This repository provides an interval-valued power spectral density function, the imprecise PSD function. Uncertainties that stem from a limited amount of available data are considered. An interval approach to define optimal bounds without considering the distribution of the data within these bounds is described. The estimation of the proposed imprecise PSD is carried out entirely in the frequency domain, using a radial basis function (RBF) network in order to approximate a basis power spectrum and to obtain basis functions representing such basis power spectrum. The individual weights of the basis functions will be optimised to obtain reasonable bounds considering the actual minimum and maximum of the data set. These bounds reflect the physics of the data as the shape is approximated to represent the overall distribution and magnitude of the individual frequencies. In particular, this means that peak frequencies, for instance, are adequately represented.
Behrendt, M.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. (2023): Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification, Mechanical Systems and Signal Processing, 189, Article 110072, DOI: 10.1016/j.ymssp.2022.110072.
The imprecise PSD can be computed by running the file example_imprecisePSD.m. Based on a set of PSD functions, the ensemble, the bounds are derived in a double-loop approach. In the outer loop, the spread of the basis functions is optimised, while in the inner loop the weights for the basis functions are optimised. Thus, the same basis functions and bias are used, to derive the upper and lower bound by optimising the respective weights. The optimisation constraints for the weights are defined in nlcon_weights.m. The results are visualised by plot_imprecisePSD.m.