Remaining useful life estimation considering threshold epistemic uncertainty with uncertain differential equation

Remaining useful life (RUL) prediction is one of the key problems in equipment operation and maintenance. In some engineering practices, sufficient degradation observations can not be obtained due to limitations in cost, technology, and time. Under these situations, several degradation models are established using uncertain processes, and based on which the RULs are predicted under belief reliability theory. Although these methods showed advantages in dealing with small sample sizes, they all regarded the failure threshold as a known constant. However, as the system will be used by a diverse range of users, the failure threshold can vary appreciably with different using scenarios. Furthermore, due to the unclear understanding and insufficient collection of the actual operation process by users, the determination of the failure threshold is quite subjective. If the threshold is simply regarded as a known constant, it will cause inaccuracies in the reliability assessment and the scheduling of maintenance, which may further lead to unnecessary losses. Therefore, this work develops a method to estimate RUL with an uncertain failure threshold based on a degradation model constructed by the uncertain differential equation. Unknown parameters in the established degradation model are estimated by the method of moment based on residuals to alleviate the problem in which observation intervals are not close enough. The effectiveness of the proposed methodology is verified through a degradation data set.