基于顺序约束的命中概率多批次试验统计评定方法

Evaluation of Hitting Probability for Multi-batch Tests Based on Ordinal Constraints

针对多批次试验中由技术状态改进所带来的异总体统计问题,研究了顺序约束条件下的命中概率指标统计评定方法。首先在X-Y向不相关情况下,将命中概率指标归结为X向和Y向的准确度和密集度参数的估计。然后根据多批次试验规律,建立各个参数之间的顺序约束关系,基于Bayes方法获得验后分布密度核函数,并采用MCMC(Markov Chain Monte Carlo)方法获得各参数的验后抽样分布,进而获得命中概率指标的抽样分布,以此计算命中概率的期望和置信限。此外,针对运动目标或末端机动的情况,分析了X-Y向相关情况下的命中概率指标计算方法。通过正交变换实现去相关处理,并在命中概率计算中引入旋转角度参数,从而解决运动目标情况下的多批次命中概率计算。最后,通过实例进行了验证,所得命中概率值优于传统方法所获得的统计结果,表明该方法对多批次试验具有良好的适应性和工程推广价值。

To solve the problem of diverse population statistics arising from the advancement of technical levels in multi-batch tests,the hitting probability evaluation method is studied based on ordinal constraints.For the condition of X-Y independence,the evaluation of hitting probability comes down to the estimation of the accuracy and precision parameters.A group of ordinal constraints are established based on the inherent rules of multi-batch tests.By virtue of MCMC（Markov Chain Monte Carlo） sampling,the Bayesian analysis is carried out to obtain the posterior kernel density and hence the sampling distribution of hitting probability.And then the expectation and confidence interval of hitting probability can be computed accordingly.Besides,for the cases of targets moving or weapons terminal maneuver,the computation of hitting probability is analyzed in the condition of X-Y correlation.Different orthogonal transforms are used to realize the decorrelation in each batch,and the parameter of rotation angle is introduced into the computation of hitting probability,thus to solve the evaluation for the special case.An example for validation is carried out,with better results than conventional methods,which shows its sound applicability and generalization in engineering.