Aircraft structure intelligent optimization method based on active learning and dynamic weighted sampling

Abstract

The invention discloses an aircraft structure intelligent optimization method based on active learning and dynamic weighted sampling. According to the method, approximate modeling is carried out on an expensive constraint function by utilizing a neural network, active learning strategy research aiming at expensive constraints in a multi-constraint optimization problem of an aircraft structure is carried out in combination with specific characteristics of a structure optimization design problem, and a multi-constraint active learning optimization method based on an augmented Lagrange multiplier method is provided. Firstly, an augmented Lagrange multiplier method is utilized to augment an original multi-constraint optimization problem into an extreme value optimization problem containing a constraint penalty term, and then solution of the extreme value optimization problem containing the constraint penalty term is fused into a dynamic correction process of an expensive constraint agent model so as to realize active learning and adaptive sampling of the agent model. The invention provides an efficient approximate optimization method for lightweight determinacy and reliability design of an aircraft structure containing expensive constraint conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent optimization and structural optimization design, and particularly relates to a method for multi-constraint optimization of an aircraft structure based on active learning and dynamic weighted sampling. BACKGROUND

[0002] Lightweight design is one of the core objectives of aircraft structure optimization, aiming to reduce redundant structures to release more design space for functional systems. However, in the process of lightweight optimization, although the objective function calculation is relatively simple, the evaluation of structural performance constraints usually relies on high-precision numerical simulation, resulting in very high computational cost. With the increasing requirements for safety and fine design of aircraft in service, the influence of uncertainty factors on structural performance is becoming more and more significant, making uncertainty analysis an indispensable part of lightweight optimization, further increasing the computational burden of structural performance constraint evaluation, and greatly reducing the efficiency of solving optimization problems. Therefore, the introduction of a surrogate model to replace high-precision numerical simulation at low cost can effectively reduce the computational load and improve the efficiency of optimization solution.

[0003] In addition, if global optimization is to be achieved in the case of a complex feasible region, intelligent optimization algorithms must be used. A large number of expensive constraint evaluations need to be carried out during the optimization process, and the repeated calls of time-consuming analysis will cause an unbearable amount of calculation. Therefore, if the number of constraint function evaluations during optimization can be reduced while ensuring the accuracy of the optimal solution, the efficiency of solving expensive constraint optimization problems represented by structural uncertainty optimization can be improved by saving the number of time-consuming analysis calls.

[0004] Currently, scholars and engineering and technical personnel at home and abroad mostly stop at the serial intelligent optimization method of first establishing a surrogate model that meets the accuracy requirements and then solving the optimization problem for the intelligent solution of complex structure optimization problems, and rarely consider the active learning intelligent optimization method of integrating optimization solution into surrogate model updating. SUMMARY

[0005] To solve the above technical problems, the application provides a kind of aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling, which adopts the loss function updating strategy based on sample weighting to realize the acceleration of active learning process.The basic idea of this method is to give higher weight to the optimization sample, i.e., the new sample point obtained by proxy model optimization, so that the model pays more attention to the influence of these samples on the decision boundary;At the same time, give smaller weight to historical samples to reduce the interference of old data to new model training.Through the design of this weighted loss function, the proxy model can preferentially evaluate the key sample points sensitive to constraints, more efficiently utilize the updated samples, improve the utilization efficiency of computing resources, and accelerate the model correction process in high-dimensional optimization problems.

[0006] The application relates to an efficient global optimization method in aircraft structure optimization, and aims to improve the optimization calculation efficiency and global optimization ability by studying the optimization strategy combining active learning, dynamic weighted sampling and intelligent proxy model for the aircraft lightweight optimization problem under the influence of multi-constraint, high calculation cost and uncertainty.The application can be widely applied to aircraft structure lightweight design, uncertainty optimization and other complex engineering structure optimization problems, and provides important theoretical basis and calculation method support for efficient and intelligent aircraft structure optimization design.

