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NASA Technical Reports Server (Ntrs) 20120017458: Representation of probability density functions from Orbit Determination Using the Particle Filter

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2016年

NASA Technical Reports Server (Ntrs) 20120017458: Representation of probability density functions from Orbit Determination Using the Particle Filter by NASA Technical Reports Server (Ntrs); NASA Technical Reports Serv... 详细信息

关键词： (ntrs) 20120017458: carpenter, j. russell covariance density determination estimates filter garrison, james mashiku, alinda k. nasa technical reports server (ntrs) nonlinearity orbit determination principal components analysis probability density functions probability theory statistical analysis

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NASA Technical Reports Server (Ntrs) 19930003211: probability density functions in Turbulent Channel Flow

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2017年

NASA Technical Reports Server (Ntrs) 19930003211: probability density functions in Turbulent Channel Flow by NASA Technical Reports Server (Ntrs); published by

关键词： (ntrs) 19930003211: channel channel flow density derivation dinavahi, surya p. g. dissipation functions kinetic energy nasa technical reports server (ntrs) probability density functions turbulent flow walls

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Single-sample unmixing and parametric end-member modelling of grain-size distributions with transformed probability density functions and their performance comparison using aeolian sediments

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SEDIMENTARY GEOLOGY 2023年第1期445卷

作者： Peng, Jun Wang, Xulong Zhao, Hui Dong, Zhibao Hunan Univ Sci & Technol Sch Earth Sci & Spatial Informat Engn Xiangtan 411201 Peoples R China Chinese Acad Sci Northwest Inst Ecoenvironm & Resources Key Lab Desert & Desertificat Lanzhou 730000 Peoples R China Chinese Acad Sci State Key Lab Loess & Quaternary Geol Inst Earth Environm Xian 710061 Peoples R China Southern Marine Sci & Engn Guangdong Lab Zhuhai 519082 Peoples R China Chinese Acad Sci CAS Ctr Excellence Tibetan Plateau Earth Sci Beijing 100101 Peoples R China Shaanxi Normal Univ Sch Geog & Tourism Xian 710119 Peoples R China

Parametric decomposition techniques including single-sample unmixing and parametric end-member model-ling are routine mathematical methods used for interpreting grain-size distributions. In this study, transformed probability density functions for the Lognormal, Weibull, Skew Normal, and Skewed Generalized Normal distri-butions are derived and efficient open-source numerical programs applying these functions are presented. These new functions contain two free shape parameters characterizing the peak position and magnitude of a unimodal distribution, and they can be more easily initialized and constrained compared to their original counterparts, as the two shape parameters can be estimated directly from the grain-size distribution or its derivatives and can only vary within very narrow intervals. This enables the decomposition to converge to both reproducible/stable and structurally/genetically reasonable solutions. The transformed functions are applied to grain-size distribu-tions of aeolian sediments collected from around the Tengger Desert, using both the single-sample unmixing and parametric end-member modelling methods, and the results of different functions are compared. The implications of the results for parametric decomposition of sediment grain-size distributions using unimodal mathematical distributions are discussed.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Single-sample unmixing Parametric end-member modelling Grain-size distributions probability density functions Structural compositions Aeolian sediments

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Healthy marine diesel engine threshold characterisation with probability density functions and ANNs

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2023年第1期238卷

作者： Castresana, Joseba Gabina, Gorka Quincoces, Inaki Uriondo, Zigor Basque Res & Technol Alliance BRTA AZTI Marine Res Txatxarramendi Ugartea Sukarrieta 48395 Spain Univ Basque Country UPV Deparment Thermal Engn EHU Alameda Urquijo s-n Bilbao 48013 Spain

