Multi-objective optimization method and system for airborne products

Abstract

The application relates to the technical field of intelligent manufacturing, and discloses a multi-target optimization method and system for an airborne product, which are used to improve the overall performance of the airborne product. The method comprises the following steps: obtaining an initial population based on a series of initial model files of a target airborne product, and determining constraint conditions and a target function of the target airborne product; the constraint conditions comprise the ranges of iteration parameters; in each iteration process of obtaining a global optimal Pareto front according to the constraint conditions, a non-dominated sorting and crowding degree calculation are performed on a tth generation population through an algorithm, a new solution of a t+1th generation is generated by applying gradient-guided Gaussian disturbance to an individual with excellent performance selected from a sorting result, and the tth generation population comprises cross offspring of a t-1th generation population; when an iteration termination condition meeting a target is reached, the iteration is terminated, and the global optimal Pareto front is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing, and particularly relates to a multi-objective optimization method and system for an airborne product. BACKGROUND

[0002] The airborne product is a composite equipment widely used in the military field, and its design needs to be balanced among multiple parameters, usually involving multiple conflicting objective functions. In practical applications, how to optimize multiple objectives simultaneously while ensuring the diversity and convergence of the solution set is a challenging problem. Currently, the design of the airborne product usually relies on experience and single-objective optimization methods, making it difficult to achieve the best balance among multiple objectives. Common multi-objective optimization methods, such as algorithms based on the Pareto front, can provide a set of non-dominated solutions, but when faced with high-dimensional objectives and complex constraint conditions, they are prone to local optimal solutions, resulting in loss of solution diversity and poor performance in certain performance indicators, affecting the combat effectiveness and economy. Therefore, there is an urgent need for a multi-objective optimization algorithm that considers strength, cost, and weight simultaneously to improve the overall performance of the airborne product. SUMMARY

[0003] The present application aims to disclose a design optimization method and system for an airborne product under multi-objective constraints to improve the overall performance of the airborne product.

[0004] To achieve the above-mentioned purpose, the multi-objective optimization method for the airborne product disclosed by the present application comprises:

[0005] Step S1, obtaining an initial population based on a series of initial model files of the target airborne product, and determining the constraint conditions and objective functions of the target airborne product; the constraint conditions include the range of each iteration parameter;

[0006] Step S2, in each iteration process of obtaining the global optimal Pareto front according to the constraint conditions, performing non-dominated sorting and crowding degree calculation on the first generation population by an algorithm, and selecting the iteration parameters of individuals with excellent performance from the sorting results to generate the parameter values in the new solution of the first generation +1 generation by applying gradient-guided Gaussian disturbance; ; the first generation population includes the offspring of the first generation -1 generation after crossover; ; the calculation formula of the parameter values of each iteration parameter in the new solution based on gradient-guided Gaussian disturbance is:

[0007]

[0008] ; wherein, is the first​​ The perturbation ratio coefficient of the generation. For gradient guiding terms, For the first The objective function at the th ... The weight of generations ; For the first Objective function In the Improvement rate of generation For the first The objective function with respect to the iteration parameters gradient, The total number of objective functions, For the first Noise amplitude control factor related to conflict level The mean is zero and the variance is Gaussian noise;

[0009] Step S3: When the iteration termination condition that satisfies the objective is reached, terminate the iteration and obtain the globally optimal Pareto front.

[0010] Preferably, The calculation formula is:

[0011] ;

[0012] ; ;

[0013] in, This is the initial disturbance scaling factor. The preset total number of iterations, For adjustment indices greater than 1, The population diversity coefficient, For the first The set of crowding levels of a generation of populations. Standard deviation, Temporary index In 1 to Within range The maximum value, For the first Pareto improvement of the generation, For the first Pareto front solution set of the generation.

[0014] Preferably, during the iteration process, The system is divided into two segments based on a pre-defined strategy. The calculation formula for the first segment is as follows: ;in, The initial noise amplitude, To adjust the parameters, This represents the maximum value in the set of conflict degrees between the two objective functions; the calculation formula for the latter part is: ;in, For the boundary distance of the iteration parameter, ; For the first The iteration parameter at the th iteration point The current value of the generation. express The maximum value in the current population. express The minimum value in the current population. To facilitate the adjustment of distance coefficients for iterative parameters.

