Embedded domain knowledge method for worst-case analysis of three-span beam under multiple patch loads

ObjectiveThis 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. MethodAn 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. ResultsCompared 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%. ConclusionThe numerical results show that the proposed method can accurately, stably, and quickly obtain the most dangerous load positions.