[0007] To achieve the above purpose, the application adopts the following technical scheme:

[0008] A kind of aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling is used for aircraft structure lightweight optimization design containing expensive constraint conditions, comprising the following steps:

[0009] First step: propose a wing structure optimization model with lightweight as target and structure reliability as constraint by combining the specific characteristics of structure optimization design problem;

[0010] Second step: the augmented Lagrange multiplier method is used to augment the original multi-constraint optimization problem into an extreme value optimization problem containing constraint penalty term;

[0011] Third step: by integrating the solution of constraint penalty term extreme value optimization problem into the dynamic correction process of expensive constraint proxy model, an active learning strategy of proxy model is proposed;

[0012] Fourth step: combine the existing active learning strategy, apply dynamic weight to the new sample points generated by optimization solution, and complete the correction and update of proxy model based on weighted samples, finally output the expensive constraint proxy model meeting the accuracy requirement;

[0013] Step 5: Based on the developed active learning strategy and dynamic weighted sampling technology, an intelligent optimization method for the lightweight design problem of the aircraft structure is constructed, and a genetic algorithm is used to solve the extreme value optimization problem constructed by the surrogate model to obtain the optimal point of the lightweight design of the aircraft structure in the feasible region.

[0014] Advantages:

[0015] The present application uses a neural network method to carry out approximate modeling on the constraint function, combines the individual characteristics of the optimization problem solution, proposes an intelligent optimization method for the aircraft structure based on active learning and dynamic weighted sampling, uses the characteristics of the Lagrange multiplier method to mutually integrate the optimization process and the surrogate model updating process to establish an active learning criterion of adaptive sampling, thereby reducing the evaluation times of the constraint conditions under the premise of ensuring effective optimization, and provides a feasible and efficient approximate optimization method for the uncertain lightweight design of the aircraft structure containing expensive constraint conditions. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 Fig. 1 is a loss function updating strategy diagram of the aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling of the present application;

[0017] Figure 2 Fig. 2 is a schematic diagram of the real objective function, constraint boundary, feasible region and optimal point in numerical example 1;

[0018] Figure 3 Fig. 3 is an approximate constraint boundary and optimal point schematic diagram of the augmented Lagrange multiplier method based on intelligent learning of the constraint surface;

[0019] Figure 4 Fig. 4 is a schematic diagram of the real objective function, constraint boundary, feasible region and optimal point in numerical example 2;

[0020] Figure 5 Fig. 5 is an approximate constraint boundary and optimal point schematic diagram of the augmented Lagrange multiplier method based on dynamic improvement of the constraint surface;

[0021] Fig. 6 (a) is a structure mass change course diagram with calculation rounds;

[0022] Fig. 6 (b) is a diagram of the optimal individual change course of each generation population;

[0023] Fig. 7 (a) is a structure mass change course diagram with calculation rounds;

[0024] Fig. 7 (b) is a diagram of the optimal individual change course of each generation population;

[0025] Figure 8 Fig. 8 is a flowchart of the aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling of the present application. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in details below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0027] As shown in Figure 8 , the present application proposes an aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling, comprising the following steps:

[0028] Step (1) proposes a wing structure optimization model combining the specific characteristics of the structure optimization design problem, taking lightweight as the target structure and reliability as the constraint.

[0029] The general structure lightweight design problem can be described by the following optimization model:

[0030] (1)

[0031] wherein, is a p-dimensional design variable is the variable corresponding to the dimension index value, and the structure size is generally selected as the design variable, and are the design upper limit and the design lower limit of , respectively, the objective function is the mass of the structure, is the defined constraint function according to the actual situation, is the index value.

