Search

Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics. These features have an uncertain effect on the remaining useful life (RUL) prediction of the equipment. The current data-driven RUL prediction method has not systematically studied the nonlinear hidden degradation modeling and the RUL distribution function. This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model. Based on the historical measured data of similar equipment, the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient. Using the on-site measured data of the target equipment, the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm. The analytical form of the RUL distribution function is derived based on the first hitting time distribution. Combined with the two case studies, the proposed method is verified to have certain advantages over the existing methods in the accuracy of prediction.

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

The degradation of data and failure data is used to make the maintenance decision of equipment in this paper. Firstly, the Wiener process is used to build the degradation model which is according to the degradation data of the equipment. Then, the random distribution coefficient of failure threshold is estimated by the failure data of the equipment, and we also derive the analytical expression of the remaining useful lifetime (RUL) distribution of the equipment. Finally, the maintenance decision model is established according to the renewal-reward theory and RUL prediction data which can achieve optimal maintenance strategy of equipment. The simulation example shows that the method in this paper can prolong the run time cost of equipment and effectively reduce the life cycle which has broad application prospects.

For the problem of remaining useful lifetime (RUL) prediction of nonlinear system, the existing methods have not systematically carried out the studies on nonlinear degradation modeling with measurement error and random effect, priori parameter estimation and the corresponding RUL prediction. In this paper, a nonlinear Wiener process is used to establish a nonlinear degradation model with the consideration of measurement error and random effect to describe the implicitness, personality difference and nonlinearity of degradation process of a class of device. The expectation maximum (EM) algorithm is used to obtain the estimates of the fixed coefficient and the priori distributions of the random coefficients in the degradation model. Using the current monitoring data of the target device, the posteriori distribution of random coefficients is iteratively updated based on Bayesian inference. Using the full-probability formula, the remaining useful lifetime distribution of device is derived based on the first hitting time (FHT) distribution. A simulation example is analyzed to verify the correctness and advantage of this method.

Number identification of maintenance equipment is an emergent problem of support resources deployment for aircraft in design and development phase. Taking maintenance mission requirements as input, queuing model of batch arrival LRU (Line Replaceable Units) based on Queuing Theory is constructed. Effects of maintenance equipment failure on queuing model are analyzed. Being subjected to the constraint of average waiting time to repair, the number of maintenance equipment required is determined, which will provide a valid method to determine the number of maintenance equipment for aircraft being developed.