Metamodeling of dynamic nonlinear structural systems through polynomial chaos NARX models

• Derivation of a reduced order metamodel of increased computational efficiency.
• Incorporation of model uncertainty via expansion on a Polynomial Chaos (PC) basis.
• Coupling of NARX and PC into a new metamodeling approach, termed the PC-NARX method.
• The excitation (load) is additionally parameterized as a model input.
• Efficient replacement of refined and computationally costly models is achieved.

This paper introduces a metamodeling strategy able to account for the uncertainties in simulating nonlinear, dynamically evolving engineering systems. Polynomial Chaos (PC) expansion is implemented for the development of stochastic metamodels capable of representing the response of numerical models with uncertain input variables. The models employed are of the Nonlinear AutoRegressive with eXogenous (NARX) input form, comprising parameters that are random variables themselves. By expanding these parameters onto an appropriately selected PC basis, the resulting PC-NARX metamodel achieves vast reduction in computational time with sufficient accuracy, yielding a suitable tool for implementations where replacement of computationally costly models is sought.