An approach for nonlinear model extraction from time-series data

We provide a numerical approach to estimating nonlinear stochastic dynamic models from time-series data. After possible dimensional reduction, time-series data can be used to construct an empirical Markov model. Spectral analysis of the Markov model is then carried out to detect the presence of complex limit cycling, almost invariant, and bistable behavior in the model. Model parameters are expressed as a linear combination of basis functions over the phase space. A least squares minimization is used to fit the basis function coefficients in order to match the spectral properties of the respective Markov operators. The approach is demonstrated on the estimation of a nonlinear stochastic model describing combustion oscillation data.