A Bayesian Degeneracy Modelling Approach Based on Iterative Optimisation of Posterior Weights

Aiming at the difficulty of a posteriori estimation bias due to insufficient quality of a priori information in Bayesian degradation modelling, this paper proposes an iterative Bayesian updating framework based on dynamic a posteriori weight adjustment. Based on the Wiener degeneration process, the progressive correction of the a priori bias is achieved by establishing the dynamic weight relationship between the prior and posterior distributions and correcting the hyperparameter estimates one by one. The sequential Bayesian updating mechanism is innovatively introduced to iteratively incorporate the field degradation data into the model with adjustable weights: in each update, the historical a posteriori hyperparameters are transformed into the dynamic prior, and the hyperparameter estimates are optimised by the Expectation Maximisation (EM) algorithm, which progressively diminishes the dominant role of the initial a priori distribution on the model. Taking the GaAs laser current degradation data as the object, the experimental results show that: with the increase of the number of a posteriori weight iterations, the mean square error (MSE) of the remaining lifetime prediction significantly decreases from 219,052 h2 in the first round of iterations to 109,993 h2 after three rounds of iterations, which is a decrease of 49.8%; the hyperparameters a and d show a linear growth (5.621 → 12.621) and an exponential decay (1.521 × 10–3 → 0.969 × 10–3), verifying the adaptive regulation ability of the dynamic weighting mechanism on the model complexity. Compared with the traditional single Bayesian updating method, the proposed framework achieves a 54.8% reduction in the average prediction error of the remaining life (331 h) through the iterative optimisation of the a posteriori weights, which provides a theoretical breakthrough and an example of engineering practice for the accurate assessment of the reliability in the case of small samples and high truncation tail scenarios.