Objectives With the continuous development of new ship designs and structural innovation in marine engineering, the traditional partial safety factor (PSF) method for verifying hull girder ultimate strength has become inadequate for meeting the refined and personalized requirements of modern ship design. The conventional Load and Resistance Factor Design (LRFD) method, which calibrates PSFs solely based on code values, exhibits significant limitations in both its underlying philosophy and optimization methodology. This method not only neglects the actual failure points and failure characteristics of ships during real navigation operations but also faces substantial challenges in realizing simultaneous multi-parameter optimization of PSFs for hull girder ultimate capacity, still-water bending moment and wave bending moment. Furthermore, the fixed PSFs specified in the current Common Structural Rules (CSR) of the International Association of Classification Societies (IACS) fail to reflect the correlation between safety factors and ship-type dimension parameters such as ship length, breadth and draft, leading to insufficient accuracy in hull girder strength assessment. To address these problems, this study carries out research on the multi-parameter optimization of PSFs for hull girder ultimate strength considering ship-type dimension parameters, aiming to establish a more scientific and applicable optimization method for PSFs and improve the accuracy and reliability of ultimate strength check and evaluation for ship structures.

Methods Based on the Global Calibration Method (GCM) and combined with the reliability analysis theory of ship structures, this study first constructed a multi-parameter expression of PSFs incorporating the principal dimensional parameters of ship types, and established a multi-parameter optimization method for PSFs of hull girder ultimate strength that takes ship-type characteristics into account, realizing the synchronous optimization of PSFs for hull girder ultimate capacity, still-water bending moment and wave bending moment. The research considered 28 types of bulk carriers with representative ship lengths (ranging from 149.6 m to 295 m) as the research object. The reliability indices and design check points for the sample ships under both hogging and sagging conditions were calculated using the improved First-Order Second-Moment (FOSM) method and the equivalent normalization method. Genetic algorithm was adopted as the multi-parameter optimization algorithm to perform the optimization calculation of PSFs. The optimization effects of the traditional LRFD and the GCM were systematically compared. Additionally, the effect of incorporating the ship length parameter (a core principal dimension) into the PSF expression on the optimization results was analyzed. . In the optimization process, different penalty functions were introduced to characterize the optimization errors, and a weight factor α was set in the GCM to balance the influence of code values and design check points on the optimization results.

Results The research results show that for bulk carriers, the GCM offers significant advantages over the traditional LRFD method in both optimization stability and result accuracy. The LRFD method leads to multiple groups of PSF combinations with the same penalty function error due to insufficient objective penalty function constraints, showing strong instability in optimization results, which is not conducive to practical engineering application. In contrast, the GCM, which comprehensively considers the ship code value points and design check points, obtained stable optimization results. Its error function was approximately 10% lower than that of the LRFD method under the same conditions. In addition, introducing the ship length parameter into the PSF expression made the expression more reasonable and in line with the actual structural characteristics of different ships. On the basis of the GCM, the optimization effect is further improved by about 0.3% after considering the ship length parameter, and the error penalty function values ε and ε* were reduced by about 0.3% and 0.6% respectively on average. Moreover, among the four multi-parameter optimization combination schemes designed in the study, the combination scheme of fixing the primary constant terms of still-water bending moment and wave bending moment and optimizing the secondary terms related to ship length and the constant term of ultimate capacity showed the best optimization effect under most weight factor α values. This scheme was particularly optimal under the hogging condition across the entire range of α values.

Conclusions This study demonstrates that in the multi-parameter optimization of PSFs for hull girder ultimate strength, the Global Calibration Method (GCM) considering ship-type parameters has more prominent technical advantages compared with the traditional Load and Resistance Factor Design (LRFD) method. By introducing the weight factor α to balance the requirements of code-specified values and the actual failure characteristics of ships, the GCM effectively resolves the instability issue inherent in the traditional method and significantly improves optimization accuracy. The introduction of ship-type dimension parameters (such as ship length) into the design of PSF expression is scientifically reasonable, which makes the PSFs more in line with the individual characteristics of different ships and further improves the optimization effect and the adaptability of the results. The research results can provide important technical support for improving the level of ultimate strength checks and evaluations for ship structures, laying a foundation for the refined design of ship hull girder strength. In the practical engineering application, the appropriate weight factor α can be selected according to the emphasis on code values or design check points, and different multi-parameter optimization combination schemes can be adopted according to the ship type and navigation area characteristics. Future research can expand the research object to more ship types such as oil tankers and container ships, and incorporate more ship-type dimension parameters such as ship breadth, draft and annual navigation time into the PSF expression to further improve the credibility and applicability of the optimization results.