Aluminum alloy net shell structure design method and system based on genetic algorithm

Abstract

The application relates to the technical field of aluminum alloy structure design, and discloses an aluminum alloy net shell structure design method and system based on a genetic algorithm. The method receives design requirement parameter input by a user, including span, height and load conditions of the net shell structure; divides the net shell structure into multiple design units corresponding to nodes or rod pieces; obtains historical performance data of aluminum alloy material, such as strength, rigidity and durability, from a database; determines the importance level and constraint level of each design unit based on the above data; generates an initial population containing multiple design schemes by using a genetic algorithm; iteratively executes selection, crossover and mutation operations to optimize the design individual; collects structure response data such as stress, strain and displacement in real time in the iteration; confirms whether a preset constraint condition is violated based on the data, and adjusts the genetic algorithm parameter if the constraint condition is violated; and outputs an optimal design result and generates a structure analysis image for the user to view.

Description

Technical Field

[0001] This invention relates to the field of aluminum alloy structure design technology, specifically to a method and system for designing aluminum alloy reticulated shell structures based on genetic algorithms. Background Technology

[0002] In the field of architectural engineering, grid shell structures are widely used in large public buildings such as stadiums, exhibition halls, and airport terminals due to their lightweight, large span, and aesthetically pleasing appearance. Aluminum alloys, with their excellent corrosion resistance, high strength-to-weight ratio, and good machinability, are gradually becoming one of the preferred materials for grid shell structures. However, the design process of aluminum alloy grid shell structures involves the intersection of multiple disciplines, including structural mechanics, materials science, and optimization algorithms, and faces numerous technical challenges.

[0003] Traditional aluminum alloy reticulated shell structure design relies heavily on engineers' experience for manual calculations and scheme adjustments. This not only results in long design cycles but also makes it difficult to achieve optimal structural performance while meeting design requirements in multiple aspects such as span, height, and load. As reticulated shell structures develop towards larger spans and greater complexity, traditional design methods are increasingly proving inadequate in handling multi-parameter constraints and multi-objective optimization problems.

[0004] Currently, while some design methods incorporate optimization algorithms, they suffer from limitations in adaptability to the properties of aluminum alloys. For example, existing methods often fail to fully utilize historical performance data of aluminum alloys, resulting in designs that do not accurately reflect the material's actual mechanical behavior. Furthermore, the distinction between the importance of structural units and constraints during optimization is not detailed enough, potentially leading to localized performance defects and an inability to balance overall structural stability and economic efficiency. In addition, the lack of a real-time acquisition and feedback adjustment mechanism for structural response data during optimization makes it difficult to guarantee the reliability and applicability of the design. These problems limit the further promotion and application of aluminum alloy reticulated shell structures in engineering practice, necessitating a more scientific and efficient design method to address these challenges. Summary of the Invention

[0005] The purpose of this invention is to provide a design method and system for aluminum alloy reticulated shell structures based on genetic algorithms, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, this invention provides a design method for aluminum alloy reticulated shell structures based on genetic algorithms, the method comprising:

[0007] The system receives design requirement parameters input by the user, including the span parameters, height parameters, and load condition parameters of the reticulated shell structure.

[0008] The reticulated shell structure is divided into multiple design units, each design unit corresponding to a node or member of the reticulated shell structure;

[0009] Historical performance data of aluminum alloy materials are obtained from the database, including strength data, stiffness data, and durability data.

[0010] Based on the historical performance data and design requirement parameters, the importance level and constraint level of each design unit are determined;

[0011] Using a genetic algorithm, an initial population is generated based on the importance level and constraint level. The initial population contains multiple design individuals, and each design individual represents a reticulated shell structure design scheme.

[0012] Genetic algorithm operations, including selection, crossover, and mutation, are performed iteratively to optimize the design of individuals;

[0013] During the iteration process, the structural response data of each individual design is collected in real time. The structural response data includes stress data, strain data, and displacement data.

[0014] Based on the structural response data, it is confirmed whether the preset constraints are violated. If they are violated, the parameters of the genetic algorithm are adjusted.

[0015] Output the design results of the reticulated shell structure corresponding to the optimal design individual; and generate structural analysis images for users to view.

[0016] Preferably, the design requirements parameters also include boundary condition parameters and material specifications of the reticulated shell structure; the historical performance data also includes fatigue life data and corrosion rate data.

[0017] Preferably, the process of determining the importance level and constraint level of each design unit is as follows: Obtain strength and stiffness data from the historical performance data of each design unit, and calculate the strength coefficient and stiffness coefficient of each design unit; based on the strength and stiffness coefficients, and combined with the load condition parameters in the design requirements parameters, calculate the importance coefficient of each design unit; compare the importance coefficient with a preset importance threshold to determine whether the importance level of the design unit is high, medium, or low; simultaneously, based on the durability data from the historical performance data, calculate the constraint coefficient of each design unit; compare the constraint coefficient with a preset constraint threshold to determine whether the constraint level of the design unit is high, medium, or low.

[0018] Preferably, the process of generating an initial population using a genetic algorithm based on the importance level and constraint level is as follows: the importance level of the design unit is used as the priority factor for population initialization, and the constraint level of the design unit is used as the control factor for population diversity; for design units with higher importance levels, a larger range of design variable variation is allocated in the initial population; for design units with higher constraint levels, stricter variable boundary restrictions are imposed in the initial population; the size of the initial population is adaptively determined based on the total number of design units of the shell structure and the complexity of the design requirement parameters.

[0019] Preferably, the iterative execution of the genetic algorithm operation is as follows: In each iteration, the fitness value of each design individual is calculated. The fitness value is based on the stress and displacement data in the structural response data, and is weighted by combining the importance level and constraint level. A selection operation is performed based on the fitness value, prioritizing the retention of design individuals with higher fitness values. When performing the crossover operation, a higher crossover probability is used for design units with higher importance levels. When performing the mutation operation, a smaller mutation length is used for design units with higher constraint levels. The iteration terminates when the fitness value converges or the maximum number of iterations is reached.

[0020] Preferably, the process of real-time acquisition of structural response data for each design unit is as follows: The mechanical behavior of each design unit under load conditions is simulated through finite element analysis, and stress data, strain data, and displacement data are extracted; the finite element analysis adopts a mesh generation method consistent with the design unit generation to ensure the accuracy of data acquisition; the acquired structural response data is updated to the database in real time for subsequent constraint confirmation.

[0021] Preferably, the process of confirming whether the preset constraints are violated is as follows: the preset constraints include stress constraints, displacement constraints and stability constraints; the real-time collected stress data is compared with the allowable stress value, and if it exceeds the allowable stress value, it is marked as a stress violation; the displacement data is compared with the allowable displacement value, and if it exceeds the allowable displacement value, it is marked as a displacement violation; based on stability analysis, if the designed individual buckles, it is marked as a stability violation; if any violation exists, a constraint violation signal is generated and the genetic algorithm parameter adjustment is triggered.

[0022] Preferably, the process of adjusting the genetic algorithm parameters is as follows: when a constraint violation signal is generated, the pressure coefficient of the selection operation is increased to increase the weight of the fitness value; the probability of the crossover operation is reduced to decrease the magnitude of the change in the design variables; the probability of the mutation operation is increased to introduce randomness to escape local optima; after parameter adjustment, the iteration continues until the constraint violation is eliminated.

[0023] Preferably, the process of generating structural analysis images is as follows: based on the structural response data of the optimal design individual, stress cloud diagrams, displacement cloud diagrams, and modal shape diagrams of the reticulated shell structure are generated; the images are rendered by a visualization engine to highlight high-stress areas and large-displacement areas; users can view the images through an interactive interface and switch between different view modes.

[0024] Preferably, the present invention also includes an aluminum alloy reticulated shell structure design system based on a genetic algorithm, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that the processor, when executing the computer program, implements the steps of the aluminum alloy reticulated shell structure design method based on the genetic algorithm described above.

