Accurately estimating gas usage is essential for the efficient functioning of gas distribution networks and saving operational costs. Traditional methods rely on centralized data processing, which poses privacy risks. Federated learning (FL) offers a solution to this problem by enabling local data processing on each participant, such as gas companies and heating stations. However, local training and communication overhead may discourage gas companies and heating stations from actively participating in the FL training process. To address this challenge, we propose a Hierarchical FL Incentive Mechanism for Gas Usage Estimation (HI-GAS), which has been testbedded in the ENN Group, one of the leading players in the natural gas and green energy industry. It is designed to support horizontal FL among gas companies, and vertical FL among each gas company and heating station within a hierarchical FL ecosystem, rewarding participants based on their contributions to FL. In addition, a hierarchical FL model aggregation approach is also proposed to improve the gas usage estimation performance by aggregating models at different levels of the hierarchy. The incentive scheme employs a multi-dimensional contribution-aware reward distribution function that combines the evaluation of data quality and model contribution to incentivize both gas companies and heating stations within their jurisdiction while maintaining fairness. Results of extensive experiments validate the effectiveness of the proposed mechanism.

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