Sloshing load inversion and stress monitoring of LNG carrier cargo containment system based on improved impulse-space superposition method

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).

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 loads in multi-regions. Using the time-shift property of the convolution integral, the Duhamel integral is reformulated and discretized into a matrix equation to predict sloshing loads at different time steps. The matrix equation is solved by least-squares. To address the instability due to noise interference and small singular values in the unit impulse load response matrix, the Tikhonov regularization method is adopted, with the optimal regularization parameter selected by 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 shear stress in the secondary plywood and vertical stress in the secondary polyurethane foam.

The algorithm's performance is systematically evaluated under both triangular and random load conditions. The application of multiple triangular sloshing loads with randomly generated characteristic shows that the predicted values agree well with actual measurements, indicating the method's ability to accurately predict multi-region triangular sloshing loads from any starting moment. For random loads, the investigation focuses on three prediction step sizes (0.5 ms, 0.25 ms, and 0.05 ms). The analysis shows 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. Stress prediction shows equally promising results. For both loading scenarios, the predicted curves for plywood shear stress and foam vertical stress agree well with actual measurements, particularly at smaller step sizes. The maximum stress peak prediction error 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.

The improved inverse impulse-space superposition method based on the Duhamel integral successfully inverts the sloshing load and the predicts hotspot stresses in the LNG carrier cargo containment system. This method combines the accuracy of experimental with the cost-effectiveness of numerical simulations, minimizing the negative effects of experimental measurement errors and numerical model simplifications. It provides a novel and reliable approach 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.