Metamodelling with independent and dependent inputs

In the cases of computationally expensive models the metamodelling technique which maps inputs and outputs is a very useful and practical way of making computations tractable. A number of new techniques which improve the efficiency of the Random Sampling-High dimensional model representation (RS-HDMR) for models with independent and dependent input variables are presented. Two different metamodelling methods for models with dependent input variables are compared. Both techniques are based on a Quasi Monte Carlo variant of RS-HDMR. The first technique makes use of transformation of the dependent input vector into a Gaussian independent random vector and then applies the decomposition of the model using a tensored Hermite polynomial basis. The second approach uses a direct decomposition of the model function into a basis which consists of the marginal distributions of input components and their joint distribution. For both methods the copula formalism is used. Numerical tests prove that the developed methods are robust and efficient.