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Adaptive self-triggered control for nonhomogeneous semi-Markov jump systems under finite-time interval

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2025年第4期239卷 592-603页

作者： Wang, Yifan Qi, Wenhai Cheng, Jun Shi, Kaibo Qufu Normal Univ Sch Engn 80 Yantai Rd Rizhao 276826 Peoples R China Guangxi Normal Univ Coll Math & Stat Guilin Peoples R China Chengdu Univ Sch Informat Sci & Engn Chengdu Peoples R China

In this paper, an adaptive self-triggered control is studied for nonhomogeneous semi-Markov jump systems under finite-time interval, which can satisfy the dual purposes of suppressing interference and saving resources. Specifically, an adaptive self-triggered mechanism is proposed different from the traditional self-triggered mechanism, in which the threshold can be adjusted dynamically to reduce interference and obtain better performance. According to the current sampling data, the next executing time is predicted to effectively avoid Zeno behavior. At the same time, the relation expressions are derived among transition probability, probability distribution function, and probability density function. Taking the transient performance into account, sufficient conditions are proposed for finite-time boundedness of the underlying nonhomogeneous semi-Markov jump systems. In order to save communication resource, the triggered mechanism and the finite-time controller are co-designed. Finally, a physical mass-spring-damper mechanical system is given to verify the effectiveness of the design method.

关键词： Adaptive self-triggered control probability distribution function Zeno behavior finite-time controller

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Wind energy feasibility and wind turbine selection studies for the city Surat,India

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Clean Energy 2024年第3期8卷 166-173页

作者： Arshi Banu P S Maanat Bhadani Hindustan Institute of Technology and Science ChennaiIndia The Doon School UttarakhandDehradunIndia

Wind energy represents a clean,abundant and cost-effective power source,fostering job growth and environmental *** wind energy harnesses several gigawatts today,its availability hinges on diverse factors,with geographical location standing *** turbines,with varying capacity ranges,saturate the *** site-specific suitability and matching the appropriate turbine to meet specific requirements are of paramount *** study aims to assess the feasibility of wind energy in Surat,Gujarat,India and select an optimal small commercial turbine for residential *** research involves Rayleigh and Weibull probability distribution functions based on yearlong velocity *** distributions are fitted with actual data,revealing the most probable velocity(v_(mf)=3 m/s)and velocity at maximum power(v_(pmax)=5 m/s).The power availability of the site has been assessed as 42.6 W/m^(2)using both graphical and analytical *** commercial turbines have been shortlisted based on on-site power criteria and their specifications are evaluated against site power availability.A comparative analysis culminates in identifying the most suitable turbine for the *** best suitable turbine for the site with an annual energy yield of 8 MW has been suggested amongst selected turbines for small-scale residential applications.

关键词： site feasibility wind energy commercial wind turbine probability distribution function rated power

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Study of several probability distribution functions for the Klein-Kramers equation

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MODERN PHYSICS LETTERS B 2024年第24期38卷

作者： Li, Yaxi Kai, Yue Shanghai Univ Engn Sci Ctr Intelligent Comp & Appl Stat Sch Math Phys & Stat Shanghai 201620 Peoples R China

In this paper, we take variable separation method to study Klein-Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy-Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.

关键词： Klein-Kramers equation probability distribution function dynamic properties variable separation method

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Cluster Optimization for Exponential, Right-Triangular, and Uniformly Distributed Data

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IEEE ACCESS 2025年 13卷 36273-36284页

作者： Bulivou, Gabiriele Reddy, Karuna G. Khan, M. G. M. Univ South Pacific Sch Informat Technol Engn Math & Phys Suva Fiji

Cluster analysis aims to categorize data objects into cohesive groups based on their intrinsic characteristics, often modeled by probability distributions. This paper presents a novel Mathematical Programming-Dynamic Programming (MP-DP) clustering method developed by the authors, applied to datasets characterized by exponential, right-triangular, and uniform distributions. The MP-DP technique optimizes cluster partitions by leveraging the probability distributions inherent in the data. We conducted a comparative evaluation to assess the performance of MP-DP against four established clustering methodologies: K-Means, Fuzzy C-Means, expectation-maximization, and Genie++ hierarchical clustering. Results from extensive simulations and real-world datasets consistently demonstrate the superior efficacy of MP-DP in achieving optimal clustering outcomes. Specifically, MP-DP excels in handling diverse data distributions and effectively mitigating the effects of noise and uncertainty, thereby enhancing clustering accuracy and reliability. This study highlights the significant advancement offered by MP-DP in clustering research. It underscores the method's potential for applications across various domains, such as healthcare, environmental monitoring, and manufacturing, where robust and efficient data clustering is essential for insightful data analysis and decision-making.

