装备试验评估中的变动统计方法研究
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摘要
随着武器装备和各类机电产品复杂度的提高,产品性状在全寿命周期中的动态变化过程也日趋复杂,相应的试验评估手段也更加多样化。这就需要融合多种数据(不同阶段、不同来源)对在研产品性状的动态变化过程进行恰当的建模与分析。在装备试验评估领域中,较为典型的就是多阶段可靠性增长试验评估、多批次和多信源条件下的武器战技指标评估。这些问题都体现出显著的“变动统计”的特点,相应统计推断结果的准确性,关系到装备接收、使用的风险。围绕装备试验评估领域中的变动统计问题开展相关研究具有重要的理论意义和应用价值。
论文以装备试验评估领域中的变动统计问题为背景,首次系统地研究了变动统计的基本理论问题,并在多阶段可靠性增长试验评估、多批次或多信源条件下的命中概率融合评估两个主要领域中,针对四大类典型问题展开了具体细致的研究工作,提出了若干创新性的变动统计方法。主要研究内容与成果如下:
1.装备试验评估中的变动统计基本理论系统地回顾了变动统计的发展历程与研究现状,提出了变动统计的主要特征。通过与其他相关研究领域的比较,提出了变动统计的基本内涵以及需要面对的几个关键的理论问题,给出了所涉及的数据预处理方法,归纳提出了三大类基本的变动统计方法:基于约束关系的多总体融合估计、基于线性模型的变动总体建模与预测、基于Bayes方法的多源验前信息融合,并对每种方法的特点和应用前景进行了分析和讨论。
2.多阶段延缓纠正可靠性增长试验评估方法分析了指数寿命型产品在这一过程中的可靠性指标变化规律。提出采用MCMC(Markov Chain Monte Carlo)方法计算顺序约束条件下的Bayes验后分布,具有较好的操作性和较高的计算精度。提出增长因子法中的一种新的变量转换原则,仅利用随机序关系和变量期望值之间的比例关系推导了变量转换方法,尽可能降低了人为因素所带来的转换原则的随意性。比较了顺序约束方法和增长因子法的特性,讨论了两类方法的选择原则。建立了各阶段失效强度之间的广义线性模型,并采用Bayes动态预测方法进行递推估计,适用于试验阶段数较多的情况。
3.多阶段含延缓纠正可靠性增长试验评估方法提出描述此类可靠性增长过程的两类模型MS-NHPP-I和MS-NHPP-I(IMulti-Stage Non-Homogeneous Poisson Process Type I & II),同时阐明了两类模型的特点、适用范围和选择原则。对于MS-NHPP-I模型,提出对阶段末尾的失效强度建立顺序约束关系。对于MS-NHPP-II模型,提出对相邻阶段衔接处的失效强度建立顺序约束关系,并采用基于Metropolis-Hastings原则的MCMC方法计算Bayes验后分布。针对多台设备同时投试的情况,提出选取特定时间的均值函数值建立比例关系,利用增长因子建立多阶段分析流程。最后,分析了两类模型中各阶段参数之间的线性关系,建立了比例强度假设下的线性模型,给出了参数估计和模型检验方法。
4.基于多批次试验信息的命中概率融合评估方法首先,针对单批次同总体数据,提出了复杂条件下(子母弹、小子样、目标旋转等)的导弹命中概率计算方法。在子母弹命中概率评估中,提出了数值积分与统计模拟相结合的计算方法。在小子样命中概率评估中,提出了二维正态分布变量的Bootstrap方法和经验Bayes方法。在此基础上,针对多批次异总体数据,分析了多批次试验过程中各个分布参数随批次的变动情况,建立了两个方向上的均值参数和方差参数的顺序约束关系,并采用MCMC方法计算上述复杂约束条件下的参数验后分布,实现了多批次异总体数据的融合估计。
5.基于多源试验信息的命中概率融合评估方法定义了有验前样本容量约束的现场样本边缘分布的ML-II(Maximun Likelihood Type II)估计以及相应的边缘密度函数值,分别记为SCML-II(prior sample Size Constrained ML II)和SCMD(prior sample Size Constrained Marginal Density),提出了基于修正权值混合验后分布的正态随机变量分布参数的融合估计方法,改进了基于仿真可信度的正态分布参数融合估计方法,所得估计值具有较小的MSE和较强的抑制“淹没”的能力。提出了多元正态分布参数估计中的SCML-II估计和SCMD值,较好地解决了两向相关情况下的命中概率融合估计问题。改进了传统的多源验前信息融合结构,在混合验前分布中加入无信息验前,并在混合验后融合权重中采用上述定义的SCMD值,从而提高了多源试验信息融合方法的适应能力。
With the increasing complexity of weapons and sorts of mechatronic products, the dynamic changing process of products lifecycle properties has become more complicated, which brings diverse test evaluation means. Sorts of data (multistage and multi-source) should be synthesized to realize the proper modeling and analysis of products performance changing during development phase. In the domain of equipments test evaluation, the typical problems are multistage reliability growth test evaluation and multi-batch or multi-source weapons tactical and technical indices evaluation. Both problems show distinct features of dynamic population statistics, and the corresponding statistical inferences veracity will greatly affect the risk of equipments acceptance and usage. It has great theoretical significance and application value to carry out studies of dynamic population statistics in the domain of equipments test evaluation.
