基于最大似然估计的点火概率曲线计算模型取点方法

Method of Point Selection for Fitting Ignition Probability Curve Based on Maximum Likelihood Estimation

关键词:  点火  曲线拟合  置信区间  实验工况  概率模型

Key words:  Ignition  Curve fitting  Confidence interval  Experimental condition  Probability model

摘要:

最佳点火能量、点火位置等关键信息可通过绘制点火概率曲线判定概率函数以提高点火成功概率。完成传统点火概率曲线的绘制需要至少300次的点火事件，以求得更加复杂的点火概率模型甚至需要更多的实验次数才能保证曲线精度。受制于点火器寿命，依据大数定律绘制点火概率曲线所需的多点数据难以保证，因此迫切需要开发一种在减少实验次数的前提下保证点火概率曲线精度的模型。本文拓展了一种点火概率计算模型，针对不同的取点方式，通过随机二项分布求得概率函数中似然函数的未知参数，从而拟合空间位置点火概率曲线和能量点火概率曲线，结合均方差评估拟合程度选取最优取点方法。研究表明，采用最优取点方法拟合的能量-点火概率曲线可以将均方差降低至0.02左右，空间位置点火概率曲线均方差降至0.04。研究表明所选取的最优取点方法可有效指导实验工况选取，并绘制出可信点火概率曲线。同等置信度下，三种点火概率曲线的实验次数均减少50%以上，实现大幅减少实验次数的目的。

Abstract:

The ignition probability curve helps to improve the probability of successful ignition by determining the key information such as the optimal ignition energy and position. Fitting the ignition probability curve in traditional method requires at least 300 experimental events. And it requires more experiments to ensure curve accuracy in a more complex ignition probability model. However, the limited service life of igniters and the difficulty in controlling the experimental variables to acquire experimental data demand an ignition probability calculation model to ensure the accuracy of experiment while reducing the number of experiments. This paper extended an ignition probability calculation model, using random binomial distribution to calculate the unknown variables of a likelihood function with different methods of point selection and fitted the ignition probability curves of space and energy. And the optimal experimental condition was selected by comparing mean square deviation. Study shows that the standard deviation of fitting probability curves of energy and space can decrease to 0.02 and 0.04 with the optimal selection. The experimental condition selection in this paper can be used to guide the design of experimental conditions effectively and fit the ignition probability curve in a reliable way. Experimental events decrease at least 50% under the same confidence level, which achieve the goal of reducing the number of experiments.