Sentence examples for stochastic coefficients from inspiring English sources

Analytical moment solutions are obtained for white noise coefficients while hybrid computer simulation was used for correlated stochastic coefficients.

Detailed applications for linear systems with stochastic coefficients under noise excitation and for a non-linear oscillator are analysed.

Deviation from the deterministic model increases with increasing variance and decreasing fluctuation frequency of the correlated stochastic coefficients.

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions.

Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients.

Both approaches are variants of a generalized Karhunen Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution.

However, each stochastic coefficient in the power load data is effectively reduced through time series modeling and Kalman filtering, each coefficient value is reduced by an order of magnitude.

Table 2 Stochastic noise coefficients before and after Kalman filtering Noise coefficient Before filtering After filtering Q 1.50e-3 1.01e-5 1.01e-5-5 1.26e-6 B 4.74e-4 4.74e-4 K 7.5.66e-5.89e-4 R 4.31e-2 5.10e-3 Fig. 5 Total variance analysis before and after Kalman filter.

And total variance method is adopted to verify the effect of modeling and filtering, namely the stochastic error coefficients before and after filtering.

As a result, the stochastic aerodynamic coefficients are described by their approximate probability density functions, which are related in turn to the aerodynamic regimes recognised for the case study.

Besides, every stochastic error coefficient is decreased effectively by total variance method, comparing with Allan variance method.