Accurately estimating the state of equipment plays an important role in ensuring the efficient operation of Industrial 4.0 systems. This paper focuses on monitoring the operating state and detecting the faults of beam pumping units under the condition of heavy noise within the Industrial Internet of Things. On the one hand, the equipment operating state monitoring system designed in this paper uses an acceleration sensor, the signal of which contains considerable noise that greatly reduces the motion state estimation accuracy. On the other hand, the complexity of the indicator diagrams of beam pumping units makes it difficult to extract features, which limits the ability to improve the fault detection accuracy. To overcome these issues, first, a period estimation method based on self-checking that employs acceleration data is proposed to effectively overcome the influence of complex noise on the estimated data period; second, a denoising method based on a physical model is proposed to effectively reduce the influence of complex noise on the acceleration-based displacement estimation; third, a method for detecting the faults of beam pumping units based on edge intelligence is proposed to effectively improve the fault detection accuracy while maintaining a low computational demand. Extensive experiments on real data verify the effectiveness of the proposed method. To our knowledge, this is the first work to discuss the impact of the quality of data on the performance of fault detection of beam pump units.