Polynomial Correlated Function Expansion

Abstract

Uncertainty quantification of civil engineering structures are often time consuming. Hence, one has to rely on equivalent models (EM) that represent the original functions with a specific level of accuracy. In this chapter, a fully equivalent operational model, referred as, Polynomial Correlated Function Expansion (PCFE) has been discussed. PCFE facilitates a systematic mapping between the input and output by expressing the output as a ranked order of component functions, with higher order component functions representing higher-order cooperative effect. The component functions are expressed in terms of extended bases and the unknown coefficients associated with the bases are determined by employing homotopy algorithm (HA). HA determines the unknown coefficients by minimizing the least-squared error and imposing an additional criteria defined as an objective function. Implementation of PCFE has been illustrated with two large scale problems. Results obtained have been compared with other popular techniques. For both the problems, PCFE outperforms popular EMs available in literature.