The condition-based maintenance of marine propulsion systems is attracting increasing interest in safety-related, financial, and environmental terms. Many researchers have studied different marine diesel engine models and fault identification techniques. However, the thresholds between a healthy and a faulty engine have not been thoroughly analysed. Thus, this study aims to determine healthy engine threshold values for multiple parameters of a marine diesel engine. To this end, an operative commercial fishing vessel was considered, and multiple engine performance variables were measured through 2020 and the first half of 2021, totalling 5181 operating hours of the main engine without any fault occurrence. Preliminary correlation and relative deviation studies suggested the analysis of some constant trend parameters with alternative modelling techniques. Hence, probability density functions (PDFs) were used to establish confidence intervals for such parameters with data from the entire year of 2020. The parameters with the highest correlation and deviation were alternatively modelled using artificial neural networks (ANNs). Four different ANNs were trained, validated, and tested with data from 2020, calculating the mean absolute percentage errors for all the predicted parameters. Finally, data from 2021 were used to validate both the PDF and ANN modelled parameter thresholds set in 2020. For the 2021 data, the confidence interval set with the PDF showed a maximum failure rate of 1.21%. Alternatively, the ANN model parameters exhibited maximum percentage errors of 1.1%, 1.22%, and 1.95% for the engine performance, cooling, and cylinder subsystems, respectively. Finally, all the obtained thresholds were summarised, providing a good source for establishing faulty engine threshold values in future fault detection studies.

关键词： Artificial neural networks probability density functions Diesel engine modelling Ship propulsion characterisation Threshold characterisation Onboard model validation

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A Formalism for Expressing the probability density functions of Interrelated Quantities

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MEASUREMENT SCIENCE REVIEW 2013年第2期13卷 50-55页

作者： Lira, I. Grientschnig, D. Pontificia Univ Catolica Chile Dept Mech Engn Santiago Chile Boehler Edelstahl Chem Labs A-8605 Kapfenberg Austria

In this paper we address measurement problems involving several quantities that are interrelated by model equations. Available knowledge about some of these quantities is represented by probability density functions (PDFs), which are then propagated through the model in order to obtain the PDFs attributed to the quantities for which nothing is initially known. A formalism for analyzing such models is presented. It comprises the concept of a, "base parameterization", which is used in conjunction with the change-of-variables theorem. The calculation procedure that results from this formalism is described in very general terms. Guidance is given on how to employ it in practice by presenting both an elementary example and a much more involved one.

关键词： probability density functions change of variables parameterizations Bayesian statistics

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Expected Cost Optimization using Asymmetric probability density functions

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IFAC Proceedings Volumes 2009年第11期42卷 744-749页

作者： Bertrand Pigeon Michel Perrier Bala Srinivasan NSERC Environmental Design Engineering Chair in Process Integration Department of Chemical Engineering école Polytechnique de Montréal C.P. 6079 Succ. Centre Ville Montréal Québec Canada H3C 3A7

Abstract In the stochastic context, expected value of the cost function is optimized either by changing the mean values of the manipulated variables or by reducing their variance. An extension is to look for an optimal shape for the entire probability density function (PDF). Though the use of asymmetric PDFs is proposed in the literature, no formal proof that justifies their use has been provided. In this paper, it is shown that an asymmetric PDF is required if and only if the cost function is asymmetric and the manipulated variable is penalised. The proof uses an analytical solution of the Fokker-Planck-Kolmogorov equation derived to calculate the shape the output PDF for scalar systems. In particular, this analytical solution is adapted to a switching proportional controller. The theoretical concepts are illustrated on a simulation example, where the advantage of choosing an asymmetric PDF is shown.

关键词： Stochastic control Optimization probability density functions Switching Algorithms

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SU-GG-T-113: Using probability density functions of Respiratory Motion to Model Motion Effects On Dose Distributions and Optimize Treatment Planning for Lung Cancers

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Medical Physics 2008年第6PART10期35卷 2751-2752页

作者： J Jin M Ajlouni F Kong S Ryu I Chetty B Movsas Henry Ford Health System Detroit MI University of Michigan Ann Arbor MI

