Accurate life prediction and reliability evaluation of lithium-ion batteries are of great significance for predictive maintenance. In the whole life cycle of a battery, the accurate description of the dynamic and stochastic characteristics of life has always been a key problem. In this paper, the concept of the digital twin is introduced, and a digital twin for reliability based on remaining useful cycle life prediction is proposed for lithium-ion batteries. The capacity degradation model, stochastic degradation model, life prediction, and reliability evaluation model are established to describe the randomness of battery degradation and the dispersion of the life of multiple cells. Based on the Bayesian algorithm, an adaptive evolution method for the model of the digital twin is proposed to improve prediction accuracy, followed by experimental verification. Finally, the life prediction, reliability evaluation, and predictive maintenance of the battery based on the digital twin are implemented. The results show the digital twin for reliability has good accuracy in the whole life cycle. The error can be controlled at about 5% with the adaptive evolution algorithm. For battery L1 and L6 in this case, predictive maintenance costs are expected to decrease by 62.0% and 52.5%, respectively.

Effective recovery after disruptions is essential to improve system resilience. For many distributed systems such as offshore wind farms and communication networks, spatial location characteristics and limited maintenance resources lead to discontinuous changes in performance during system recovery. However, the stepwise performance is frequently ignored. The coupling relationship between the system and maintenance teams makes it difficult to improve the system resilience from the recovery perspective. In this article, a new method that combines the resilience importance measure and enhanced pigeon-inspired optimization (PIO) is presented to optimize the system resilience under stepwise recovery conditions. First, this study proposes a resilience-oriented importance measure that evaluates the recovery priority for each component. Second, an optimization model is established to minimize the system resilience loss by joint optimization of recovery sequence and task assignment under the conditions of multiple maintenance teams. Third, the resilience importance measure is combined with roulette wheel selection to form a high-quality intitle swarm of PIO. Fourth, an importance measure-based PIO with a Gaussian mutation and adaptive crossover operator is designed to find an optimization solution for system resilience. Finally, the recovery of a network system consisting of 32 nodes and 71 edges is studied. Compared with the stochastic method and traditional PIO, the proposed method in this study reduces the system resilience loss by 48.87 and 15.54%, respectively.

The scarcity of time-series data constrains the accuracy of online reliability assessment. Data expansion is the most intuitive way to address this problem. However, conventional small-sample reliability evaluation methods either depend on prior knowledge or are inadequate for time series. This article proposes a novel autoaugmentation network, the worm Wasserstein generative adversarial network, which generates synthetic time-series data that carry realistic intrinsic patterns with the original data and expands a small sample without prior knowledge or hypotheses for reliability evaluation. After verifying the augmentation ability and demonstrating the quality of the generated data by manual datasets, the proposed method is demonstrated with an experimental case: the online reliability assessment of lithium battery cells. Compared with conventional methods, the proposed method accomplished a breakthrough in the online reliability assessment for an extremely small sample of time-series data and provided credible results.