scarce measurement-data system means that the input or output of one system are sampled at scarce time series. Thus, the sampled data are incomplete in scarce measurement-data systems. In this paper, the parameter estimation of scarce measurement-data multiple input multiple output Hammerstein Box-Jenkins (S-MIMO-H-BJ) systems is studied. To make full use of the system data without adding unknown parameters, the particle filtering method is applied to obtain unknown states and variables in scarce measurement-data systems. Thus, the maximum likelihood Levenberg Marquardt (ML-LM) iterative method based on particle filtering (ML-LM-I-PF) is derived. To verify the superiority of the proposed algorithm, the ML-LM iterative method based on auxiliary model (ML-LM-I-AM) is also derived. Finally, using these two algorithms, unknown parameters in the S-MIMO-H-BJ numerical example and the two-tank level system are identified. Simulations prove that these two methods can all estimate S-MIMO-H-BJ models effectively, but the ML-LM-I-PF method behaves better because it has smaller calculation amount and more accurate parameter estimation.
稀缺测量数据系统是指一个系统的输入或输出采样时间序列稀缺。因此,在稀缺测量数据系统中,采样数据是不完整的。本文研究了稀缺测量数据多输入多输出哈默斯坦箱-詹金斯(S-MIMO-H-BJ)系统的参数估计。为了充分利用系统数据而不增加未知参数,本文采用粒子滤波方法来获取稀缺测量数据系统中的未知状态和变量。因此,得出了基于粒子滤波的最大似然 Levenberg Marquardt(ML-LM)迭代法(ML-LM-I-PF)。为了验证所提算法的优越性,还推导出了基于辅助模型的 ML-LM 迭代方法(ML-LM-I-AM)。最后,利用这两种算法,确定了 S-MIMO-H-BJ 数值示例和双罐电平系统中的未知参数。仿真证明,这两种方法都能有效估计 S-MIMO-H-BJ 模型,但 ML-LM-I-PF 方法的计算量更小,参数估计更准确,因此表现更好。
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引用次数: 0
Numerical simulation and error analysis for a novel fractal–fractional reaction diffusion model with weighted reaction 带加权反应的新型分形-分数反应扩散模型的数值模拟与误差分析
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-21 DOI: 10.1016/j.matcom.2024.11.013
Lihong Zhang , Keke Lu , Bashir Ahmad
A new fractal-fractional reaction diffusion model with weighted reaction is investigated in this paper. Using Chelyshkov polynomials, we construct the associated Chelyshkov operator matrix to solve this diffusion model. An error estimation is obtained for validation of our method. Numerical examples indicate that the proposed method is easy to apply and produce accurate results. It is imperative to mention that the fractal-fractional reaction diffusion model and the proposed numerical method offer an efficient approach to handle the issues related to the diffusion phenomenon.
本文研究了一种带有加权反应的新分形-分形反应扩散模型。利用切利什科夫多项式,我们构建了相关的切利什科夫算子矩阵来求解该扩散模型。为了验证我们的方法,我们进行了误差估计。数值示例表明,所提出的方法易于应用,并能产生精确的结果。值得一提的是,分形-分数反应扩散模型和所提出的数值方法为处理与扩散现象相关的问题提供了一种有效的方法。
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引用次数: 0
A parsimonious dynamic mixture for heavy-tailed distributions 重尾分布的拟动态混合物
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-20 DOI: 10.1016/j.matcom.2024.11.011
Marco Bee
Dynamic mixture distributions are convenient models for highly skewed and heavy-tailed data. However, estimation has proved to be challenging and computationally expensive. To address this issue, we develop a more parsimonious model, based on a one-parameter weight function given by the exponential cumulative distribution function. Parameter estimation is carried out via maximum likelihood, approximate maximum likelihood and noisy cross-entropy. Simulation experiments and real-data analyses suggest that approximate maximum likelihood is the best method in terms of RMSE, albeit at a high computational cost. With respect to the version of the dynamic mixture with weight equal to the two-parameter Cauchy cumulative distribution function, the reduced flexibility of the present model is more than compensated by better statistical and computational properties.
