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Research on the behavior of fiber orientation probability distribution function in the planar flows

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第4期6卷 257-264页

作者：周锟林建忠 Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University

The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fok- ker-Planck equation was solved numerically to validify the theoretical solutions. The stable orientation and orientation period of fiber were obtained. The results showed that the fiber orientation distribution is dependent on the relative not absolute magnitude of the matrix rate-of-strain of flow. The effect of fiber aspect ratio on the orientation distribution of fiber is insignificant in most conditions except the simple shear case. It was proved that the results for a planar flow could be generalized to the case of 3-D fiber direction vector.

关键词： Fiber suspension flow Orientation distribution probability distribution function

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The choice of droplet size probability distribution function for oil spill modeling is not trivial

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MARINE POLLUTION BULLETIN 2021年 163卷 111920-111920页

作者： Faillettaz, Robin Paris, Claire B. Vaz, Ana C. Perlin, Natalie Aman, Zachary M. Schlueter, Michael Murawski, Steven A. Univ Miami Rosenstiel Sch Marine & Atmospher Sci 4600 Rickenbacker Causeway Miami FL 33149 USA IFREMER STH F-56100 Lorient France Univ Western Australia Sch Mech & Chem Engn Ctr Energy Crawley WA 6009 Australia Hamburg Univ Technol Inst Multiphase Flows Eissendorfer Str 38 D-21073 Hamburg Germany Univ S Florida Coll Marine Sci 140 7th Ave S St Petersburg FL 33701 USA

The droplet size distribution (DSD) formed by gas-saturated oil jets is one of the most important characteristics of the flow to understand and model the fate of uncontrolled deep-sea oil spills. The shape of the DSD, generally modeled as a theoretical lognormal, Rosin-Rammler or non-fundamental distribution function, defines the size and the mass volume range of the droplets. Yet, the fundamental DSD shape has received much less attention than the volume median size (d50) and range of the DSD during ten years of research following the Deepwater Horizon (DWH) blowout. To better understand the importance of the distribution function of the droplet size we compare the oil rising time, surface oil mass, and sedimented and beached masses for different DSDs derived from the DWH literature in idealized and applied conditions, while keeping d50 constant. We highlight substantial differences, showing that the probability distribution function of the DSD for far-field modeling is, regardless of the d50, consequential for oil spill response.

关键词： Droplet size distribution DSD Oil spill Oil spill model Oil model Deepwater Horizon Blowout d50 probability distribution function

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Wind-tunnel experiments of Aeolian sand transport reveal a bimodal probability distribution function for the particle lift-off velocities

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CATENA 2022年 217卷

作者： Jiang, Chan-Wen Parteli, Eric J. R. Dong, Zhi-Bao Zhang, Zheng-Cai Qian, Guang-Qiang Luo, Wan-Yin Lu, Jun-Feng Xiao, Feng-Jun Mei, Fan-Min Shaanxi Normal Univ Sch Geog & Tourism Xian 710000 Peoples R China Weinan Normal Univ Coll Environm & Life Sci Key Lab Ecol & Environm River Wetlands Shaanxi Pr Weinan 714000 Peoples R China Univ Duisburg Essen Fac Phys Lotharstr 1 D-47057 Duisburg Germany Chinese Acad Sci Northwest Inst Ecoenvironm & Resources Lanzhou 730000 Peoples R China Xian Polytech Univ Sch Environm & Chem Engn Xian 710048 Peoples R China

The probability distribution function (PDF) of the lift-off velocities of Aeolian (wind-blown) sand particles - i.e., the velocities with which the particles rebound or are ejected from the bed owing to a granular-bed collision - is an important parameter in models of sediment transport and dust emission. However, in order to reliably describe this distribution function, measurements of the individual particle trajectories near the sand bed during sediment transport are required. Such measurements are challenging due to the high particle concentration near the bed, which makes it difficult to track the dynamics of the particles involved in the lift-off process. Here we seek to overcome this difficulty by applying an experimental method for grain trajectory detection, which allows us to obtain a large number of near-bed lift-off particle trajectories during sand transport in a boundary layer wind tunnel. The PDFs of horizontal and vertical lift-off velocities all were found to display a bimodal distribution at a height smaller than 1 mm from the bed. The first and second maxima in the distribution curve of horizontal and vertical lift-off velocities occur at around 0.25 and 1.0 ms(-1), and at 0 and 1.0 ms(-1), respectively. Moreover, the first maximum is mainly associated with splashed particles, whereas the second peak is mainly caused by rebound particles. However, the lift-off velocities far from the bed follow a unimodal distribution, in agreement with previous experiments. Our results are providing, thus, unprecedented insights about near-bed transport processes over wind-blown soils, and have implication for modelling granular-bed interactions in Aeolian sand transport and geomorphodynamic models.

