To enhance the application effectiveness of the decomposition-based optimization method in the large-scale optimization design of ship cabin structures, a constraint progressive relaxation adjustment strategy and a computational resource allocation strategy are proposed that consider both the contribution of the sub-problem to the objective and the margin of constraints of the sub-problem.

Constraint progressive relaxation adjustment strategy: initially, a tightened constraint boundary is given and then gradually relaxed until it recovers to the original constraint boundary, enabling all sub-problems to be more fully optimized. Computational resource allocation strategy: optimization computing resources are comprehensively allocated based on the contribution of the sub-problem to the objective and the margin of constraints of the sub-problem. The two strategies are then combined and their coupling effects analyzed.

Compared with the original algorithm, under the same computational resources, the cabin weight is reduced by 10.3% and 7.0% when using the constraint progressive relaxation adjustment strategy and computational resource allocation strategy respectively, and the weight is reduced by 22.2% when both strategies are applied simultaneously, relative to the weight obtained by the original optimization method.

The proposed strategies are effective and possess value for the decomposition-based large-scale optimization of ship structures.

This paper proposes a domain knowledge-driven large-scale optimization algorithm for ship cabin structures based on a decomposition optimization framework.

The proposed algorithm combines domain mechanical knowledge with a general black box optimization algorithm, groups the design variables into location variables and size variables, and decomposes the original problem into a series of low-dimensional subproblems. Due to the monotonicity and locality of each bending stress, shear stress, and deformation constraint, subproblems with larger constraint margins are prioritized for optimization. All of the location variables are grouped into one subproblem, and the corresponding subproblem's objective function is to maximize the minimum constraint margin. Each girder size variable is separately grouped, and the corresponding subproblem's objective function is the weight of the cabin structure. Additionally, a surrogate model is introduced to quickly predict the constraints of each subproblem, and the sample infill criterion is adopted only in the constraint surrogate model.

The experimental results show that the algorithm can reduce the overall weight of the cabin structure by 43.5% compared to the upper bound.

The proposed algorithm has higher optimization efficiency and can obtain a better optimization solution compared to both the differential evolution algorithm directly using the using finite element method and the general black box optimization algorithm.

In the fields of underwater vehicles and aerospace, ring-stiffened cylindrical shells are widely used. Achieving a refined design for such structures is crucial to reducing structural weight while meeting strength and stability requirements. This study focuses on solving the optimization challenges of ring-stiffened cylindrical shells, with each rib as a design variable, to overcome the difficulties in automatically distinguishing whether the buckling mode is global or local. Additionally, it aims to improve the effectiveness and efficiency of the collaborative decomposition optimization algorithm with the assistance of domain knowledge.

To achieve these objectives, ResNet is trained for the buckling mode image recognition of ring-stiffened cylindrical shells. Using Abaqus for parametric modeling, numerous finite element simulations are conducted under different design variable combinations to generate buckling mode image datasets under various conditions. These images are preprocessed and divided into training, validation, and test sets for training the ResNet101 model. Meanwhile, based on domain knowledge regarding the coupling relationship between design variables and constraint quantities in ring-stiffened cylindrical shell design, specific grouping and resource allocation strategies are proposed.

The experimental results show that the trained ResNet has an outstanding performance in identifying the buckling modes of ring-stiffened cylindrical shells, with an accuracy rate of 98%. In this case, the volume of the optimized solution using the domain knowledge-driven algorithm is significantly reduced compared to the initial solution. Specifically, the volume is reduced by 38.4% compared to the initial solution, and further reduced by an average of 7.06% using this algorithm compared to the solution without domain knowledge.

In conclusion, combining the neural network-based image recognition technology with the collaborative decomposition optimization algorithm, supported by domain knowledge, effectively solves the optimization problem of ring-stiffened cylindrical shells with different ribs. The high recognition accuracy of the neural network ensures the accurate stability constraint calculations, and the innovative strategies based on domain knowledge enhance the algorithm’s optimization performance and provide a valuable reference for designing ring-stiffened cylindrical shells in related fields.

In order to explore the characteristics of optimization design schemes of titanium alloy double layer stiffened cylindrical shell structures under different length-to-diameter ratios and calculation pressures, a mathematical model for the lightweight optimization of such structures is established.

The main control program of the genetic algorithm is established in MATLAB, and the ultimate bearing capacity is calculated and checked by finite element software ANSYS. The differences of optimization schemes between titanium alloy single layer stiffened cylindrical shells and titanium alloy double layer stiffened cylindrical shells under different length-to-diameter ratios and different calculation pressures are then compared and analyzed.