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] This invention provides a genetic algorithm-based design method for aluminum alloy reticulated shell structures. By receiving user-input design requirements parameters, it can accurately grasp the core design indicators of the reticulated shell structure, such as span, height, and load conditions, providing clear target guidance for subsequent design processes. The reticulated shell structure is divided into multiple design units, each corresponding to a node or member, achieving refined decomposition of the structural design and facilitating targeted processing of each component. Historical performance data of aluminum alloy materials, covering key information such as strength, stiffness, and durability, is obtained from a database, allowing the design process to fully rely on the actual performance characteristics of the material and avoiding design deviations caused by insufficient consideration of material properties.

[0027] Based on historical performance data and design requirements, the importance and constraint levels of each design unit are determined. This allows for differentiated treatment of different units during the design optimization process, giving more attention to important and highly constrained units, thus achieving a rational allocation of resources in the overall structural design. A genetic algorithm is used to generate an initial population based on the importance and constraint levels, ensuring the diversity and relevance of the initial design schemes and laying a solid foundation for subsequent optimization iterations. Iterative execution of the selection, crossover, and mutation operations of the genetic algorithm continuously optimizes individual designs, gradually approaching a better design solution.

[0028] During the iterative process, structural response data, including stress, strain, and displacement, is collected in real time. This allows designers to promptly grasp the mechanical behavior of the structure under different working conditions, providing a direct basis for the confirmation of constraints. Based on the structural response data, it is confirmed whether preset constraints are violated. If a violation is found, the genetic algorithm parameters are adjusted, forming a dynamic feedback optimization mechanism that can promptly correct deviations during the design process and prevent deviations from the optimization direction. The optimal design individual corresponding to the reticulated shell structure is output, and structural analysis images are generated for users to view. This not only provides specific design solutions for engineering practice but also allows users to intuitively understand the structural performance through visualization, enhancing the readability and operability of the design scheme. Attached Figure Description

[0029] Figure 1 This is a schematic diagram illustrating the working principle of the aluminum alloy reticulated shell structure design method based on genetic algorithm described in this invention.

[0030] Figure 2 A flowchart for determining the importance and constraint levels of design units;

[0031] Figure 3 A flowchart for generating the initial population;

[0032] Figure 4 This is a stress distribution cloud map of an aluminum alloy reticulated shell structure.

[0033] Figure 5 This is a comparison chart showing the effect of adjusting the design parameters of an aluminum alloy mesh shell structure based on a genetic algorithm. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] Please see Figure 1 This invention provides a design method and system for aluminum alloy reticulated shell structures based on genetic algorithms. The method includes:

[0036] The process begins by receiving user-inputted design requirements parameters, including the span, height, and load conditions of the reticulated shell structure. These parameters define the structure's fundamental geometric and mechanical properties. The reticulated shell structure is then divided into multiple design units, each corresponding to a node or member, thus decomposing the macroscopic design problem into microscopic optimizable units. Historical performance data of the aluminum alloy material, encompassing strength, stiffness, and durability, is retrieved from a database. This data, based on past engineering cases and experimental accumulation, ensures design reliability. Based on the historical performance data and design requirements parameters, the importance and constraint levels of each design unit are determined. The importance level reflects the unit's criticality within the overall structure, while the constraint level represents the limit conditions the unit must meet. A genetic algorithm is used to generate an initial population based on the importance and constraint levels. This initial population contains multiple design individuals, each representing a complete reticulated shell structure design scheme. The encoding method maps design variables such as cross-sectional dimensions or material type to chromosomes. The genetic algorithm iteratively executes operations, including selection, crossover, and mutation, to progressively optimize the design individuals, evaluating their performance in each generation. During the iterative process, structural response data for each design individual is collected in real time. This data includes stress, strain, and displacement, obtained through numerical simulation or sensor feedback. Based on the structural response data, it is determined whether preset constraints are violated, such as excessive stress or displacement. If violations are found, the parameters of the genetic algorithm are dynamically adjusted to guide the search direction. The optimal design individual corresponding to the reticulated shell structure is output, satisfying all design requirements. A structural analysis image is generated for user viewing, visually displaying stress distribution or deformation patterns to aid decision-making. The entire method achieves automated and adaptive optimization, reducing manual intervention and improving design efficiency.

[0037] Example 1: See Figure 2In practical implementation, a design method for aluminum alloy reticulated shell structures based on genetic algorithms includes design requirements parameters such as boundary condition parameters and material specifications. Boundary condition parameters specify the support type of the structure, such as fixed support, hinged support, or elastic support. These parameters are input through the user interface and stored in system memory. Material specifications include physical properties of the aluminum alloy, such as grade, density, elastic modulus, and Poisson's ratio. These parameters are derived from a material library or user-defined settings. Historical performance data also includes fatigue life data and corrosion rate data. Fatigue life data is obtained through accelerated fatigue testing in the laboratory and represents the number of failure cycles of the material under cyclic loading. Corrosion rate data is derived based on environmental exposure experiments and reflects the degradation rate of the material in specific humidity, temperature, or chemical media. These data are extracted from the database and used to enhance the reliability of the design. The process of determining the importance and constraint levels of each design unit is implemented as follows: First, obtain the strength and stiffness data from the historical performance data of each design unit. The strength data includes yield strength and tensile strength values, and the stiffness data includes elastic modulus and shear modulus values. Calculate the strength coefficient and stiffness coefficient for each design unit. The strength coefficient is obtained by comparing the actual strength value with the standard allowable strength value, and the stiffness coefficient is obtained by normalizing the actual stiffness value with the reference stiffness value. Based on the strength and stiffness coefficients, and combined with the load condition parameters in the design requirements (including the magnitude and distribution of static load, live load, wind load, and snow load), calculate the importance coefficient for each design unit. The importance coefficient uses a weighted summation method, where the weights of the strength and stiffness coefficients are dynamically adjusted according to the load type; for example, the weight of the stiffness coefficient increases when wind load is dominant. The importance coefficient is compared with the preset importance threshold, which is set according to the structural safety level. For example, the importance coefficient is greater than 0.8 for high importance level, between 0.5 and 0.8 for medium importance level, and less than 0.5 for low importance level, thereby determining the importance level of the design unit as high importance level, medium importance level, or low importance level.

[0038] Simultaneously, based on durability data from historical performance data, including fatigue life and corrosion rate data, a constraint coefficient is calculated for each design unit. This constraint coefficient is derived by combining the ratio of fatigue life to design life with the ratio of corrosion rate to allowable rate. The constraint coefficient is then compared to a preset constraint threshold, which is set based on engineering specifications and empirical values. For example, a high constraint level corresponds to a constraint coefficient below 0.3, a medium constraint level corresponds to a constraint coefficient between 0.3 and 0.6, and a low constraint level corresponds to a constraint coefficient above 0.6. This determines whether the design unit is classified as high, medium, or low constraint level. This process is automatically executed by the algorithm module, and the results are stored in a unit attribute table.

[0039] In some embodiments, the processing of boundary condition parameters includes analyzing the degree-of-freedom constraints of the support points; the selection of material specification parameters is based on cost and performance optimization objectives; and the acquisition of historical performance data involves database queries and caching mechanisms to ensure real-time data availability. In the calculation of importance coefficients, the weight allocation of load condition parameters is based on load combination coefficients. For example, the combined effect of dead load and live load is represented by a weighting factor. When calculating constraint coefficients, fatigue life data considers the influence of stress amplitude, and corrosion rate data incorporates an environmental correction factor. The preset importance threshold and preset constraint threshold can be adjusted through the user configuration interface to adapt to different engineering standards. The determination results of importance level and constraint level are used for the generation of the initial population in the subsequent genetic algorithm.

[0040] Optionally, acquiring strength and stiffness data can include data preprocessing steps, such as outlier filtering and smoothing. Durability data calculation can integrate time-related models to simulate long-term performance changes. Importance coefficient calculation can employ multiple regression methods, introducing interaction terms to improve accuracy. Constraint coefficient calculation can combine probability distribution models to handle uncertainty. The process of determining importance and constraint levels can be iterative, adjusting thresholds based on preliminary results to ensure reasonable classification. It is understood that expanding design requirements parameters makes the design more closely aligned with actual engineering conditions, enriching historical performance data enhances the predictive ability of material behavior, and refining the classification of importance and constraint levels provides precise input for optimization algorithms. In practical implementation, the definition of boundary condition parameters includes geometric and mechanical constraints; the selection of material specification parameters affects the weight and cost trade-offs; the application of fatigue life data involves damage accumulation calculations; and the integration of corrosion rate data needs to consider the effects of protective measures. When calculating importance coefficients, the dynamic weights of load condition parameters are based on risk analysis; in constraint coefficient calculations, multi-source fusion of durability data improves robustness.

