scholarly journals Weighted Measurement Fusion White Noise Deconvolution Filter with Correlated Noise for Multisensor Stochastic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xin Wang ◽  
Shu-Li Sun ◽  
Kai-Hui Ding ◽  
Jing-Yan Xue
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Gaussian White Noise ◽  
Minimum Variance ◽  
Seismic Exploration ◽  
Global Optimality ◽  
Correlated Noise ◽  
Noise Input ◽  
Time Invariant ◽  
Correlated Noises

For the multisensor linear discrete time-invariant stochastic control systems with different measurement matrices and correlated noises, the centralized measurement fusion white noise estimators are presented by the linear minimum variance criterion under the condition that noise input matrix is full column rank. They have the expensive computing burden due to the high-dimension extended measurement matrix. To reduce the computing burden, the weighted measurement fusion white noise estimators are presented. It is proved that weighted measurement fusion white noise estimators have the same accuracy as the centralized measurement fusion white noise estimators, so it has global optimality. It can be applied to signal processing in oil seismic exploration. A simulation example for Bernoulli-Gaussian white noise deconvolution filter verifies the effectiveness.

Internal Resonance Energy Harvesting

2015 ◽  
Vol 82 (3) ◽  
Author(s):  
Li-Qun Chen ◽  
Wen-An Jiang
Keyword(s):  
Energy Harvesting ◽  
White Noise ◽  
Frequency Response ◽  
Internal Resonance ◽  
Energy Harvester ◽  
Multiple Scales ◽  
Gaussian White Noise ◽  
Resonance Energy ◽  
Correlated Noise ◽  
Amplitude Frequency Response

Internal resonance is explored as a possible mechanism to enhance vibration-based energy harvesting. An electromagnetic device with snap-through nonlinearity is proposed as an archetype of an internal resonance energy harvester. Based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude–frequency response relationships of the displacement and the power in the first primary resonances with the two-to-one internal resonance. The amplitude–frequency response curves have two peaks bending to the left and the right, respectively. The numerical simulations support the analytical results. Then the averaged power is calculated under the Gaussian white noise, the narrow-band noise, the colored noise defined by a second-order filter, and the exponentially correlated noise. The results demonstrate numerically that the internal resonance design produces more power than other designs under the Gaussian white noise and the exponentially correlated noise. Besides, the internal resonance energy harvester can outperform the linear energy harvesters with the same natural frequencies and in the same size under Gaussian white noise.

Globally Optimal Weighted Fusion White Noise Deconvolution Estimator

2013 ◽  
Vol 823 ◽  
pp. 422-427
Author(s):  
Xiao Jun Sun
Keyword(s):  
White Noise ◽  
Discrete Systems ◽  
Covariance Matrices ◽  
Seismic Exploration ◽  
Global Optimality ◽  
Communication Signal ◽  
Weighted Fusion ◽  
Wide Range ◽  
Gaussian Input ◽  
Linear Discrete Systems

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. A globally optimal weighted fusion white noise deconvolution estimator is presented for the multisensor linear discrete systems using the Kalman filtering method. It is derived from the centralized fusion white noise deconvolution estimator so that it is identical to the centralized fuser, i.e. it has the global optimality. Compared with the existing globally suboptimal distributed fusion white noise estimators, the proposed white noise fuser is given based on the local Kalman predictors, and the computation of complex covariance matrices is avoided. A simulation for the Bernoulli-Gaussian input white noise shows the effectiveness of the proposed results.

Stochastic transitions in the Schlögl reaction model with nonextensive statistical noise and Gaussian white noise

2018 ◽  
Vol 32 (31) ◽  
pp. 1850349
Author(s):  
Peirong Guo ◽  
Wei Xu ◽  
Haiyan Wang ◽  
Ruoxing Mei
Keyword(s):  
White Noise ◽  
Colored Noise ◽  
First Passage Time ◽  
Gaussian White Noise ◽  
Correlated Noise ◽  
Degree Relative ◽  
Steady State Probability ◽  
Deviation Degree ◽  
Theoretical Results ◽  
Statistical Noise

In this paper, we investigate the stochastic transitions in a bistable Schlögl chemical reaction subjected to a nonextensive statistical noise (NESN) and a Gaussian white noise. The NESN is a correlated noise, and able to describe heavy-tailed noise distributions with certain deviation degree relative to Gaussian colored noise. With a unified-colored noise approximation method, the theoretical results of the steady state probability density function (PDF) and mean first passage time (MFPT) are obtained to demonstrate the influences of NESN. The validity of theoretical results has been confirmed by numerical simulations of the PDFs. Besides, stochastic P-bifurcation is discovered based on the changing of PDFs. The results show that the NESN will keep the conversion rate of substrate and the generation rate of products in the low state. Finally, from the MFPT, we find that the intensity and deviation degree of NESN, and Gaussian noise intensity can decrease the switching time between two states.

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.

scholarly journals Optimal Linear Estimators for Time-Delay Systems with Fading Measurements and Correlated Noises

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yazhou Li ◽  
Jiayi Li ◽  
Xin Wang
Keyword(s):  
Time Delay ◽  
Minimum Variance ◽  
Delay Systems ◽  
Multiplicative Noises ◽  
Linear Estimators ◽  
Discrete Linear Systems ◽  
Estimation Problems ◽  
Optimal Linear ◽  
State Augmentation ◽  
Correlated Noises

The optimal linear estimation problems are investigated in this paper for a class of discrete linear systems with fading measurements and correlated noises. Firstly, the fading measurements occur in a random way where the fading probabilities are regulated by probability mass functions in a given interval. Furthermore, time-delay exists in the system state and observation simultaneously. Additionally, the multiplicative noises are considered to describe the uncertainty of the state. Based on the projection theory, the linear minimum variance optimal linear estimators, including filter, predictor, and smoother are presented in the paper. Compared with conventional state augmentation, the new algorithm is finite-dimensionally computable and does not increase computational and storage load when the delay is large. A numerical example is provided to illustrate the effectiveness of the proposed algorithms.

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