Construction of a probabilistic model for impedance matrices

Impedance matrices allow for the coupling of domains with very different properties, and possibly modeled with different methods. This paper presents the construction of a probabilistic model for such matrices, using a nonparametric method that allows for the consideration of data errors as well as model errors. To enable the application of this method in the case of a domain for which no Finite Element model is available, the identification of a “hidden state variables model” – from the knowledge of the impedance matrix at a discrete set of frequencies – is also described. Finally the construction of the probabilistic model of the impedance of a pile foundation on a layered unbounded soil illustrates the capabilities of the method.