118 A. Hatstatt and K. E. Tatsis where ˜Al denotes the l-th row of matrix ˜Aand accordingly, ˜bl is the l-th entry of ˜b. Therefore, the vector σw of unknown variance terms is computed using the generalized inverse of ˜A. Application The methodology presented in Section is herein applied for the modeling of vibration response signals obtained from wind turbine systems. To this end, the NREL 5MW onshore wind turbine [13] is simulated using FAST software for various operational and environmental conditions, which are defined by the mean wind speed and the turbulence intensity. For each sample of these conditional variables, a 10 minute period is simulated and the acceleration signals in bothxandy directions are extracted from two positions of the tower. The signals are sampled at 50 Hz and are subsequently truncated to 1-minute intervals and transformed into the Fore-Aft (FA) and Side-to-Side (SS) directions. The corresponding SCADA variables are also extracted for the 1-minute intervals. Thereafter, a GPLF model is learned in order to be used as generative model that can translate SCADA variables into 1-min time series, whose spectral characteristics are in accordance with those obtained from simulations. The aim of the generated time series is to emulate the original signal, not only in terms of its spectral content and statistical properties, but also in terms of the loading cycles, which are responsible for the accumulation of fatigue damage. A schematic overview of the workflow followed in this case study is presented in Fig. 1 Workflow description: 10 Minutes Simulation with software FAST of a 5MW baseline Offshore Wind Turbine Various operating conditions Mean Wind Speed Turbulence Intensity Time series for Loads, Displacements, Accelerations at 50 HZ SCADA data at 0.017 HZ Evaluation of Fatigue Damage based on time series at 50 HZ and accuracy evaluation of the prediction Generative Data Driven Model construction (GM) Use of GM Ground Truth Prediction Pseudo time series for Accelerations at 50 HZ Fig. 1 General workflow description As underlined in the section of the methodology, the optimization algorithm implies the knowledge of certain hyperparameters, which can be extracted from statistical metric of the signal. In this specific case study, it is assumed that certain characteristics of the response are available from the design, such as the eigenfrequencies and the damping of the system, while some further information can be extracted from the available SCADA data. As such, the dynamics of the acceleration signals of the two modes in each direction, namely FA and SS, are assumed to be governed by a harmonic oscillator kernel,
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