| The primary contributions of this thesis are associated with the development of a new method for exploring the relationships between inputs and outputs for large scale computer simulations. Primarily, the proposed design space exploration procedure uses a hierarchical partitioning method to help mitigate the curse of dimensionality often associated with the analysis of large scale systems. Closely coupled with the use of a partitioning approach, is the problem of how to partition the system. This thesis also introduces and discusses a quantitative method developed to aid the user in finding a set of good partitions for creating partitioned metamodels of large scale systems.; The new hierarchically partitioned metamodeling scheme, the lumped parameter model (LPM), was developed to address two primary limitations to the current partitioning methods for large scale metamodeling. First the LPM was formulated to negate the need to rely on variable redundancies between partitions to account for potentially important interactions. While variable redundancies improve the accuracy of the partitioned metamodel, they do so at the cost of significantly reducing the efficiency of the partitioned metamodeling process. By using a hierarchical structure, the LPM addresses the impact of neglected, direct interactions by indirectly accounting for these interactions via the interactions that occur between the lumped parameters in intermediate to top-level mappings. Secondly, the LPM was developed to allow for hierarchical modeling of black-box analyses that do not have available intermediaries with which to partition the system around.; The second contribution of this thesis is a graph-based partitioning method for large scale, black-box systems. The graph-based partitioning method combines the graph and sparse matrix decomposition methods used by the electrical engineering community with the results of a screening test to create a quantitative method for partitioning large scale, black-box systems. An ANOVA analysis of the results of a screening test can be used to determine the sparse nature of the large scale system. With this information known, the sparse matrix and graph theoretic partitioning schemes can then be used to create potential sets of partitions to use with the lumped parameter model. |