[0032] When considering non-probabilistic interval uncertainty, it is assumed that the interval variable in the structure is wherein represents the lower limit of the interval variable , and represents the upper limit of the interval variable . Under the premise of given design variable , the limit state function of the structure can be expressed as:

[0033] (2)

[0034] Thus, the non-probabilistic interval reliability measurement index and of the structure system under the condition of given design variable can be calculated. The structure optimization design model with reliability as the constraint can be expressed as:

[0035] (3)

[0036] or

[0037] (4)

[0038] where, and are the safety and failure indices of the license, respectively.

[0039] In practical applications, for the performance evaluation of complex structures of aircraft, the main means at present is to use finite element software to model and simulate the structure, so in the optimization problem of complex structure, the calculation of each constraint function generally needs to call simulation analysis, which is quite time-consuming; and single reliability evaluation needs multiple constraint function calculations, so it is more time-consuming, so in the optimization model, the constraint condition belongs to expensive constraint. In contrast, because the estimation of the structure quality is extremely simple, the single time consumption of the objective function in the above optimization model can be almost ignored. Based on this, it can be summarized that the characteristics of the multi-disciplinary constraint lightweight design of the aircraft structure, that is, the calculation of the objective function of the structure quality estimation is simple, but the calculation of the constraint function involving multi-disciplinary analysis is large, which affects the optimization efficiency.

[0040] In view of the above problems, the expensive constraint function is approximated by training a neural network surrogate model, and a new active learning method suitable for expensive constraint structure optimization is studied, so as to reduce the number of time-consuming structure simulations in the optimization process and improve the optimization efficiency under the premise of ensuring the accuracy of the optimal solution.

[0041] Step (2) uses the augmented Lagrange multiplier method to augment the original multi-constraint optimization problem into an extreme value optimization problem containing constraint penalty terms.

[0042] The augmented Lagrange multiplier method is a penalty function method, which is used to convert the constraint problem into an unconstrained problem for solving. Unlike the exterior point penalty function method and the interior point penalty function method, the augmented Lagrange multiplier method does not need to make the penalty factor tend to infinity, avoids the ill-posed problem, and has good convergence properties, and has become one of the most commonly used means for solving constraint optimization problems.

[0043] In the inequality constraint problem, for the dimensional constraint function, a dimensional slack variable is introduced, which is converted into the following equality constraint problem:

[0044] (5)

[0045] Therefore, the dimensional optimization variable , the slack variable , the multiplier vector and the scalar penalty factor the augmented Lagrangian function with slack variable :

[0046] (6)

[0047] Thus the original problem is transformed into solving

[0048] (7)

[0049] Firstly, we need to minimize with respect to the slack variable and transform it into a problem of minimizing only . By the method of penalty, we rewrite as

[0050] (8)

[0051] Thus we know that when the minimum point of is

[0052] (9)

[0053] When , the minimum point of is

[0054] (10)

[0055] Combining the above two cases, we can get

[0056] (11)

[0057] Then we can get the augmented Lagrangian function of the inequality constrained problem, which is independent of the slack variable , denoted as :

[0058] (12)

[0059] Thus the original problem is transformed into

[0060] (13)

[0061] In order to get more accurate results, we take the iterative strategy, take a larger penalty factor , and modify the multiplier , the multiplier in the k+1th iteration is obtained , the correction formula is as follows:

[0062] (14)

[0063] wherein, is the optimal point in the kth iteration. As can be seen from the formula, the multiplier will gradually converge with iteration, and when the constraint condition is met, the basic , otherwise it will be amplified.

[0064] Step (3) by integrating the solution of the constraint penalty term extreme value optimization problem into the dynamic correction process of the expensive constraint surrogate model, an active learning strategy of the surrogate model is proposed.

[0065] Based on the augmented Lagrange multiplier method, the expensive constraint problem can be converted into an unconstrained expensive objective function problem, and in theory, the existing technology can be used to realize approximate optimization through active learning of the objective function. However, as can be seen from the objective function of the augmented Lagrange multiplier method, there is a complex interface at , and the approximate modeling at the interface is difficult, and in the constraint optimization problem, the approximate accuracy at the complex interface is particularly important, so the traditional approximate optimization method is not suitable for such problems. Based on this, the present application proposes an active learning strategy for dynamic improvement of approximate constraint boundary.