Purpose: Respiratory motion is an important factor potentially contributing to excessive normal tissue irradiation in radiotherapy of lung cancers. This study uses the motion probability density function (PDF) to model the motion effects on dose distributions and incorporates this information to optimize treatment planning for lung cancers. Method and Materials: PDFs were calculated from the respiratory motion signals of 10 representative patients. Motion effects were evaluated by convolving static dose distributions with various PDFs. Based on a differential dose prescription with relative lower dose to the clinical target volume (CTV) than to the gross tumor volume (GTV), two strategies were proposed to incorporate PDFs into optimization of treatment planning. The first strategy used the GTV-based-ITV to ensure full dose to the GTV, and utilized the motion induced dose gradient to cover the CTV. The second strategy was to find an intensity-modulated static dose distribution to best match the prescription dose gradient. Results: Motion effect on dose distributions was minimal in the axial direction. A 10-mm motion amplitude induced a 3% dose reduction in the peripheral zone of the target. The motion effect was remarkable in the cranial-caudal direction. It varied with the motion amplitude, but tended to be similar for various respiratory patterns. We found that the motion-induced gradients resulting from motion with amplitudes of 10–15 mm would adequately cover the CTV (60–70% of the GTV dose). For motions <10 mm, motion-induced gradients were much larger and a planning CTV margin was needed to sufficiently cover the CTV. For motions > 15 mm, an intensity modulated static dose distribution was generated to decrease the dose to the normal tissue beyond the CTV without compromising the GTV coverage. Conclusion: The effect of respiratory motion on dose gradients can be utilized to individualize treatment planning and minimize the lung dose.

关键词： Dosimetry probability density functions Lungs Cancer Medical treatment planning Biomedical modeling Tissues Radiation therapy

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A new possibilistic-based clustering method for probability density functions and its application to detecting abnormal elements

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SCIENTIFIC REPORTS 2024年第1期14卷 1-15页

作者： Tran-Nam, Hung Nguyen-Trang, Thao Che-Ngoc, Ha Lang Univ Inst Computat Sci & Artificial Intelligence Lab Appl & Ind Math Ho Chi Minh City Vietnam Lang Univ Fac Fundamental Sci Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Math & Stat Appl Anal Res Grp Ho Chi Minh City Vietnam

Cluster analysis can also detect abnormalities besides building a basis for identifying elements into clusters. Detecting abnormalities is a highly developed feature in the field of unsupervised learning. However, existing studies have mainly focused on discrete data, not probability density functions. This paper enables a possibilistic approach to solving the clustering for probability density functions dealing with abnormal elements. First, the data are extracted using the density function. Then, they are passed through the proposed algorithm to produce a possibilistic partition. Finally, a decision rule is established to recognize which function is abnormal. We compare the proposed algorithm with baseline algorithms in clustering PDFs, such as k-means, FCF, and Self-Updated Clustering. The results of three numerical examples applied to the image are typical for this new method. Furthermore, The proposed algorithm reaches accuracy at 100% over simulated benchmark data and outperforms baseline methods. Additionally, two last examples apply to image data reaching G-mean up from 96 to 100% (Sensitivity: 92-100% and Specificity: 100%). The proposed method can be researched and used to understand the internal structures of big data in the digital age through the probability density functions.

关键词： Detecting abnormal Image extraction Possibilistic clustering probability density functions Unsupervised learning

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Control of the Output probability density functions for a Class of Nonlinear Stochastic Systems

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IFAC Proceedings Volumes 1998年第4期31卷 95-99页

作者： Hong Wang Department of Paper Science UMIST Manchester M60 1QD U. K

Following the recent developments on the modelling and control of the output probability density functions for linear stochastic systems (Wang, 1997, 1998), this paper presents an extented solution to the control of the probability density function for the output of a class of nonlinear stochastic systems. This is based on the fact that there exist many control systems where the requirements are set to control the shape of the probability density function of the system output, rather than the actual values of the system output. At first, the representation of dynamic model is discussed. This is then followed by the construction of a nonlinear control algorithm. An application to a papermaking process has been made and desired results have been obtained.

关键词： Nonlinear systems neural networks probability density functions stochastic systems control

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MOMENT EXPANSION REPRESENTATION OF probability density-functions

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AMERICAN JOURNAL OF PHYSICS 1981年第6期49卷 552-555页

作者： GILLESPIE, DT Research Department Naval Weapons Center China Lake California 93555

A discussion is given of a formal way of representing probability density functions in terms of their central moments and the derivatives of the Dirac delta function. This generalized function representation is then used (a) to obtain an expression giving the value of density function at any point and (b) to exhibit an alternative way of deriving the Kramers–Moyal expansion from the Smoluchowski equation.

关键词： Dirac equation probability density functions

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