An aircraft low-cost element verification method based on counterfactual reasoning

Abstract

The application relates to the technical field of aircraft design and cost optimization, and discloses an aircraft low-cost factor verification method based on counterfactual reasoning, which comprises the following steps: based on the historical design scheme of an aircraft and the corresponding total cost, constructing an influence factor dataset and a total cost dataset; calculating the Pearson correlation coefficient between the cost influence factors and the total cost, so as to determine the first key cost influence factor; constructing a multiple linear regression model by using the influence factor dataset, and determining the second key cost influence factor by solving the regression coefficient vector of the multiple linear regression model, and then performing consistency judgment on the first key cost influence factor; then, a benchmark scheme is constructed, and a counterfactual reasoning verification method is adopted to further perform reliability verification on the key cost influence factors, so as to determine the final key cost influence factors, thereby providing support for aircraft design.

Description

Technical Field

[0001] This invention relates to the field of aircraft design and cost optimization technology, specifically to a method for verifying low-cost elements of aircraft based on counterfactual reasoning, which is applicable to the rapid identification and quantitative verification of key cost elements in the aircraft development stage. Background Technology

[0002] Modern aircraft are powerful and complex, and their costs are influenced by a combination of factors, including scale parameters, system composition, design schemes, material prices, and manufacturing processes. Traditional cost estimation methods (such as empirical estimation and engineering estimation methods) rely mainly on historical references and designers' experience, making it difficult to reveal the deep causal transmission mechanisms between aircraft costs and cost factors. This results in a lack of scientific understanding of cost components and makes it difficult to positively guide designers' initial cost forecasts. Especially during the feasibility study stage, designers cannot accurately determine the true causal effect of hypothetical decisions such as "adjusting the airframe size," "changing the proportion of composite materials," or "simplifying design complexity" on costs, leading to cost reduction measures that are not targeted and have limited effectiveness.

[0003] In recent years, with the rapid development of aircraft, cost has become its core competitiveness. At present, the main method to reduce the cost of aircraft is to rely on mass production to average the unit price, and there is a lack of guiding methods and design principles to consider cost factors in the design stage. Summary of the Invention

[0004] The purpose of this invention is to provide a method for verifying low-cost elements of aircraft based on counterfactual reasoning, which is used to reason and determine the key low-cost components of an aircraft, thereby providing support for aircraft design.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A low-cost element verification method for aircraft based on counterfactual reasoning includes:

[0007] Step 1: Obtain the historical design schemes and corresponding total costs of the aircraft, determine the cost influencing factors of the aircraft, and construct the influencing factor dataset and the total cost dataset;

[0008] Step 2: For each cost-influencing factor in the influencing factor dataset, calculate the Pearson correlation coefficient between the cost-influencing factor and the total cost to determine the first key cost-influencing factor.

[0009] Step 3: Construct a multiple linear regression model using the influencing factor dataset; determine the second key cost influencing factor by solving the regression coefficient vector of the multiple linear regression model; determine whether to proceed to step 4 based on the consistency judgment between the second key cost influencing factor and the first key cost influencing factor.

[0010] Step 4: Based on the influencing factor dataset, determine the mean value of each cost influencing factor to construct a benchmark scheme; use the multiple linear regression model to determine the total cost estimate corresponding to the benchmark scheme.

[0011] Step 5: Construct corresponding counterfactual solutions for the second key cost impact factor; obtain the total cost estimate for each counterfactual solution through the multiple linear regression model; determine the final key cost impact factor based on the relationship between the baseline solution and the total cost estimates of all counterfactual solutions.

[0012] Furthermore, the cost-influencing factors include scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors;

[0013] By combining expert scoring and normalization methods, the scale element value, component element value, scheme complexity element value, material cost element value, and process complexity element value of each historical design scheme are determined, thereby constructing a scale element vector. Component vector Solution complexity element vector Material cost element vector and process complexity element vector To construct the influencing factors dataset .

[0014] Furthermore, a random perturbation is added to the total cost of each historical design scheme to form a total cost dataset. :

[0015] ;

[0016] in, , For the first A random perturbation that conforms to a normal distribution from a historical design scheme; , The number of historical design schemes; For the first The total cost of a historical design scheme after adding random perturbations; Random perturbation A random value that conforms to a normal distribution within a preset cost range; superscript This indicates transpose.