[0066] In the augmented Lagrange function, there are structure mass function and multi-disciplinary constraint function, and in fact, only the expensive constraint needs to be replaced by an approximate model, that is:

[0067] (15)

[0068] wherein, is an approximate model.

[0069] The most direct active learning strategy is to take the optimal point as a new sample point and update the approximate model of the expensive constraint , until the optimal solution change value of two learning rounds is less than the tolerance. The active learning strategy is a prediction optimal point criterion.

[0070] Step (4) combines the existing active learning strategy, applies a dynamic weight to the new sample points generated by optimization solution, and updates and corrects the surrogate model based on the weighted samples, and finally outputs the expensive constraint surrogate model meeting the accuracy requirement.

[0071] Although the historical samples and the updated samples are comprehensively considered, the importance of the samples is not distinguished. Obviously, the value of the historical samples for constructing the initial surrogate model is much less than the updated samples calculated. Therefore, for the multi-dimensional problem requiring a large number of historical sample points, the strategy will require more updated samples to realize the correction of the surrogate model, thereby slowing down the solution speed of the optimization problem. Based on the above consideration, the application proposes a sample-weighted loss function updating strategy to realize the acceleration of the active learning process. The basic idea of the method is to give higher weight to the optimization samples, i.e. the new sample points obtained by the surrogate model optimization, through the updating of the loss function, so as to make the model pay more attention to the influence of these samples on the decision boundary; at the same time, the historical samples, i.e. the old data, are given smaller weight to reduce the interference of the new model training. Through the design of the weighted loss function, the model can efficiently utilize the updated samples to accelerate the correction process of the surrogate model in the high-dimensional optimization problem. The schematic diagram is as shown in Figure 1 . Figure 1 In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result.

[0072] (16)

[0073] In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result. In the formula, y represents the neural network prediction value of the i-th initial sample point, and y represents the absolute difference between the neural network prediction value and the real calculation result.

[0074] Step (5) constructs an intelligent optimization method for the lightweight design problem of the aircraft structure based on the developed active learning strategy and the dynamic weighted sampling technology.

[0075] By minimizing the augmented Lagrangian function constructed based on the surrogate model, new sample points are obtained in the design domain, and the approximate model is updated. Active learning is carried out in each multiplier method iteration until the approximate accuracy requirements are met. It is worth noting that although a neural network surrogate model is used as the constraint function, as sampling proceeds, the approximate accuracy of the model gradually improves, and its prediction results will gradually approach the true function. Therefore, the optimal solution finally obtained can meet the true constraint conditions. The steps of the proposed method are given below:

[0076] Step 5.1 Define the augmented Lagrangian function based on the optimization model, initial penalty factor and multiplier vector, then collect a small number of sample points in the design domain, call the expensive constraint function to calculate the initial training sample set, establish the initial neural network, and give the initial multiplier vector , let the multiplier method iteration count ;

[0077] Step 5.2: Multiplier vector based on the current multiplier method iteration , using a hybrid genetic algorithm based on the gradient method to solve the augmented Lagrangian function about Solving for the minimum point And calculate the expensive constraint function value ;

[0078] Step 5.3 Judgment Approximate accuracy at

[0079] (17)

[0080] in, Represents the minimum point The true expensive constraint function value at , Represents the minimum point The expensive constraint function value predicted by the surrogate model at If the above formula is established, it means that the accuracy of the prediction result of the minimum point proxy model meets the requirements and proceed to step 5.4. Otherwise, the true expensive constraint function value at the minimum point is set to As a new training sample, the neural network proxy model is dynamically updated by retraining the training set by applying dynamic weights, and returning to step 5.2;

[0081] Step 5.4: Minimum point As the optimal solution of the current multiplier method iteration step, calculate the true expensive constraint value at this point, and then update the multiplier vector of the augmented Lagrangian function according to the following formula and the calculated true expensive constraint value of the optimal point:

[0082] (18)

[0083] Step 5.5 If the multiplier vector or the optimal value meets the convergence requirement, end the calculation process and output the current optimal design point and the optimal objective function value, otherwise, enter the next multiplier method iteration step, bring the new multiplier vector into the augmented Lagrange function, let , return to step 5.2.

