Modeling and analysis of cyclic inhomogeneous Markov processes: a wind turbine case study

TL;DR

This paper introduces a method to reconstruct cyclic inhomogeneous Markov processes from data, demonstrated on wind turbine measurements, enabling analysis of their stochastic dynamics through time-dependent transition matrices and Kramers-Moyal coefficients.

Contribution

The paper presents a novel approach to model and analyze cyclic inhomogeneous Markov processes using measured data, with specific application to wind turbine systems.

Findings

Successful reconstruction of cyclic inhomogeneous Markov processes from wind turbine data

Derivation of time-dependent Kramers-Moyal coefficients from transition matrices

Discussion of potential applications of the method in stochastic process analysis

Abstract

A method is proposed to reconstruct a cyclic time-inhomogeneous Markov pro- cess from measured data. First, a time-inhomogeneous Markov model is fit to the data, taken here from measurements on a wind turbine. From the time-dependent transition matrices, the time-dependent Kramers-Moyal coefficients of the corresponding stochastic process are computed. Further applications of this method are discussed.