Study on Vibration Characteristic Evaluation of Nonlinear Vibration System with Gaps by Transition Probability Density Function

2004 ◽  
Vol 2004.41 (0) ◽  
pp. 209-210
Author(s):  
Masanori SHINTANI ◽  
Hiroyuki IKUTA ◽  
Hajime TAKADA ◽  
Tadashi KOTERA ◽  
Fumiyasu NISHIKAWA
Keyword(s):  
Probability Density Function ◽  
Nonlinear Vibration ◽  
Probability Density ◽  
Density Function ◽  
Transition Probability ◽  
Vibration Characteristic ◽  
Vibration System ◽  
Transition Probability Density ◽  
Nonlinear Vibration System

Study on Nonlinear Vibration Characteristic Evaluation of Nonlinear Vibration System With Gaps by Transition Probability Density Function

2004 ◽  
Author(s):  
Masanori Shintani ◽  
Hiroyuki Ikuta ◽  
Hajime Takada
Keyword(s):  
Probability Density Function ◽  
Nonlinear Vibration ◽  
Probability Density ◽  
Density Function ◽  
Transition Probability ◽  
Probability Density Functions ◽  
Force Characteristic ◽  
Density Functions ◽  
Restoring Force ◽  
Transition Probability Density

In this paper, the transition probability density functions between response velocity and response displacement in nonlinear vibration systems which have the restoring force characteristic of a cubic equation are governed by the Fokker-Planck Equation. The experimental probability density functions are compared with analytical results. The analytical model of the cubic equation as Duffing Equation is proposed by the restoring force characteristic of the nonlinear vibration system with gaps in the experiments. However, a slight difference for the frequency range of the transfer function was shown by simulation results. Then, it is considered using transition probability density functions in the response characteristic. For stationary random input waves, the probability density function between the response displacement and the response velocity are easily estimated by the Fokker-Planck Equation and the Duffing Equation. The slight difference of the transfer function of the response acceleration is evaluated by the scattering of the restoring force characteristic estimated by the probability density function and self-natural frequency curve. The R.M.S. value and the transfer function of the experimental results are compared with the analytical results. It is thought that the estimation of the probability density function of the response has validity. It is thought that the evaluation of the nonlinear vibration characteristics by the probability density function is valid.

scholarly journals Numerical simulation of the two-locus Wright-Fisher stochastic differential equation with application to approximating transition probability densities

2020 ◽  
Author(s):  
Zhangyi He ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Differential Equation ◽  
Natural Selection ◽  
Probability Density Function ◽  
Stochastic Differential Equation ◽  
Probability Density ◽  
Density Function ◽  
Genetic Recombination ◽  
Transition Probability ◽  
Superior Performance ◽  
Transition Probability Density

AbstractOver the past decade there has been an increasing focus on the application of the Wright-Fisher diffusion to the inference of natural selection from genetic time series. A key ingredient for modelling the trajectory of gene frequencies through the Wright-Fisher diffusion is its transition probability density function. Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time, which presents opportunities for investigating natural selection while accounting for genetic recombination and local linkage. However, most existing methods for computing the transition probability density function of the Wright-Fisher diffusion are only applicable to one-locus problems. To address two-locus problems, in this work we propose a novel numerical scheme for the Wright-Fisher stochastic differential equation of population dynamics under natural selection at two linked loci. Our key innovation is that we reformulate the stochastic differential equation in a closed form that is amenable to simulation, which enables us to avoid boundary issues and reduce computational costs. We also propose an adaptive importance sampling approach based on the proposal introduced by Fearnhead (2008) for computing the transition probability density of the Wright-Fisher diffusion between any two observed states. We show through extensive simulation studies that our approach can achieve comparable performance to the method of Fearnhead (2008) but can avoid manually tuning the parameter ρ to deliver superior performance for different observed states.

Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation

1983 ◽  
Vol 20 (04) ◽  
pp. 754-765 ◽  
Author(s):  
Etsuo Isobe ◽  
Shunsuke Sato
Keyword(s):  
Differential Equation ◽  
Probability Density Function ◽  
Stochastic Differential Equation ◽  
Probability Density ◽  
Density Function ◽  
Series Expansion ◽  
Transition Probability ◽  
Transition Probability Density ◽  
Hermite Expansion ◽  
Functional Series

In this paper we deal with the Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation. The so-called Wiener kernels which appear in the functional series expansion are expressed in terms of the transition probability density function of the process.

Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation

1983 ◽  
Vol 20 (4) ◽  
pp. 754-765 ◽  
Author(s):  
Etsuo Isobe ◽  
Shunsuke Sato
Keyword(s):  
Differential Equation ◽  
Probability Density Function ◽  
Stochastic Differential Equation ◽  
Probability Density ◽  
Density Function ◽  
Series Expansion ◽  
Transition Probability ◽  
Transition Probability Density ◽  
Hermite Expansion ◽  
Functional Series

In this paper we deal with the Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation. The so-called Wiener kernels which appear in the functional series expansion are expressed in terms of the transition probability density function of the process.

On the Use of the Posterior Crame´r-Rao Lower Bound for Damage Estimation in Structural Health Management

2009 ◽  
Author(s):  
Jun Jason Zhang ◽  
Wenfan Zhou ◽  
Narayan Kovvali ◽  
Antonia Papandreou-Suppappola ◽  
Aditi Chattopadhyay
Keyword(s):  
Probability Density Function ◽  
Lower Bound ◽  
Probability Density ◽  
Density Function ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Transition Probability ◽  
Estimation Error ◽  
Stochastic Dynamic ◽  
Transition Probability Density

The use of the posterior Crame´r-Rao lower bound (PCRLB) as a lower bound for the mean-squared estimation error (MSEE) of progressive damage is investigated. The estimation problem is formulated in terms of a stochastic dynamic system model that describes the random evolution of damage and provides measurement uncertainty. Based on whether the system is linear or nonlinear, sequential Monte Carlo techniques are used to approximate the posterior probability density function and thus obtain the damage state estimate. The resulting MSEE is compared to the lower bound offered by the PCRLB that is obtained from the implied state transition probability density function and the measurement likelihood function. The progressive estimation results and the PCRLB are demonstrated for fatigue crack estimation in an aluminum compact-tension (CT) sample subjected to variable-amplitude loading.

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