[0084] (19)

[0085] wherein, is the optimal objective function value of the kth iteration step of the multiplier method, indicates the convergence error tolerance of the multiplier vector, indicates the convergence error tolerance of the optimization target.

[0086] Embodiment:

[0087] In order to more fully understand the characteristics of the present application and its applicability to engineering practice, the present application provides three verification examples, including two numerical optimization examples and one engineering optimization example taking a wing structure as the object, including deterministic optimization design and reliability optimization design.

[0088] (1) Numerical example 1: double-constraint optimization problem

[0089] Consider an optimization problem with two constraint conditions as shown in the formula,

[0090] (20)

[0091] In the above formula, indicates the two-dimensional optimization variable of the objective function corresponding to the optimization problem and the optimal solution of the optimization problem is known . Next, the intelligent optimization method based on active learning and dynamic weighted sampling is used to solve the optimization problem. The objective function contour and design feasible region are shown in Figure 2 . Due to the high degree of nonlinearity of the constraint function , the feasible region of this optimization problem is relatively complex. Using the intelligent optimization method based on active learning and dynamic weighted sampling to solve the optimization model, after a single run, the objective function value at the optimal point and the true constraint function value are:

[0092] (21)

[0093] The approximate constraint boundary and its training samples are shown in Figure 3The optimal point obtained by the proposed method is consistent with the true solution, and the optimal solution is consistent with the true solution and falls on the constraint boundary. The sample points collected by the proposed method are mainly concentrated near the potential optimal point on the possible constraint boundary, so the number of training samples is less. This is because the intelligent optimization method based on active learning and dynamic weighted sampling not only makes full use of the prior information of the constraint function (i.e. the predicted value), but also more locally locates the sampling area of active learning by optimizing the objective function of the model, i.e. near the point that minimizes the objective function in the given feasible region.

[0094] Next, in order to illustrate the robustness of the proposed algorithm, the optimization method is repeated 10 times, and the number of constraint function calls and the statistical values of the optimal solution are listed in the table.

[0095] Table 1 Optimization results of Example 1

[0096]

[0097] It should be noted that in the intelligent optimization method based on active learning and dynamic weighted sampling, the true constraint function is called at the optimal point obtained at each optimization to verify the approximation accuracy of the point, but not all optimal points are used as training samples of the Gaussian process model. Therefore, the number of true constraint function calls shown in the table is more than the number of training samples shown in the figure.

[0098] As shown in Table 1, in terms of average value, the proposed optimization method can obtain a high-precision optimal solution. In addition, if only the results shown in this example are considered, for optimization problems with local optimal solutions, the intelligent optimization method based on active learning and dynamic weighted sampling may fall into local optimization. This problem will be examined in the following examples.

[0099] (2) Numerical example 2: constrained optimization problem with local optimal solution

[0100] Consider the optimization problem shown in the following formula:

[0101] (22)

[0102] The contour lines of the objective function and the design feasible region are shown in Figure 4 The feasible region of this problem is two disconnected regions, there is a local optimal solution and a global optimal solution .

[0103] The following section uses an intelligent optimization method based on active learning and dynamic weighted sampling to solve the optimization problem and examine the global optimization capability of the proposed method. To demonstrate the optimization efficiency of the proposed method, a genetic algorithm is also used to directly solve the optimization model and compare the number of times each constraint function is called during the optimization process of each method.

