Multi-innovation identification method for fractional Hammerstein state space model with colored noise

Abstract

The paper proposes an identification method for the fractional Hammerstein state space model with colored noise. The traditional identification algorithms of this model suffer from problems such as parameter coupling, unknown intermediate state variables, difficulty in processing noise signal coloring, and low identification accuracy. The proposed method is based on the principle of multiple innovations and involves constructing the partial derivative system of the system output to the system parameters, calculating the sensitivity function for the fractional order, and using historical data with current data to obtain the objective function and its gradient and Hessian matrix. The parameters and fractional orders are then iteratively updated through the Levenberg–Marquardt algorithm. The algorithm's robustness is verified through multiple Monte Carlo experiments under different signal-to-noise ratios on an academic example, and its practicability is demonstrated by applying it to an actual heating system.