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On the contrary, the proposed randomized optimization method with stochastic sampling requires the solution of only a few (e.g., 5 or 6) finite element problems (large linear systems) per optimization step.
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In contrast, the methods with stochastic strategies can have solutions that are near the global optimum within a reasonable amount of time.
Combining these novel methods with stochastic search algorithms to explore the combinatorial search space using both high-performance computing and expert knowledge to limit the search space will be required to explore genetic associations in an era of plentiful genome-wide data.
The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs.
In this paper, a stochastic homogenization method that couples the state-of-the-art computational multi-scale homogenization method with the stochastic finite element method, is proposed to predict the statistics of the effective elastic properties of textile composite materials.
Integration of the structural creep analysis by the Model B3 and the age-adjusted effective modulus method with the stochastic seismic analysis by the pseudo-excitation method is then proposed.
By employing the Lyapunov Krasovskii functional method with the stochastic analysis approach, several delay-independent criteria, which are in the form of linear matrix inequalities (LMIs), are established to ensure the existence of the desired multi-sensor H∞ fusion filters.
In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface.
An excellent method to deal with stochastic variables is Monte Carlo analysis.
Since the discrimination method is done with stochastic characteristics of signals in time domain without application of any deterministic index, more reliable and accurate classification is achieved.
By integrating these homogenization methods with the stochastic finite element method and structural reliability methods, the reliability of composites can be investigated with a limit state function based on a chosen failure criterion.
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