<p>This study investigates the stability of a crane X-shaped double-boom frame, incorporating the mechanical analysis of a simplified model. A theoretical calculation method is proposed for the structure under study by integrating the deflection slope equation. Calculation results were validated using finite element analysis, with the super-lift mast on a ring rail crane as an example. The approximate solution shows a 3.1 % deviation from the example, meeting the criteria for practical engineering applications. This study examines the influence of the hinge point location on the results and proposes a generalized regression neural network model optimized using the Northern Goshawk optimization algorithm to fit the data. The optimized model achieves a test set R² value of 0.989, satisfying accuracy requirements. The proposed theoretical framework provides valuable insights for similar structural designs and demonstrates potential for practical engineering implementation.</p>