The escalating occurrence of ship-pier collisions poses a substantial threat to coastal bridge infrastructures. To avert such accidents, various specifications have introduced several impact force models, yet engineers strive for accurate predictions. This study presents a framework for predicting impact forces by combining a precise finite element (FE) model, machine learning algorithms, and fast Fourier transform (FFT). Firstly, a reliable FE model is constructed to simulate barge collisions with a double-column pier, encompassing analyses of energy transformation, structural damage, time-frequency impact forces, and structural response. Subsequently, a machine learning approach combined with FFT is employed to predict the impact force, with a discussion on the impact force's sensitivity to barge weight and velocity. The study also presents two potential applications of the proposed framework. Numerical results demonstrate that the framework accurately predicts the duration and frequency series of impact forces. The sensitivity analysis reveals the importance of closely monitoring barge weight in comparison to velocity during the design and management stages. Additionally, the study reveals that increasing barge velocity and weight prolongs the impact duration and amplifies the response peak, with time-series responses primarily concentrated in a limited low-frequency band. In summary, this study not only proposes a novel and accurate framework for predicting the time-history of impact forces through time-frequency analysis but also offers valuable insights into preventing catastrophic ship-pier collisions and mitigating their impact on coastal bridge infrastructure.