Generalized probability density function and applications to the experimental data in electrical circuits and systems

2020 ◽  
Vol 48 (12) ◽  
pp. 2266-2279
Author(s):  
Ali Özyapıcı ◽  
Bülent Bilgehan ◽  
Zehra B. Şensoy
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Electrical Circuits ◽  
Generalized Probability

Microstructural Constitutive Equation for Sprain Analysis

2008 ◽  
Author(s):  
Zheying Guo ◽  
Raffaella De Vita
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Constitutive Equation ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Damage Evolution ◽  
Linear Elastic ◽  
Proposed Model ◽  
Collagenous Tissues

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

scholarly journals Providing a New Approach for Modeling and Parameter Estimation of Probability Density Function of Noise in Digital Images

2015 ◽  
Vol 37 ◽  
pp. 182
Author(s):  
Hanif Yaghoobi ◽  
Keivan Maghooli ◽  
Alireza Ghahramani Barandagh
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Digital Images ◽  
Image Sensors ◽  
Arrival Process ◽  
Mean And Variance ◽  
Two Parameters ◽  
Generalized Probability

The main part of the noise in digital images arises when taking pictures or transmission. There is noise in the imagescaptured by the image sensors of the real world. Noise, based on its causes can have different probability density functions.For example, such a model is called the Poisson distribution function of the random nature of photon arrival process that isconsistent with the distribution of pixel values measured. The parameters of the noise probability density function (PDF)can be achieved to some extent the properties of the sensor. But, we need to estimate the parameters for imaging settings. Ifwe assume that the PDF of noise is approximately Gaussian, then we need only to estimate the mean and variance becausethe Gaussian PDF with only two parameters is determined. In fact, in many cases, PDF of noise is not Gaussian and it hasunknown distribution. In this study, we introduce a generalized probability density function for modeling noise in imagesand propose a method to estimate its parameters. Because the generalized probability density function has multipleparameters, so use common parameter estimation techniques such as derivative method to maximize the likelihood functionwould be extremely difficult. In this study, we propose the use of evolutionary algorithms for global optimization. Theresults show that this method accurately estimates the probability density function parameters.

A Detailed Validation Study of Multi-Environment Eulerian Probability Density Function Transport Method for Modeling Turbulent Nonpremixed Combustion

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Rakesh Yadav ◽  
Abhijit Kushari ◽  
Vinayak Eswaran ◽  
Atul K. Verma
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Current Model ◽  
Combined Effect ◽  
Current Work ◽  
Nonpremixed Combustion ◽  
Turbulent Nonpremixed ◽  
Transport Method

The current work involves the validation of presumed shape multi-environment Eulerian probability density function (PDF) transport method (MEPDF) using direct quadrature method of moments (DQMOM)-interaction by exchange with mean (IEM) approach for modeling turbulence chemistry interactions in nonpremixed combustion problems. The joint composition PDF is represented as a collection of finite number of Delta functions. The PDF shape is resolved by solving the governing transport equations for probability of occurrence of each environment and probability-weighted mass fraction of species and enthalpy in Eulerian frame for each environment. A generic implementation of the MEPDF approach is carried out for an arbitrary number of environments. In the current work, the MEPDF approach is used for a series of problems to validate each component of MEPDF approach in an isolated manner as well as their combined effect. First of all, a nonreactive turbulent mixing problem with two different Reynolds numbers (Re = 7000 and 11,900) is used for validation of the mixing and correction terms appear in the MEPDF approach. The second problem studied is a diffusion flame with infinitely fast chemistry having an analytical solution. The reaction component is validated by considering a 1D premixed laminar flame. In order to validate the combined effect of mixing and turbulence chemistry interactions, two different turbulent nonpremixed problems using global one-step chemistry are used. The first reactive problem used is H2 combustion (DLR Flame H3), while the second reactive validation case is a pilot-stabilized CH4 flame. The current predictions for all validation problems are compared with experimental data or published results. The study is further extended by modeling a turbulent nonpremixed H2 combustion using finite-rate chemistry effects and radiative heat transfer. The current model predictions for different flame lengths as well as minor species are compared with experimental data. The current model gave excellent predictions of minor species like OH. The differences in the current predictions with experimental data are discussed.

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