基于随机参数逆高斯过程的加速退化建模方法

为了将随机参数退化模型应用于加速退化试验以提高可靠性评估结果的准确性，本文以逆高斯过程为例研究了基于随机参数退化模型的加速退化建模方法。利用加速系数不变原则推导出逆高斯过程各参数在不同应力下应满足的关系式，由此建立参数的加速模型，计算出加速系数，进而将加速应力下的退化数据等效折算到工作应力下。采用了随机参数的共轭先验分布，并且利用最大期望算法估计出随机参数的超参数值。仿真试验验证了所提方法的可行性和有效性，实例应用说明了所提方法具有较好的工程应用价值。

Accelerated degradation modeling method based on Inverse Gaussian processes with random parameters

In order to apply degradation models with random parameters to accelerated degradation tests to improve the accuracy of reliability evaluation, an accelerated degradation modeling method based on degradation models with random parameters was studied with Inverse Gaussian processes taken as examples. First, acceleration coefficient constant principle was used to deduce the relationships that the parameters of Inverse Gaussian process should satisfy under different stresses. Then, the acceleration models of parameters were constructed and acceleration coefficients were computed. So accelerated degradation data was extrapolated from accelerated stress levels to normal stress level. The conjugate prior distributions of random parameters were used and maximization expectation algorithm was utilized to estimate hyper-parameters. Simulation tests validate the feasibility and effectiveness of the proposed method, and a case study demonstrates that the proposed method has good engineering application value.