[0015] Preferably, during the iteration process, a surrogate model is used to predict the objective function of each individual.

[0016] Preferably, the surrogate model corresponding to at least one objective function uses radial basis functions to approximate the objective function.

[0017] Preferably, when the predicted value of the surrogate model exceeds the range of existing training points, the corresponding predicted value is replaced with the real objective function value obtained based on finite element simulation and added to the training set to trigger the update operation of the surrogate model.

[0018] Preferably, the iteration termination condition includes when the number of iterations reaches or the Pareto improvement of M consecutive iterations meets the preset convergence characteristics, where M is an integer greater than or equal to 3.

[0019] Preferably, the airborne product is a tail fin, the objective function includes a strength objective function, a weight objective function, and a cost objective function, and the constraints include the width and thickness ranges corresponding to the chordal and transverse stiffeners, respectively.

[0020] To achieve the above objectives, the present invention also discloses a multi-objective optimization system for airborne products, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0021] The present invention has the following beneficial effects:

[0022] 1. By introducing gradient-based perturbations, the algorithm's search capability is enhanced, ensuring that the perturbation direction aligns with the current optimization priority. For example, if a certain generation has a high cost improvement rate, the gradient term tends to guide the parameters towards cost reduction, thus avoiding getting trapped in local optima. Simultaneously, an adaptive strategy can be used to adjust the perturbation magnitude as the number of iterations increases, ensuring a large perturbation amplitude in early iterations (global search) and a small amplitude in later iterations (local fine-tuning).

[0023] 2. By integrating dynamic adjustment mechanisms based on objective function weights, perturbation mechanisms, and perturbation adjustments driven by objective conflict degree into multi-objective genetic algorithms, effective optimization of airborne product components across multiple objectives such as strength, cost, and weight can be achieved. Furthermore, by employing reasonable population search strategies, the algorithm's global search capability can be enhanced, avoiding the local optimum problem common in optimization algorithms, improving the quality of solutions for multi-objective optimization, adapting to the needs of complex problems, and thereby improving the overall performance of the target airborne product.

[0024] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0025] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0026] Figure 1 This is a schematic diagram of the iterative parameter distribution of the tail fin disclosed in an embodiment of the present invention.

[0027] Figure 2 This is a flowchart of a multi-objective optimization method for airborne products disclosed in an embodiment of the present invention. Detailed Implementation

[0028] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0029] Example 1

[0030] This embodiment discloses a multi-objective optimization method for airborne products, which are based on... Figure 1 The following explanation uses the tail fin as an example to illustrate the typical component structure shown. Figure 2 The flowchart shown includes the following steps:

[0031] Step S1: Obtain an initial population based on a series of initial model files of the target airborne product, and determine the constraints and objective function of the target airborne product; the constraints include the range of each iteration parameter.

[0032] Typically, the objective functions for a tail fin include maximizing strength, minimizing cost, and minimizing weight. Therefore, three objective functions are defined as follows: , , ;in, For the strength target of the component, The stress on a component is to be minimized, thereby indirectly maximizing its strength. For the cost of components, It is a function of production costs and is usually related to materials, processes, and production scale; The weight of the component. The weight is the weight of the component, which is usually a function of the component's geometry and density.

[0033] In this embodiment, as Figure 1 As shown, the iteration parameters of the tail fin can be set as the width and thickness of the chordal and lateral stiffeners, respectively. Here, the numerical index 1 represents the width of the lateral stiffener, 2 represents the width of the chordal stiffener, 3 represents the thickness of the chordal stiffener, 4 represents the rear lug, 5 represents the front lug, and 6 represents the thickness of the lateral stiffener. The corresponding constraints include the width and thickness ranges of the chordal and lateral stiffeners, respectively; while the front and rear lugs are fixed constraints. The initial model file is usually an STP file. In subsequent iterations, the model file corresponding to the new solution generated by the mutation is also updated accordingly. Typically, there is a one-to-one correspondence between the solution and the model file.

[0034] Step S2: In each iteration of obtaining the globally optimal Pareto front based on the constraints, the algorithm is used to... The population is subjected to non-dominated sorting and crowding calculation. Iterative parameters are selected from the sorting results to choose individuals with superior performance. Applying gradient-guided Gaussian perturbation generates the first Parameter values ​​in the new solution of +1 generation The first The first generation of the population includes the second generation. -1 generation crossover offspring.

