A Rudder System Optimization Design Method Based on Nonprobabilistic Reliability Theory

Abstract

This invention relates to the field of ship design technology and discloses a rudder system optimization design method based on nonprobabilistic reliability theory, comprising the following steps: S1: Determine the mechanical performance design values ​​of key components of the rudder system based on nonprobabilistic reliability indices, conduct parameter sensitivity analysis to determine the sensitive variables affecting the rudder stock torque, construct a parameterized model library, and generate a sample space through automated simulation scripts; S2: Call the parameterized model library to generate a three-dimensional model, perform finite element calculations of the rudder-propeller combination, simulate the hydrodynamic performance of the rudder system under different rudder angle conditions, and compare and analyze the results with reference data and standard calculations. By integrating nonprobabilistic reliability theory and comparing nonprobabilistic reliability indices and convex set models, parameter uncertainties are effectively handled, the reliability of the rudder system design is improved, and the optimization ideas of portal frame structures are used to reduce design constraints and improve efficiency.

Description

Technical Field

[0001] This invention relates to the field of ship design technology, specifically to a rudder system optimization design method based on nonprobabilistic reliability theory. Background Technology

[0002] As the core control component for ships to achieve steering and maintain course, the reliability of the steering system directly affects the ship's navigation safety, operational efficiency, and economy. In the field of ship design, steering system design needs to comprehensively consider multiple factors such as hydrodynamic characteristics, structural strength, material properties, and adaptability to operating conditions. It is an interdisciplinary task involving fluid mechanics, structural mechanics, and shipbuilding engineering.

[0003] Traditional rudder system design methods are based on deterministic theory, primarily relying on shipbuilding industry standards (such as the International Association of Classification Societies (IACS) standards and national classification society regulations) and empirical charts. The process typically involves: initially determining key parameters such as rudder blade area and rudder stock diameter based on the ship's main dimensions (length, beam, draft, etc.); calculating the normal force, tangential force, and rudder stock torque on the rudder blade using empirical formulas; then performing strength checks according to regulatory requirements; and finally determining the design scheme. However, this method has significant limitations: First, the uncertainties in the parameters are not adequately considered. The loads (such as wave impact and water velocity), material properties (such as elastic modulus and fatigue limit), and manufacturing errors (such as rudder blade thickness deviation and assembly clearance) faced by the rudder system in actual operation are all random and ambiguous. Traditional methods use a single benchmark value for calculation, making it difficult to quantify the impact of these uncertainties on the reliability of the rudder system, potentially leading to over-design (increasing costs) or under-design (creating safety hazards). For example, in ocean shipping routes with frequent winds and waves, the actual impact force on the rudder blade may be more than 30% higher than the specified value, and traditional designs do not incorporate such fluctuations, posing a risk of structural failure. Secondly, the design efficiency and ability to compare multiple options are weak. Traditional design relies on manual modeling and calculation. Each adjustment to a scheme requires repeated parameter modifications, mechanical analysis, and strength checks, making the process cumbersome and time-consuming. For different ship types (such as dry cargo ships and bulk carriers) or different operating conditions of the same ship type (such as fully loaded and empty), the model needs to be rebuilt and calculated, making it difficult to quickly compare and optimize multiple options. Taking an 84,500-ton dry cargo ship as an example, it takes 3-5 days to complete a single optimization of the rudder system parameters using traditional methods, while the ship design phase often requires the evaluation of more than 10 schemes, resulting in a lengthy design cycle. Secondly, there is insufficient synergy between hydrodynamic performance and structural design. The hydrodynamic performance of the rudder system (such as lift coefficient and drag coefficient) and structural parameters (such as rudder blade shape and rudder stock diameter) are strongly coupled. In traditional design, fluid analysis and structural strength calculations are often disconnected: hydrodynamic parameters are estimated using empirical formulas, which deviate from the actual flow field; structural design relies only on simplified mechanical models, failing to fully consider the influence of complex flow fields on structural stress. For example, uneven pressure distribution on the rudder blade surface under large rudder angle conditions may lead to localized stress concentrations, but traditional methods using average pressure calculations struggle to capture such details, affecting design accuracy. Nonprobabilistic reliability theory, with interval analysis and convex set models at its core, can quantify parameter uncertainty without requiring a large amount of sample data. It assesses structural reliability through nonprobabilistic reliability indices and has demonstrated significant advantages in fields such as civil engineering. Introducing it into rudder system design can overcome the shortcomings of traditional methods and achieve effective control over uncertainty. Combined with parametric modeling and automated simulation, it can also improve design efficiency and the ability to compare multiple solutions, providing a completely new solution for modern ship rudder system design. Summary of the Invention

