Parameter Space Reduction Using Approximate Canonical Correlation Analysis
Jon M. Wallace · 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2004
Reducing a highly dimensional space to a more manageable one is an important step for time-consuming engineering design, analyses, and optimization studies. While conducting such a reduction is routinely accomplished for single response, single analysis scenarios; a reduction method for complex analysis spaces involving multiple layers of analyses and parameters is needed. A new parameter screening approach which is well suited for complex analysis spaces is proposed. The approach is based on an approximation to a venerable multi-variate statistical technique called canonical correlation. Canonical correlation is simply a measure of the level of statistical correlation between two sets of parameters. Where canonical correlation has traditionally been applied using statistics computed from several sets of data, it is implemented here using an e‐cient analytical approximation to such statistics. The usefulness of this technique is demonstrated on a turbine engine component study consisting of multiple analyses and a multitude of parameter subsets driven by engine system operating conditions. As a result, signiflcant interrelationships between analyses, categories of parameters, as well as global and local input parameters, which would otherwise go unnoticed, are revealed and quantifled.