Blockchain-based Federated Learning for Industrial Metaverses: Incentive Scheme with Optimal AoI

The emerging industrial metaverses realize the map-ping and expanding operations of physical industry into virtual space for significantly upgrading intelligent manufacturing. The industrial metaverses obtain data from various production and operation lines by Industrial Internet of Things (IIoT), and thus conduct effective data analysis and decision-making, thereby en-hancing the production efficiency of the physical space, reducing operating costs, and maximizing commercial value. However, there still exist bottlenecks when integrating metaverses into IIoT, such as the privacy leakage of sensitive data with commercial secrets, IIoT sensing data freshness, and incentives for sharing these data. In this paper, we design a user-defined privacy-preserving framework with decentralized federated learning for the industrial metaverses. To further improve privacy protection of industrial metaverse, a cross-chain empowered federated learning framework is further utilized to perform decentralized, secure, and privacy-preserving data training on both physical and virtual spaces through a hierarchical blockchain architecture with a main chain and multiple subchains. Moreover, we introduce the age of information as the data freshness metric and thus design an age-based contract model to motivate data sensing among IIoT nodes. Numerical results indicate the efficiency of the proposed framework and incentive mechanism in the industrial metaverses.