[0035] In this step, the general formula for calculating the values ​​of each iteration parameter in the new solution based on the gradient-guided Gaussian perturbation is:

[0036] ;in, For the first The perturbation ratio coefficient of the generation. For gradient guiding terms, For the first The objective function at the th ... The weight of generations ; For the first Objective function In the The improvement rate of the generation (an improvement rate greater than zero indicates a better improvement). Indicates that all objective functions are in the th order. (total improvement rate of each generation) For the first The objective function with respect to the iteration parameters gradient, The total number of objective functions. For the first Noise amplitude control factor related to conflict level The mean is zero and the variance is Gaussian noise.

[0037] In this embodiment, The calculation formula is: ; ; ;in, This is the initial disturbance scaling factor. The preset total number of iterations, For adjustment indices greater than 1, The population diversity coefficient, For the first The set of crowding levels of a generation of populations. Standard deviation, Temporary index In 1 to Within range The maximum value, For the first Pareto improvement of the generation, For the first Pareto front solution set of the generation.

[0038] In this embodiment, during the iteration process, The system is divided into two segments based on a preset self-adjustment strategy. The calculation formula for the first segment is as follows: ;in, The initial noise amplitude, To adjust the parameters, This represents the maximum value in the set of conflict degrees between the two objective functions; the calculation formula for the latter part is: ;in, For the boundary distance of the iteration parameter, ; For the first The iteration parameter at the th iteration point The current value of the generation. express The maximum value in the current population. express The minimum value in the current population. A convenient distance adjustment coefficient (the value range can be 0.5-3.0, according to the parameter boundary range, the range is narrow, and a large value is taken to enhance the inhibition of the boundary distance on the disturbance, so as to avoid the parameter exceeding the effective range) is taken for the iteration parameter. Optionally, the division strategy of the front and rear two sections can be reasonably set according to the experience value and the total number of iterations (for example, assuming that the total number of iterations is set to 1100 times, the first 800 times are set as the front section, and the last 300 times are set as the rear section); so that the iteration process of the present embodiment in the front section is relatively extensive, and the iteration process in the rear section further deepens the subtle differences between the iteration parameters.

[0039] It is worth noting that the improvement rate and the improvement degree of the present embodiment are two different concepts. For the target changes of stress, weight, cost, etc., the stress of the tail wing is reduced from 227MPa to 222MPa, and the improvement rate is 2.2%. The improvement degree is a comprehensive quantitative index for all target functions. From a certain level, the improvement rate focuses on the local improvement of a single performance, while the improvement degree is used to measure the overall improvement index of the Pareto frontier based on multiple targets. In addition, in the calculation formula of the above gradient-guided Gaussian disturbance, a solution includes the values of multiple iteration parameters, and each iteration parameter is calculated based on the same disturbance formula to obtain the corresponding value in the next generation solution. In other words, for a single iteration parameter, the calculation formula can also be described as: ; so that if After considering diversity, the values of different iteration parameters in the process of generating the Sth generation new solution are usually inconsistent.

[0040] In a specific implementation scenario, the data in the iteration process of the tail wing part is shown in Table 1:

[0041] Table 1: Iteration data table

[0042]

[0043] In the above table 1, the chord-wise stiffener width is 20mm, the chord-wise stiffener thickness is 13mm, the transverse stiffener width is 20mm, and the transverse stiffener thickness is 13mm. The initial population solution; based on the algorithm of the present embodiment after multiple optimization iterations, an optimal solution satisfying the optimization requirement is obtained at the iteration step of 1100 steps:

[0044] The chord-wise stiffener width is 12.02mm, the chord-wise stiffener thickness is 11.4mm, the transverse stiffener width is 10.17mm, and the transverse stiffener thickness is 11mm.

[0045] ​Step S3, when the iteration termination condition of the target is reached, terminate the iteration and obtain the global optimal Pareto front. The iteration termination condition includes that the number of iterations reaches or the degree of Pareto improvement of M consecutive generations meets the preset convergence characteristics, and M is an integer greater than or equal to 3.

