Reliability analysis for structural systems relies on an accurate surrogate model. Currently, several multiple Kriging methods are utilized to calculate the failure probability. However, existing multiple Kriging methods for the reliability analysis have generally not incorporated model form selection into the modeling process, resulting in inaccurate probability of failure estimates. To overcome the shortcomings of existing multiple Kriging methods, this article presents an adaptive Bayesian model averaging-based multiple Kriging method. The proposed method utilizes Bayesian model averaging to incorporate an ensemble of individual Kriging models, each composed of different basis functions. The effect heredity principle is employed to enhance the model search efficiency, and the Occam's Window selection strategy is implemented to remove the Kriging models with poor prediction performance from the candidate set. For the final ensemble predictions, each single Kriging model is weighted based on its corresponding posterior model probability. Four benchmark examples are applied to validate the proposed new methods. Results revealed that the proposed method notably improves efficiency and accuracy estimates of failure probability.

Remaining useful life (RUL) prediction is vital for the safety of engineering assets. In the real scenario, due to the lack of failure data and variable working conditions, the accuracy of predictive RUL is significantly compromised as models struggle to generalize across diverse operating environments. Existing solutions manage to shift the degradation information from the ideal laboratory environment to the complex real-world environment. However, they fail to consider the heterogeneity of operating machines under different working conditions. This ignorance of inherent properties will eventually hamper the accuracy of RUL prediction. Consequently, a novel Bayesian adversarial Fast Linear Attention with a Single Head (FLASH) Transformer with feature disentanglement model (BAFTFD) was proposed in this article to tackle with the problem. The proposed BAFTFD model can disentangle the private feature representations from the raw data, preserving the shared feature representation for the prediction. The adversarial training method is also exploited to facilitate the transfer of degradation knowledge. Besides, the feature extractor is equipped with the effective FLASH Transformer model to retain the most informative degradation features for model training, improving the efficiency of feature extraction. Moreover, considering the impact of insufficient training data, inherent data noise on the trustworthiness of the predictive results, the Bayesian DL method is adopted to quantify the prediction uncertainties, ensuring the reliability of maintenance decisions. Two commercial turbofan datasets are leveraged to validate the designed model.