[0041] In some embodiments, fuzzy logic can be introduced to handle boundary cases in importance level determination, and constraint level determination can be combined with machine learning models to adaptively learn thresholds. A historical performance data update mechanism ensures data timeliness. The preset importance threshold is set with reference to industry standards such as building structure codes, and the preset constraint threshold is determined based on life cycle analysis. The output format of importance and constraint levels is structured data, facilitating algorithm calls.

[0042] Optionally, standardization methods such as Z-score normalization can be used when calculating the strength coefficient; anisotropic characteristics can be considered when calculating the stiffness coefficient; sensitivity analysis can be introduced to optimize weights when calculating the importance coefficient; and safety factor adjustments can be added when calculating the constraint coefficient. The determination process can be logged for traceability, and the results of importance and constraint levels can be visualized to assist user verification. It can be understood that this implementation enhances the comprehensiveness and accuracy of the design by expanding parameters and data. Automatic determination of importance and constraint levels reduces subjective errors and lays a solid foundation for genetic algorithm optimization. In specific implementation, the processing of boundary condition parameters includes boundary element analysis integration; the selection of material specification parameters supports multi-objective optimization; the application of fatigue life data involves crack propagation models; and the processing of corrosion rate data includes chemical kinetic simulation. When calculating the importance coefficient, the spatial distribution of load condition parameters is discretized using finite element meshes; in the constraint coefficient calculation, the time series of durability data is solved using difference equations. The adjustment of the preset importance threshold is based on Monte Carlo simulation, the optimization of the preset constraint threshold is achieved through response surface methodology, and the determination algorithms for importance and constraint levels are executed in parallel to improve computational efficiency.

[0043] In practical implementation, the weighted summation method used for calculating importance coefficients involves the dynamic determination of weighting factors and the synthesis calculation of coefficients. The weighting factors are not fixed values ​​but are dynamically allocated based on the load type and spatial distribution characteristics in the load condition parameters. For example, for reticulated shell structures, the weight allocation under wind load will be significantly different from that under snow load. The implementation process begins with the analysis of load condition parameters, converting the input static load, live load, wind load, and other parameters into a unified load effect vector. This vector represents the standard internal force or displacement response caused by various loads on the design unit. Subsequently, the system presets a basic weight for each type of load effect. This basic weight comes from the load combination coefficients specified in the structural design code; for example, the partial factor for dead load is 1.2, and for live load, it is 1.4. The core of dynamic adjustment lies in introducing a sensitivity analysis module. This module evaluates the sensitivity of the internal forces or displacements of each design unit to different load types through a finite number of rapid finite element calculations. The foundation weight of the load type with high sensitivity will be corrected by an amplification factor, which is directly proportional to the sensitivity value. The importance coefficient of each design unit is calculated by weighting and summing its strength coefficient, stiffness coefficient, and dynamically adjusted weighting factor. The summation model is a linear weighted model to ensure that the calculation results have clear physical meaning and comparability.

[0044] The optional multiple regression method for calculating importance coefficients focuses on mining patterns from historical successful design case data to build a predictive model. This method does not directly rely on preset weights, but rather establishes a data-driven mapping relationship between strength coefficients, stiffness coefficients, load parameters, and a target importance level. The implementation requires a dataset containing a large number of completed or validated aluminum alloy reticulated shell structure design cases. Each case in the dataset includes the strength coefficients, stiffness coefficients, load details, and importance scores obtained from expert evaluation or subsequent performance inversion for each design unit. The system uses strength coefficients, stiffness coefficients, and quantified load parameters (such as load intensity and load location coordinates) as independent variables, and the importance score as the dependent variable, employing a multiple linear regression algorithm for model fitting. The multiple linear regression algorithm estimates the coefficients of the regression equation using the least squares method. These coefficients are equivalent to the weights in a weighted summation, but they are based on the best fit of historical data, not on pre-set parameters. After obtaining the regression model, for a new design project, you only need to input the strength coefficient, stiffness coefficient and load condition parameters of the current design unit, and you can directly predict its importance coefficient using the regression equation. This method is especially suitable for scenarios with rich historical data accumulation and can automatically learn complex nonlinear relationships.

[0045] Example 2: See Figure 3In practical implementation, the process of generating the initial population using a genetic algorithm based on importance and constraint levels is specifically implemented as follows: The importance level of the design unit is used as the priority factor for population initialization. This principle is reflected in the design of the chromosome encoding scheme. The chromosome consists of gene sequences representing all design unit variables. Genes corresponding to design units with high importance levels are arranged at the front of the chromosome sequence, allowing these key unit variables to be prioritized and optimized in the early stages of genetic operations. The constraint level of the design unit is used as the control factor for population diversity. The random generation range of variables for design units with high constraint levels is strictly limited during initialization. This limitation is achieved by setting narrower upper and lower bounds for variables, thus pre-excluding individuals that clearly do not meet the constraints during the introduction of population diversity, avoiding waste of computational resources. For design units with higher importance levels, a larger range of design variable mutations is allocated to the initial population. Specifically, wider initialization boundaries are set for the definition variables of these design units. For example, the cross-sectional area variable can be uniformly and randomly generated between 50% and 150% of the standard value. This wide initial allocation helps to fully explore the potential optimal solutions of these key units in a broad design space during the early stages of the search. For design units with higher constraint levels, stricter variable boundary restrictions are imposed on the initial population. The initialization boundary of variables for design units with higher constraint levels is compressed. For example, the variation range of node coordinates is limited to within ±5% of the theoretical value. This compression strategy ensures that each individual in the initial population meets the basic constraints, laying a feasible foundation for subsequent optimization.

[0046] The initial population size is adaptively determined based on the total number of design units in the reticulated shell structure and the complexity of the design requirements parameters. The total number of design units directly determines the length of the chromosome genes, while the complexity of the design requirements parameters is a comprehensive indicator that considers factors such as the types and number of load conditions, the complexity of boundary conditions, and the diversity of material specifications. The adaptive determination process is implemented through an empirical formula, which uses the total number of design units as the basic variable and multiplies it by a complexity factor. The complexity factor is divided into multiple levels according to the complexity of the parameters, with each level corresponding to a specific multiplier, thereby dynamically calculating a reasonable population size. This ensures that the population contains sufficient diversity to avoid premature convergence, while also avoiding computational inefficiency due to excessive size. The initial population is generated using a pseudo-random number generation algorithm combined with a boundary check mechanism. For each gene locus on the chromosome, the importance level and constraint level of its corresponding design unit are determined. Random initial values ​​are generated according to the preset variable boundary range. During the generation process, design units with high constraint levels undergo secondary verification to ensure that their values ​​fall within the allowable range. For design units with high importance levels, they are allowed to take random values ​​within a wider range to increase population diversity.

[0047] In some embodiments, chromosome encoding can directly represent the actual values ​​of design variables using real-number encoding, or it can use binary encoding to discretize continuous variables before representation. Design units with high importance levels may be allocated more bits in the binary encoding to improve representation accuracy. Variable boundary constraints can be implemented using mapping functions, mapping randomly generated values ​​to allowable intervals. Design units with high constraint levels use strict mapping functions, while those with high importance levels use relaxed mapping functions. The adaptive formula for population size can further incorporate computational resource constraints as an adjustment factor, appropriately reducing the population size when available computational resources are limited, and increasing the population size when resources are sufficient to improve optimization quality.

