CAJ | 학술논문

为解决复杂系统多失效模式相关性难以判别与量度的问题，提出一种基于竞争风险理论的多失效模式统计相关性分析模型。采用多元对数正态分布建立系统的联合失效分布，构造基于条件概率的极大似然函数，运用模拟退火算法对极大似然估计值进行优化求解。在大样本条件下，凭借Fisher信息矩阵获得极大似然估计量的渐近协方差矩阵，并采用Delta方法推导出相关矩阵的方差。建立相关性p值假设检验过程，判别各竞争失效模式间的相关关系与相关程度。通过对燃料电池发动机的故障数据进行分析，验证所建模型的可行性和有效性，为竞争失效系统的可靠性预测和分配提供理论依据，为研究最优维修策略提供技术基础。
위해결복잡계통다실효모식상관성난이판별여량도적문제，제출일충기우경쟁풍험이론적다실효모식통계상관성분석모형。채용다원대수정태분포건립계통적연합실효분포，구조기우조건개솔적겁대사연함수，운용모의퇴화산법대겁대사연고계치진행우화구해。재대양본조건하，빙차Fisher신식구진획득겁대사연고계량적점근협방차구진，병채용Delta방법추도출상관구진적방차。건립상관성p치가설검험과정，판별각경쟁실효모식간적상관관계여상관정도。통과대연료전지발동궤적고장수거진행분석，험증소건모형적가행성화유효성，위경쟁실효계통적가고성예측화분배제공이론의거，위연구최우유수책략제공기술기출。
To overcome the difficulties in discriminating and measuring the correlation between multiple failure modes of complex systems, a statistical correlation analysis model for multiple failure modes is proposed based on competing risks theory. The combined failure distribution of the system is established with multivariate log-normal distribution, and a conditional probability-based maximum likelihood function is constructed with its esti-mates optimized by using simulated annealing algorithm. In large sample condition, the asymptotic covariance matrix of maximum likelihood estimates is obtained by means of Fisher information matrix, and then Delta method is used to derive the variance of correlation matrix. Then, p-values hypothesis testing procedures are developed to discrimi-nate the relationship and degree of correlation between competing failure modes. Finally an analysis on the fault data of a fuel cell engine is conducted to verify the feasibility and effectiveness of the model built. The research provides a theoretical basis for the reliability prediction and allocation of competing failure system and a technical foundation for the study on optimal maintenance strategy.