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The method of multiple scales is used to obtain the first-order approximation of response.
The method of multiple scales is utilized to obtain the first order approximation of response.
Multidimensional fitting or approximation of response functions exponentially increase their complexity and computational cost with the number of dimensions responding to the well-known "curse of dimensionality".
The cross correlation function of Preisach hysteretic force and response in the covariance equation is evaluated based on the switching probability analysis and the Gaussian approximation of response process and an explicit expression for the cross correlation function is given for the case of symmetric Preisach weighting function.
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This paper reports the approximation quality of response surfaces as metamodels for key results from computational fluid dynamics (CFD) gas explosion simulations.
This paper proposes an iterative RSM framework, where Gaussian process (GP) regression models are applied for the approximation of the response surface.
The conclusions obtain provide a valuable approximation of pavement response.While PMARP is a static finite element program, the properties of inertia and damping of the pavement structure were not included in consideration.
By the new equivalent forms of the variance-based sensitivity indices and the multiplication approximation of the response function, the proposed method can simultaneously estimate all the order effects by repeatedly making use of the same sample points.
Zones of convergence and divergence of the response series are presented graphically, for a range of the non-dimensional non-linear parameter and the number of terms included in the approximation of a response harmonic.
In the analysis procedure, the approximation of the response, y, was determined using a quadratic polynomial regression model as a function of the pyrolysis parameters using Eq. 1, which has linear and quadratic terms in addition to an interaction term, where b is the regression coefficient, χ is the independent parameter, and e is the experimental error.
In order to improve the efficiency, the accuracy and the robustness of the sampling-based methods for estimating the variance-based sensitivity indices, a new efficient method based on the combination of the unconditional expectation, the conditional expectation and the multiplication approximation of the response function is proposed in this paper.
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