[0017] Furthermore, after determining the Pearson correlation coefficient between each cost-influencing factor and all total costs, the Pearson correlation coefficients are ranked from largest to smallest to determine the top [cost-influenced factors]. The cost influencing factor corresponding to each Pearson correlation coefficient is the first key cost influencing factor; among which This is the default value.

[0018] Furthermore, based on the influencing factors dataset, the scale factor values ​​for each historical design scheme are... Component values Scheme complexity element values Material cost element value and process complexity factor values Together as a sample , sample As an independent variable Total cost after adding random perturbations As dependent variable The multiple linear regression model is as follows:

[0019] ;

[0020] In the above formula, the regression coefficient vector , This is a constant term, with a value of 1. These are the regression coefficients corresponding to scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors, respectively. It is a random error vector;

[0021] By sampling the influencing factor dataset Substituting into the multiple linear regression model, the least squares method is used to solve for the regression coefficient vector. ,get The value of .

[0022] Furthermore, the regression coefficients are sorted in descending order to determine the top... The cost impact factor corresponding to each regression coefficient is the second key cost impact factor; then determine whether the first key cost impact factor and the second key cost impact factor are the same; if they are the same, proceed to step 4.

[0023] Furthermore, for the influencing factor dataset, the mean of the scale factor is obtained by averaging the cost impact factor values ​​corresponding to all historical design schemes. The mean of the constituent elements can be obtained using the same method. Mean of the complexity factor of the solution Mean of material cost factors Mean value of process complexity factor The baseline scheme is then expressed as ( , , , , );

[0024] The benchmark scheme ( , , , , ) as independent variable Substituting into the aforementioned multiple linear regression model, the resulting dependent variable As a total cost estimate .

[0025] Furthermore, each counterfactual scenario for the second key cost impact factor includes an optimization scenario and a deterioration scenario; the optimization scenario refers to reducing the mean of the second key cost impact factor while keeping the mean of the other cost impact factors unchanged, based on the baseline scenario; the deterioration scenario refers to increasing the mean of the second key cost impact factor while keeping the mean of the other cost impact factors unchanged, based on the baseline scenario.

[0026] The optimized and deteriorated solutions for each second key cost factor are substituted into the multiple linear regression model as independent variables to obtain the corresponding total cost estimates. If the total cost estimates corresponding to the deteriorated solutions of all second key cost factors are greater than the total cost estimates of the benchmark solution, and the total cost estimates corresponding to the optimized solutions of the second key cost factors are all less than the total cost estimates of the benchmark solution, then all second key cost factors are considered to be the final key cost factors.

[0027] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the counterfactual reasoning-based low-cost element verification method for aircraft.

[0028] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the counterfactual reasoning-based low-cost element verification method for aircraft.

[0029] Compared with the prior art, the present invention has the following technical features:

[0030] 1. Low verification cost: The data-driven approach generates a dataset of influencing factors without the need to build physical models or conduct physical experiments, which greatly reduces R&D costs and time. The sample generation and calculation process can be completed on a regular computer.

[0031] 2. High logical rigor: By comparing the "benchmark solution - optimized solution - worsening solution", the causal impact of a single cost factor on the total cost is accurately separated, avoiding interference from the coupling of multiple factors, and the conclusions are highly reliable.

[0032] 3. High practicality and scalability: The logic of this method conforms to engineering practice. It can adjust the cost-influencing factors according to different types of aircraft, support the expansion and verification of new factors (such as R&D cycle and testing costs), and adapt to different scenario requirements. Attached Figure Description

[0033] Figure 1 This is a schematic flowchart of the method of the present invention;

[0034] Figure 2 A diagram showing the relationship between cost influencing factors and total cost;

[0035] Figure 3 The results of Pearson correlation coefficient calculation in this embodiment of the invention;

[0036] Figure 4 This is the result of solving the regression coefficient vector in this embodiment of the invention;

[0037] Figure 5 This is a comparison of the total cost estimate of the counterfactual solution for the second key cost impact factor in this invention embodiment with the baseline solution;

[0038] Figure 6 This is a total cost distribution diagram for scale factors, component factors, and scheme complexity factors. Detailed Implementation

[0039] This invention provides a low-cost component verification method for aircraft based on counterfactual reasoning. Employing a data-driven approach, it offers advantages such as low cost, rigorous logic, and strong scalability, making it suitable for cost optimization and design decision support during the aircraft development phase. See also... Figure 1 The present invention includes the following steps:

[0040] Step 1: Obtain the historical design schemes and corresponding total costs of the aircraft, determine the cost influencing factors of the aircraft, and construct the influencing factor dataset and the total cost dataset.

