Research on the efficiency of reduced-basis approach in computations of structural problems and its improvements

摘要

In this article, procedure and efficiency of the reduced-basis approach in structural design computation are studied. As a model order reduction approach, it provides fast evaluation of a structural system in explicitly parameterized formulation. Theoretically, the original structural system is reduced to obtain a reduced system by being projected onto a lower dimensional subspace. However, in practice, it is a time-consuming process due to the iterations of adaptive procedure in subspace construction. To improve the efficiency of the method, some characteristics are analyzed. First, the accuracy of the subspace is evaluated and computational costs of procedures with different approaches are studied. Results show that the subspaces constructed by greedy adaptive procedures with different beginnings have the same accuracy. It is instructive that accuracy of the subspace is guaranteed by adaptive procedure. And the computational costs depend on the number of iterations in adaptive procedure. Thus, a modified adaptive procedure is proposed to reduce the computational costs and guarantee the accuracy. The modified adaptive procedure begins with experimental design methods to obtain a set of samples rather than a single sample and ends with the adaptive procedure. The start set of samples are selected by the following experimental design methods: 2k factorial design, standard Latin design and Latin hypercube design. By being integrated with the experimental design, the modified adaptive procedure saves computational costs and retains the same accuracy as traditional procedure does. As an example, the outputs of a vehicle body front compartment subjected to a bending load are illustrated. It is proved that the proposed procedure is efficient and is applicable to many other structural design contexts.