Surrogate modeling of nonstationary systems with uncertain properties L.D. Avenda˜ no-Valencia, E.N. Chatzi & M.D. Spiridonakos Institute of Structural Engineering, Department of Civil, Environmental and Geomatic Engineering ETH Z¨ urich, Stefano-Franscini-Platz 5, 8093 Z¨ urich, Switzerland ABSTRACT: The present study aims at developing a surrogate modeling method able to represent both non-stationarity and the propagation of uncertainties in the dynamic response of complex structures with time- dependent characteristics. Toward this end, AutoRegressive (ARX) models with random time-varying parame- ters are introduced. More specifically, the parameters of the introduced model are expanded on a multidimen- sional basis, with one of the dimensions corresponding to a scheduling variable dependent of time and the rest of them to the probability space of the uncertain input parameters. Linear parameter varying basis functions and polynomial chaos basis are utilized for this purpose with the resulting Polynomial Chaos Linear Parameter Varying ARX (PC-LPV-ARX) model being fully described by a finite number of deterministic coefficients of projection that may be estimated by a linear maximum likelihood method. In order to illustrate the workings of the method, the whole procedure is applied for the construction of a surrogate model of the vibration response of a wind turbine blade under normal operation. The surrogate is estimated from simulated data obtained by FAST (an aeroelastic computer-aided engineering tool for the simulation of horizontal axis wind turbines), while the value of the average wind speed within each analysis period is assumed to be uncertain following a normal dis- tribution. In overall, this study aims at demonstrating the effectiveness and applicability of the proposed method for the estimation of non-stationary surrogate models of low order that are capable of accurate approximation of large scale numerical models. 1 INTRODUCTION Despite the rapid increase of computational resources and the development of hardware and software so- lutions for distributed computing, the accompanying growth in the complexity of numerical models, as well as the necessity for more detailed descriptions of both structural geometry and mechanical properties, ren- der the use of highly detailed numerical models al- most prohibitive for complex, large structures. At the same time, by taking into account the uncertainties in- volved at various levels of the model description, the analyst is faced with the task of performing a large number of simulations in order to obtain a statistical description of the structural response characteristics (Queipo et al. 2005, Forrester and Keane 2009, Yang et al. 2013, Nguyen et al. 2014). This problem is even more pronounced in the case when the stochastic dynamic response structure of interest is characterized by time-dependent statisti- cal moments, namely non-stationary (Poulimenos & Fassois 2006). The non-stationarity property is mani- fested either in systems with time-varying properties (mass distribution, stiffness, and/or damping), or in systems with time-invariant properties operating un- der non-stationary loading, including the case of tran- sient dynamics. Important examples of this type of systems are civil structures subject to seismic exci- tations, structures with variable geometry, wind tur- bines, offshore platforms, and so on. The accurate modeling of such systems necessitates the represen- tation of their dynamics for the complete evolution of the non-stationary phenomenon, leading to compli- cated and computationally expensive models (Hansen et al. 2006, Taflanidis et al. 2014). The assumption of stationarity has to be abandoned whenever the non-stationarity is an important com- ponent of the dynamic response of the structure. In consequence, the well established and known rep- resentations of the structure, either in the time or frequency domain – such as impulse response func- tion, frequency response function, modal models, and the like – are not advisable as surrogate represen- tations. Alternatively, time-dependent and linear pa- rameter varying ARX models (TARX and LPV-ARX, respectively) can be used to effectively represent non- stationary processes (Bamieh & Giarr´ e 2002, Pouli- menos & Fassois 2006). At the same time, in the case of non-stationary stochastic dynamic loading, which might often be the case, the statistical characteris-