The suitability of the approximation criterion on the first output from the area comparison for distribution probability density of fluctuations of the harmonic signal in gaussian random noise

2016 ◽  
Author(s):  
N. A. Vostretsov ◽  
A. F. Zhukov
Keyword(s):  
Probability Density ◽  
Random Noise ◽  
Harmonic Signal ◽  
Distribution Probability ◽  
Approximation Criterion

scholarly journals A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems

2011 ◽  
Vol 468 (2139) ◽  
pp. 759-783 ◽  
Author(s):  
D. Venturi ◽  
T. P. Sapsis ◽  
H. Cho ◽  
G. E. Karniadakis
Keyword(s):  
Probability Density Function ◽  
Evolution Equation ◽  
Probability Density ◽  
Density Function ◽  
Random Noise ◽  
Functional Integral ◽  
Excitation Density ◽  
Numerical Verification ◽  
Markovian Systems ◽  
Excitation Probability

By using functional integral methods, we determine a computable evolution equation for the joint response-excitation probability density function of a stochastic dynamical system driven by coloured noise. This equation can be represented in terms of a superimposition of differential constraints, i.e. partial differential equations involving unusual limit partial derivatives, the first one of which was originally proposed by Sapsis & Athanassoulis. A connection with the classical response approach is established in the general case of random noise with arbitrary correlation time, yielding a fully consistent new theory for non-Markovian systems. We also address the question of computability of the joint response-excitation probability density function as a solution to a boundary value problem involving only one differential constraint. By means of a simple analytical example, it is shown that, in general, such a problem is undetermined, in the sense that it admits an infinite number of solutions. This issue can be overcome by completing the system with additional relations yielding a closure problem, which is similar to the one arising in the standard response theory. Numerical verification of the equations for the joint response-excitation density is obtained for a tumour cell growth model under immune response.

Conditional sampling and other measurements in a plane turbulent wake

1973 ◽  
Vol 57 (3) ◽  
pp. 549-582 ◽  
Author(s):  
R. M. Thomas
Keyword(s):  
Probability Density ◽  
Random Noise ◽  
Longitudinal Velocity ◽  
Time Derivative ◽  
Longitudinal Component ◽  
Longitudinal Velocity Component ◽  
Mean Velocity ◽  
Instantaneous Position ◽  
Probability Densities ◽  
Intermittency Factor

A series of hot-wire measurements has been carried out in a plane wake to investigate the structure of the turbulence boundary and the relation of its instantaneous position to the behaviour in the core of the flow. The principal measured quantities are as follows: mean velocity profile; intermittency factor; burst rate; mean of the longitudinal component of velocity conditioned upon various specified interface positions; autocorrelation of the intermittency signal; probability densities a t the half-intermittency point for the time between bursts and the duration of a burst; probability density for the longitudinal velocity component and its time derivative at various points across the wake; probability density a t the half-intermittency point for the same quantities in the turbulent and irrotational zones separately. In addition, the profile of the second moment of the probability density for the time between bursts has been obtained indirectly and part of the theory of Phillips (1955) has been shown to be applicable in the intermittent region.The present measurements appear to indicate that the turbulence boundary in the wake resembles that in other plane flows more closely than has been supposed hitherto. The theory of normally distributed random noise was found to explain many of the observed statistical properties of the turbulence boundary.

The Movement Planning of Mobile Robots in Performing Search Task Based on Probability Theory

2019 ◽  
Vol 20 (9) ◽  
pp. 560-567
Author(s):  
S. L. Zenkevich ◽  
А. V. Nazarova ◽  
Meixin Zhai
Keyword(s):  
Probability Density ◽  
Target Detection ◽  
Continuous Distribution ◽  
Search Time ◽  
Target Position ◽  
Movement Planning ◽  
Probability Density Distribution ◽  
Optimal Distribution ◽  
Search Area ◽  
Distribution Probability

The article is devoted to the development of searching and covering task in different areas, for example, for extinguishing fires, during search operations in the air, on the ground, etc. Two probabilistic models were created based on the characteristics of the sensors and the search zone, that is, the probability density of the target position and the conditional probability of detecting the target by the sensor under the conditions that the target is at the point of observation (depending on the distance between the sensor and the point of observation). Based on these models, the parameters and the search procedure were analyzed; more precisely, the relationship and formulas between the target detection probability, the search time and other parameters were found. The main difference of the proposed research lies in the fact that by optimizing the obtained relations and formulas it is possible to obtain an optimal distribution of time in the search process, as a result, to increase the probability of target detection. In the research process, at first, the case where the distribution probability of target position in the search area represents a discrete form (network map) is investigated, then a formula for the probability of target detection in a discrete and continuous probe is obtained. Using the method of Lagrange multipliers and dynamic programming, the optimal distribution of search time in each cell was obtained. Further, according to the result obtained, the study was expanded to a continuous distribution probability of target position in the search area, the functional probability of detecting the target of search time, probability density of target and the search trajectory (velocity) was derivated. As a result of solving this functional, for a given search time and probability density distribution of target, optimal control (trajectory and speed) was obtained. The simulation confirmed the efficiency of the proposed search method. The simulation result shows that the greater the probability density of target and the slower the agent’s movement speed, the greater the probability of target detection, for some values of the search parameters, the difference in probabilities of target detection reaches 75.3 %.

Local Similarity in Nonlinear Random Vibration

1999 ◽  
Vol 66 (1) ◽  
pp. 225-235 ◽  
Author(s):  
S. Krenk ◽  
J. B. Roberts
Keyword(s):  
Energy Level ◽  
Spectral Density ◽  
Probability Density ◽  
Phase Plane ◽  
Duffing Oscillator ◽  
Random Noise ◽  
Kolmogorov Equation ◽  
Response Analysis ◽  
Local Similarity ◽  
Highly Nonlinear

A response analysis procedure is developed for oscillators with highly nonlinear stiffness and light nonlinear damping excited by non-white wide-band random noise based on local similarity between the random response and the deterministic response at the same energy level of the corresponding undamped oscillator. The analysis consists of three parts: introduction of modified phase plane variables, derivation of an approximate general form of the probability density of the response energy. for non-white excitation, and derivation of the spectral density function of the response from the conditional covariance function for a given energy level. The use of modified phase plane variables leads to a completely symmetric formulation and reformulates the stiffness nonlinearity as a nonlinear variation of the instantaneous angular frequency, and thereby a local rescaling of time. The probability density is obtained by averaging the full Fokker-Plank-Kolmogorov equation using local similarity, thus avoiding some theoretical problems associated with the traditional averaging of the stochastic differential equations. The use of local similarity with the exact undamped solution in the derivation of the conditional spectral density leads to a spectral density estimate, that contains the higher harmonic components explicitly. Comparisons of theoretical predictions with digital simulation estimates of both the probability and spectral densities for the Duffing oscillator demonstrate the accuracy of the theory.

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