To address the issues of node overload and failure caused by resource constraints in Industrial Internet of Things （IIoT） edge computing environments， this paper proposed a fault-tolerant method based on edge intelligence — Sparse Graph ATtention-based Generative Adversarial Network （SGAT-GAN）. This method integrated a fault prediction mechanism and employed a Fault Embedding Encoder （FEE） to achieve real-time fault detection， classification， and prediction， thereby enhancing the system’s fault-tolerance capability. On this basis， this method combined Generative Adversarial Network （GAN） with a preemptive migration strategy to select the optimal strategy for intelligent fault recovery， thereby providing an efficient and intelligent solution for IIoT edge computing systems. Experimental results in a Raspberry Pi-based edge environment demonstrate that this method outperforms four state-of-the-art methods — Proactive Coordinated Fault Tolerance （PCFT）， Clustering-based Multiple Objective Dynamic Load Balancing technique （CMODLB）， self-supervised deep proxy-based edge computing fault tolerance method DeepFT， and Preemptive migration prediction Generative Adversarial Network （PreGAN） — in terms of average detection precision and average classification accuracy of faults. Specifically， compared with the best-performing state-of-the-art method PreGAN， the proposed method achieves improvements of 1.96 and 1.62 percentage points in these two metrics， respectively， validating its effectiveness and superiority in enhancing the reliability of IIoT edge computing systems.