关键词： Aeolian saltation Lift-off velocity distribution High-speed photography probability distribution function Impact-entrainment processes

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probability distribution functions of Velocity Fluctuations and Quadrant Analysis on Turbulent Flow Around a Horizontal Cylinder Across a Channel Bed

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WATER 2025年第7期17卷 958-958页

作者： Kumar, Sandeep Kumar, Bimlesh Pu, Jaan H. Hanmaiahgari, Prashanth Reddy Indian Inst Technol Dept Civil Engn Kharagpur 721302 India Indian Inst Technol Guwahati Dept Civil Engn Gauhati 781039 India Univ Bradford Fac Engn & Digital Technol Bradford BD7 1DP England

An experiment is conducted to investigate the turbulent flow field close to a wall-fastened horizontal cylinder. The evolution of the flow field is analyzed by evaluating turbulent flow characteristics and fluid dynamics along the lengthwise direction. The approach flow velocity retards in the immediate upstream area of the cylinder. At the crest level of the cylindrical pipe, the turbulence characteristics such as Reynolds stresses and turbulence intensities are attaining their peaks. Gram-Charlier (GC) series-based Hermite polynomials yield probability density functions that better match experimental data than those from Gram-Charlier (GC) series-based exponential distributions, demonstrating the superiority of the Hermite polynomial method. Quadrant analysis reveals that sweeps (Q4) dominate intermediate and free-surface zones, while ejections (Q2) prevail near the bed, both being primary contributors to Reynolds shear stress (RSS). The stress component remains minimal or zero for all events when hole size H >= six. Larger hole sizes (>= five) drastically reduced the stress fraction, approaching zero. The stress fraction was highest near the cylinder, decreasing with distance and eventually plateauing. The study enhances the understanding of flow hydraulics around cylindrical objects in rough-bed natural streams.

关键词： probability distribution function Gram-Charlier Hermite polynomials bursting events turbulence

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A Novel Methodology to Estimate probability Density function of Voltage Sag Duration and Failure Rates on Power distribution Systems

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IEEE ACCESS 2023年 11卷 16863-16874页

作者： Cebrian, Juan C. Giacomini Jr, Jairo Carneiro, Carlos A. Silva, Gabriela B. Morales-Paredes, Helmo K. Sao Paulo State Univ UNESP Inst Sci & Engn BR-18409010 Itapeva SP Brazil Sao Paulo State Univ UNESP Inst Sci & Technol BR-18087180 Sorocaba SP Brazil

Voltage sags and power interruptions are important power quality problems that affect sensitive customers, mainly because they cause annual massive economical losses to the industrial sector as a result of unexpected production process disruptions. In this sense, to propose corrective and preventive measures and improve the power quality of the distribution systems, stochastic methodologies have been proposed in the literature to estimate annual voltage sags and power interruptions. However, these methodologies, generally, use typical cumulative distribution functions of voltage sag duration (PSgD), which may not reflect the real estate of the network under study. To solve this constraint, this paper proposes a novel methodology to estimate a proper PSgD considering information of the distribution network (i.e., topology and coordination schemes of the protection system) and the stochastic behaviors of short-circuits that can affect the distribution system. Moreover, the proposed methodology allows estimating permanent failure rates and average repair time considering known or expected values of reliability indicators. The results show that this proposed methodology is capable to adapt from an initial PSgD curve to another one with fidelity, in order to achieve real values of expected annual power interruptions.

关键词： distribution networks power interruption probability distribution function reliability indicators voltage sag

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Variable Amplitude Loading Strains Data distribution using probability Density function and Power Spectral Density

Variable Amplitude Loading Strains Data Distribution using P...

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8th International Conference on Fracture and Strength of Solids (FEOFS) 2010

作者： Lennie, A. Nopiah, Z. M. Abdullah, S. Baharin, M. N. Nuawi, M. Z. Arifin, A. Univ Kebangsaan Malaysia Fac Engn & Built Environm Ukm Bangi 43600 Selangor Malaysia

ISBN: (纸本)9780878492107

This paper presents a relative study on variable amplitude (VA) strain data distribution using the approach of probability density function (PDF) and power spectral density (PSD). PDF is a technique to identify the probability of the value falling within a particular interval, and a PSD is to measure the power of a signal by converting it from the time domain to the frequency domain. The objective of this study is to observe the applicability of both techniques in detecting the pattern behaviour in terms of energy and probability distribution. For this reason, a set of case study data consist of nonstationary VA pattern with a random behaviour was used. This kind of data was measured by fixing a strain gauge that connected to the strain data acquisition on the lower suspension arm of a mid-sized sedan car. The data was measured for 60 seconds at the sampling rate of 500 Hz, which gave 30,000 discrete points. The distribution of collected data was then calculated and analysed in the form of both PDF and PSD, and they were then compared for further analysis. The findings from this study are expected for determining the pattern behaviour that exists in VA strain signals.

关键词： Energy Variable amplitude loadings probability distribution function Power spectral density

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

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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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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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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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probability distribution functions of succession quotas in the case of Markov dependent trials

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1997年第3期49卷 531-539页

作者： Antzoulakos, DL Philippou, AN UNIV CRETE DEPT ECONRETHIMNON 74100GREECE UNIV PATRAS DEPT MATHPATRAS 26100GREECE

The exact probability distribution functions (pdf's) of the sooner and later waiting time random variables (rv's) for the succession quota problem are derived presently in the case of Markov dependent trials. This is done by means of combinatorial arguments. The probability generating functions (pgf's) of these rv's are then obtained by means of enumerating generating functions (enumerators). Obvious modifications of the proofs provide analogous results for the occurrence of frequency quotas and such a result is established regarding the pdf of a frequency and succession quotas rv. Longest success and failure runs are also considered and their joint cumulative distribution function (cdf) is obtained.

关键词： sooner and later problems frequency quota succession quota Markov dependent trials probability distribution function probability generating function cumulative distribution function binomial expressions longest run enumerator

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