[0004] The purpose of this invention is to provide a rudder system optimization design method based on nonprobabilistic reliability theory to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a rudder system optimization design method based on nonprobabilistic reliability theory, comprising the following steps: S1: Determine the mechanical performance design values ​​of key components of the rudder system based on non-probabilistic reliability indices, conduct parameter sensitivity analysis to determine the sensitive variables affecting the rudder stick torque, construct a parameterized model library, and generate a sample space through automated simulation scripts; S2: Call the parametric model library to generate a three-dimensional model, perform finite element calculation of the rudder propeller combination, simulate the hydrodynamic performance of the rudder system under different rudder angle conditions, and compare and analyze the results with reference data and standard calculations. S3: Determine the allowable mechanical parameters of key components of the rudder system, construct a multi-objective optimization model, and combine the failure probability comparison results of interval convex set and ellipsoidal convex set models for optimization design reference, providing quantitative basis for rudder stock diameter, rudder blade thickness and rudder blade selection.

[0006] As a further explanation of the present invention, in S1, the mechanical performance design values ​​of key components of the rudder system are determined based on non-probabilistic reliability indicators, and the sensitive variables affecting the torque of the rudder stock are determined. The sensitive variables include the span ratio, lift coefficient, drag coefficient, inertial force coefficient, normal force coefficient, friction coefficient of the upper and lower rudder bearings, torque coefficient, and drag coefficient.

[0007] As a further explanation of the present invention, when constructing the parametric model library in S1, the core structural parameters of the rudder system are defined parametrically, different ship type parameter association rules are preset, and a three-dimensional model is automatically generated after inputting key parameters; the automated simulation script covers the process of model import, mesh generation, boundary condition application, solution parameter setting and result output.

[0008] As a further explanation of the present invention, in S1, an interval convex set model is used to describe the uncertainty range of the sensitive variable. The variable follows a normal distribution, and 50 sample spaces are constructed by Latin hypercube sampling.

[0009] As a further explanation of the present invention, in S2, a three-dimensional model of the target ship's rudder system is generated by calling a parametric model library, and a simulation calculation model and a rudder-propeller combination finite element model are constructed using hydrodynamic software, setting boundary conditions such as incoming flow velocity, water depth, and material properties.

[0010] As a further explanation of the present invention, S2 runs an automated simulation script to simulate the hydrodynamic performance under different rudder angle conditions such as 0°, 5°, 15°, 20°, 25°, 30°, and 35°, calculates the normal force, tangential force, and rudder stock torque, and outputs the velocity flow field distribution, pressure distribution, and hydrodynamic coefficient curves.

[0011] As a further explanation of the present invention, in S2, the simulation results are compared with the standard calculation results, and the standard calculation torque is... The influence of different rudder angles on hydrodynamic performance was analyzed by the deviation rate.

[0012] As a further explanation of the present invention, in S3, the allowable mechanical parameters of key components of the rudder system are determined, such as the allowable torque of the rudder stock and the allowable stress of the rudder blade, etc., and a multi-objective optimization model is constructed. With reliability and economy as objectives and the rudder stock diameter as variables, the Pareto optimal solution set is solved by intelligent optimization algorithm in combination with constraints.

[0013] As a further explanation of the present invention, in S3, the sensitivity coefficients of sensitive variables are calculated, and highly sensitive variables are optimized first; the failure probabilities of the interval convex set model and the ellipsoidal convex set model are compared to clarify the difference in reliability.

[0014] As a further explanation of the present invention, S3 establishes a formula relating the rudder stock diameter and the rudder blade thickness, and combines the comparison results of the convex set model to provide a quantitative reference for rudder blade selection, thereby realizing the optimized design of the rudder system.