关键词： Clustering algorithms probability distribution Dynamic programming Programming Noise Clustering methods Partitioning algorithms Heuristic algorithms Distributed databases Uncertainty Cluster analysis dynamic programming technique mathematical programming problem optimum cluster partitions probability distribution function

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Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

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Journal of Earth Science 2024年第1期35卷 248-262页

作者： Linfeng Wang Jixu Zhang Wanchun Xia Xiaoming Huang Guojin Tan Key Laboratory of Geological Hazards Mitigation for Mountainous Highway and Waterway Chongqing Jiaotong UniversityChongqing 400074China School of Transportation Southeast UniversityNanjing 211189China College of Transportation Jilin UniversityChangchun 130012China

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is ***,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion ***,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is ***,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is *** calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical *** the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.

关键词： toppling perilous rock bidirectional earthquake fuzzy failure criterion dynamic stability fuzzy reliability Newmark-βmethod probability distribution function

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Probabilistic cellular automata simulation of microstructure evolution: the role of model parameters on precision and uncertainty

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MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 2025年第1期33卷

作者： Seyed-Salehi, Majid K N Toosi Univ Technol Fac Mat Sci & Engn Tehran *** Iran

Probabilistic cellular automata (PCA) is a widely used and cost-efficient method for simulating microstructural evolution. In this method, probabilistic state change rules determine the evolution of cell states at each time step. However, its stochastic nature introduces inherent uncertainty, leading to non-repeatable results. Most microstructural simulation studies assess the accuracy of simulations by comparing predicted results with experimental observations, neglecting uncertainties in mathematical models and algorithms. In this study, the precision and stochastic behavior of microstructure evolution in the PCA simulations were investigated. The probabilities of transformations of cell states at each time step were formulated, and discrete probability distribution functions (dPDF) were introduced to analyze the frequency distribution of simulation outcomes. The performance and consistency of these dPDFs were assessed by comparing statistical analyzes of PCA simulation results with dPDF predictions, revealing that the variance of simulation results is less than that of the binomial distribution function. Additionally, the effects of modeling parameters, such as model size, cellular resolution, and probability distribution of state changes in two- and three-dimensional PCA modeling, on the precision and reliability of simulation results were studied. In PCA models, simulation uncertainty inversely relates to the square root of model size. Furthermore, in 2D simulations, uncertainty is inversely proportional to the square root of the cellular resolution, while in 3D simulations, it is inversely proportional to the cellular resolution itself. These findings provide a simple and computationally efficient method for evaluating PCA simulation uncertainty and determining optimal simulation parameters, including model size, cellular resolution, and dimensionality.

关键词： probabilistic cellular automata probability distribution function uncertainty assessment microstructure evolution

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Nonlinear probabilistic modeling of incipient fault in underground cables

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ELECTRIC POWER SYSTEMS RESEARCH 2025年 241卷

作者： Hosseini, Zahra Samet, Haidar Ghanbari, Teymoor Shiraz Univ Sch Elect & Comp Engn Dept Power & Control Shiraz Iran Eindhoven Univ Technol Dept Elect Engn Eindhoven Netherlands Shiraz Univ Sch Adv Technol Shiraz Iran

The incipient fault in underground cables is a well-known fault that occurs because of cable insulation failure and water penetration. For assessment of the suggested detection methods for such a fault, one could use practical data from the real field or a suitable model for the generation of data in different conditions. This paper presents a model for incipient faults in underground cables, by which the required data close to the real records can be provided. Although there are various arc models for different arc types, there is no specific model for incipient faults in underground cables. Eight models based on polynomial functions are proposed here for incipient fault modeling. Actual records based on a laboratory setup are used in the models' identification process. The proposed models are nonlinear and dynamic, in which the model parameters are changed every half cycle based on some probability functions. The optimal model orders are attained for the proposed models. For every model parameter, several probability distribution functions (PDFs) are tested and the most fitted one with the actual data is chosen.