动态混合分布是高度倾斜和重尾数据的便捷模型。然而,事实证明估算具有挑战性且计算成本高昂。为了解决这个问题,我们基于指数累积分布函数给出的单参数权重函数,开发了一种更简洁的模型。参数估计通过最大似然法、近似最大似然法和噪声交叉熵进行。模拟实验和实际数据分析表明,近似极大似然法是均方根误差(RMSE)最小的方法,尽管计算成本较高。与权重等于双参数考奇累积分布函数的动态混合物版本相比,本模型的灵活性有所降低,但统计和计算特性更好,足以弥补这一不足。
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引用次数: 0
Numerical analysis of an age-structured model for HIV viral dynamics with latently infected T cells based on collocation methods 基于配位方法的潜伏感染T细胞的HIV病毒动力学年龄结构模型的数值分析
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-20 DOI: 10.1016/j.matcom.2024.09.028
Mengna Li, Zhanwen Yang
In this paper, we consider the numerical threshold for an age-structured HIV model with latently infected T cells. Based on the continuous collocation methods, a semi-discrete scheme is constructed by discretizing the age variable and a numerical basic reproduction number Rh is provided. With the study of higher-order convergence to the real basic reproduction number R0, the relations between Rh and local stability of disease-free are presented. From the viewpoint of full discretization, an equivalent block-Leslie matrix expression is obtained by embedding into a piecewise-discontinuous polynomial space rather than the piecewise-continuous polynomial space. An implicit full-discrete scheme is considered based on a linearly implicit Euler (IMEX) method, of which the computational cost is almost the same as an explicit scheme. It is more important that the dynamical behavior of the age-semi-discretization system is also preserved for any time step whenever Rh is the threshold for the numerical dynamical system of the age-semi-discretization. Finally, numerical applications are shown to HIV models to illustrate our analysis.
在本文中,我们考虑的数值阈值年龄结构的HIV模型与潜伏感染的T细胞。在连续配置方法的基础上,构造了年龄变量离散化的半离散格式,并给出了数值基本再现数Rh。通过对实基本繁殖数R0的高阶收敛性的研究,给出了Rh与无病局部稳定性的关系。从完全离散化的角度出发,通过嵌入到一个分段不连续的多项式空间而不是分段连续的多项式空间中,得到了一个等价的块- leslie矩阵表达式。考虑了一种基于线性隐式欧拉(IMEX)方法的隐式全离散格式,其计算成本与显式格式几乎相同。更重要的是,当Rh为半离散化的数值动力系统的阈值时,系统的动力学行为在任何时间步长都保持不变。最后,通过HIV模型的数值应用来说明我们的分析。
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引用次数: 0
Competition-based two-stage evolutionary algorithm for constrained multi-objective optimization 基于竞争的约束多目标优化两阶段进化算法
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-19 DOI: 10.1016/j.matcom.2024.11.009
Lupeng Hao , Weihang Peng , Junhua Liu , Wei Zhang , Yuan Li , Kaixuan Qin
In recent years, the emergence of constrained multi-objective evolutionary algorithms (CMOEAs) has made it increasingly difficult to balance between the diversity and convergence of algorithms. To address this challenge, this paper proposes a competition-based two-stage evolutionary algorithm, named CP-TSEA, for constrained multi-objective problems. In the first stage, a ɛ constraint boundary relaxation learning mechanism was applied to the auxiliary population. This mechanism not only improved the diversity of the population but also enhanced the global search capability by relaxing the constraints, allowing infeasible solutions with higher fitness rankings to participate in the evolution. In the second stage, an equal-probability competitive strategy was used to select high-quality parents from the elite mating pool to ensure that the population could converge quickly to the optimal solution. The two-stage approach not only improved the exploration ability of the algorithm, but also was able to select higher quality solutions and prevent them from falling into local optima. Additionally, the solution selection in the elite environment employed a three-criteria ranking method to maintain a balance between population diversity and convergence. In terms of experiments, CP-TSEA was compared with seven advanced CMOEAs across five test suites, and the comprehensive data showed that CP-TSEA significantly outperformed its competitors. In addition, CP-TSEA also achieved the best values in six real-world problems, which further confirmed its scalability in real-world applications.
近年来,约束多目标进化算法(CMOEAs)的出现使得算法的多样性和收敛性之间的平衡变得越来越困难。为了应对这一挑战,本文针对约束多目标问题提出了一种基于竞争的两阶段进化算法,命名为 CP-TSEA。在第一阶段,对辅助种群采用了ɛ约束边界松弛学习机制。该机制不仅提高了种群的多样性,还通过放松约束增强了全局搜索能力,允许适配度排名较高的不可行解参与进化。在第二阶段,采用等概率竞争策略从精英交配池中选择优质亲本,以确保种群能快速收敛到最优解。两阶段方法不仅提高了算法的探索能力,还能选择更高质量的解,防止它们陷入局部最优。此外,精英环境下的解选择采用了三标准排序法,以保持群体多样性和收敛性之间的平衡。在实验方面,CP-TSEA 与七种先进的 CMOEA 在五个测试套件中进行了比较,综合数据显示,CP-TSEA 的性能明显优于竞争对手。此外,CP-TSEA 还在六个实际问题中取得了最佳值,这进一步证实了其在实际应用中的可扩展性。
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引用次数: 0
Long time behavior of a Lotka–Volterra competition system with two dynamical resources and density-dependent motility 具有两种动态资源和密度依赖性运动的 Lotka-Volterra 竞争系统的长期行为
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-18 DOI: 10.1016/j.matcom.2024.11.008
Jianping Gao, Wenyan Lian
In this paper, we consider a Lotka–Volterra competition system with two dynamical resources and density-dependent motility under the homogeneous Neumann boundary condition. Here, we put the two competing species into a predator–prey system, and assume that the two competing species as predators can feed on different preys and that the preys as resources admit temporal dynamics including spatial movement, intrinsic birth–death kinetics and loss due to predation. When the distributions of prey’s resources can be homogeneous, by using some proper Lyapunov functionals and applying LaSalle’s invariant principle, we obtain that the solution can converge to the positive steady state exponentially or to the competitive exclusion steady states algebraically as time goes to infinity. Our finding shows that the consideration of temporal dynamics on the resources can lead to the coexistence of two competitors in some parameter conditions regardless of their dispersal rates. When the distributions of prey’s resources are spatially heterogeneous, we conduct several numerical simulations in different combinations of dispersal strategy and the distributions of prey’s resources, and we show that the non-random dispersal and heterogeneous distributions of prey’s resources can affect the fates of two competitors.