[0041] Obtain historical design schemes for the aircraft and their corresponding total costs; historical design schemes include completed design schemes, abandoned design schemes during the development process, and design schemes estimated by engineers based on experience.

[0042] Identify the cost influencing factors of the aircraft, including scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors; see the cost influencing factor-total cost relationship diagram. Figure 2 Combining expert scoring and normalization methods, the scale element value, component element value, scheme complexity element value, material cost element value, and process complexity element value of each historical design scheme were determined, as follows:

[0043] (1) Scale factor.

[0044] The number of historical design schemes is recorded as follows: There is a direct causal relationship between scale factors and aircraft diameter, aircraft length, and aircraft weight; firstly, the aircraft diameter, aircraft length, and aircraft weight in all historical design schemes are normalized.

[0045] Through formula Calculate the first Scale element values ​​of historical design schemes ;in, , , The first Normalized aircraft diameter, normalized aircraft length, and normalized aircraft weight in each historical design scheme.

[0046] (2) Components.

[0047] The constituent elements can be characterized by the number of parts in the aircraft; after experts score the constituent elements of each historical design scheme and then normalize the results, the final result is obtained. Component values ​​of a historical design scheme .

[0048] (3) Scheme complexity factor.

[0049] The complexity of a solution can be characterized by factors such as the process scale and the ease of implementation of historical design solutions. The complexity of each historical design solution is scored by experts and then normalized to obtain the final solution. The complexity factor of a historical design scheme .

[0050] (4) Material cost factors.

[0051] Material cost elements are represented by the total material costs of the aircraft in all historical design schemes; the material costs of all historical design schemes are normalized to obtain the... Material cost element value of each historical design scheme .

[0052] (5) Factors related to process complexity.

[0053] The complexity of the manufacturing process can be characterized by the number of production steps in the aircraft; experts score the complexity of each historical design scheme and then normalize the scores to obtain the final score. The process complexity factor value of a historical design scheme .

[0054] ;

[0055] Among them, superscript Indicates transpose; Represents a vector of scale elements; Represents the vector of constituent elements; Represents the vector of factors related to the complexity of the solution; Represents a vector of material cost elements; Represents a vector of process complexity elements; .

[0056] Based on the sample feature vectors, the following dataset of influencing factors is constructed:

[0057] ;

[0058] For each historical design scheme, a random perturbation is added to the total cost to form the total cost dataset. :

[0059] ;

[0060] in, , For the first Total cost and random disturbances of a historical design scheme; For the first The total cost of a historical design scheme after adding random perturbations; Random perturbation The cost range is a random value that conforms to a normal distribution within a preset cost range; the preset cost range may be, for example, an interval consisting of the maximum and minimum total costs of all historical design schemes.

[0061] Step 2: For each cost influencing factor in the influencing factor dataset, calculate the Pearson correlation coefficient between the cost influencing factor and all total costs to determine the first key cost influencing factor.

[0062] Calculate the Pearson correlation coefficient between each cost-influencing factor and all total costs using the following formula:

[0063] ;

[0064] in, This represents a certain cost-influencing factor in the influencing factors dataset. Pearson correlation coefficient with all total costs; Indicating cost influencing factors The Values ​​of cost-influencing factors; For all The mean; For all The mean.

[0065] Sort the Pearson correlation coefficients from largest to smallest to determine the top... The cost factor corresponding to each Pearson correlation coefficient is the first key cost factor.

[0066] The Pearson correlation coefficient can quantify the degree of correlation between cost-influencing factors and total cost. If the Pearson correlation coefficient is greater than 0, the cost-influencing factors and total cost are positively correlated, and the closer the value is to 1, the stronger the influence of cost-influencing factors on total cost.

