  The emerging industrial metaverses realize the mapping 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 enhancing 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.