[0104] The approximate constraint bounds and optimal points obtained by the proposed method are as follows: Figure 5 As shown. Figure 5 Figure 5 It can be seen that under the guidance of the active learning strategy, the newly added sample points are concentrated near the possible optimal point and successfully capture both the local and global optimal points. This is because the proposed method uses an approximate constraint function (i.e., a proxy model) to replace the true constraint function in the augmented Lagrangian function, incorporating areas where constraint misjudgment may occur into the approximate feasible domain, thereby enhancing the global exploration capability of active learning.

[0105] Similar to Numerical Example 1, the robustness of the proposed method is examined through repeated runs. The comparison methods include an intelligent optimization method based on active learning and dynamic weighted sampling, and a direct optimization method based on a genetic algorithm. The table shows the statistical values ​​of the results obtained from 10 repeated runs. To illustrate the optimization efficiency of the proposed method, the table also lists the number of calls to each true constraint function.

[0106] Table 2 Optimization results of Example 2

[0107]

[0108] As can be seen from Table 2, the optimal solutions obtained by the genetic algorithm and the proposed intelligent optimization method based on active learning and dynamic weighted sampling are highly consistent with the reference solutions provided in the literature, which once again verifies the global optimization capability of the proposed method. In terms of optimization efficiency, the number of calls to expensive constraints during operation of the proposed method is significantly less than that of the case of directly using the genetic algorithm. In addition, Both methods listed in show good robustness in repeated runs.

[0109] (3) Engineering example: Lightweight optimization design of aircraft wing structure

[0110] This example will use the proposed method to carry out weight reduction optimization design of the wing structure of a hypersonic aircraft. The design variables of the optimization problem are the thickness of the skin, ribs and beams. 、 、 , the objective function is the structural quality. The constraints are the structural fundamental frequency, maximum stress, and flutter velocity. Therefore, evaluating these constraints requires time-consuming finite element simulation analysis, which is expensive.

[0111] Design variables The initial value of is 2mm, and the design domain is ; Structural stiffness reliability and strength reliability The constraints are:

[0112] (twenty three)

[0113] Among them, the allowable values ​​are ; From this, the following mathematical model of deterministic structural optimization design can be established:

[0114] (twenty four)

[0115] The deterministic optimization problem is solved using a direct optimization method and an intelligent optimization method based on active learning and dynamic weighted sampling. First, the direct optimization method is used to solve the problem, and the genetic algorithm is selected as the optimization algorithm. The optimization process is shown in Figure 6 (a) and Figure 6 (b).

[0116] After 7500 operations, the objective function converges to 3.482 kg, and the optimal design point is: mm.

[0117] Next, the intelligent optimization methods based on active learning and dynamic weighted sampling proposed in the present invention were used to solve the problem. After repeated operation 10 times, the results are shown in Tables 3 and 4.

[0118] Table 3 Wing deterministic weight reduction optimization results

[0119]

[0120] Table 4 Best optimization results obtained after repeated runs

[0121]

[0122] Table 3 shows the statistical results after 10 repeated runs. From the perspective of the dispersion of the results, the proposed method has good robustness. In terms of structural weight reduction effect, the proposed method can calculate the optimal solution that is highly consistent with the reference solution. In terms of optimization efficiency, the proposed method can effectively reduce the number of calls to expensive constraints during the optimization process.

[0123] Table 4 lists the best data among the 10 groups of optimization results, which once again confirms that the approximate optimization method proposed in the present invention has good optimization accuracy.

[0124] Taking uncertainty into further consideration, a reliability optimization design is carried out for the above wing structure. The three constraints in the deterministic optimization model are replaced by a system reliability constraint, resulting in the following reliability optimization model:

[0125] (25)

[0126] wherein, Area ratio index representing non-probabilistic interval reliability measure, allowable value Suppose that the material elastic modulus has 5% dispersion, and the load has 10% dispersion, the reliability index is calculated by using the proposed active learning method.