[0067] The number of historical design schemes in one embodiment of the present invention is These 200 historical design proposals cover aircraft diameters ranging from 0.3 to 1 meter, lengths from 2 to 10 meters, and weights from 50 to 20,000 kilograms. The Pearson correlation coefficient calculation results for the examples are shown below. Figure 3 The calculation results are as follows:

[0068] Scale factor (0.636842) > Scheme complexity factor (0.519766) > Component factor (0.431967) > Process complexity factor (0.245168) > Material cost factor (0.201675); where the values ​​in parentheses are Pearson correlation coefficients.

[0069] In the embodiment, it is set In this embodiment, the first key cost impact factor is determined to be: scale factor, scheme complexity factor, and component factor.

[0070] Step 3: Construct a multiple linear regression model using the influencing factor dataset; determine the second key cost influencing factor by solving the regression coefficient vector of the multiple linear regression model; and determine whether to proceed to step 4 based on the consistency judgment between the second key cost influencing factor and the first key cost influencing factor.

[0071] Based on the influencing factors dataset, the scale element values ​​for each historical design scheme are... (i.e., scale element vector) The (each component), component value Scheme complexity element values Material cost element value and process complexity factor values Together as a sample , sample As an independent variable Total cost after adding random perturbations As dependent variable The multiple linear regression model is as follows:

[0072] ;

[0073] In the above formula, the regression coefficient vector , The constant term takes the value 1. These are the regression coefficients corresponding to scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors, respectively. It is a random error vector, for example, it can be a vector composed of random errors that conform to a normal distribution.

[0074] By sampling the influencing factor dataset Substituting into the multiple linear regression model, the least squares method is used to minimize the sum of squared errors. Solving for the regression coefficient vector ,get The value of .

[0075] The regression coefficients are sorted in descending order to determine the top... The cost impact factor corresponding to each regression coefficient is the second key cost impact factor; then it is determined whether the first key cost impact factor and the second key cost impact factor are the same. If they are not the same, it indicates that there is no explicit correlation between the cost impact factor of the aircraft and the total cost, and the analysis ends or returns to step 1 to replace other cost impact factors and re-analyze; otherwise, proceed to the next step.

[0076] In one embodiment of the present invention, such as Figure 4 As shown, the solution results are as follows:

[0077] Scale factor (0.612327) > Component factor (0.347457) > Scheme complexity factor (0.32138) > Process complexity factor (0.209688) > Material cost factor (0.187127); where the values ​​in parentheses are regression coefficients.

[0078] In this embodiment, the second key cost impact factor is ultimately determined to be: scale factor, component factor, and solution complexity factor, which is consistent with the first key cost impact factor in step 3 (this is not considered during the judgment). (Rank the regression coefficients); then proceed to the next step.

[0079] Step 4: Based on the influencing factor dataset, determine the mean value of each cost influencing factor to construct a benchmark scheme; use the multiple linear regression model to determine the total cost estimate corresponding to the benchmark scheme.

[0080] For the influencing factor dataset The average value of each cost-influence factor is obtained by averaging all the cost-influence factor values; for example, for the scale factor, the average value is calculated by averaging all the cost-influence factor values. The mean of the scale factor is obtained by averaging the cost impact factors corresponding to each historical design scheme. The mean of the constituent elements can be obtained using the same method. Mean of the complexity factor of the solution Mean of material cost factors Mean value of process complexity factor The baseline scheme is then expressed as ( , , , , ).

[0081] The benchmark scheme ( , , , , ) as independent variable Substituting into the aforementioned multiple linear regression model, the resulting dependent variable As a total cost estimate .

[0082] Although steps 2 and 3 have identified and verified the key cost-influencing factors, these steps are based on data from historical design schemes. While random disturbances and random error vectors have been introduced to simulate real-world scenarios, biases in the conclusions may still exist. Therefore, this invention proposes a counterfactual reasoning verification method in step 5 to further verify the reliability of the key cost-influencing factors.

