scholarly journals On estimation of $$L_{r}$$-norms in Gaussian white noise models

2020 ◽  
Vol 177 (3-4) ◽  
pp. 1243-1294
Author(s):  
Yanjun Han ◽  
Jiantao Jiao ◽  
Rajarshi Mukherjee
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Noise Models

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

Driver Steering Control and a New Perspective on Car Handling Qualities

2005 ◽  
Vol 219 (10) ◽  
pp. 1041-1051 ◽  
Author(s):  
R S Sharp
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Design Parameters ◽  
Steering Wheel ◽  
Steering Control ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Handling Qualities ◽  
Gaussian White Noise Process ◽  
Low Pass

The article is about steering control of cars by drivers, concentrating on following the lateral profile of the roadway, which is presumed visible ahead of the car. It builds on previously published work, in which it was shown how the driver's preview of the roadway can be combined with the linear dynamics of a simple car to yield a problem of discrete-time optimal-linear-control-theory form. In that work, it was shown how an optimal ‘driver’ of a linear car can convert the path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering wheel displacement commands to cause the car to follow the previewed path with an attractive compromise between precision and ease. Recognizing that real roadway excitation is not so rich in high frequencies as white-noise, a low-pass filter is added to the system. The white-noise sample values are filtered before being seen by the driver. Numerical results are used to show that the optimal preview control is unaltered by the inclusion of the low-pass filter, whereas the feedback control is affected diminishingly as the preview increases. Then, using the established theoretical basis, new results are generated to show time-invariant optimal preview controls for cars and drivers with different layouts and priorities. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through simulation. A new performance criterion with handling qualities implications is set up, involving the minimization of the preview distance required. The sensitivities of this distance to variations in the car design parameters are calculated. The influence of additional rear wheel steering is studied from the viewpoint of the preview distance required and the form of the optimal preview gain sequence. Path-following simulations are used to illustrate relatively high-authority and relatively low-authority control strategies, showing manoeuvring well in advance of a turn under appropriate circumstances. The results yield new insights into driver steering control behaviour and vehicle design optimization. The article concludes with a discussion of research in progress aimed at a further improved understanding of how drivers control their vehicles.

STOCHASTIC RESONANCE IN SATURATION NONLINEARITIES BASED ON SIGNAL DETECTION

2008 ◽  
Vol 08 (02) ◽  
pp. L229-L235 ◽  
Author(s):  
LEI ZHANG ◽  
JUN HE ◽  
AIGUO SONG
Keyword(s):  
Signal Detection ◽  
White Noise ◽  
Stochastic Resonance ◽  
Gaussian White Noise ◽  
Detection Performance ◽  
Sinusoidal Signal ◽  
Signal Noise ◽  
Noise Ratio

Recently, it was reported that some saturation nonlinearities could effectively act as noise-aided signal-noise-ratio amplifiers. In the letter we consider the signal detection performance of saturation nonlinearities driven by a sinusoidal signal buried in Gaussian white noise. It is showed that the signal detection statistics still undergo a nonmonotonic evolution as noise is raised. We also particularly show that an improvement of the SNR in terms of the first harmonic does not imply the possibility to improve the signal detection performance through stochastic resonance. The study might also complement other reports about stochastic resonance in saturation nonlinearities.

scholarly journals Wavelet Co-movement Significance Testing with Respect to Gaussian White Noise Background

2018 ◽  
Vol 16 ◽  
pp. 01002
Author(s):  
Jitka Poměnková ◽  
Eva Klejmová ◽  
Tobiáš Malach
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Real Data ◽  
Significance Testing ◽  
Noise Background ◽  
Advantages And Disadvantages ◽  
The United Kingdom ◽  
Long Run ◽  
Short Run ◽  
White Noise Background

The paper deals with significance testing of time series co-movement measured via wavelet analysis, namely via the wavelet cross-spectra. This technique is very popular for its better time resolution compare to other techniques. Such approach put in evidence the existence of both long-run and short-run co-movement. In order to have better predictive power it is suitable to support and validate obtained results via some testing approach. We investigate the test of wavelet power cross-spectrum with respect to the Gaussian white noise background with the use of the Bessel function. Our experiment is performed on real data, i.e. seasonally adjusted quarterly data of gross domestic product of the United Kingdom, Korea and G7 countries. To validate the test results we perform Monte Carlo simulation. We describe the advantages and disadvantages of both approaches and formulate recommendations for its using.

Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise

2018 ◽  
Vol 28 (13) ◽  
pp. 1830043 ◽  
Author(s):  
Meng Su ◽  
Wei Xu ◽  
Guidong Yang
Keyword(s):  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Response Analysis ◽  
State Variables ◽  
Van Der Pol ◽  
Impact System ◽  
The Impact

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

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