关键词： Incipient fault Polynomial arc model probability distribution function Underground cable

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Evaluation of probability distribution functions applied to tree diameter in a mixed uneven Kiker (Robinia pseudoacacia) stand of Kashmir Himalaya, India

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CURRENT SCIENCE 2021年第4期121卷 573-577页

作者： Masoodi, Tariq H. Shah, Immad A. Dar, Meraj U. Din Sofi, Parvez A. Mugloo, Javeed A. Sher E Kashmir Univ Agr Sci & Technol Kashmir SKU Fac Forestry Benhama 191202 India SKUAST K Div Silviculture & Agroforestry Ganderbal 191201 India

probability distribution is of significance to predict tree distribution and estimate productivity in different ages as well as thinning out in forest stands to ensure optimized and stable stands. Statistical probability distributions, viz. lognormal, Weibull, exponential and gamma were used to fit tree-diameter data generated from the Manasbal forest stand of Kashmir Himalaya, India containing a heterogeneous population of trees with the objective to determine the best probability distribution of tree diameter. To estimate the parameters of the fitted distributions, the method of maximum likelihood was used. The various distributions were evaluated using different goodness-of-fit tests, viz. Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling statistics, and the best distribution pertaining to the forest stand was ascertained. Lognormal distribution fitted the data well and could be used in modelling, planning and scheduling the forest stand in the study region.

关键词： Diameter class goodness-of-fit statistics forest stands probability distribution function Robinia pseudoacacia

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Simulation of the fiber orientation through a finite element approach to solve the Fokker-Planck equation

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JOURNAL OF NON-NEWTONIAN FLUID MECHANICS 2024年 331卷

作者： Al Ayoubi, Nazih Assaad Digonnet, Hugues Silva, Luisa Binetruy, Christophe Renault, Thierry Comas-Cardona, Sebastien Nantes Univ Inst Rech Genie Civil & Mecan GeM CNRS Ecole Cent NantesUMR 6183 1 Rue Noe F-44321 Nantes France FORVIA 14 Rue Petits Bois F-35400 St Malo France

This work aims to introduce a groundbreaking approach by directly computing the Fokker-Planck equation, providing a mesoscopic scale orientation indicator based on the 2D-probability density function (PDF) of the fibers' orientation state. Unlike conventional methods that rely on pre-averaged quantities and closure approximations, our method offers enhanced accuracy and information preservation. The model's enhanced accuracy can be served as a foundational tool for future studies, enabling the development of comprehensive models describing the fluid-flow coupling problem with precision. Consequently, this advancement facilitates the simulation of real-case scenarios, such as the dynamic motion of fibers during the injection phase of molten thermoplastics within a mold cavity. The novelty of this work lies in its application of the Streamline-Upwind/Petrov-Galerkin (SUPG) finite element method, on both orientation and physical spaces. Our model shows the potential to improve the understanding and prediction of fiber behavior in industrial applications, offering valuable insights into process optimization and design. Implemented within a finite element framework, a comprehensive investigation is conducted into the effects of mesh refinement, time scheme, and time stepping on the computational modeling of the PDF evolution, aiming to strike an optimal balance between model precision and computational efficiency. The validation tests were conducted for the case of simple shear flow to examine the influence of the interaction coefficient C-I and the fiber shape factor lambda on the resolution of the probability distribution function. The numerical results demonstrate the evolution of fiber orientation over time under Poiseuille flow conditions.

关键词： Fiber orientation probability distribution function Fokker-Planck equation Finite element method Numerical modeling

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On the continuous probability distribution attribute weight of belief rule base model

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JOURNAL OF SUPERCOMPUTING 2024年第16期80卷 23225-23270页

作者： Zhang, Yunyi Huang, Hongbin Du, Ye He, Wei Beijing Jiaotong Univ Beijing Key Lab Secur & Privacy Intelligent Transp Beijing 100000 Peoples R China Beijing Jiaotong Univ Beijing Lab Natl Econ Secur Early Warning Engn Beijing 100000 Peoples R China Harbin Normal Univ Harbin 150025 Peoples R China

In current researches on belief rule base (BRB), input parameters are tended to be expressed in the form of quantitative values through expert knowledge combined with optimization methods. A singular quantitative value fails to capture the statistical properties, leading to irrational outcomes. Therefore, an attempt on attribute weights is made in this paper, and a new model with probability distribution attribute weights (pdw) called BRB-pdw is proposed. The combination of two attributes is in detail discussed, where attribute weights are described as random variables with specific probability distribution. To characterize the output of probability distribution attribute weight, a new concept of expectation of activation weight is proposed. In addition, the BRB-pdw is extended to multiple attributes to demonstrate its universality. Furthermore, fundamental properties and characteristics of the BRB-pdw are further validated by rigorous mathematical derivation. Finally, practicability of the BRB-pdw is validated with NASA lithium battery open dataset, and experiments show that the BRB-pdw model is more robust while maintaining precision.

关键词： Belief rule base (BRB) Attribute weight Random variable probability distribution function probability inference

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