mNARX - A novel surrogate model for the uncertainty quantification of dynamical systems

Abstract

Modelling the dynamic response of civil structures is vital for many applications, including structural health monitoring, reliability analysis and design optimization. These systems often feature responses governed by highly uncertain exogenous excitations, for example, ground motions, wind, or wave loads. To quantify the effects of this uncertainty, many evaluations of the underlying numerical models are usually required. Therefore, in the presence of expensive simulations, surrogate models become necessary as a fast-to-evaluate proxy. However, for many time-dependent systems it is difficult to build surrogates that provide precise and stable predictions. Additional non-linearity is introduced by controllers that actively change the system properties depending on multiple state variables. One approach to surrogate such systems is to use non-linear auto-regressive with exogenous input (NARX) models, which exploit the temporal coherence of the system response and its strong dependence on the exogenous excitations. Constructing a stable and accurate NARX model, however, is often unattainable when the system response is highly non-linear, the dimensionality of the exogenous input is high, or when data is scarce. In this work, we present a novel approach called manifold NARX (mNARX) to tackle this class of problems. mNARX takes advantage of prior knowledge about the physics of the system to incrementally build an input manifold suitable for efficiently surrogating the dynamic system response. We showcase its efficiency on an aero-servo-elastic (ASE) wind turbine simulation benchmark. ASE simulators take turbulent wind as input, and model selected time-dependent quantities of interest (QoIs), such as power output or blade and tower loads. The exogenous input wind field is a spatio-temporal random field with high spatial dimensionality. Furthermore, most QoIs are affected by both the control system and rotor orientation, making the mapping from the exogenous inputs to the QoIs even more complex. Within the mNARX framework, we first predict physically meaningful auxiliary quantities, such as control and state variables, based on a NARX model built on a truncated set of time-dependent spectral coefficients of the wind input. We then use these predictions in conjunction with the spectral coefficients to form an exogenous input manifold onto which the final QoI NARX model is constructed. We demonstrate that this sequential approach leads to accurate predictions over a long time horizon, even in the presence of complex localized spectral features. Finally, we show that the training of this chain of surrogate models and its evaluation are computationally inexpensive, up to multiple orders of magnitude cheaper than its original ASE simulator counterpart.