There are two critical calculation pressures in the optimization design of titanium alloy stiffened cylindrical shells, and the optimization design is divided into three types: the stability constraint type of ultimate bearing capacity constraint control optimization design, the strength constraint type of strength constraint control optimization design, and the joint constraint type of strength and ultimate bearing capacity constraint joint control optimization design. The larger the length-to-diameter ratio, the greater the critical calculation pressure. Under the same calculation pressure and length-to-diameter ratio, the weight of the double layer shell optimization scheme is lighter than that of the single layer shell, and the critical calculation pressure of the double layer shell optimization design is smaller than that of the single layer shell under the same length-to-diameter ratio.

The results of this study can provide useful references for the optimization design of titanium alloy double layer stiffened cylindrical shell structures.

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.

In order to explore the effects of different stiffening configurations on the bearing capacity and anti-blast performance of double stiffened cylindrical shells, a numerical study is made of the responses of four kinds of double stiffened cylindrical shells under hydrostatic pressure and underwater explosion load.

First, finite element models of stiffened cylindrical shells with different structural forms are established. Next, finite element software ANSYS is used to calculate and analyze the influence of each structural form on the strength, stability and ultimate bearing capacity of the cylindrical shell. Finally, finite element software Abaqus/Explicit is used to calculate and analyze the influence of each structural form on the deformation deflection and plastic strain of the cylindrical shell under explosion load.

Compared with a traditional single stiffened cylindrical shell with the same mass, the I-shaped double stiffened cylindrical shell has a great advantage in carrying capacity. When the explosion load level is low, the anti-blast performance of a double cylindrical shell with small rib spacing is similar, but decreases when the explosion load level is high.

The reasonable design of double stiffened cylindrical shells can yield better design schemes for bearing capacity and anti-blast performance.

As a new type of pressure-resistant structure, the titanium alloy sandwich cylindrical shell has not yet been studied comprehensively. The topology of the core layer needs to be confirmed using the optimization method. This paper carries out the core topology optimization of titanium alloy pressure- resistant sandwich cylindrical shells.

An unreinforced cylindrical shell with high thickness is selected as the analysis object, and the axisymmetric element is used to calculate the structural stresses via ANSYS. The cylindrical shell is divided into the upper, middle and lower regions along the thickness direction. The structures of the middle region are set as the design variables, and a two-stage topology optimization mathematical model of its core structure is proposed. Based on Matlab, the main control program of the genetic algorithm is established to carry out the core layout optimization of the unreinforced cylindrical shell along the axial direction only and both the axial direction and radial direction respectively.

The optimal core topological form consists of equidistant ribs connecting the inner shell and outer shell vertically.

A sandwich cylindrical shell under hydrostatic pressure is a reasonable pressure-resistant structure.

The optimization of midship sections is characterized by the large amount of design variables and the complex constraints. Most relevant research applied the intelligent optimization algorithm embedded with the rule-based calculation program (e.g., Mars2000) from classification society to deal with this issue, which has a large computation cost. Therefore, a general fast optimization method based on sensitivity ranking is proposed for the optimization of midship sections.

Firstly, the sensitivity of each constraint about each design variable was evaluated. According to the result of sensitivity, the order of design variables to be modified can be obtained when each constraint is violated. Whether the constraint is only related to local variables or not can be determined as well. During optimization iteration, based on the constraint violation of the current scheme, variable adjustment can be made with the above sensitivity information, and the sensitivity result was updated periodically. Finally, minor adjustment of optimized schemes based on coordinate alternation was employed to further improve the optimization effect.

The optimization result of an oil tanker midship section shows that the proposed method can achieve a 5.195% reduction of weight.

Compared with the intelligent optimization algorithm nesting Mars2000 directly, the optimization effect of the proposed method is satisfactory, and the time cost is only 5.58% of the former. The advantage of the proposed method in time cost is quite obvious.

To solve the difficulties of numerous design parameters and time-consuming computation of ship cabin structure optimization, a collaborative optimization method of surrogate model for cabin structure based on sub-model decomposition is proposed.

A grillage was selected at a time, and the sub-model of grillage structure was established based on the finite element model of the current cabin scheme. The surrogate model was constructed for the grillage structure response and optimized based on the sub-model. After the optimization solution of the grillage was obtained, the cabin model was updated, and then the next grillage was optimized. This iteration stopped until one or more rounds of collaborative optimization including all grillages were completed. Finally, a small-scale adjustment of cabin structure size was conducted to obtain the final optimization solution.

The optimization result of a ship cabin structure shows that, compared with the cabin structure optimization method based on the dimensionality reduction surrogate model from the point of view of overall optimization, under the equivalent computational cost, the weight in the optimization result of the proposed method is further reduced by 2.86%, and the structural weight is reduced by 4.96% eventually.

The proposed method has better optimization results and better application value on the structure optimization problem of the high-dimensional ship hull.