[0015] Compared with the prior art, the beneficial effects of the present invention are: By integrating nonprobabilistic reliability theory and comparing nonprobabilistic reliability indices with convex set models, parameter uncertainties can be effectively handled, improving the reliability of the rudder system design. The optimization ideas of portal frame structures can be used to reduce design constraints and improve efficiency. By introducing parametric modeling and automated simulation, the parametric model library enables rapid modeling, automated scripts shorten simulation time, support parallel computing under multiple operating conditions, reduce human error, and significantly improve design efficiency. A multi-objective optimization algorithm is adopted to balance reliability and economy, solve the Pareto optimal solution set, provide multi-dimensional choices for design, and combine sensitivity analysis to focus on key variables, making optimization more targeted; It achieves bidirectional verification through standardized calculations and finite element simulations, broadens the perspective of reliability analysis by comparing the failure probabilities of convex set models, provides a scientific basis for the selection of rudder system parameters, reduces design costs, and improves ship handling performance. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process steps S1, S2, and S3 of the present invention; Figure 2 This is a schematic diagram of the process of S1 of the present invention; Figure 3 This is a schematic diagram of the process of S2 in this invention; Figure 4 This is a schematic diagram of the process of S3 in this invention; Figure 5 This is a schematic diagram of the process for establishing the parameterized model library in S1 of the present invention; Figure 6 This is a schematic diagram of the process for developing automated simulation scripts in S1 of the present invention; Figure 7 This is a schematic diagram of the sample space construction process in S1 of the present invention; Figure 8 This is a schematic diagram of the model construction and setup process in S2 of the present invention; Figure 9 This is a schematic diagram of the rudder system inflow simulation calculation model of the present invention; Figure 10 This is a schematic diagram of the finite element calculation model of the rudder propeller combination of the present invention. Detailed Implementation

[0017] In the following description, various embodiments of the invention will be described with reference to the accompanying drawings.

[0018] Example 1: Please refer to Figures 1-10 The present invention provides a technical solution: S1, Parameter Sensitivity Analysis and Foundation Construction Based on the operational characteristics of an 84,500-ton dry cargo ship (mainly traveling on near-sea routes with moderate load fluctuations), and using non-probabilistic reliability indicators, combined with the ship's full-load displacement, speed, and typical route sea state data, the mechanical performance design values ​​of key rudder components are determined: the design value of the bending moment resistance that the rudder stock needs to withstand is 280 kN·m, and the design value of the bending strength of the rudder blade material is 300 MPa. Eight sensitive variables that significantly affect rudder stock torque were selected, including span ratio (reference value 2.8, range 2.5-3.1), lift coefficient (reference value 1.15, range 1.0-1.3), and drag coefficient (reference value 0.22, range 0.19-0.25). An interval convex set model was used to describe the uncertainty range of these variables. The parametric model library pre-sets parameter association rules for this ship type (length 190m, beam 30m, draft 10.5m). For example, the ratio of rudder blade area to ship length is set to 0.0085. After inputting the principal dimension parameters, the model library automatically generates a 3D model including the rudder stock, rudder blade, and upper and lower rudder bearings. Model details include the rudder blade edge fillet radius (150mm) and the thickness of the rudder stock and rudder blade connecting flange (80mm). The developed automated simulation script covers the entire process: geometric integrity is automatically checked during model import; a hybrid mesh is used for mesh generation (triangular mesh, 50mm on the rudder surface; tetrahedral mesh, 100mm inside); the boundary condition setting module is linked to a sea state database, automatically matching typical incoming current speeds (14kN) and seawater density (1025kg / m³) along the route. 3 The simulation parameters were set to a time step of 0.01s and a total simulation duration of 10s to ensure the capture of transient flow field characteristics. Fifty sample spaces were generated using Latin hypercube sampling, with each sample containing the specific values ​​of eight sensitive variables, covering the distribution range of all variables.

[0019] S2, Finite Element Calculation of the Rudder-Propeller Combination The 3D model generated by the parametric model was imported into hydrodynamic software to construct a rudder system inflow simulation model and a rudder-propeller combination finite element model. The rudder blade material was selected from CCSB marine steel plate, with an elastic modulus of 206 GPa and a Poisson's ratio of 0.3. The rudder stock was made of 42CrMo alloy structural steel with a yield strength of 600 MPa. An automated simulation script was run to simulate seven rudder angle conditions: 0°, 5°, 15°, 20°, 25°, 30°, and 35°.

[0020] Real-time monitoring data during simulation showed that at a rudder angle of 0°, the pressure distribution on the rudder blade surface was uniform, with a maximum pressure of approximately 18 kPa; at a rudder angle of 15°, a pressure peak (32 kPa) appeared at the leading edge of the rudder blade, and the pressure gradient at the tail increased significantly. The velocity flow field showed that a vortex region with a length of approximately 5 m formed behind the rudder blade; at a rudder angle of 30°, the rudder stock torque reached its maximum value of 185 kN·m, with a deviation rate of 4.1% from the standard calculated value (193 kN·m), verifying the accuracy of the model. The flow field animation showed that as the rudder angle increased, the velocity difference between the two sides of the rudder blade intensified, with the velocity on the left side reaching 18 kN and the velocity on the right side approximately 12 kN, resulting in a significant increase in lateral force.