[0127] The reliability optimization problem is solved by using the direct optimization method and the intelligent optimization method based on active learning and dynamic weighted sampling respectively, and the optimization process of the direct optimization method is shown in Fig. 7 (a) and Fig. 7 (b).

[0128] After 7500 operations, the objective function converges to 3.743 kg, and the optimal design point is: mm.

[0129] After repeated running for 10 times, the results are shown in Table 5 and Table 6.

[0130] Table 5 Wing reliability weight reduction optimization results

[0131]

[0132] Table 6 Optimal optimization results obtained by repeated running

[0133]

[0134] As shown in Table 5 and Table 6, for the reliability optimization design problem, the proposed method can obtain an optimal solution similar to the reference solution and basically meet the reliability constraint; from the perspective of optimization efficiency, the intelligent optimization method based on active learning and dynamic weighted sampling requires fewer training samples, and the above phenomenon not only reflects the effectiveness of the proposed optimization method, but also embodies the superiority of the intelligent optimization method based on active learning and dynamic weighted sampling in solving expensive constraint optimization problems, because the optimization design and the calculation requirement of expensive constraint approximation are integrated in active learning, so the intelligent optimization method based on active learning and dynamic weighted sampling is superior in terms of solving accuracy and efficiency.

[0135] The above is only the specific steps of the present application, and does not constitute any limitation on the protection scope of the present application; it can be applied to other structural optimization design fields, and any technical solution formed by equivalent transformation or equivalent replacement falls within the protection scope of the present application.

[0136] Some parts of the present application are not described in detail, which are known to those skilled in the art.

Claims

1. An aircraft structure multi-constraint optimization method based on active learning and dynamic weighted sampling for lightweight optimization design of aircraft structure with expensive constraint conditions, characterized in that, The method comprises the following steps: Step 1: a wing structure optimization model is proposed by combining the specific characteristics of the structure optimization design problem and taking lightweight as the target and structure reliability as the constraint; Step 2: the original multi-constraint optimization problem is augmented into an extreme value optimization problem containing a constraint penalty term by using an augmented Lagrange multiplier method; Step 3: an active learning strategy of the proxy model is proposed by integrating the solution of the constraint penalty term extreme value optimization problem into the dynamic correction process of the expensive constraint proxy model; Step 4: the existing active learning strategy is combined to apply a dynamic weight to the new sample points generated by optimization solution and complete the correction and update of the proxy model based on the weighted samples, and finally an expensive constraint proxy model meeting the accuracy requirement is output; Step 5: an intelligent optimization method for the aircraft structure lightweight design problem is constructed based on the developed active learning strategy and dynamic weighted sampling technology, and a genetic algorithm is used to solve the extreme value optimization problem constructed by the proxy model to obtain the optimal point of the aircraft structure lightweight design in the feasible region.

2. The method of claim 1, wherein, The step 1 comprises: The structure lightweight design problem is described by the following optimization model: （1） in, is the p-dimensional design variable is the dimensional index value corresponding to the variable. Generally, the structural size is selected as the design variable. and They are The design upper bound and design lower bound of the objective function For the quality of the structure, Defined according to actual conditions A constraint function, is the index value; When considering non-probabilistic interval uncertainty, it is assumed that the interval variables in the structure are in Represents interval variables The lower bound Represents interval variables The upper bound of Under the premise of , the limit state function of the structure is expressed as: （2）。 3. The method of claim 2, wherein, The step 1 further comprises: Non-probabilistic interval reliability measure of structural system under given design variables The structural optimization design model with reliability as constraint is represented as:​​ （3） Or （4） wherein, and are the safety and failure indices, respectively.