[0048] Optionally, the initial population generation can utilize Latin hypercube sampling instead of completely random sampling to ensure a more uniform distribution of the initial population within the design space. This is particularly beneficial for design units with high importance levels, where Latin hypercube sampling ensures good coverage of variable values ​​across a wide range. Variable boundary constraints can be designed as a combination of soft and hard constraints. Hard constraints are used to strictly limit the range of design units with extremely high constraint levels, while for design units with medium or lower constraint levels, a small number of individuals can be allowed to slightly exceed the boundary, but a penalty term is applied. Adaptive population size determination can incorporate a learning mechanism, dynamically adjusting parameters in the formula based on feedback from the optimization effects of similar historical projects, making the population size setting more precise. In essence, prioritizing importance ensures the optimization priority of key regions, controlling diversity to reduce ineffective searches using constraint levels, balancing exploration and utilization through differentiated allocation of variable ranges, and improving computational efficiency through adaptive population size. In practical implementation, chromosome encoding needs to be compatible with subsequent genetic operations. Real-number encoding facilitates direct arithmetic crossover and Gaussian mutation, while binary encoding is suitable for single-point crossover and bit-flip mutation. The logic for variable boundary constraints needs to be consistent with the input requirements of the finite element analysis model to ensure that each generated individual is an analyzable and effective structural design. The adaptive process for population size needs to consider the current load status of the computer system in real time. In a parallel computing environment, the number of computing nodes can be dynamically allocated to match the population size requirements.

[0049] In some embodiments, design units with high importance levels can use heuristic rules to generate partial initial values ​​during initialization. For example, roughly reasonable cross-sectional dimensions can be estimated based on simple beam theory or empirical formulas as part of the initial values, and then combined with randomly generated values ​​to form the initial population, thereby accelerating the convergence process. Boundary constraints on design units with high constraint levels can introduce a tolerance mechanism, allowing a very small tolerance range during the initialization phase to prevent insufficient diversity in the initial population due to overly strict boundaries. The adaptive determination of the population size can be designed as a dynamically adjusted mode during iteration, using a larger population for global exploration in the early stages of optimization and reducing the population size for local fine-tuning in the later stages.

[0050] Optionally, the initial population generation can incorporate orthogonal experimental design methods. For design units with high importance levels, orthogonal arrays can be used to arrange the combinations of variable values, covering more possible combinations with fewer individuals. The implementation of variable boundary constraints can incorporate the concept of fuzzy boundaries. For design units with medium to low constraint levels, the variable boundary can be a transitional interval rather than an absolute limit, with the probability distribution gradually decreasing within the interval. The adaptive formula for population size can integrate machine learning prediction models to predict the optimal population size based on the characteristic parameters of the design problem, achieving truly intelligent setting. It is understandable that the quality of the initial population directly affects the efficiency and results of genetic algorithm optimization. Guided by importance and constraint levels, the initial population contains both diversity and high feasibility, providing a good starting point for subsequent iterative optimization. In specific implementation, the chromosome encoding scheme needs to be closely integrated with the shell structure parameterized modeling module to ensure accurate mapping from genes to design variables. The setting of variable boundary constraints needs to consider the characteristics of aluminum alloy materials and processing limitations to ensure that the generated design scheme is not only mechanically sound but also feasible in engineering practice. The adaptive population size algorithm needs to be robust and able to handle different types and sizes of reticulated shell structure design problems, automatically determining the appropriate initial population size from small, simple reticulated shells to large, complex reticulated shells.

[0051] In practical implementation, the pseudo-random number generation algorithm combined with the boundary checking mechanism is implemented as follows: The pseudo-random number generation algorithm uses a linear congruential generator to generate a pseudo-random number sequence uniformly distributed between 0 and 1. The algorithm calculates using a recursive formula, where each random number is obtained by multiplying the previous random number by a large constant and adding a fixed increment, then taking the modulus, thus generating a pseudo-random sequence with good statistical properties. The boundary checking mechanism is activated immediately after each pseudo-random number is generated. The checking process identifies the corresponding boundary constraints based on the type of the design unit variable being initialized. The boundary constraints come from two parts: one is the absolute physical boundary based on engineering common sense and material properties, and the other is the permissible boundary dynamically adjusted according to the constraint level of the design unit. For design units with high constraint levels, the permissible boundary is usually within the absolute physical boundary, which is a more stringent interval. The generated pseudo-random number is linearly mapped to the entire absolute physical boundary range of the variable to obtain an initial value. Subsequently, the boundary checking logic determines whether this initial value falls within the permissible boundary of the current design unit. If the value exceeds the permissible boundary, a correction function is triggered. The correction function projects the value towards the center of the permissible boundary to ensure that it falls within the valid area. For design units with high importance but low constraint levels, their permissible boundaries are basically consistent with the absolute physical boundaries. The generated random values ​​can usually pass the boundary check without correction after mapping, thus ensuring that these key variables have sufficient diversity in the initialization phase.

[0052] In its implementation, the Latin hypercube sampling method aims to replace simple random sampling to obtain an initial population with a more uniform distribution in the variable space. The core idea is to precisely divide the range of values ​​for each design variable into several equally probable intervals, with the number of intervals strictly equal to the planned number of individuals in the initial population. The process begins by processing each design variable independently. For each variable, its probability distribution type is determined; in the absence of prior knowledge, it is usually assumed to be a uniform distribution. The range of values ​​for this variable is then divided into N non-overlapping intervals of equal length, where N is the set initial population size. Subsequently, the Latin hypercube sampling method performs a random permutation sampling for each variable, generating a random permutation from 1 to N for each variable. This permutation defines the order in which samples are drawn from each interval, ensuring that each interval is drawn exactly once, thus achieving complete coverage in the dimension of a single variable. The specific generation of sample values ​​involves randomly selecting a sample value from the i-th interval of the first variable, the j-th interval of the second variable, and so on, up to the k-th interval of the n-th variable, according to the permutation order. Here, i, j, ..., k are indices determined by the permutation order. These sample values ​​are combined to form an individual in the initial population. This combination method ensures that in the multidimensional variable space, each interval in each dimension has exactly one sample point projection, thus achieving more efficient and uniform coverage of the design space statistically. This is particularly beneficial for exploring the wide range of variable spaces of design units with high importance levels.

[0053] Example 3: In specific implementation, the iterative execution of the genetic algorithm is as follows: In each iteration, the fitness value of each design individual is calculated. The fitness value is based on the stress and displacement data in the structural response data, and is weighted by combining the importance level and constraint level. The stress data comes from the maximum equivalent stress value output by the finite element analysis, and the displacement data is taken from the maximum absolute value of the nodal displacement. The weighted calculation process is completed through a fitness function, which normalizes the stress and displacement data and linearly combines them with weight coefficients. The weight coefficients are dynamically adjusted according to the importance level and constraint level of the design unit. For example, the stress data weight of a design unit with a high importance level is increased, and the displacement data weight of a design unit with a high constraint level is increased, to ensure that the optimization objective focuses on key areas and constraints. A selection operation is performed based on the fitness value, using a roulette wheel selection method. The selection probability of each design individual is proportional to its fitness value. Design individuals with higher fitness values ​​have a higher probability of being selected, thus preferentially retaining superior genes. Before the selection operation, the fitness value is usually scaled, such as using linear scaling or exponential scaling, to control the selection pressure and avoid premature convergence. When performing crossover operations, a higher crossover probability is used for design units with higher importance levels. The crossover probability value is set according to the importance level classification. The crossover probability of design units with high importance levels can be set to 0.9 or higher, the crossover probability of design units with medium importance levels is set to 0.7 to 0.9, and the crossover probability of design units with low importance levels is set to 0.5 to 0.7. The crossover method can be single-point crossover or arithmetic crossover, depending on the coding scheme. The crossover point is preferentially selected near the gene segment corresponding to the design unit with high importance level to promote the exchange of key information.