[0021] S3, Optimized Design Reference According to ship classification regulations, the allowable torque of the rudder stock is determined to be 200 kN·m, and the allowable stress of the rudder blade is determined to be 290 MPa. The failure probability of the rudder system calculated using the interval convex set model is 0.0023, while the result calculated using the ellipsoidal convex set model is 0.0017, a difference of 26%. The difference is mainly attributed to the different methods of describing the uncertainty of the friction coefficient. Sensitivity analysis software calculations show that the torque coefficient (sensitivity coefficient 0.78) and lift coefficient (0.75) have the most significant impact on the rudder stock torque.

[0022] Optimizations were made to key variables: the torque coefficient was reduced from 0.32 to 0.30 by increasing the contact area of ​​the key connecting the rudder stock and the rudder blade (from 0.05m). 2 Increased to 0.06m 2 The lift coefficient was optimized by modifying the rudder blade profile, shifting the maximum thickness position from 30% chord length to 35% chord length, thus reducing flow separation. The final optimized scheme was: rudder stock diameter 270mm (5mm less than the initial scheme), rudder blade thickness 26mm (gradually tapering to 15mm at the edge), rudder blade chord length 4.8m, and span 2.1m. After application on a real ship, monitoring via the navigation data recorder (VDR) showed that the maximum torque of the rudder system in 12-level winds and waves was 192kN·m, which did not exceed the allowable value, improving reliability by 16%; material usage was reduced by 8%, the design cycle was shortened by 30 days compared to traditional methods, and the number of design constraints was reduced by 25%, verifying the accuracy of the model. The ship's maneuverability was significantly improved, meeting the requirements for safe navigation and economical operation.

[0023] Working Principle: During use, by comparing non-probabilistic reliability indices and convex set models, uncertain parameters are transformed into quantifiable reliability metrics for analysis. This provides a basis for determining the design values ​​of the mechanical properties of key components in the rudder system of an 84,500-ton dry cargo ship. Parametric modeling and automated simulation enable efficient operation of the design process. The parametric model library quickly generates a 3D model of the rudder system based on preset ship type rules. The automated simulation script completes model import, mesh generation, boundary condition setting, solution solving, and result output according to predetermined logic, significantly shortening the design cycle and reducing human intervention errors. A multi-objective optimization algorithm balances the reliability and economy of the rudder system, and an intelligent algorithm searches for the Pareto optimal solution set, providing multiple options for the design.

[0024] Example 2: Please refer to Figures 1-10 The present invention provides a technical solution: S1, Parameter Sensitivity Analysis and Foundation Construction The 80,000-ton dry cargo ship is primarily used on trans-Pacific routes. It has a design draft of 12m and a full-load displacement of 82,000 tons, requiring it to withstand greater wave loads. Based on non-probabilistic reliability indicators, the design value for the rudder stock bending moment resistance is determined to be 320 kN·m, and the rudder blade bending strength is 310 MPa. Among the sensitive variables, the normal force coefficient has a significant impact; the baseline value is 1.3, with a range of 1.1-1.5, due to the ship's large rudder blade (area 38m²). 2 The normal force increases significantly at large rudder angles.

[0025] The parametric model library is adapted to its main dimensions (length 210m, beam 34m), with a preset rudder stock length and draft ratio of 0.3 (i.e., 3.6m). The generated 3D model, after inputting parameters, includes a double rudder bearing structure, with the upper rudder bearing 1.8m above the deck and the lower rudder bearing 0.6m above the bottom. An automated script improves the mesh accuracy to 50mm, and the incoming current velocity is set to 15kN. Considering the influence of ocean currents on the Pacific route, a velocity disturbance simulation of ±2kN is added. When sampling 50 sets of samples, the sampling density of the normal force coefficient is significantly increased to ensure coverage of values ​​under extreme sea conditions.

[0026] S2, Finite Element Calculation of the Rudder-Propeller Combination Simulations show that the rudder stock torque reaches 210 kN·m at a rudder angle of 25°, compared to the standard calculated value of 218 kN·m, a deviation rate of 3.7%. Flow field analysis revealed a significant turbulent region at the leading edge of the rudder blade at a large rudder angle of 35°, with a turbulence intensity of 15%, causing local pressure fluctuations exceeding ±5 kPa, which can easily trigger rudder blade vibration. Pressure contour plots showed that the flow velocity at the gap between the rudder blade and the stern of the hull reached as high as 22 kN, forming a low-pressure area. The gap size needs to be optimized (increasing from 300 mm to 400 mm) to reduce interference.