4. The method of claim 1, wherein, The step 2 comprises: In the inequality-constrained problem dimensionality-reduced constraint function dimensionality-relaxed variable into the following equality-constrained problem: （5） whereby the augmented Lagrangian function with relaxation variables optimization variables , relaxation variables , multiplier vector and scalar penalty factor can be defined as : （6） Therefore, the original problem is transformed into solving （7）。 5. The method of claim 4, wherein, The step 2 further comprises: Let On slack variables Minimize, which is transformed into a problem in Minimize; by the method of Lagrange multipliers Rewrite as: （8） The minimum point of when is （9） When , The minimum point of f(x) is: （10） Comprehensive consideration of the above two cases gives: （11） An augmented Lagrangian function of the inequality constrained problem can then be obtained, which is denoted by L(λ,μ,ζ) = L(λ,μ,ζ) + ζT(μ - g(x)) : （12） Therefore, the original problem is transformed into （13） Take an iterative strategy, take a larger penalty factor And by revising the multiplier in the kth iteration Get the multiplier in the k+1th iteration The revision formula is as follows: （14） wherein, is the optimal point in the kth iteration, the multiplier will gradually converge with iterations, and when the constraint condition is met, substantially satisfies , otherwise will be amplified.

6. The method of claim 1, wherein, The step 3 comprises: The expensive constraint in the augmented Lagrange function is replaced by an approximate model, that is: （15） wherein is an approximation model; The most direct active learning strategy is to select the optimal point as the new sample point and update the approximation model of the expensive constraint until the change of the optimal solution of two learning rounds is less than a tolerance; this active learning strategy is the predicted optimal point criterion.

7. The method of claim 1, wherein, The step 4 comprises: The weighted loss function is designed as follows: （16） in, Indicates the The absolute difference between the neural network prediction value and the actual calculation result of the initial sample point, Indicates the The absolute difference between the neural network prediction value and the actual calculation result of the optimized sample point; Indicates the indivual dimensional sample points and subscripts Then the classification of the sample point is represented by It represents the initial sample points, if the subscript is It represents the Optimized sample points; Indicates the The neural network prediction value of the initial / optimized sample points, Indicates the The actual calculation results of the initial / optimized sample points.

8. The method of claim 1, wherein, The step 5 comprises: Step 5.1 Define the augmented Lagrangian function according to the optimization model and the initial penalty factor and multiplier vector, then collect a small number of sample points in the design domain, call the expensive constraint function to calculate the initial training sample set, establish the initial neural network, and give the initial multiplier vector Let the multiplier method iteration step count be .

9. The method of claim 8, wherein, The step 5 further comprises: Step 5.2: multiplier vector based on the current multiplier method iteration step , the augmented Lagrangian function with respect to the solving the minimum point and computing the expensive constraint function value .

10. The method of claim 1, wherein, The step 5 further comprises: Step 5.3 judging approximate accuracy （17） wherein, the real expensive constraint function value at the minimum point, the real expensive constraint function value at the minimum point, the predicted expensive constraint function value at the minimum point by the surrogate model, the predicted expensive constraint function value at the minimum point by the surrogate model, denotes a threshold value; if the above equation is satisfied, it means that the accuracy of the minimum point predicted by the surrogate model meets the requirements and enters step 5.4, otherwise, the real expensive constraint function value at the minimum point as a new training sample and retrain the training set by applying a dynamic weight to realize dynamic updating of the neural network surrogate model, and return to step 5.

2. Step 5.4 Find the minimizer of the Lagrangian function As the optimal solution of the current multiplier method iteration step, the true expensive constraint value at this point is computed, and then the multiplier vector of the augmented Lagrangian function is updated according to the following formula and the computed true expensive constraint value of the optimal point: （18） Step 5.5 If the multiplier vector or the optimal value satisfies the convergence requirement, end the calculation process and output the current optimal design point and the optimal objective function value, otherwise, enter the next multiplier iteration step to bring the new multiplier vector into the augmented Lagrangian function, let , return to step 5.2; （19） wherein, is the optimal objective function value for the kth iteration step of the multiplier method, denotes a convergence error tolerance for the multiplier vector, denotes a convergence error tolerance for the optimization objective.

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