[0054] When performing mutation operations, a smaller step size is used for design units with higher constraint levels. The step size is determined by multiplying a step size control factor by the variable range. The step size control factor is set to 0.01 to 0.05 for design units with high constraint levels, 0.05 to 0.1 for design units with medium constraint levels, and 0.1 to 0.2 for design units with low constraint levels. Uniform mutation or Gaussian mutation is used, and the mutation probability is uniformly set to a low value, such as 0.1. However, for design units with high constraint levels, the step size is reduced to ensure minor adjustments and avoid compromising feasibility. The iteration termination condition is the convergence of the fitness value or the reaching of the maximum number of iterations. The fitness value convergence is determined based on the rate of change of the optimal fitness value being less than a preset threshold for several consecutive generations. The maximum number of iterations is preset to 500 to 2000 times based on the problem size. During the iteration process, each generation of the population undergoes selection, crossover, and mutation operations to generate a new population and re-evaluate the fitness until the termination condition is met.

[0055] The specific formula for calculating fitness value can be expressed as:

[0056]

[0057] in: Represents the fitness value. This represents the stress weighting coefficient. This represents the actual stress value. Indicates the allowable stress value. This represents the displacement weighting coefficient. This represents the actual displacement value. Indicates the allowable displacement value. Indicates the total number of design units. This represents the importance level adjustment factor for the i-th design unit. This represents the constraint level influence term for the i-th design unit. The stress weight coefficient and displacement weight coefficient are obtained through the mapping between importance level and constraint level. Design units with higher importance levels correspond to increased stress weight coefficients, and design units with higher constraint levels correspond to increased displacement weight coefficients. The importance level adjustment factor is calculated based on the importance level quantification value. The constraint level influence term is used to penalize constraint violations, ensuring that the fitness value fully reflects the structural performance.

[0058] In some embodiments, the selection operation can use a tournament selection method instead of roulette wheel selection. Tournament selection randomly selects a small number of individuals for comparison, and the individual with the highest fitness value wins and is selected. This method reduces the dependence on the absolute size of fitness values ​​and is more suitable for scenarios with small differences in fitness values. The crossover operation can use a multi-point crossover approach, setting multiple crossover points on the chromosome. This is particularly suitable for situations where high-importance design units are widely distributed, increasing the degree of gene mixing. The mutation operation can employ a non-uniform mutation strategy, where the mutation step size decreases with the number of iterations. Larger mutations are allowed early on to explore the space, while mutations are reduced later for finer searching. This strategy, combined with constraint level control of the step size, can balance global and local searches.

[0059] In some embodiments, fitness value calculation can incorporate a penalty term to handle constraint violations. When stress or displacement exceeds the allowable value, the fitness value decays linearly or quadratically according to the degree of violation. The penalty coefficient is related to the constraint level, with higher constraint levels resulting in more severe penalties for design units. The selection operation can be combined with an elite retention strategy, directly retaining the individuals with the highest fitness values ​​in each generation to the next generation to prevent the loss of superior individuals. The number of elites is typically set to 5% to 10% of the population size. Crossover and mutation probabilities can be dynamically adjusted based on population diversity. When the population fitness variance is small, the probabilities are increased to introduce diversity; when the variance is large, the probabilities are decreased to stabilize convergence.

[0060] In some embodiments, the iteration termination condition can incorporate a time limit or a user interruption mechanism, terminating immediately when the optimization runtime exceeds a preset limit or when the user manually stops the process, ensuring practicality. Fitness value convergence can be determined using a sliding window averaging method, calculating the average rate of change of fitness values ​​over the most recent several generations to avoid misjudgments due to single-generation fluctuations. The maximum number of iterations can be adaptively set based on the total number of design units; the number of iterations increases when the number of units is high and decreases when the number of units is low, thereby improving efficiency.

[0061] Optionally, the weighted calculation of fitness values ​​can employ a nonlinear combination approach, such as converting stress and displacement data into utility functions before weighting. These utility functions reflect the diminishing marginal returns of performance. Selection operations can utilize a general random selection method, iterating through all individuals using a single random number to improve efficiency and reduce bias. Crossover operations can employ a hybrid strategy, using arithmetic crossover for high-importance design units to smooth changes, and single-point crossover for low-importance design units to maintain diversity. In essence, fitness value calculation integrates multi-source data to ensure comprehensive evaluation, selection operations guide the inheritance of superior genes, crossover operations focus on optimizing key units, mutation operations maintain constraint feasibility, and termination conditions balance convergence and efficiency. In practical implementation, weight coefficient adjustments need to be synchronized with the importance and constraint level mapping table, which is predefined based on engineering experience or historical data. The setting of crossover and mutation probabilities needs to consider the encoding method; real-number encoding is suitable for arithmetic operations, while binary encoding is suitable for point operations. The iterative process requires monitoring population diversity indicators, such as gene entropy values, to prevent premature convergence.

[0062] It is understandable that the iterative execution of genetic algorithm operations constitutes the core loop of optimization. Each generation generates new solutions through selection, crossover, and mutation. Fitness values ​​guide the search direction, while importance and constraint levels fine-tune operational parameters, enabling the optimization process to possess both global exploration and local development capabilities. In practical implementation, the iterative loop needs to be efficiently integrated with the finite element analysis module. Fitness evaluation may account for the majority of computation time; therefore, algorithm parameter settings must balance accuracy and speed. Flexible combinations of termination conditions ensure that optimization can reliably terminate under different scenarios and output usable results.

[0063] In practice, the roulette wheel selection method is implemented as follows: This method simulates a roulette wheel game, where the area of ​​the sector occupied by each individual on the wheel is proportional to its fitness value. Individuals with higher fitness values ​​have larger sector areas and a higher probability of being selected. The implementation begins by normalizing the fitness values ​​of all designed individuals in the current population. Each individual's fitness value is divided by the sum of the fitness values ​​of all individuals in the population to obtain the selection probability of each individual, ensuring that the sum of all selection probabilities is 1. Then, the cumulative probability of each individual is calculated. The cumulative probability of the first individual equals its own selection probability; the cumulative probability of the second individual equals the sum of the cumulative probability of the first individual and the selection probability of the second individual, and so on. An individual's cumulative probability should be 1. This cumulative probability sequence actually divides the [0,1] interval into several continuous sub-intervals, with the length of each sub-interval corresponding to the selection probability of an individual. Generate a uniformly distributed random number in the range [0,1]. This random number is equivalent to the pointer position on a roulette wheel. Starting from the first individual, check whether the random number is less than or equal to the cumulative probability of the current individual. When the random number falls into the cumulative probability interval corresponding to an individual, that individual is selected to enter the mating pool. This selection process is repeated until the number of individuals in the mating pool is the same as the original population size. During this process, individuals with higher fitness values ​​have a higher probability of being hit by the random number because their cumulative probability interval is larger, and therefore have more opportunities to be selected.

[0064] In its implementation, the tournament selection method serves as an alternative to the roulette wheel selection method. Its implementation is based on a small-scale competition mechanism. This method does not rely on the global fitness ratio but selects superior individuals through local competition. The implementation process requires determining the size of the tournament, i.e., the number of individuals randomly selected in each competition. The tournament size is typically a small integer, such as 2, 3, or 5. Smaller sizes result in less selection pressure and better preservation of diversity, while larger sizes lead to greater selection pressure and faster convergence. For each new individual to be selected, the tournament selection method performs the following operations: randomly select the tournament-sized number of individuals from the current population to form a temporary competition group. This sampling process uses replacement, meaning the same individual may be selected multiple times to participate in different tournaments. Within this temporary competition group, the fitness values ​​of each individual are compared, and the individual with the highest fitness value is directly selected as the winner and replicated into the new population. This selection process is repeated until the size of the new population reaches the predetermined value. The advantage of the tournament selection method lies in its simplicity and high computational efficiency. It does not rely on scaling of the global fitness value and is not sensitive to extreme fitness values. At the same time, the selection pressure can be flexibly controlled by adjusting the size of the tournament. In small-scale tournaments, even individuals with lower fitness values ​​have a chance to win, which helps maintain population diversity. In large-scale tournaments, only the best individuals can win, which accelerates the convergence process.