[0046] Preferably, with reference to Figure 2 In the iteration process of the embodiment, a surrogate model can be used to predict the target function of each individual. The surrogate model can approximately predict the value of the target function. In the process of using the surrogate model to approximate the complex physical simulation, the surrogate model learns the simulation data to establish a mathematical expression of the target function and the constraint condition, and then quickly evaluates the performance of the structure in the multi-objective optimization process, thereby reducing the time and resource consumption of target function calculation in each optimization. The mechanism based on the surrogate model is prior art. Some surrogate models can use existing radial basis functions (including but not limited to Gaussian basis functions and the like) to approximate the target function, which will not be described in detail. Further, when the predicted value of the surrogate model exceeds the range of the existing training points, the corresponding predicted value is replaced by the real target function value obtained based on the finite element simulation and is added to the training set to trigger the update operation of the surrogate model.

[0047] To sum up, in the embodiment, the "perturbation to generate a new solution" is the core link of the "mutation operation" in the multi-objective optimization algorithm, which can combine dynamic weight adjustment, hierarchical perturbation mechanism, target conflict degree driving and adaptive strategy. The specific steps and mathematical logic are as follows:

[0048] Preparation before perturbation: first, the algorithm performs non-dominated sorting (selects high-quality individuals according to the Pareto front criterion) and crowding degree calculation on the current generation (such as the t-th generation) population, and selects individuals with excellent performance from the sorting results as parent individuals (that is, the basis solution to be perturbed); at the same time, the dynamic weights of the current generation of target functions are calculated to determine the optimization priority of each target (intensity, cost, weight).

[0049] Perturbation formula and parameter analysis: new solution is generated by applying gradient-guided Gaussian perturbation to the parent individual , wherein the iteration logic of the (t-1)-th generation, the t-th generation and the (t+1)-th generation is in a continuous progressive relationship, and the core revolves around the "population update-evaluation-selection" cycle. The specific cycle process can be as follows:

[0050] Parent selection: from the (t-1)-th generation, a certain number of individuals are selected as the parent population of the t-th generation in combination with the crowding degree calculation results (select individuals with high crowding degree to avoid solution set concentration), to ensure that the parent individuals have performance advantages and diversity.

[0051] Cross operation: adopt simulated binary crossover (SBX) to cross the individuals in the parent population to generate the cross offspring (e.g., combine the chord-wise stiffener parameters of parent A with the transverse stiffener parameters of parent B to generate a new parameter combination), further expanding the population diversity.

[0052] Disturbance generation of new solution: apply gradient-guided Gaussian disturbance to the cross offspring and part of the parent individuals (to avoid the direct loss of high-quality parents) to generate a candidate new solution population of the t-th generation (including the cross offspring disturbance solution and the parent disturbance solution).

[0053] Objective function evaluation: use the updated surrogate model of the t-1-th generation to quickly calculate the objective function values (strength, cost, weight) of the candidate new solutions; for a small number of new solutions with large surrogate model prediction error (e.g., solutions with iteration parameters beyond the range of existing training points), supplement direct finite element simulation to obtain the true objective function values.

[0054] Surrogate model updating: add the "parameter-real target value" data of the candidate new solutions to the training set, and re-fit the surrogate model coefficients to obtain the updated surrogate model of the t-th generation.

[0055] Population screening and t-th generation output: combine the candidate new solutions with the Pareto front solution set of the t-1-th generation, perform non-dominated sorting and crowding degree calculation, and screen out the Pareto front solution set of the t-th generation (i.e., the optimal solution set of the t-th generation), which is used as the parent source of the t+1-th generation.

[0056] Embodiment 2

[0057] The embodiment discloses a multi-objective optimization system of an airborne product, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the corresponding method of the above embodiment when executing the computer program.

[0058] The multi-objective optimization method and system of the airborne product disclosed in the above two embodiments of the application have the following beneficial effects:

[0059] 1. By introducing gradient-based disturbance, the search ability of the algorithm is enhanced, and the disturbance direction is ensured to be consistent with the current optimization priority; for example, if the cost improvement rate is high in a certain generation, the gradient term is more inclined to guide the parameter to change in the direction of reducing the cost; and local optimal solution is avoided. At the same time, the disturbance amplitude can be adjusted by an adaptive strategy to decrease with the increase of the iteration number, ensuring that the disturbance amplitude is large in the early stage (global search) and small in the later stage (local fine tuning).