For the dynamic population statistics problems in equipments test evaluation, the essential theoretical problems are systematically studied for the first time. In both important domains of multistage reliability growth evaluation and multi-batch or multi-source hit probability synthetic evaluation, concrete and detailed studies are given to four types of representative problems, and several innovative approaches are proposed. The leading contents and outcomes are as follows.
1. The basic theory of dynamic population statistics in equipments test evaluation. After a systematical review of developments of dynamic population statistics, the essential features of dynamic population statistics are presented. By compare with other related subjects, the thesis grasps its basic connotation and several key theoretical problems. The preprocessing methods involved are analyzed, and three elementary approaches of dynamic population statistics are summarized and presented with discussion of their features and prospects: constraints based multi-population integrated estimation, linear model based dynamic population forecasting and Bayesian based multi-source prior information fusion.
2. Evaluation approaches of multistage reliability growth test with delayed fix mode. The reliability changing rules of exponential life type products are analyzed firstly. The MCMC (Markov Chain Monte Carlo) method is introduced to the computation of the ordinal constrained Bayesian posterior, and it’s easy to operate with high precision. Different acquisition ways of improvement factor and different conversion rules of adjacent stages failure rates are compared and discussed. In the improvement factor approach, a new conversion principle is put forward, which uses only the proportional relation and stochastic order relation and can restrain the arbitrary decision by human. Both approaches by improvement factor and ordinal constraint respectively are compared, and the general choosing rules are discussed. For the case of more stages, the linear model and Bayesian dynamic forecasting are introduced to realize the incursive estimation of failure rates.
3. Evaluation approaches of multistage reliability growth test with hybrid fix modes (instant & delayed fix modes). Two models for such process are presented: MS-NHPP-I&II (Multi-Stage Non-homogeneous Poisson Process Type I&II), followed with their features, application domains and choosing rules. For MS-NHPP-I, the ordinal constraints of failure intensities are established at stage terminals. For MS-NHPP-II, ordinal constraints of failure intensities are established at stage conjunctions. The Bayesian posterior is computed by MCMC based on Metropolis-Hastings principle. For multiple equipments tested simultaneously, the proportional relations are established on the mean value function at a particular point. And then by improvement factor, the multistage analysis diagram is established. Finally, by analysis of the linear relation of stage parameters in both models, the linear model is established based on the proportional intensity assumption, followed with parameters estimations and model check approaches.
4. Evaluation approaches of hit probability based on multi-batch test data. Firstly, the computations of missile hit probability are analyzed under complex conditions (cluster warhead, small sample size, target rotation, etc.) For the cluster warhead, a method of numerical integral mixed with statistical simulation is proposed. For small sample size, the altered Bootstrap and empirical Bayesian methods are presented for the bivariate normal variable. Based on the above, the distribution parameters variations are analyzed for the multi-batch test, and the ordinal constraints of the mean and variance parameters of both directions are established accordingly. By MCMC, the parameter posteriors can be obtained under complex constraints thus to realize the multi-batch test data fusion.
5. Evaluation approaches of hit probability based on multi-source test data. The thesis defines the prior sample size constrained ML-II (Maximum Likelihood Type II) estimation of the field data and the corresponding marginal density, denoted respectively as SCML-II (prior sample Size Constrained ML-II) and SCMD (prior sample Size Constrained Marginal Density). A novel way of fusion estimation of normal distribution parameters is presented based on mixed posterior with modified weights. Based on it, the simulation credibility based test evaluation method is improved for smaller MSE (Mean Square Error) and stronger capacity to restrain from obliteration phenomenon. As a further extension, the SCML-II and SCMD of multivariate normal distribution parameters are put forward to solve the hit probability computation with bidirectional correlation. Finally, the conventional fusion structure of multi-source prior information is improved for better applicability by adding the non-informative prior to the mixed prior and using SCMD in the mixed posterior weights.