[0065] Example 4: In specific implementation, the process of real-time acquisition of structural response data for each design individual is as follows: Finite element analysis is used to simulate the mechanical behavior of each design individual under load conditions. The finite element analysis employs commercial software or a custom numerical calculation program. Load conditions include static load, live load, wind load, and seismic load. During the simulation, the geometric model of the design individual is discretized into a finite element mesh, with each mesh node corresponding to a design element node. The mesh element type is selected as beam or rod element based on the characteristics of the member. The analysis solver calculates nodal displacements and element internal forces based on the stiffness matrix method. When extracting stress data, the stress data includes equivalent stress, principal stress, and shear stress values. Nodal stress is obtained through Gaussian point stress interpolation. Strain data is derived from the displacement field using geometric equations. Displacement data is directly read from the nodal displacement vectors, including linear and angular displacement components. After data extraction, it is stored in a structured array format. The finite element analysis employs a mesh generation method consistent with the design unit meshing. The mesh generation algorithm is based on the design unit topology, with each design unit corresponding to one or more finite element elements. The mesh size is adaptively adjusted according to the element length to ensure mesh refinement in stress concentration regions. The accuracy of data acquisition is guaranteed through mesh convergence verification, i.e., the mesh is progressively refined until the response data variation is less than the tolerance. The acquired structural response data is updated to a database in real time. The database is either a time-series database or a relational database. The update operation is performed immediately after the finite element analysis of each design unit is completed. The data record includes a design unit identifier, timestamp, stress data array, strain data array, and displacement data array, used for subsequent constraint verification and optimization history tracking.

[0066] Referring to Table 1, the process for confirming whether preset constraints are violated is specifically implemented as follows: Preset constraints include stress constraints, displacement constraints, and stability constraints. Stress constraints are defined as allowable stress values, which are calculated based on the yield strength and safety factor of the aluminum alloy material. Displacement constraints are defined as permissible displacement values, which are set based on the span ratio and functional requirements of the reticulated shell structure. Stability constraints are verified through buckling analysis, which calculates the critical load factor. Real-time collected stress data is compared with the permissible stress values, with the comparison performed unit by unit. For each design unit, the maximum stress value is extracted and compared with the corresponding permissible stress value. If the stress data exceeds the permissible stress value, it is marked as a stress violation, and the degree of violation is recorded as the stress ratio. Displacement data is compared with permissible displacement values, using the global maximum displacement value or the displacement value of key nodes. If the displacement data exceeds the permissible displacement value, it is marked as a displacement violation, and the degree of violation is recorded as the displacement ratio. Based on stability analysis, the linear eigenvalue buckling method is used. After applying the design load, the eigenvalue problems of the stiffness matrix and geometric stiffness matrix are solved. If the minimum eigenvalue is less than 1.0, the individual design is determined to have buckled and is marked as a stability violation. If any violation occurs, a constraint violation signal is generated. The constraint violation signal is a digital signal that includes the violation type, violation unit identifier, and violation degree value, and triggers the genetic algorithm parameter adjustment module. The adjustment operation is completed before the next iteration.

[0067] Table 1: Preset Constraint Parameter Table

[0068]

[0069] In practical implementation, finite element analysis simulation can integrate multi-physics coupling, such as considering the thermal stress effect under temperature load, and extending load condition parameters to include temperature distribution parameters. Real-time data update mechanisms can employ incremental update strategies, transmitting only changed data to reduce database load. Constraint violation signal generation can be tiered, with warning levels categorized based on the severity of the violation. Stress data comparison can incorporate local average stress methods to smooth out stress concentration effects, and displacement data comparison can set independent constraints for displacements in different directions. Stability analysis can utilize nonlinear buckling analysis to improve accuracy, but this is computationally expensive and suitable for design verification.

[0070] Constraint violation signals can be encoded as binary vectors, with each bit representing a type of constraint violation state, facilitating rapid parsing by the genetic algorithm module. Database updates can incorporate data compression algorithms, such as lossless compression for storing historical data. Real-time data acquisition ensures the optimization process is based on accurate mechanical responses, and the constraint verification mechanism promptly corrects infeasible designs, improving optimization efficiency. In practical implementation, finite element analysis mesh generation needs to balance computational accuracy and speed, and mesh consistency ensures accurate data mapping. Constraint parameter settings must conform to engineering standards, and violation marking logic should robustly handle boundary conditions. Data acquisition can be parallelized, with multiple design individuals' finite element analyses executed simultaneously to accelerate the optimization cycle. Constraint verification can introduce fuzzy logic to handle gray areas approaching thresholds.

[0071] In practice, the specific implementation process of mesh convergence verification is a crucial step in ensuring the accuracy and reliability of finite element analysis results. This process assesses the stability of the numerical solution by systematically changing the mesh density. The verification process begins by generating a series of finite element models with different mesh sizes. The coarsest mesh model is generated based on the basic size of the design element. Each subsequent model is obtained by refining the mesh size of the previous model by a specific ratio (e.g., 0.8 times), forming a sequence of meshes from coarse to fine. The same finite element analysis is performed on each mesh model, extracting structural response data at key locations, which typically include stress concentration areas, near constraint boundaries, and at the maximum displacement. Specific values ​​for each model at these locations, such as the maximum equivalent stress and maximum displacement, are recorded. Subsequently, the relative rate of change of key response data between two adjacent mesh models is calculated. When the relative rate of change between two consecutive refined models is less than a preset tolerance value (e.g., 1% or 0.5%), the numerical solution is considered to have converged, and the mesh size used at this point is considered sufficiently accurate. If the convergence criterion is not met, the mesh will be refined and the analysis process will be repeated until the convergence condition is met. The determined mesh parameters will be applied to the finite element analysis of all design units to ensure the consistency of data acquisition.

[0072] In practical implementation, the linear eigenvalue buckling method for stability constraint verification is based on the linearization assumption to analyze the buckling behavior of a structure under load. This method requires establishing the stiffness matrix and geometric stiffness matrix of the structure in the finite element model. The stiffness matrix describes the elastic properties of the structure in a stress-free state, while the geometric stiffness matrix reflects the influence of the initial stress state on the structural stiffness. The calculation of the geometric stiffness matrix depends on the initial stress distribution generated by the individual structure under the load conditions. These two matrices are combined to form the mathematical expression of the eigenvalue problem. Solving this generalized eigenvalue problem yields a series of eigenvalues ​​and their corresponding eigenvectors. Each eigenvalue represents a buckling load factor, and the eigenvector describes the shape of the corresponding buckling mode. Stability is determined by checking the smallest positive eigenvalue. If the smallest positive eigenvalue is less than a preset threshold (usually 1.0), it indicates that the structure will buckle under the applied load conditions, thus marking it as a stability violation. Linear eigenvalue buckling analysis has high computational efficiency and is suitable for frequent calls during the genetic algorithm iteration process. However, its results are relatively conservative and are mainly used for preliminary screening. For cases close to the threshold, more precise nonlinear analysis may be needed for verification.

[0073] See Figure 4 This diagram, generated from real-time structural response data collected through finite element analysis, shows a stress cloud map of an aluminum alloy reticulated shell structure optimized using a genetic algorithm. The diagram uses a Cartesian coordinate system to represent the spatial extent of the reticulated shell structure; the color scale on the right represents stress values, with a gradient from dark blue to dark red visually representing stress distribution differences. The dark red area at the center of the cloud map indicates a high stress concentration zone, reflecting significant stress on members or nodes under load, requiring close verification of whether the allowable stress constraints of the aluminum alloy material are met. The surrounding blue-green areas have lower stress levels, indicating relatively safe structural performance. In the design process, this diagram is a crucial visualization element in the closed loop of real-time structural response data acquisition, constraint violation confirmation, and genetic algorithm parameter optimization. On one hand, it helps engineers quickly identify high-stress-risk areas, providing an intuitive basis for determining the importance level of design units; on the other hand, it quantifies the distribution of structural mechanical properties through color differences, verifying the effectiveness of the genetic algorithm in optimizing structural strength, ensuring that the final design meets requirements such as span and load while achieving reasonable and safe stress distribution. It serves as a vital bridge between algorithm optimization and engineering application for aluminum alloy reticulated shell structures.