[0027] S3, Optimized Design Reference The allowable torque was set at 230 kN·m. The failure probabilities of the interval convex set and ellipsoidal convex set models were 0.0027 and 0.0020, respectively, with a difference rate of 26%. Multi-objective optimization focused on "anti-turbulence performance" and "manufacturing cost." Torque loss was reduced by adjusting the friction coefficient of the upper and lower rudder bearings (from 0.12 to 0.10, using a bronze-steel friction pair). The final design featured a rudder stock diameter of 290 mm, a rudder blade thickness of 27 mm, and a leading edge radius increased to 200 mm to suppress turbulence. Real-ship testing showed that at a rudder angle of 35°, the vibration acceleration decreased from 0.15g to 0.08g, and the maintenance cycle was extended by 15%, verifying the model's accuracy. Ship maneuverability was significantly improved, meeting the requirements for safe navigation and economical operation.

[0028] Working Principle: During use, by comparing non-probabilistic reliability indices and convex set models, uncertain parameters are transformed into quantifiable reliability metrics for analysis. This provides a basis for determining the design values ​​of the mechanical properties of key components in the rudder system of an 80,000-ton dry cargo ship. Parametric modeling and automated simulation enable efficient operation of the design process. The parametric model library quickly generates a 3D model of the rudder system based on preset ship type rules. The automated simulation script completes model import, mesh generation, boundary condition setting, solution solving, and result output according to predetermined logic, significantly shortening the design cycle and reducing human intervention errors. A multi-objective optimization algorithm balances the reliability and economy of the rudder system, and an intelligent algorithm searches for the Pareto optimal solution set, providing multiple options for the design.

[0029] Example 3: Please refer to Figures 1-10 The present invention provides a technical solution: S1, Parameter Sensitivity Analysis and Foundation Construction The 82,600-ton bulk carrier mainly transports coal and ore, with a high proportion of heavy-load operation (over 90%), and inertial forces have a significant impact on the rudder system. Based on non-probabilistic reliability indicators, the design value of the rudder stock bending moment resistance is determined to be 350 kN·m, the rudder blade bending strength is 320 MPa, and the baseline value of the inertial force coefficient among the sensitive variables is 0.22, with a range of 0.18-0.26.

[0030] The parametric model library, designed for its heavy-load characteristics, pre-defines a thickened rudder blade area (increasing thickness by 20% within 1 / 3 of the chord length from the root). The main dimensions are a length of 220m, a beam of 36m, and a draft of 12.5m. The generated model, after importing the parameters, includes an internal reinforcing rib structure (500mm spacing). The automated script sets the incoming current velocity to 16kN and the mesh accuracy to 50mm. Considering the impact of cargo center of gravity shift on the rudder system forces, a ±3° heel simulation is added.

[0031] S2, Finite Element Calculation of the Rudder-Propeller Combination At a 30° rudder angle, the simulated torque is 230 kN·m, while the specified value is 239 kN·m, resulting in a deviation rate of 3.8%. Flow field analysis shows that under heavy load conditions at a 20° rudder angle, the pressure distribution on the rudder blade is uneven, with a maximum pressure difference reaching 40 kPa. This is because cargo displacement causes the hull to tilt, resulting in a deviation in the water flow's angle of attack on the rudder blade. Stress contour plots reveal stress concentration at the connection between the rudder blade root and the rudder stock (maximum 280 MPa), close to the allowable value.

[0032] S3, Optimized Design Reference The permissible torque is 250 kN·m. The failure probabilities of the interval and ellipsoidal models are 0.0029 and 0.0021, respectively, with a difference rate of 28%. The lift coefficient was optimized (reduced from 1.35 to 1.28) by adjusting the trailing edge inclination angle of the rudder blade (increased from 15° to 18°), while simultaneously increasing the thickness of the root stiffener (from 25 mm to 30 mm). The final solution has a rudder stock diameter of 300 mm and a rudder blade thickness of 29 mm. After application, the sailing resistance was reduced by 4%, the fuel consumption per voyage was reduced by 8 tons, the structural stress concentration phenomenon was eliminated, and the reliability was improved by 19%. This verified the accuracy of the model, significantly improved the ship's maneuverability, and met the requirements for safe navigation and economical operation of the ship.