[0083] Step 5: Construct corresponding counterfactual solutions for the second key cost impact factor; obtain the total cost estimate for each counterfactual solution through the multiple linear regression model; determine the final key cost impact factor based on the relationship between the baseline solution and the total cost estimates of all counterfactual solutions.

[0084] Each counterfactual scenario for a second key cost impact factor includes an optimization scenario and a worsening scenario. The optimization scenario involves reducing the mean of the second key cost impact factor (e.g., by reducing it according to a first preset ratio) while keeping the mean of the remaining cost impact factors unchanged. The worsening scenario involves increasing the mean of the second key cost impact factor (e.g., by increasing it according to a second preset ratio; the first and second preset ratios can be the same or different, for example, both can be 50%) while keeping the mean of the remaining cost impact factors unchanged.

[0085] Finally, the optimized and deteriorated solutions for each of the second key cost factors are substituted into the multiple linear regression model as independent variables to obtain the corresponding total cost estimates. If the total cost estimates for the deteriorated solutions of all the second key cost factors are greater than the total cost estimate for the benchmark solution, then... Meanwhile, the estimated total cost of the optimized solutions for the second key cost factor is lower than the estimated total cost of the benchmark solution. If so, all second key cost impact factors are considered final key cost impact factors.

[0086] In steps 2 and 3, it has been determined that the first and second key cost influencing factors are both scale factors, component factors, and solution complexity factors. Taking the scale factor as an example, the construction process of the optimal and deteriorating solutions in the counterfactual scenario is as follows:

[0087] In the benchmark scheme ( , , , , Based on this, the average of the scale factors will be used. Shrink to While keeping other means unchanged, we obtain an optimized solution for scale factors; the mean of scale factors is... Increase to While keeping the other means constant, we obtain the deterioration scheme for scale factors; the optimization scheme and the deterioration scheme for scale factors are used as independent variables respectively. Substituting into the aforementioned multiple linear regression model, the resulting dependent variable This is the estimated total cost.

[0088] like Figure 5 As shown, this figure compares the estimated total cost of the counterfactual solution for the second key cost impact factor in this invention with the baseline solution. For better illustration, the estimated total cost of the counterfactual solutions for other cost impact factors is also calculated in the figure.

[0089] pass Figure 5 It can be seen that the estimated total cost of the worsened solutions for scale, component, and complexity factors in the examples is greater than the estimated total cost of the baseline solution, while the estimated total cost of the optimized solutions is less than the estimated total cost of the baseline solution. This indicates that scale, component, and complexity factors are the key cost factors influencing the final cost.

[0090] The counterfactual reasoning results in the embodiment are consistent with the conclusions of steps 2 and 3, verifying that scale, composition and scheme complexity are key factors in determining the total cost of the aircraft, and that scale has a significant impact on the total cost.

[0091] Draw a total cost distribution map for scale factors, component factors, and solution complexity factors, such as... Figure 6 As shown in the figure, there is a positive correlation between scale, composition, and scheme complexity and total cost. That is, the smaller the scale, the simpler the composition, and the lower the scheme complexity, the lower the total cost of aircraft design, thus providing scientific and reasonable support for the overall design decision of aircraft.