[0074] Example 5: In specific implementation, the process of adjusting the genetic algorithm parameters is as follows: When a constraint violation signal is generated, the pressure coefficient of the selection operation is increased. The pressure coefficient is an influencing factor that controls the selection intensity. The increase of the pressure coefficient is achieved by modifying the fitness value scaling function. For example, the slope of the linear scaling function is increased from 1.0 to 1.2, making the difference in selection probability between individuals with high fitness values ​​and those with low fitness values ​​more significant. Increasing the weight of the fitness value means assigning a higher multiplier to the fitness value when calculating the selection probability, thereby significantly increasing the probability of individuals violating the constraints being eliminated. The probability of the crossover operation is reduced. The crossover probability is gradually reduced from the default baseline value of 0.7 with a preset step size of 0.1, and can be reduced to a minimum of 0.4. This strategy of reducing the magnitude of changes in design variables is achieved by reducing the frequency of gene exchange between parent individuals, thus slowing down the overall evolution speed of the population and avoiding the generation of more new individuals violating the constraints due to drastic changes. The probability of mutation is increased, starting from a default baseline of 0.1 and gradually increasing in preset steps of 0.05, up to a maximum of 0.2. This mechanism of introducing randomness to escape local optima is achieved by increasing the possibility of random changes in gene loci within the population. Even under increased selection pressure and decreased crossover probability, a certain level of population diversity can still be maintained. The iterative process after parameter adjustment includes updating the genetic algorithm control parameter register and applying the adjusted parameters to the genetic operations of the next generation of the population until constraint violation signals disappear. The criterion for constraint violation elimination is that no constraint violation signals are detected for three consecutive generations.

[0075] The process of generating structural analysis images is specifically implemented as follows: Based on the structural response data of the optimally designed individual, stress contour maps, displacement contour maps, and modal shape maps of the reticulated shell structure are generated. Stress contour maps are generated by mapping the nodal stress values ​​obtained from finite element analysis onto a color gradient; high-stress areas are represented using warm colors such as red, and low-stress areas using cool colors such as blue. Displacement contour maps are generated by color-coding the nodal displacement vector magnitudes; large displacement areas are marked with dark colors. Modal shape maps extract natural frequencies and mode shapes through eigenvalue analysis and display vibration modes using deformation animation. The images are rendered using a visualization engine based on a 3D graphics library such as OpenGL or DirectX. Techniques for highlighting high-stress and large-displacement areas include isosurface rendering, color enhancement, and boundary reinforcement, making key areas more prominent in the image. Users can view the images through an interactive interface that provides mouse and keyboard event handling functions and allows switching between different view modes, including isometric view, top view, bottom view, and section view. Enhanced user experience operations include zoom, pan, rotate, and animation playback control.

[0076] In practical implementation, the pressure coefficient can be adjusted using a dynamic adaptive strategy, automatically determining the increment based on the severity of constraint violations; a larger increase in pressure coefficient occurs when the constraint violation signal is strong. The reduction in crossover probability can be phased: decreasing to 0.6 for the first violation, 0.5 for subsequent violations, and 0.4 for severe violations, achieving fine-grained control. The increase in mutation probability can be correlated with the number of iterations; appropriately reducing the mutation probability in later iterations improves convergence accuracy. Optionally, the pressure coefficient adjustment for selection operations can be combined with population diversity indicators; when population diversity is too low, the pressure coefficient can be appropriately reduced to avoid premature convergence. The adjustment of crossover probability can be tailored to different gene segments, with lower reductions in crossover probability for gene segments corresponding to design units with higher importance levels. The increase in mutation probability can employ a non-uniform strategy: Gaussian mutation for continuous variables and uniform mutation for discrete variables.

[0077] Optionally, a relaxation factor can be introduced into the constraint violation elimination process to allow occasional minor violations to proceed without triggering readjustment. The visualization engine's rendering can employ a hierarchy of details technique, dynamically adjusting the mesh detail level based on the view zoom level to balance rendering quality and performance.

[0078] It is understandable that the parameter adjustment mechanism enables the genetic algorithm to have adaptive optimization capabilities, while the image generation function provides intuitive design feedback; the combination of the two forms a complete design verification closed loop. In practical implementation, the adjustment amounts of the stress coefficient, crossover probability, and mutation probability need to be determined through extensive experimentation to ensure a reasonable range, avoiding over-adjustment that could lead to oscillations in the optimization process. Visualization rendering needs to be tightly integrated with the geometric modeling engine to ensure consistency between graphical and analytical data. In some embodiments, constraint violation signals can be categorized into different types, corresponding to different parameter adjustment strategies: stress violations primarily increase selection stress, displacement violations primarily decrease crossover probability, and stability violations primarily increase mutation probability. Image generation can add time-series animation functionality to demonstrate the structural response changes as loads are gradually applied. The interactive interface can integrate annotation tools, allowing users to add annotations and measurement data to the images.

[0079] Optionally, parameter adjustments can be logged historically to form an adjustment strategy knowledge base for parameter initialization in similar projects. The visualization engine can support virtual reality display modes, providing an immersive structural browsing experience. The image export function can generate standard format reports, including key data tables and 3D images. In specific implementations, the pressure coefficient adjustment formula for selected operations can be designed as a function of the degree of violation; the higher the degree of violation, the greater the increase in the pressure coefficient. The adjustment of crossover probability can consider the population fitness variance; the smaller the variance, the greater the reduction. The adjustment of mutation probability can introduce random perturbations to prevent the adjustment process from becoming too regularized. The lighting model for visualization rendering can be optimized, using Phong shading or physically based rendering techniques to improve image realism. The view switching of the interactive interface can preset multiple standard perspectives and support saving and recalling custom perspectives. The image generation process can be batch-processed, automatically generating multi-angle views and comparison views for comprehensive evaluation of design results.

[0080] In practical implementation, the adjustment method for the pressure coefficient involves a dynamic feedback mechanism. When the system detects a constraint violation signal, the pressure coefficient, as a key parameter for controlling the intensity of the selected operation, is immediately adjusted. The adjustment of the pressure coefficient is based on the type and severity of the constraint violation signal. The violation signal analysis module extracts the violation type (such as stress violation, displacement violation, or stability violation) and the violation severity value (such as stress ratio or displacement ratio). Based on a preset mapping table, the increment of the pressure coefficient is determined. The mapping table divides the violation severity into multiple levels, each level corresponding to a pressure coefficient increase. For example, a minor violation (…) For violations of severity (1.0-1.2), the stress coefficient is increased by 0.1; for moderate violations (1.2-1.5), it is increased by 0.2; and for severe violations (greater than 1.5), it is increased by 0.3. The baseline value of the stress coefficient is usually set to 1.0. The adjusted stress coefficient is applied to the fitness value scaling function, which can be linear or exponential. Linear scaling multiplies the fitness value by the stress coefficient, amplifying the difference between high-fitness and low-fitness individuals, thereby increasing the intensity of survival of the fittest in the selection operation. The adjustment process is executed automatically, and the parameter register is updated before each iteration to ensure that the genetic algorithm responds quickly to changes in constraint states.

[0081] The implementation of the visualization engine rendering method begins with the preprocessing of structural response data. The preprocessing stage converts the raw data output from the finite element analysis (such as nodal stresses, displacements, and mode shape vectors) into a format recognizable by the visualization engine. The data standardization module normalizes stress or displacement values ​​to the 0-1 range for color mapping. The color mapping algorithm uses linear interpolation or nonlinear transformation to map data values ​​to predefined color gradients. For example, in the stress contour plot, the minimum value is mapped to blue, the maximum value to red, and intermediate values ​​are generated with smooth transition colors through HSV color space interpolation. The displacement contour plot undergoes similar processing but may use different color schemes for differentiation. The generation of the mode shape diagram involves geometric deformation calculations, converting the mode shape vectors... Superimposed on the original mesh geometry, the deformation effect is amplified for observation using a displacement scaling factor. The visualization engine is implemented based on the OpenGL or WebGL graphics API. The rendering pipeline includes vertex shaders to handle geometric transformations, fragment shaders to apply color and lighting models, and lighting models that use Phong shading or a simpler diffuse model to enhance the 3D effect. Interactive functions are implemented through event listeners. User input, such as mouse movement, triggers the view transformation matrix to update, enabling rotation, scaling, and translation. View mode switching is accomplished by switching camera parameters and rendering parameters. For example, isometric views use orthographic projection, and perspective views use perspective projection. All rendering operations are completed in real time in the graphics buffer to ensure smooth image updates.