[0033] Working Principle: During use, by comparing non-probabilistic reliability indices and convex set models, uncertain parameters are transformed into quantifiable reliability metrics for analysis. This provides a basis for determining the design values ​​of the mechanical properties of key components of the rudder system in an 82,600-ton bulk carrier. Parametric modeling and automated simulation enable efficient operation of the design process. The parametric model library quickly generates a 3D model of the rudder system based on preset ship type rules. The automated simulation script completes model import, mesh generation, boundary condition setting, solution solving, and result output according to predetermined logic, significantly shortening the design cycle and reducing human intervention errors. A multi-objective optimization algorithm balances the reliability and economy of the rudder system, and an intelligent algorithm searches for the Pareto optimal solution set, providing multiple options for the design.

[0034] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0035] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A rudder system optimization design method based on nonprobabilistic reliability theory, characterized in that, Includes the following steps: S1: Parameter sensitivity analysis and basic construction: Based on non-probabilistic reliability indicators, determine the mechanical performance design values ​​of key components of the rudder system, conduct parameter sensitivity analysis to determine the sensitive variables affecting the rudder stock torque, construct a parameterized model library and generate a sample space through automated simulation scripts; S2: Finite element calculation of rudder and propeller combination. The parameterized model library is called to generate a three-dimensional model, and finite element calculation of rudder and propeller combination is performed to simulate the hydrodynamic performance of the rudder system under different rudder angle conditions and compare and analyze the results with reference data and standard calculations. S3: Optimize design reference, determine the allowable mechanical parameters of key components of the rudder system, construct a multi-objective optimization model, and combine the failure probability comparison results of interval convex set and ellipsoidal convex set models to provide optimization design reference, providing quantitative basis for rudder stock diameter, rudder blade thickness and rudder blade selection.

2. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: The sensitive variables affecting rudder stick torque mentioned in S1 include the span ratio λ and the lift coefficient C. L Drag coefficient C D Inertial force coefficient C M Normal force coefficient C N The coefficient of friction of the upper and lower rudder bearings Torque coefficient K T and drag coefficient C R .

3. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: When constructing the parametric model library in S1, the core structural parameters of the rudder system are defined parametrically, and the association rules of parameters for different ship types are preset. After inputting key parameters, a three-dimensional model is automatically generated. The automated simulation script covers the process of model import, mesh generation, boundary condition application, solution parameter setting, and result output.

4. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: When constructing the sample space, S1 uses an interval convex set model to describe the uncertainty range of the sensitive variables. The variables follow a normal distribution, and the probability density function is... ,in The mean, The standard deviation is determined based on ship design specifications, historical test data, or engineering experience.

5. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: S1 uses the Latin hypercube sampling method to sample the sensitive variable, and the formula is as follows: , For the j-th sample value of the i-th variable, for Uniform random numbers, Given the inverse function of the standard normal distribution, obtain 50 sample spaces with variable sampling covering the range of values ​​and following a normal distribution.

6. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: The S2 simulation included rudder angles of 0°, 5°, 15°, 20°, 25°, 30°, and 35°, and calculated the normal force. Tangential force and rudder stick torque ,in Let S be the density of seawater and S be the area of ​​the rudder blade. For hydrodynamic coefficient, This is the axial force.

7. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: S2 outputs velocity-flow field distribution at different rudder angles. Pressure distribution on the rudder blade surface and hydrodynamic coefficient curve , And compare it with the standard calculation results, the standard calculation torque K is the correction factor, and L is the length of the rudder stick lever arm.

8. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: The multi-objective optimization model in S3 takes the reliability and design economy of the rudder system as optimization objectives, and the rudder stock diameter, rudder blade thickness, and hydrodynamic coefficient as design variables. Combined with the constraints of ship specifications, the Pareto optimal solution set is solved by intelligent optimization algorithm.

9. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: In S3, calculate the sensitivity coefficient of the sensitive variable to the rudder stick torque. Torque versus variable X i The partial derivatives, The average torque value is based on... Prioritize the optimization of highly sensitive variables by sorting by absolute value.

10. The rudder system optimization design method based on nonprobabilistic reliability theory according to claim 1, characterized in that: Establish rudder stock diameter in S3 With rudder blade thickness The relational formula, The allowable shear stress, k is the safety factor, and W is the section modulus. The comparison results of failure probabilities in the convex set model provide a quantitative reference for rudder blade selection.

Images