Advances and Applications in Statistics
Volume 42, Issue 2, Pages 119 - 156
(October 2014)
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STOCHASTIC MODELING OF WAVE EQUATION WITH UNCERTAINTIES IN INITIAL AND BOUNDARY CONDITIONS
Shiang-Jen Wu
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Abstract: This study proposes an alternative stochastic modeling framework to quantify the uncertainty propagation of spatiotemporal variables due to variations in initial and boundary conditions by incorporating the explicit numerical solutions of the 1-D wave equation with the expected value operator. Spatiotemporal semivariogram models are employed to deal with the correlation of the variables in time and space. The proposed model is validated by comparing it with the Monte Carlo simulation (MCS) model associated with the explicit numerical solution of the wave equation in the calculation of statistical properties of model outputs, i.e., the mean and coefficient of variance (CV). The results of numerical experiments show that the proposed model can produce excellent approximations of the mean and inferior approximations of the CV as compared to those of the MCS model. Furthermore, by means of the proposed models with varying CV values for the initial and boundary conditions, respectively, we can quantify the resulting effect from conditions based on the estimations of the wave displacement; therefore, it is possible to conclude that their uncertainties are mainly attributed to the variation of the boundary condition. |
Keywords and phrases: wave equation, Monte Carlo simulation, expected value operator, spatiotemporal semivariogram. |
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