Bayesian Frequency Domain Identification of LTI Systems with OBFs kernels

Regularised Frequency Response Function (FRF) estimation based on Gaussian process regression formulated directly in the frequency-domain has been introduced recently The underlying approach largely depends on the utilised kernel function, which encodes the relevant prior knowledge on the system under consideration. In this paper, we show how to construct a rich class of kernel functions, directly in the frequency-domain, based on Orthonormal Basis Functions (OBFs), which is capable of representing a wide range of dynamical properties, e.g., stability, resonance frequencies, damping, etc, in terms of the poles of the employed basis functions that are treated as hyperparameters to efficiently shape the model class, i.e., the prior in the corresponding Bayesian setting. This class of kernel functions also implicitly guarantees the stability of the estimated FRF. The generating poles of the OBFs are tuned along with other hyperparameters, e.g., noise variance, by maximising the marginal likelihood. Multiple case studies are considered to show the potential of the considered kernels.