在本文中,我们考虑的是在均质 Neumann 边界条件下具有两种动态资源和密度依赖性运动的 Lotka-Volterra 竞争系统。在此,我们将两个竞争物种置于捕食者-猎物系统中,并假设作为捕食者的两个竞争物种可以捕食不同的猎物,作为资源的猎物具有时间动力学特性,包括空间运动、内在的出生-死亡动力学和捕食导致的损失。当猎物资源的分布可以是同质的时,通过使用一些适当的 Lyapunov 函数并应用拉萨尔不变原理,我们可以得到,随着时间的无穷大,解可以指数收敛到正稳态或代数收敛到竞争排斥稳态。我们的发现表明,在某些参数条件下,考虑资源的时间动态会导致两个竞争者共存,而不管它们的扩散率如何。当猎物资源的分布在空间上具有异质性时,我们对不同的扩散策略和猎物资源分布组合进行了多次数值模拟,结果表明,猎物资源的非随机扩散和异质性分布会影响两个竞争者的命运。
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引用次数: 0
Algorithmic modelling of a complex redundant multi-state system subject to multiple events, preventive maintenance, loss of units and a multiple vacation policy through a MMAP 通过 MMAP 建立受多重事件、预防性维护、单元损失和多重休假政策影响的复杂冗余多状态系统的算法模型
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-16 DOI: 10.1016/j.matcom.2024.11.005
Juan Eloy Ruiz-Castro , Hugo Alaín Zapata-Ceballos
A complex multi-state redundant system undergoing preventive maintenance and experiencing multiple events is being considered in a continuous time frame. The online unit is susceptible to various types of failures, both internal and external in nature, with multiple degradation levels present, both internally and externally. Random inspections are continuously monitoring these degradation levels, and if they reach a critical state, the unit is directed to a repair facility for preventive maintenance. The maintenance place is managed by a repairperson, who follows a multiple vacation policy dependent on the operational status of the units. The repairperson is responsible for two primary tasks: corrective repair and preventive maintenance. The time durations within the system follow phase-type distributions, and the model is constructed utilizing Markovian Arrival Processes with marked arrivals. A variety of performance measures, including transient and stationary distributions, are calculated using matrix-analytic methods. This methodology allows for the representation of significant outcomes and the general behavior of the system in a matrix-algorithmic structure. To enhance the model's efficiency, both costs and rewards are incorporated into the analysis. A numerical example is presented to showcase the model's flexibility and effectiveness in real-world applications.
一个复杂的多状态冗余系统正在进行预防性维护,并在连续的时间框架内经历多个事件。在线设备容易出现各种类型的故障,既有内部故障,也有外部故障。随机检查将持续监测这些退化程度,如果达到临界状态,设备将被送往维修设施进行预防性维护。维修地点由一名维修人员管理,他根据设备的运行状况实行多次休假政策。维修人员主要负责两项任务:纠正性维修和预防性维修。系统内的时间长度遵循阶段型分布,模型利用马尔可夫到达过程(Markovian Arrival Processes)构建,带有到达标记。使用矩阵分析方法计算了各种性能指标,包括瞬态和静态分布。这种方法允许在矩阵算法结构中表示重要结果和系统的一般行为。为了提高模型的效率,成本和回报都纳入了分析。通过一个数值示例,展示了该模型在实际应用中的灵活性和有效性。
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引用次数: 0
On numerical resolution of shape optimization bi-Laplacian eigenvalue problems 关于形状优化双拉普拉卡特征值问题的数值求解
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-16 DOI: 10.1016/j.matcom.2024.11.007
Abdelkrim Chakib , Ibrahim Khalil , Azeddine Sadik
In this paper, we deal with the numerical resolution of some shape optimization models for the volume-constrained buckling and clamped plate bi-Laplacian eigenvalues problems. We propose a numerical method using the Lagrangian functional, Hadamard’s shape derivative and the gradient method combined with the finite elements discretization, to determine the minimizers for the first ten eigenvalues for both problems. We investigate also numerically the maximization of some quotient functionals, which allows us to obtain the optimal possible upper bounds of these spectral quotient problems and establish numerically some conjectures. Numerical examples and illustrations are provided for different and various cost functionals. The obtained numerical results show the efficiency and practical suitability of the proposed approaches.
