In industry 4.0, Industrial Cyber–Physical Systems (ICPS) integrate industrial machines with computer control and data analysis. Federated Learning (FL) improves this by enabling collaborative machine learning and improvement while maintaining data privacy. This method improves the security, and intelligence of industrial processes. FL-based frameworks proposed in the literature do not perform rigorous validation of collaborators’ behaviors, especially with regard to reliability and operational correctness. In contrast, non-FL-based cyber–physical systems have already been verified in the literature using formal methods. Therefore, there is a significant gap in the application of these verification techniques to FL-based systems. To fill this gap, we explore the possibility of introducing formal verification into FL-based cyber–physical systems, starting with our FedGA-Meta published framework. Thus, our research focuses on expanding our FedGA-Meta framework in the context of Industry 4.0, this paper delves into a comprehensive validation of the framework’s operational reliability and correctness within ICPS based on FL. To achieve this, we employ Timed Computation Tree Logic (TCTL) for the precise specification of system requirements, coupled with Labeled Transition Systems (LTS) to construct the ICPS semantic in detail. Through the usage of Uppaal for both simulation and model-checking purposes, we rigorously test the framework under a variety of operational scenarios. This approach allows us to confirm the system’s reliability and correctness, ensuring that the FedGA-Meta framework operates effectively and as intended within the demanding environments of Industry 4.0.

中文翻译：

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确保联合的正确性：工业信息物理系统中联邦学习的形式验证


在工业 4.0 中，工业信息物理系统 （ICPS） 将工业机器与计算机控制和数据分析集成在一起。联邦学习 （FL） 通过在维护数据隐私的同时实现协作机器学习和改进来改善这一点。这种方法提高了工业流程的安全性和智能性。文献中提出的基于 FL 的框架没有对合作者的行为进行严格的验证，尤其是在可靠性和操作正确性方面。相比之下，非基于 FL 的信息物理系统已经在文献中使用形式化方法进行了验证。因此，这些验证技术在基于 FL 的系统中的应用存在重大差距。为了填补这一空白，我们探索了将形式验证引入基于 FL 的信息物理系统的可能性，从我们的 FedGA-Meta 发布的框架开始。因此，我们的研究重点是在工业 4.0 的背景下扩展我们的 FedGA-Meta 框架，本文深入探讨了基于 FL 的 ICPS 中该框架的运行可靠性和正确性的全面验证。为了实现这一目标，我们采用定时计算树逻辑 （TCTL） 来精确规范系统需求，并结合标记转换系统 （LTS） 来详细构建 ICPS 语义。通过将 Uppaal 用于仿真和模型检查目的，我们在各种操作场景中对框架进行了严格测试。这种方法使我们能够确认系统的可靠性和正确性，确保 FedGA-Meta 框架在工业 4.0 的苛刻环境中有效运行并按预期运行。