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The inertial vibration of the force measurement system (FMS) has a large influence on the force measuring result of aircraft, especially on some tests carried out in high-enthalpy impulse facilities, such as in a shock tunnel. When force tests are conducted in a shock tunnel, the low-frequency vibrations of the FMS and its motion cannot be addressed through digital filtering because of the inertial forces, which are caused by the impact flow during the starting process of the shock tunnel. Therefore, this paper focuses on the dynamic characteristics of the performance of the FMS. A new method—i.e., deep-learning-based single-vector dynamic self-calibration (DL-based SV-DSC) of an impulse FMS, is proposed to increase the accuracy of aerodynamic force measurements in a shock tunnel. A deep-learning technique is used to train the dynamic model of the FMS in this study. Convolutional neural networks with a simple structure are applied to describe the dynamic modeling so that the low-frequency vibration signals are eliminated from the test results of the shock tunnel. By validation of the force test results measured in a shock tunnel, the current trained model can realize intelligent processing of the balance signals of the FMS. Based on this new method of dynamic calibration, the reliability and accuracy of force data processing are well verified.