Contribution of vibrational sources during operation is one of the crucial pieces of information to be identified. For contribution analysis, there are many different approaches such as classical transfer path analysis (TPA) formulation and the cross-talk cancellation method, etc. Among these, data-driven methods based on machine learning approaches have recently been proposed, showing prominent validation results using numerical and lab-scale experimental datasets [1, 2]. In this study, the deep learning framework for operational TPA is enhanced to handle non synchronously measured source-side and target responses. To address the non-synchronous measurement problem, a time-lag estimator is developed using a deep neural network together with a time-lag augmentation scheme. The introduced time-lag estimator is combined with a DeepONet that predicts underwater radiated noise (URN) propagated from ship equipment vibration. The DeepONet consists of one branch network to estimate the input–output relations between equipment vibrations and URN, and several trunk networks to identify the functions of frequency, ship velocity, and operational conditions. The constructed DeepONet is trained using an acquired dataset measured under real environments at sea for a surface ship. The training is conducted with a sequential training scheme: an auto-encoder/decoder for vibration input is first trained, and next, with the encoder frozen, the URN predictor is trained. After training the DeepONet, it is used to estimate the contributions of each vibration input by turning off the corresponding input of the trained model. This contribution analysis procedure is validated by comparing the summation of all contributions with measured responses. The contribution analysis results are consistent with long-stacked engineering general sense, demonstrating the effectiveness of the proposed framework.