Gaussian Mixture Model Clustering-Based Knock Threshold Learning in Automotive Engines

Abstract

In this article, a Gaussian mixture model (GMM) clustering-based method is proposed to learn the optimal threshold of the knock intensity metric, which minimizes the probability of the judgment error of the knock event. First, statistical analysis of knock intensity on an experimental database measured from a gasoline engine test bench is conducted and the results show that GMM has better fitting performance than the single Gaussian model. Then, the learning problem which consists of two subproblems is formulated based on the assumption that the probability distribution model of knock intensity is a two-component GMM. The first subproblem is a clustering problem in which parameters of the two-component GMM are optimized to maximize the likelihood of obtaining the measurements. The second subproblem is also an optimization problem in which the probability of the judgment error is formulated as a function of the threshold. The solution to the problem is the required threshold decision. The convergence analysis of the proposed method is implemented. Furthermore, the proposed method is also validated in the experimental database. The proposed method is expected to be applied in the real-world application to save time, labor effort on the knock threshold calibration.