论文以装备试验评估领域中的变动统计问题为背景,首次系统地研究了变动统计的基本理论问题,并在多阶段可靠性增长试验评估、多批次或多信源条件下的命中概率融合评估两个主要领域中,针对四大类典型问题展开了具体细致的研究工作,提出了若干创新性的变动统计方法。主要研究内容与成果如下:
1.装备试验评估中的变动统计基本理论系统地回顾了变动统计的发展历程与研究现状,提出了变动统计的主要特征。通过与其他相关研究领域的比较,提出了变动统计的基本内涵以及需要面对的几个关键的理论问题,给出了所涉及的数据预处理方法,归纳提出了三大类基本的变动统计方法:基于约束关系的多总体融合估计、基于线性模型的变动总体建模与预测、基于Bayes方法的多源验前信息融合,并对每种方法的特点和应用前景进行了分析和讨论。
2.多阶段延缓纠正可靠性增长试验评估方法分析了指数寿命型产品在这一过程中的可靠性指标变化规律。提出采用MCMC(Markov Chain Monte Carlo)方法计算顺序约束条件下的Bayes验后分布,具有较好的操作性和较高的计算精度。提出增长因子法中的一种新的变量转换原则,仅利用随机序关系和变量期望值之间的比例关系推导了变量转换方法,尽可能降低了人为因素所带来的转换原则的随意性。比较了顺序约束方法和增长因子法的特性,讨论了两类方法的选择原则。建立了各阶段失效强度之间的广义线性模型,并采用Bayes动态预测方法进行递推估计,适用于试验阶段数较多的情况。
3.多阶段含延缓纠正可靠性增长试验评估方法提出描述此类可靠性增长过程的两类模型MS-NHPP-I和MS-NHPP-I(IMulti-Stage Non-Homogeneous Poisson Process Type I & II),同时阐明了两类模型的特点、适用范围和选择原则。对于MS-NHPP-I模型,提出对阶段末尾的失效强度建立顺序约束关系。对于MS-NHPP-II模型,提出对相邻阶段衔接处的失效强度建立顺序约束关系,并采用基于Metropolis-Hastings原则的MCMC方法计算Bayes验后分布。针对多台设备同时投试的情况,提出选取特定时间的均值函数值建立比例关系,利用增长因子建立多阶段分析流程。最后,分析了两类模型中各阶段参数之间的线性关系,建立了比例强度假设下的线性模型,给出了参数估计和模型检验方法。
4.基于多批次试验信息的命中概率融合评估方法首先,针对单批次同总体数据,提出了复杂条件下(子母弹、小子样、目标旋转等)的导弹命中概率计算方法。在子母弹命中概率评估中,提出了数值积分与统计模拟相结合的计算方法。在小子样命中概率评估中,提出了二维正态分布变量的Bootstrap方法和经验Bayes方法。在此基础上,针对多批次异总体数据,分析了多批次试验过程中各个分布参数随批次的变动情况,建立了两个方向上的均值参数和方差参数的顺序约束关系,并采用MCMC方法计算上述复杂约束条件下的参数验后分布,实现了多批次异总体数据的融合估计。
5.基于多源试验信息的命中概率融合评估方法定义了有验前样本容量约束的现场样本边缘分布的ML-II(Maximun Likelihood Type II)估计以及相应的边缘密度函数值,分别记为SCML-II(prior sample Size Constrained ML II)和SCMD(prior sample Size Constrained Marginal Density),提出了基于修正权值混合验后分布的正态随机变量分布参数的融合估计方法,改进了基于仿真可信度的正态分布参数融合估计方法,所得估计值具有较小的MSE和较强的抑制“淹没”的能力。提出了多元正态分布参数估计中的SCML-II估计和SCMD值,较好地解决了两向相关情况下的命中概率融合估计问题。改进了传统的多源验前信息融合结构,在混合验前分布中加入无信息验前,并在混合验后融合权重中采用上述定义的SCMD值,从而提高了多源试验信息融合方法的适应能力。
With the increasing complexity of weapons and sorts of mechatronic products, the dynamic changing process of products lifecycle properties has become more complicated, which brings diverse test evaluation means. Sorts of data (multistage and multi-source) should be synthesized to realize the proper modeling and analysis of products performance changing during development phase. In the domain of equipments test evaluation, the typical problems are multistage reliability growth test evaluation and multi-batch or multi-source weapons tactical and technical indices evaluation. Both problems show distinct features of dynamic population statistics, and the corresponding statistical inferences veracity will greatly affect the risk of equipments acceptance and usage. It has great theoretical significance and application value to carry out studies of dynamic population statistics in the domain of equipments test evaluation.
