Objectives The sloshing load is one of the most important and complex loads in the LNG carrier cargo containment system, but it is difficult to calculate or measure accurately due to the simplifications in numerical simulations and model experiments. To obtain accurate time-history characteristics of the sloshing load and enable real-time health monitoring of the LNG carrier cargo containment system, the inverse impulse-space superposition method is used to measure the local response of the structure and deduce the sloshing load and the response of high-stress regions (hotspots).

Methods Based on the improved inverse impulse-space superposition method, an inverse mathematical model of measuring point positions and sloshing load positions is established to predict multi-region loads. By utilizing the time-shift property of the convolution integral, the Duhamel integral is reformulated and discretized into a matrix equation, enabling the prediction of sloshing loads under various time steps. The matrix equation is solved using the least-squares method. To address the instability of the least-squares method caused by noise interference and small singular values in the unit impulse load response matrix, the Tikhonov regularization method is adopted, and the optimal regularization parameter is selected using the L-curve method. Based on the improved impulse-space superposition method, a response prediction mathematical model for sloshing load positions and hotspot positions is established to predict multi-hotspot stress, such as the shear stress of the secondary plywood and the vertical stress of the secondary polyurethane foam.

Results The algorithm's performance is systematically evaluated under both triangular and random load conditions. The application of multiple sets of triangular sloshing loads with randomly generated characteristic values demonstrates that the predicted values show good agreement with actual measurements, indicating the method's capability to accurately predict multi-region triangular sloshing loads from any arbitrary starting moment. For random load conditions, the investigation focuses on three distinct prediction step sizes (0.5 ms, 0.25 ms, and 0.05 ms). The analysis reveals a strong correlation between prediction accuracy and step-size reduction. At the finest resolution of 0.05 ms, the predicted load curve successfully captures all peak features of the actual load profile. While minor fluctuations occur in zero-value regions without prominent peaks, primarily due to noise interference and small singular values, comprehensive error analysis across all regions demonstrates that step-size reduction effectively minimizes prediction errors. Specifically, the maximum load peak pressure error for individual regions decreases from 21.861% to 9.530%, with corresponding average errors decreasing from 10.081% to 4.023%. Similarly, temporal accuracy improves significantly, with maximum load peak time errors decreasing from 0.900 ms to 0.050 ms and average errors decreasing from 0.256 ms to 0.022 ms. The analysis of stress prediction demonstrates equally promising results. For both loading scenarios, the predicted curves for plywood shear stress and foam vertical stress exhibit strong agreement with actual measurements, particularly at smaller step sizes. The maximum error in stress peak prediction remains within 1% for selected hotspots. In the most challenging cases, the maximum peak stress error reaches 5.267% for plywood shear stress and 2.644% for foam vertical compressive stress, with peak time errors not exceeding 0.15 ms.

Conclusions The improved inverse impulse-space superposition method based on the Duhamel integral successfully achieves the inversion of the sloshing load and the prediction of hotspot stresses in the LNG carrier cargo containment system. This method combines the accuracy of experimental approaches with the cost-effectiveness of numerical simulations while minimizing the negative effects of experimental measurement errors and numerical model simplifications. It provides a novel approach and a reliable technical means for assessing the safety of LNG carriers and other ship-ocean structures. Although the current study adopts a uniform load model and does not fully account for the internal non-uniformity of actual sloshing loads in different regions, it still serves as a valuable reference for future research in this field.