Q2S2: Merging Qualitative Information in Sequential DOE

Sequential sampling refers to a set of design of experiment (DOE) methods where the next sample point is determined by information from previous experiments. This paper introduces a qualitative and quantitative sequential sampling (Q2S2) technique, in which optimization and user knowledge is used to guide the efficient choice of sample points. This method combines information from multiple fidelity sources including computer simulation models of the product, first principals involved in design, and designer’s qualitative intuitions about the design. Both quantitative and qualitative information from different sources are merged together to arrive at a new sampling strategy. This is accomplished by introducing the concept of a confidence function, C, which is represented as a field that is a function of the decision variables, x, and the performance parameter, f. We compare the sampling plans generated by Q2S2 to previously known sample plans on five test functions using various metrics. In each case, the performance of Q2S2 is highly encouraging.

Cumulative global metamodels with uncertainty — a tool for aerospace integration

The integration of multidisciplinary data is key to supporting decisions during the development of aerospace products. Multidimensional metamodels can be automatically constructed using limited experimental or numerical data, including data from heterogeneous sources. Recent progress in multidimensional response surface technology, for example, provides the ability to interpolate between sparse data points in a multidimensional parameter space. These analytical representations act as surrogates that are based on and complement higher fidelity models and/or experiments, and can include technical data from multiple fidelity levels and multiple disciplines. Most importantly, these representations can be constructed on-the-fly and are cumulatively enriched as more data become available. The purpose of the present paper is to highlight applications of these cumulative global metamodels (CGM), their ease of construction, and the role they can play in aerospace integration. A simple metamodel implementation based on a radial basis function network is presented. This model generalises multidimensional data while simultaneously furnishing an estimate of the uncertainty on the prediction. Four examples are discussed. The first two illustrate the efficiency of surrogate-based design/optimisation. The third applies CGM concepts to a data fusion application. The last example is used to visualise extrapolation uncertainty, based on computational fluid dynamics data.