scholarly journals Statistical Taylor series expansion : An approach for Epistemic uncertainty propagation in Markov reliability models

2019 ◽  
Author(s):  
Katia Bachi ◽  
Karim Abbas ◽  
Bernd Heidergott
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Chebyshev Inequality ◽  
Model Output ◽  
Reliability Models ◽  
The Impact

In this paper we develop a new Taylor series expansion method for computing model output metrics under epistemic uncertainty in the model input parameters. Specifically, we compute the expected value and the variance of the stationary distribution associated with Markov reliability models. In the multi-parameter case, our approach allows to analyze the impact of correlation between the uncertainty on the individual parameters the model output metric. In addition, we also approximate true risk by using the Chebyshev' inequality. Numerical results are presented and compared to the corresponding Monte Carlo simulations ones.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

Rationalize the irrational and fractional expressions in nonlinear analysis

2016 ◽  
Vol 30 (04) ◽  
pp. 1650068 ◽  
Author(s):  
Yongfeng Yang ◽  
Tingdong Jiang ◽  
Zhong Ren ◽  
Junyao Zhao ◽  
Zheng Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Series Expansion ◽  
Taylor Series ◽  
Impact Force ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Stochastic Bifurcation ◽  
Bifurcation And Chaos ◽  
Integral Process ◽  
Series Expansion Method

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

scholarly journals A New Localization Algorithm Based on Taylor Series Expansion for NLOS Environment

2016 ◽  
Vol 16 (5) ◽  
pp. 127-136 ◽  
Author(s):  
Jin Ren ◽  
Jingxing Chen ◽  
Wenle Bai
Keyword(s):  
Neural Network ◽  
Series Expansion ◽  
Taylor Series ◽  
Rbf Neural Network ◽  
Taylor Series Expansion ◽  
Localization Algorithm ◽  
Location Accuracy ◽  
Location Algorithm ◽  
Adaptive Ability ◽  
The Impact

Abstract In Non-Line-Of-Sight (NLOS) environment, location accuracy of Taylorseries expansion location algorithm degrades greatly. A new Taylor-series expansion location algorithm based on self-adaptive Radial-Basis-Function (RBF) neural network is proposed in this paper, which can reduce the impact on the positioning accuracy of NLOS effectively on the basis of the measurement error correction. RBF neural network has a faster learning characteristic and the ability of approximate arbitrary nonlinear mapping. In the process of studying, RBF neural network adjusts to the quantity of the nodes according to corresponding additive strategy and removing strategy. The newly-formed network has a simple structure with high accuracy and better adaptive ability. After correcting the error, reuse Taylor series expansion location algorithm for positioning. The simulation results indicate that the proposed algorithm has high location accuracy, the performance is better than RBF-Taylor algorithm, LS-Taylor algorithm, Chan algorithm and LS algorithm in NLOS environment.

scholarly journals An Alternative Approach to Energy Eigenvalue Problems of Anharmonic Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Okan Ozer ◽  
Halide Koklu
Keyword(s):  
Series Expansion ◽  
Excellent Agreement ◽  
Taylor Series ◽  
Taylor Expansion ◽  
Eigenvalue Problems ◽  
Energy Eigenvalue ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Energy Eigenvalues ◽  
Alternative Approach

Energy eigenvalues of quartic and sextic type anharmonic potentials are obtained by using an alternative method called asymptotic Taylor expansion method (ATEM) which is an approximate approach based on the asymptotic Taylor series expansion of a function. It is shown that the energy eigenvalues found by ATEM are in excellent agreement with the existing results.

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