基于马尔可夫链蒙特卡罗的实时可靠性预测方法研究

针对一般的非线性性能退化轨道模型中误差项方差未知的情况,研究基于贝叶斯方法的实时性能退化可靠性预测问题.为了处理未知的误差项方差,引入相应的标准差的无信息先验分布,并进一步结合退化轨道模型中随机参数的先验分布,利用马尔可夫链蒙特卡罗方法得到随机参数及误差项标准差的联合后验分布的采样值,进而实时预测产品在未来一段时间内的可靠度.基于疲劳裂纹增长数据的数值仿真实验表明,该方法可以有效地预测到产品可靠性的下降,从而可以为预测维护提供依据.

REAL-TIME RELIABILITY PREDICTION METHOD BASED ON MARKOV CHAIN MONTE CARLO

In order to predict the product's real-time reliability when the variance of error terms in its nonlinear degradation path model was unknown,a Bayesian analysis method was presented.The noninformative prior of the standard deviation of error terms was introduced for Bayesian analysis.Then,given the prior density of the random coefficients in the degradation path model,the Markov Chain Monte Carlo method was adopted to generate samples of joint posterior distribution of random coefficients and unknown standard deviation.By these posterior samples,the product's reliability during a certain period in the future was predicted.The numerical example by use of fatigue crack growth data shows the effectiveness of the proposed method.