دانلود رایگان مقاله تولید برای مدل سازی راه حل مشکلات ارزیابی غیر مخرب تصادفی

Abstract

A novel algorithm for creating a computationally efficient approximation of a system response that is defined by a boundary value problem is presented. More specifically, the approach presented is focused on substantially reducing the computational expense required to approximate the solution of a stochastic partial differential equation, particularly for the purpose of estimating the solution to an associated nondestructive evaluation problem with significant system uncertainty. In order to achieve this computational efficiency, the approach combines reduced-basis reduced-order modeling with a sparse grid collocation surrogate modeling technique to estimate the response of the system of interest with respect to any designated unknown parameters, provided the distributions are known. The reduced-order modeling component includes a novel algorithm for adaptive generation of a data ensemble based on a nested grid technique, to then create the reduced-order basis. The capabilities and potential applicability of the approach presented are displayed through two simulated case studies regarding inverse characterization of material properties for two different physical systems involving some amount of significant uncertainty. The first case study considered characterization of an unknown localized reduction in stiffness of a structure from simulated frequency response function based nondestructive testing. Then, the second case study considered characterization of an unknown temperature-dependent thermal conductivity of a solid from simulated thermal testing. Overall, the surrogate modeling approach was shown through both simulated examples to provide accurate solution estimates to inverse problems for systems represented by stochastic partial differential equations with a fraction of the typical computational cost.

4. Conclusion

A novel approach was presented for creating a computationally efficient polynomial approximation (i.e., surrogate model) of a system response with respect to any designated unknown parameters, including parameters that may be considered to have significant uncertainty and/or parameters that are entirely unknown and sought to be determined through a nondestructive evaluation procedure. To enhance the overall efficiency of the approach, a novel algorithm was included as an intermediate step for creating a reduced-basis type reduced-order model of the system of interest. This intermediate step was based upon a technique to use nested grids to adaptively generate a data ensemble that is representative of the potential system response with respect to the unknown parameters. The overall approach would then use this computationally efficient ROM to create the surrogate model rather than a full-order model (e.g., traditional finite element analysis) at a substantial computational savings. This approach to generate an ROM was shown to provide a more accurate representation of the system of interest in comparison to a commonly used approach of randomly generating the response field ensemble. The overall surrogate modeling approach was then evaluated through numerically simulated example inverse problems based on characterization of material properties for two different systems, involving solid mechanics and heat transfer, respectively. Not only did the two examples consider different physical processes, but they also consider two different ways that uncertainty could be present and significant within NDE applications. The first example showed that the surrogate modeling approach could be used to computationally efficiently and accurately estimate the statistical moments of the parameters for an unknown stiffness distribution for a dynamically tested solid with uncertainty in the applied actuation. Lastly, the surrogate modeling approach was shown to be able to provide a single estimate, again both efficiently and accurately, of the parameters for an unknown temperature-dependent thermal conductivity for a solid in which the inverse problem objective was to match the statistical moments of the measured temperature field given an uncertain applied heat flux.