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.

中文翻译：

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基于高斯混合模型聚类的爆震阈值学习

本文提出了一种基于高斯混合模型（GMM）聚类的方法来学习爆震强度度量的最佳阈值，从而将爆震事件判断错误的可能性降到最低。首先，对从汽油发动机试验台测得的实验数据库的爆震强度进行统计分析，结果表明，GMM的拟合性能优于单一高斯模型。然后，基于爆震强度的概率分布模型为两成分GMM的假设，提出了由两个子问题组成的学习问题。第一个子问题是聚类问题，其中优化了两组分GMM的参数以最大化获得测量值的可能性。第二个子问题也是一个优化问题，其中将判断错误的概率表示为阈值的函数。解决问题的方法是所需的阈值决策。对该方法进行了收敛性分析。此外，该方法在实验数据库中也得到了验证。所提出的方法有望在实际应用中应用，以节省爆震阈值校准的时间和劳力。