Umbrella drills for small vertical shaft construction are limited by wellbore space and require lower weight for easy portability, safe and reliable structure, and less prone to resonance. In this paper, the model is simplified, and the simulation data are obtained by parametric solution method, and the relationship between input parameters and output response is described by surrogate model; Using Sobol’s sensitivity analysis method for parameter analysis, using fuzzy analytic hierarchy process to transform multi-objective optimization problems into a single objective optimization model for comprehensive optimization, reducing the complexity of the optimization model; Improve the locust optimization algorithm and apply it to the optimization solution in this article. The results show that the quality, stress, and displacement deformation of the optimized results have been improved, and the environmental excitation frequency is more than 30% away from adjacent frequencies, indicating an improvement in vibration resistance performance.