广义维修高档数控机床的贝叶斯可靠性评估理论及应用研究

Reliability test and reliability assessment are the important parts of reliability technology for numerically controlled (NC) machine tools. To improve the reliability of the domestic high-grade NC machine tools, whose optimal design of reliability test, reliability assessment and accuracy verification of assessment methods will be studied in this project. In view of the features of imperfect repair and small sample failure data for high-grade NC machine tools, based on the theory of generalized renewal process (GRP) for repairable systems and Bayesian principle, reliability assessment models for multiple NC machine tools with time truncation test will be developed. Using Fisher information matrix method and Markov chain Monte Carlo (MCMC) method, etc, some problems including effect analysis of reliability assessment results with different prior information of model parameters and posterior sampling methods will be discussed. Through theoretical simulation and practical verification, some reliability testing techniques and reliability assessment methods for high-grade NC machine tools will be presented. The proposed assessment methods can save testing costs and eliminate the uncertainty of assessment models with small sample data by using the optimal testing design and incorporating prior information with testing information for machine tools, and thus its assessment results are more reasonable. The studies can provide a scientific basis for improving machine tools reliability and for reducing maintenance costs, and have an important theoretical and engineering application value.

可靠性试验和可靠性评估是数控机床可靠性技术的重要组成部分。为了提高国产高档数控机床的可靠性，拟开展其可靠性试验设计、可靠性评估及评估方法准确性的验证研究。首先根据高档数控机床的不完全维修及少样本故障数据的特点，基于可修系统广义更新过程（GRP）理论及贝叶斯（Bayes）原理，拟建立多台广义维修数控机床时间截尾试验的Bayes可靠性评估模型。其次应用Fisher信息矩阵法及马尔科夫链蒙特卡洛（MCMC）等方法，研究评估模型中参数先验信息和后验分布抽样方法对可靠性评估结果的影响。最后通过理论仿真及实际工程应用验证，拟提出高档数控机床的可靠性试验技术及可靠性评估方法。所提方法基于最佳可靠性试验设计，综合应用数控机床先验及试验信息，可节约试验成本并消除少样本数据评估模型的不确定性，所得评估结果更趋合理。项目的研究可为提高高档数控机床可靠性及减少维修费用提供科学依据，具有重要的理论和工程应用价值。

应用可修系统广义更新过程理论及贝叶斯原理建立了多台广义维修高档数控机床时间截尾试验的Bayes可靠性评估模型，主要研究内容包括数控机床可靠性试验优化设计及仿真验证；广义维修数控机床的Bayes可靠性评估；广义维修可靠性评估方法准确性验证及实际工程应用。提出了高档数控机床的可靠性试验技术及可靠性评估方法，该方法可节约试验成本并消除少样本数据评估模型的不确定性。在可靠性优化设计方面，为了保证可靠性优化设计问题的可靠性约束条件，在一次二阶矩可靠性优化设计方法的基础上，提出了一种基于四阶矩的单环可靠性设计优化方法。该方法通过把可靠性优化问题转变为单环的确定性优化问题，与双环的可靠性优化设计方法相比，提高了优化效率。同时为了克服求解高度非线性结构功能函数可靠性优化设计时出现的低效率和优化结果不稳定的缺点，提出了改进的共轭梯度方法。该方法通过修正共轭梯度法的相关参数和算法，探寻最优设计点的方向，可提高求解效率。与常用方法相比，改进的共轭梯度方法具有更高的效率和更好的鲁棒性。项目的研究为提高高档数控机床可靠性及减少维修费用提供科学依据，具有重要的理论和工程应用价值。