本文涉及体积受限屈曲和夹紧板双拉普拉卡特征值问题的一些形状优化模型的数值解析。我们提出了一种使用拉格朗日函数、哈达玛形状导数和梯度法结合有限元离散化的数值方法,以确定这两个问题前十个特征值的最小值。我们还对一些商函数的最大化进行了数值研究,从而获得了这些谱商问题的最佳可能上限,并在数值上建立了一些猜想。我们针对不同的成本函数提供了数值示例和说明。所获得的数值结果表明了所提出方法的效率和实用性。
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引用次数: 0
Finite-time synchronization analysis for the generalized Caputo fractional spatio-temporal neural networks 广义卡普托分数时空神经网络的有限时间同步分析
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-13 DOI: 10.1016/j.matcom.2024.11.006
Xianghu Liu, Yanfang Li, Guangjun Xu
This paper is concerned with finite-time synchronization analysis for the generalized Caputo fractional spatio-temporal neural networks with time delay(GCFSTNN). The generalized Caputo type fractional derivative are defined, two novel generalized Caputo fractional differential inequalities are proved. Meanwhile, some control strategies are designed to get the finite-time synchronization results. Finally, numerical examples and simulation results are showed to demonstrate validation of finite-time synchronization conditions.
本文关注带时延的广义卡普托分数时空神经网络(GCFSTNN)的有限时间同步分析。定义了广义卡普托分数导数,证明了两个新的广义卡普托分数微分不等式。同时,设计了一些控制策略以获得有限时间同步结果。最后,展示了数值示例和仿真结果,以证明有限时间同步条件的有效性。
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引用次数: 0
A perception-guided CNN for grape bunch detection 用于葡萄串检测的感知引导型 CNN
IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-12 DOI: 10.1016/j.matcom.2024.11.004
Vittoria Bruni , Giulia Dominijanni , Domenico Vitulano , Giuliana Ramella
Precision Viticulture (PV) is becoming an active and interdisciplinary research field since it requires solving interesting research issues to concretely answer the demands of specific use cases. A challenging problem in this context is the development of automatic methods for yield estimation. Computer vision methods can contribute to the accomplishment of this task, especially those that can replicate what winemakers do manually. In this paper, an automatic artificial intelligence method for grape bunch detection from RGB images is presented. A customized Convolutional Neural Network (CNN) is employed for pointwise classification of image pixels and the dependence of classification results on the type of input color channels and grapes color properties are studied. The advantage of using additional perception-based input features, such as luminance and visual contrast, is also evaluated, as well as the dependence of the method on the choice of the training set in terms of the amount of labeled data. The latter point has a significant impact on the practical use of the method on-site, its usability by non-expert users, and its adaptability to individual vineyards. Experimental results show that a properly trained CNN can discriminate and detect grape bunches even under uncontrolled acquisition conditions and with limited computational load, making the proposed method implementable on smart devices and suitable for on-site and real-time applications.
精准葡萄栽培(PV)正在成为一个活跃的跨学科研究领域,因为它需要解决一些有趣的研究问题,以具体满足特定用途的需求。在此背景下,一个具有挑战性的问题是开发产量估算的自动方法。计算机视觉方法可以帮助完成这项任务,尤其是那些可以复制酿酒师手工操作的方法。本文介绍了一种从 RGB 图像中自动检测葡萄串的人工智能方法。采用定制的卷积神经网络(CNN)对图像像素进行点分类,并研究了分类结果对输入颜色通道类型和葡萄颜色属性的依赖性。此外,还评估了使用其他基于感知的输入特征(如亮度和视觉对比度)的优势,以及该方法在标记数据量方面对训练集选择的依赖性。后一点对该方法的现场实际使用、非专业用户的可用性以及对各个葡萄园的适应性都有重大影响。实验结果表明,即使在不受控的采集条件下,经过适当训练的 CNN 也能在有限的计算负荷下分辨和检测葡萄串,这使得所提出的方法可以在智能设备上实现,并适用于现场和实时应用。
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引用次数: 0
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Mathematics and Computers in Simulation
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