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Ultrasonic wave-assisted underwater flux-cored arc welding (FCAW) has the potential to control the dynamic bubble and then improve arc stability. In this study, the four indexes evaluation methods to determine arc stability, i.e., oscillograms, cyclograms, probability distribution, variation coefficients of the welding current and arc voltage, were conducted to study the effect of ultrasonic wave on the arc stability. Results show that it is reasonable to evaluate the variation in arc stability with the welding parameters including wire feed speed and arc voltage, or without/with an ultrasonic wave by using the four indexes evaluation methods. Further, the control of the dynamic bubble induced by the exertion of ultrasonic wave can be used to explain why the arc stability is improved. The key points to excellent arc stability depend on both the designation of the welding parameters and reasonable control of the bubble with structural integrity. Therefore, through the novel method which combines optimized welding parameters with a stable bubble environment, the achieved welding process can effectively reduce the bubble disturbance and enhance the arc stability. Results presented in the paper aim to understand the combined influence mechanism of welding parameters and ultrasonic wave on the arc stability in underwater wet welding.