This paper proposes a method for improving the efficiency and accuracy of finding the worst-case positions of wheel patch loads on deck grillage.

The proposed method combines the domain knowledge of ship structural mechanics with the simplified model. According to the specified girder to be analyzed, the method first applies concentrated forces to different positions on the corresponding girder of the deck grillage in advance, then selects several suitable girders according to the response value to form a simplified intersecting beam system model. It then carries out the worst-case analysis using the genetic algorithm and domain knowledge. Keeping the order positions of worst-case loads in the simplified model unchanged, the loads are applied to deck grillage girders with similar modes to the simplified model for traversal or perturbation, and finally the dangerous positions are obtained.

The worst-case positions are calculated using three methods: the direct search method for the deck grillage, direct search method for the deck grillage with domain knowledge, and combined domain knowledge and simplified model method. The numerical results show that compared with the direct search method without any strategy, the maximum bending normal stress and shear stress of the girder obtained by the proposed method can be increased by 16.1% and 26.9% respectively. The computational resources are only about 1/32 of that obtained by the direct search method and 1/8 of that obtained by the direct search method with domain knowledge. Moreover, the difference between the three-run results obtained by the proposed method is small.

The proposed method can quickly, effectively, and robustly identify the dangerous load positions of a deck girder under multiple wheel patch loads.

This paper seeks to solve the problem in which directly invoking an optimization algorithm for the worst-case analysis of a three-span beam structure under multiple wheel patch loads raises the possibility of falling into the local optimal solution rather than the global solution.

An analysis method comprising embedded domain knowledge with the general black-box optimization algorithm is proposed for the worst-case analysis of the beam. On the one hand, the position of each wheel patch load is defined as a design variable, so there is no need to specify the relative position of the group of wheel patch loads inadvance,which is more universal; on the other, by integrating knowledge of ship structural mechanics, such as “large stress resulting from the close aggregation of loads in order of magnitude, large bending moment and shear force usually generated by the load in the mid span of the beam and near the support”, into the optimization algorithm, a strategy for generating dangerous initial populations based on the genetic algorithm （GA） and the overall translational strategy of the wheel patch load are proposed respectively, thereby reducing the possibility of falling into the local optimal solution. The theoretical bending moment and shear force distribution of a three-span beam under a single wheel patch load are derived respectively. The theoretical most dangerous positions of multiple wheel patch loads are then determined by enumerating all possible combinations to verify the correctness of the proposed algorithm.

Compared with the classical method using GAs without domain knowledge and under the same computational resources, the most dangerous bending normal stress and shear stress increase by 5.98% and 8.59% respectively under six wheel patch loads, and the error between the calculation results and the theoretical solution is less than 0.5%.

The numerical results show that the proposed method can accurately, stably, and quickly obtain the most dangerous load positions.