For the dynamic population statistics problems in equipments test evaluation, the essential theoretical problems are systematically studied for the first time. In both important domains of multistage reliability growth evaluation and multi-batch or multi-source hit probability synthetic evaluation, concrete and detailed studies are given to four types of representative problems, and several innovative approaches are proposed. The leading contents and outcomes are as follows.
1. The basic theory of dynamic population statistics in equipments test evaluation. After a systematical review of developments of dynamic population statistics, the essential features of dynamic population statistics are presented. By compare with other related subjects, the thesis grasps its basic connotation and several key theoretical problems. The preprocessing methods involved are analyzed, and three elementary approaches of dynamic population statistics are summarized and presented with discussion of their features and prospects: constraints based multi-population integrated estimation, linear model based dynamic population forecasting and Bayesian based multi-source prior information fusion.
2. Evaluation approaches of multistage reliability growth test with delayed fix mode. The reliability changing rules of exponential life type products are analyzed firstly. The MCMC (Markov Chain Monte Carlo) method is introduced to the computation of the ordinal constrained Bayesian posterior, and it’s easy to operate with high precision. Different acquisition ways of improvement factor and different conversion rules of adjacent stages failure rates are compared and discussed. In the improvement factor approach, a new conversion principle is put forward, which uses only the proportional relation and stochastic order relation and can restrain the arbitrary decision by human. Both approaches by improvement factor and ordinal constraint respectively are compared, and the general choosing rules are discussed. For the case of more stages, the linear model and Bayesian dynamic forecasting are introduced to realize the incursive estimation of failure rates.
3. Evaluation approaches of multistage reliability growth test with hybrid fix modes (instant & delayed fix modes). Two models for such process are presented: MS-NHPP-I&II (Multi-Stage Non-homogeneous Poisson Process Type I&II), followed with their features, application domains and choosing rules. For MS-NHPP-I, the ordinal constraints of failure intensities are established at stage terminals. For MS-NHPP-II, ordinal constraints of failure intensities are established at stage conjunctions. The Bayesian posterior is computed by MCMC based on Metropolis-Hastings principle. For multiple equipments tested simultaneously, the proportional relations are established on the mean value function at a particular point. And then by improvement factor, the multistage analysis diagram is established. Finally, by analysis of the linear relation of stage parameters in both models, the linear model is established based on the proportional intensity assumption, followed with parameters estimations and model check approaches.
4. Evaluation approaches of hit probability based on multi-batch test data. Firstly, the computations of missile hit probability are analyzed under complex conditions (cluster warhead, small sample size, target rotation, etc.) For the cluster warhead, a method of numerical integral mixed with statistical simulation is proposed. For small sample size, the altered Bootstrap and empirical Bayesian methods are presented for the bivariate normal variable. Based on the above, the distribution parameters variations are analyzed for the multi-batch test, and the ordinal constraints of the mean and variance parameters of both directions are established accordingly. By MCMC, the parameter posteriors can be obtained under complex constraints thus to realize the multi-batch test data fusion.
5. Evaluation approaches of hit probability based on multi-source test data. The thesis defines the prior sample size constrained ML-II (Maximum Likelihood Type II) estimation of the field data and the corresponding marginal density, denoted respectively as SCML-II (prior sample Size Constrained ML-II) and SCMD (prior sample Size Constrained Marginal Density). A novel way of fusion estimation of normal distribution parameters is presented based on mixed posterior with modified weights. Based on it, the simulation credibility based test evaluation method is improved for smaller MSE (Mean Square Error) and stronger capacity to restrain from obliteration phenomenon. As a further extension, the SCML-II and SCMD of multivariate normal distribution parameters are put forward to solve the hit probability computation with bidirectional correlation. Finally, the conventional fusion structure of multi-source prior information is improved for better applicability by adding the non-informative prior to the mixed prior and using SCMD in the mixed posterior weights.
引文
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