[0092] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for verifying low-cost elements of an aircraft based on counterfactual reasoning, characterized in that, include: Step 1: Obtain the historical design schemes and corresponding total costs of the aircraft, determine the cost influencing factors of the aircraft, and construct a dataset of influencing factors and a dataset of total costs; the cost influencing factors include scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors. Among them, the scale factor has a direct causal relationship with the aircraft diameter, aircraft length, and aircraft weight; the composition factor is characterized by the number of aircraft parts; the scheme complexity factor is characterized by the process scale and the ease of implementation of the historical design scheme; the material cost factor is characterized by the total material cost of the aircraft in the historical design scheme; and the process complexity factor is characterized by the number of production steps of the aircraft. By combining expert scoring and normalization methods, the scale element value, component element value, scheme complexity element value, material cost element value, and process complexity element value of each historical design scheme are determined, thereby constructing a scale element vector. Component vector Solution complexity element vector Material cost element vector and process complexity element vector To construct the influencing factors dataset ; Step 2: For each cost-influencing factor in the influencing factor dataset, calculate the Pearson correlation coefficient between the cost-influencing factor and all total costs to determine the first key cost-influencing factor, including: After determining the Pearson correlation coefficient between each cost-influencing factor and all total costs, the Pearson correlation coefficients are sorted from largest to smallest to determine the top [cost-influenced factors]. The cost influencing factor corresponding to each Pearson correlation coefficient is the first key cost influencing factor; among which This is the default value; Step 3: Construct a multiple linear regression model using the influencing factor dataset; determine the second key cost influencing factor by solving the regression coefficient vector of the multiple linear regression model; based on the consistency judgment between the second key cost influencing factor and the first key cost influencing factor, determine whether to proceed to step 4, including: Based on the influencing factors dataset, the scale element values ​​for each historical design scheme are... Component values Scheme complexity element values Material cost element value and process complexity factor values Together as a sample , sample As an independent variable Total cost after adding random perturbations As dependent variable The multiple linear regression model is as follows: ； In the above formula, the regression coefficient vector , For constant terms, These are the regression coefficients corresponding to scale factors, component factors, scheme complexity factors, material cost factors, and process complexity factors, respectively. It is a random error vector; By sampling the influencing factor dataset Substituting into the multiple linear regression model, the least squares method is used to solve for the regression coefficient vector. ,get The possible values ​​of ; The regression coefficients are sorted in descending order to determine the top... The cost impact factor corresponding to each regression coefficient is the second key cost impact factor; then determine whether the first key cost impact factor and the second key cost impact factor are the same; if they are the same, proceed to step 4; Step 4: Based on the influencing factor dataset, determine the mean value of each cost influencing factor to construct a benchmark scheme; use the multiple linear regression model to determine the total cost estimate corresponding to the benchmark scheme. Step 5: Construct corresponding counterfactual solutions for the second key cost impact factor; obtain the total cost estimate for each counterfactual solution through the multiple linear regression model; determine the final key cost impact factor based on the relationship between the baseline solution and the total cost estimates of all counterfactual solutions.

2. The method for verifying low-cost elements of an aircraft based on counterfactual reasoning according to claim 1, characterized in that, For each historical design scheme, a random perturbation is added to the total cost to form the total cost dataset. : ； in, , For the first The total cost of each historical design scheme and random perturbations that conform to a normal distribution; , The number of historical design schemes; For the first The total cost of a historical design scheme after adding random perturbations; Random perturbation A random value that conforms to a normal distribution within a preset cost range; superscript This indicates transpose.

3. The method for verifying low-cost elements of an aircraft based on counterfactual reasoning according to claim 1, characterized in that, For the influencing factors dataset, the mean of the scale factor is obtained by averaging the cost impact factor values ​​corresponding to all historical design schemes. The mean of the constituent elements can be obtained using the same method. Mean of the complexity factor of the solution Mean of material cost factors Mean value of process complexity factor The baseline scheme is then expressed as ( , , , , ); The benchmark scheme ( , , , , ) as independent variable Substituting into the aforementioned multiple linear regression model, the resulting dependent variable As a total cost estimate .

4. The method for verifying low-cost elements of an aircraft based on counterfactual reasoning according to claim 1, characterized in that, Each counterfactual scenario for the second key cost impact factor includes an optimization scenario and a deterioration scenario. The optimization scenario is based on the baseline scenario, which reduces the mean of the second key cost impact factor while keeping the mean of the other cost impact factors unchanged. The deterioration scenario is based on the baseline scenario, which increases the mean of the second key cost impact factor while keeping the mean of the other cost impact factors unchanged. The optimized and deteriorated solutions for each second key cost factor are substituted into the multiple linear regression model as independent variables to obtain the corresponding total cost estimates. If the total cost estimates corresponding to the deteriorated solutions of all second key cost factors are greater than the total cost estimates of the benchmark solution, and the total cost estimates corresponding to the optimized solutions of the second key cost factors are all less than the total cost estimates of the benchmark solution, then all second key cost factors are considered to be the final key cost factors.

5. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the low-cost element verification method for aircraft based on counterfactual reasoning as described in any one of claims 1-4.

6. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by a processor, it implements the low-cost aircraft element verification method based on counterfactual reasoning as described in any one of claims 1-4.

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