[0060] 2. By integrating dynamic adjustment mechanisms based on objective function weights, perturbation mechanisms, and perturbation adjustments driven by objective conflict degree into multi-objective genetic algorithms, effective optimization of airborne product components across multiple objectives such as strength, cost, and weight can be achieved. Furthermore, by employing reasonable population search strategies, the algorithm's global search capability can be enhanced, avoiding the local optimum problem common in optimization algorithms, improving the quality of solutions for multi-objective optimization, adapting to the needs of complex problems, and thereby improving the overall performance of the target airborne product.

[0061] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for multi-objective optimization of an airborne product, characterized in that, The method comprises the following steps: S1, obtaining an initial population based on a series of initial model files of a target airborne product, and determining constraint conditions and an objective function of the target airborne product; the constraint conditions comprise ranges of iteration parameters; Step S2: In each iteration of obtaining the globally optimal Pareto front based on the constraints, the algorithm is used to... The population is subjected to non-dominated sorting and crowding calculation. Iterative parameters are selected from the sorting results to choose individuals with superior performance. Applying gradient-guided Gaussian perturbation generates the first Parameter values ​​in the new solution of +1 generation The first The first generation of the population includes the second generation. -1 generation crossover offspring; Wherein, a calculation formula for taking values of each iteration parameter in a new solution based on gradient-guided Gaussian perturbation is: ; wherein, is a disturbance scaling factor of the th iteration, is a gradient guide term, is a weight of the th objective function at the th iteration, ; is an improvement rate of the th objective function at the th iteration, is a gradient of the th objective function with respect to an iteration parameter , is a total number of objective functions, is a noise amplitude control factor related to the th iteration and the degree of conflict, is a Gaussian noise with a mean of zero and a variance of . S3, terminating iteration and obtaining a global optimal Pareto front when an iteration termination condition of meeting a target is reached; Wherein, the airborne product is a tail fin, the objective function comprises a strength objective function, a weight objective function and a cost objective function, and the constraint conditions comprise ranges of widths and thicknesses of chordwise and transverse stiffeners respectively.

2. The method of multi-objective optimization of an airborne product on board an aircraft according to claim 1, characterized in that, The calculation formula is: ； ； ； wherein, is an initial perturbation scaling factor, is a preset total number of iterations, is an adjustment index greater than 1, is a population diversity factor, is a crowding degree set of the th generation population, is a standard deviation, is a temporary index in a range of 1 to a maximum value, is a maximum value, is a Pareto improvement degree of the th generation, is a Pareto front solution set of the th generation.

3. The method of multi-objective optimization of an airborne product according to claim 1 or 2, characterized in that, In the iteration process, will According to the preset strategy, it is divided into two sections, and the calculation formula of the front section is: ; wherein, is an initial noise amplitude, is an adjustment parameter, is the maximum value in the set of two objective function conflict degrees; The calculation formula of the latter section is: ; wherein, is an iteration parameter boundary distance, ; is the first iteration parameter in the current value of the first generation, denotes the maximum value in the current population, denotes the minimum value in the current population, is an iteration parameter convenient distance adjustment coefficient.

4. The method of multi-objective optimization of an airborne product on board an aircraft according to claim 3, characterized in that, In the iteration process, a surrogate model is used to predict the objective function of each individual.

5. The method of multi-objective optimization of an airborne product on board an aircraft according to claim 4, characterized in that, The surrogate model corresponding to at least one objective function uses a radial basis function to approximate the objective function.

6. The method of multi-objective optimization of an airborne product on board an aircraft according to claim 5, characterized in that, When a predicted value of the surrogate model exceeds a range of existing training points, the corresponding predicted value is replaced by a real objective function value obtained based on finite element simulation and added to the training set to trigger an updating operation of the surrogate model.

7. The method of multi-objective optimization of an airborne product on board an aircraft according to claim 6, characterized in that, The iteration termination condition comprises that the iteration number reaches or the degree of Pareto improvement of continuous M generations meets a preset convergence characteristic, and M is an integer greater than or equal to 3.

8. A multi-objective optimization system for an airborne product, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein, The processor executes the computer program to implement the method of any one of claims 1 to 7.

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