[0082] The implementation of the pressure coefficient adjustment method further includes historical log recording. The system records the pressure coefficient value, violation signal, and iteration algebra for each adjustment, which is used for subsequent analysis and optimization trend. The adjustment logic can also integrate a learning mechanism to automatically optimize the mapping table parameters by analyzing historical optimization data, thereby improving adjustment accuracy. The processing of violation signals supports parallel computing, allowing multiple violation types to be processed simultaneously and the pressure coefficient to be adjusted comprehensively, ensuring the comprehensiveness of adjustment decisions. In the data preprocessing stage of the visualization engine rendering method, data compression technology can be added, such as using octrees or LOD (Level of Detail) models to manage large-scale mesh data, improving rendering efficiency. The color mapping algorithm can support custom color schemes, allowing users to adjust the appearance of cloud maps according to their preferences. The interactive function can be extended to support multi-touch, facilitating operation on mobile devices. The rendering engine can also integrate screenshot and animation export functions to automatically generate image materials required for design reports.

[0083] In the implementation of the pressure coefficient adjustment method, the adjustment amount of the pressure coefficient can be designed as an adaptive variable, dynamically fine-tuned according to the population diversity index to avoid premature convergence caused by excessive pressure. The violation degree calculation can adopt a weighted average method to integrate the influence of multiple violation signals. The update of the mapping table can be optimized through machine learning algorithms, adjusting the level classification based on historical successful cases. In the implementation of the visualization engine rendering method, the rendering quality can be improved through anti-aliasing techniques, such as MSAA or FXAA, to reduce image jaggedness. Physical constraints can be added to the geometric deformation calculation to prevent unreasonable deformations when displaying vibration modes. The interactive interface can integrate annotation tools, allowing users to add text annotations or measurement lines to the image, enhancing the analysis function. The implementation process of the pressure coefficient adjustment method ensures that the genetic algorithm quickly converges to the feasible region when constraints are violated. The visualization engine rendering method provides intuitive visual feedback to help users understand the design performance. The combination of the two forms a complete optimization verification loop.

[0084] See Figure 5 This figure, presented as a bar chart, visually compares the changes in three key parameters of the genetic algorithm before and after constraint violations, covering three types of parameters: selection pressure coefficient, crossover probability, and mutation probability. This parameter adjustment mechanism is the core of the genetic algorithm's adaptive optimization: when a violation of stress, displacement, or stability constraints is detected, a combined strategy of increasing selection pressure, decreasing crossover probability, and increasing mutation probability is employed. This strategy strengthens the inheritance of superior genes while maintaining population diversity, ensuring that the algorithm can quickly converge to the optimal design scheme that satisfies the constraints. This embodies the closed-loop logic of dynamic feedback-parameter adaptive adjustment-optimization iteration in the design of aluminum alloy reticulated shell structures, and is one of the key technologies for achieving automated and intelligent structural design.

[0085] 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.

[0086] 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 design method for aluminum alloy reticulated shell structures based on genetic algorithms, characterized in that, Includes the following steps: The system receives design requirement parameters input by the user, including the span parameters, height parameters, and load condition parameters of the reticulated shell structure. The reticulated shell structure is divided into multiple design units, each design unit corresponding to a node or member of the reticulated shell structure; Historical performance data of aluminum alloy materials are obtained from the database, including strength data, stiffness data, and durability data. Based on the historical performance data and design requirement parameters, the importance level and constraint level of each design unit are determined; Using a genetic algorithm, an initial population is generated based on the importance level and constraint level. The initial population contains multiple design individuals, and each design individual represents a reticulated shell structure design scheme. Genetic algorithm operations, including selection, crossover, and mutation, are performed iteratively to optimize the design of individuals; During the iteration process, the structural response data of each individual design is collected in real time. The structural response data includes stress data, strain data, and displacement data. Based on the structural response data, it is confirmed whether the preset constraints are violated. If they are violated, the parameters of the genetic algorithm are adjusted. Output the design results of the reticulated shell structure corresponding to the optimal design individual; and generate structural analysis images for users to view; The process of determining the importance level and constraint level of each design unit is as follows: obtain the strength data and stiffness data from the historical performance data of each design unit, and calculate the strength coefficient and stiffness coefficient of each design unit; based on the strength coefficient and stiffness coefficient, and in combination with the load condition parameters in the design requirement parameters, calculate the importance coefficient of each design unit; The importance coefficient is compared with the preset importance threshold to determine whether the importance level of the design unit is high, medium or low; at the same time, the constraint coefficient of each design unit is calculated based on the durability data in the historical performance data; the constraint coefficient is compared with the preset constraint threshold to determine whether the constraint level of the design unit is high, medium or low. The process of generating an initial population using a genetic algorithm based on the importance and constraint levels is as follows: the importance level of the design unit is used as the priority factor for population initialization, and the constraint level of the design unit is used as the control factor for population diversity; for design units with higher importance levels, a larger range of design variable variation is allocated in the initial population; for design units with higher constraint levels, stricter variable boundary constraints are imposed in the initial population; the size of the initial population is adaptively determined based on the total number of design units in the shell structure and the complexity of the design requirements parameters.

2. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 1, characterized in that, The design requirements parameters also include boundary condition parameters and material specifications for the reticulated shell structure; the historical performance data also includes fatigue life data and corrosion rate data.

3. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 2, characterized in that, The process of iteratively executing the genetic algorithm operation is as follows: In each iteration, the fitness value of each design individual is calculated. The fitness value is based on the stress data and displacement data in the structural response data, and is weighted by combining the importance level and constraint level. The selection operation is performed based on the fitness value, prioritizing the retention of design individuals with higher fitness values; when performing the crossover operation, a higher crossover probability is used for design units with higher importance levels; when performing the mutation operation, a smaller mutation length is used for design units with higher constraint levels; the iteration termination condition is when the fitness value converges or the maximum number of iterations is reached.

4. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 3, characterized in that, The process of real-time acquisition of structural response data for each design unit is as follows: The mechanical behavior of each design unit under load conditions is simulated through finite element analysis, and stress, strain, and displacement data are extracted. The finite element analysis uses a mesh generation method consistent with the design unit division to ensure the accuracy of data acquisition. The acquired structural response data is updated to the database in real time for subsequent constraint confirmation.

5. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 4, characterized in that, The process for confirming whether the preset constraints have been violated is as follows: The preset constraints include stress constraints, displacement constraints, and stability constraints; the real-time collected stress data is compared with the allowable stress value, and if it exceeds the allowable stress value, it is marked as a stress violation; the displacement data is compared with the allowable displacement value, and if it exceeds the allowable displacement value, it is marked as a displacement violation. Based on stability analysis, if the designed individual buckles, it is marked as a stability violation; if any violation exists, a constraint violation signal is generated, and the genetic algorithm parameters are adjusted.

6. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 5, characterized in that, The process of adjusting the genetic algorithm parameters is as follows: when a constraint violation signal is generated, the pressure coefficient of the selection operation is increased to increase the weight of the fitness value; the probability of the crossover operation is reduced to decrease the magnitude of the change in the design variables; the probability of the mutation operation is increased to introduce randomness to escape local optima; after parameter adjustment, the iteration continues until the constraint violation is eliminated.

7. The design method for aluminum alloy reticulated shell structures based on genetic algorithms according to claim 6, characterized in that, The process of generating structural analysis images is as follows: Based on the structural response data of the optimal design individual, stress cloud diagrams, displacement cloud diagrams, and modal shape diagrams of the reticulated shell structure are generated; the images are rendered by a visualization engine to highlight high-stress areas and large-displacement areas; users can view the images through an interactive interface and switch between different view modes.

8. A design system for aluminum alloy reticulated shell structures based on a genetic algorithm, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the aluminum alloy reticulated shell structure design method based on genetic algorithm as described in any one of claims 1 to 7.

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