Mixture Density Networks-Based Knock Simulator

The engine knock simulator is useful for the evaluation of the feedback knock controllers and also the calibration of the feedforward control input without experiments in spark-ignition engines. This article proposes a mixture density network (MDN)-based statistical simulator of the engine knock for spark-ignition engines. The simulator can output the simulated knock intensity by the operating condition, which has a consistent probability distribution with the real engine. The statistical analysis is conducted based on the experimental data. According to the analysis results, several important properties about the knock intensity have been revealed. The logarithm of knock intensity is independent and identically distributed under an identical operating condition, whose probability distribution can be approximated by Gaussian mixture model (GMM). The parameter vector of the GMM is a function of the engine's operation condition. Based on these statistical properties of engine knock, we formulate the problem of establishing a statistical simulator, which includes two subproblems. The first one is how to approximate the function from the operating condition to the parameters of the GMM. The second one is how to output the simulated random data of logarithm of knock intensity that obeys a given distribution. The MDN and the accept-reject algorithm are applied to solve the two subproblem, respectively. Finally, we conducted experimental data-based validations to verify the proposed method.