The value range of the failure threshold will generate an uncertain influence on the prediction results for the remaining useful life (RUL) of equipment. Most of the existing studies on the RUL prediction assume that the failure threshold is a fixed value, as they have difficulty in reflecting the random variation of the failure threshold. In connection with the inadequacies of the existing research, an in-depth analysis is carried out to study the effect of the random failure threshold (RFT) on the prediction results for the RUL. First, a nonlinear degradation model with unit-to-unit variability and measurement error is established based on the nonlinear Wiener process. Second, the expectation-maximization (EM) algorithm is used to solve the estimated values of the parameters of the prior degradation model, and the Bayesian method is used to iteratively update the posterior distribution of the random coefficients. Then, the effects of three types of RFT constraint conditions on the prediction results for the RUL are analyzed, and the probability density function (PDF) of the RUL is derived. Finally, the degradation data of aero-turbofan engines are used to verify the correctness and advantages of the method.

中文翻译：

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考虑随机故障阈值的设备剩余使用寿命预测方法

故障阈值的取值范围会对设备剩余使用寿命（RUL）的预测结果产生不确定的影响。现有的关于 RUL 预测的大多数研究都假设故障阈值是一个固定值，因为它们难以反映故障阈值的随机变化。结合现有研究的不足，深入分析随机失效阈值（RFT）对RUL预测结果的影响。首先，基于非线性维纳过程建立具有单元间可变性和测量误差的非线性退化模型。其次，使用期望最大化（EM）算法求解先验退化模型的参数估计值，使用贝叶斯方法迭代更新随机系数的后验分布。然后，分析了三种RFT约束条件对RUL预测结果的影响，推导了RUL的概率密度函数(PDF)。最后，利用航空涡扇发动机的退化数据验证了该方法的正确性和优势。