Airport flight area green operation evaluation method based on multi-dimensional gradient optimization

Abstract

The invention discloses an airport flight area green operation evaluation method based on multi-dimensional gradient optimization, and the method comprises the following steps: carrying out data collection and standardization processing; constructing a green operation scoring function according to the collected index data, and introducing a weight vector in the scoring function to reflect the influence of each index; calculating Hessian matrix elements to obtain a final covariance matrix; carrying out weight constraint optimization by using a Lagrange multiplier method; updating and scoring the dynamic weight; and outputting the green operation score. Compared with the prior art, high-precision evaluation of the green operation state of the airport flight area is realized under the condition of limited data volume, so that the evaluation result is more in line with the actual environment condition, and the model can automatically optimize weight distribution according to the real-time environment change; the applicability and flexibility of the evaluation system in different airports and different time periods are ensured, the dependence on the data volume is low, and global judgment can be provided for green operation management of the airports.

Description

Technical Field

[0001] The present invention relates to the field of airport environmental monitoring and intelligent analysis, and particularly to an evaluation method for the green operation of an airport apron based on multi-dimensional gradient optimization. Background Art

[0002] In recent years, with the improvement of environmental protection awareness, the green operation of the airport apron has become an important part of airport management. The green operation evaluation method can evaluate the environmental protection status of the airport by comprehensively evaluating environmental indicators such as air quality, noise level, carbon emissions, and water resource use. The existing green operation evaluation methods mainly include the following categories:

[0003] 1. Weighted average method: This method assigns fixed weights to different indicators according to their importance, and calculates the weighted average of the indicator data to obtain a comprehensive score. This method is simple to calculate, but in practical applications, it often lacks the reflection of the complex relationships between different environmental factors, and is prone to causing distortion of the evaluation results.

[0004] 2. Data-driven evaluation model: Some green operation evaluation systems adopt data-driven machine learning or neural network models, which are trained through a large amount of historical data to achieve the prediction and evaluation of the green operation status. These models can capture the non-linear relationships in the data, but have high requirements for the amount of data, and the environmental monitoring data in the airport apron is relatively small, so they are usually not applicable to such models.

[0005] 3. Expert scoring method: This method relies on the experience of environmental protection experts to subjectively score each indicator. This method is relatively simple and has a certain degree of interpretability, but the evaluation results are relatively subjective and it is difficult to maintain consistency in different environments.

[0006] The existing technologies have the following deficiencies in the evaluation of the green operation of the airport apron:

[0007] 1. Lack of fine analysis of the relationships between indicators: The current weighted average method and expert scoring method fail to accurately describe the non-linear associations between different environmental factors. In the airport apron scenario, each indicator may affect each other, and ignoring these associations will lead to a decrease in the accuracy of the green operation score.

[0008] 2. Data dependence problem: Data-driven models (such as neural networks) have high dependence on a large amount of data. However, in practical applications, the amount of monitoring data in the airport is limited and cannot support the training of complex models, resulting in the inapplicability of such methods to this scenario.

[0009] 3. Insufficient dynamic adjustment of weight setting: Most of the existing methods adopt a fixed weight allocation method, which is difficult to adjust the indicator weights at any time to reflect environmental changes and cannot flexibly adapt to the green operation requirements of different airports and periods. Summary of the Invention

[0010] The object of the present invention is to propose a green operation evaluation method for airport apron based on multi-dimensional gradient optimization aiming at existing problems, which aims to help airport managers evaluate the green operation status in the apron in real time and accurately, and provide a scientific basis for airport environmental management and decision-making.

[0011] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0012] A green operation evaluation method for airport apron based on multi-dimensional gradient optimization, and the method flow is as follows.

[0013] Step A: Conduct data collection and standardization processing

[0014] Collect the green operation index data of the airport apron, conduct standardization processing on each index, and convert it into data with the same dimension.

[0015] Step B: Construct a multi-dimensional green scoring function

[0016] According to the collected index data, construct a green operation scoring function, and introduce a weight vector in the scoring function to reflect the influence of each index.

[0017] Step C: Calculate the elements of the Hessian matrix

[0018] Calculate the covariance matrix based on the normalized data, conduct standardization processing to obtain the standardized covariance matrix, and add a regularization term to improve numerical stability to obtain the final covariance matrix.

[0019] Step D: Use the Lagrange multiplier method for weight constraint optimization

[0020] Introduce the Lagrange multiplier method to optimize the scoring function, and obtain the optimal weight W that satisfies the weight and constraint conditions * and the value of the Lagrange multiplier λ. The Lagrange multiplier λ provides the specific direction and amplitude of how to adjust the weight during the optimization process, so as to maximize the scoring function while satisfying the constraints.

[0021] Step E: Dynamic weight update and scoring

[0022] When scoring each time, first calculate the optimal weight W * , and then substitute it into the scoring function to calculate the final green operation score. For the optimal weight W * , use the gradient descent method for iterative update. By dynamically updating the weight, the evaluation model can adapt to different environmental changes.

[0023] Step F: Output the green operation score.

[0024] Preferably, in step A, the standardized index matrix is defined as follows:

[0025] X = [x 1 , x 2 ,..., x n

[0026] where x i represents the standardized value of the i-th index.

[0027] Preferably, in step B, the green operation scoring function is f(X, W), and the introduced weight vector is W = [w 1 , w 2 ,..., w n . The formula for the constructed green operation scoring function is as follows:

[0028]

[0029] where g(x i ) is a monotonically increasing function for non-linear transformation of index data. Common choices include logarithmic functions or exponential functions; H ij represents the element in the Hessian matrix, which is used to characterize the second-order non-linear relationship between indices.

[0030] Preferably, the functional expression of the monotonically increasing function g(x) is as follows:

[0031] g(x) = ln(x + 1)

[0032] According to the above definition, g(x) can be sensitive at low values and weaken the growth rate at high values, which is suitable for environmental indicators with large data fluctuations;

[0033] Therefore, the green scoring function f(X, W) can be expressed as:

[0034]

[0035] Preferably, the specific calculation method of step C is as follows:

[0036] a. For the elements of the covariance matrix of m observation samples (i.e., environmental data at m time points), they can be expressed as:

[0037]

[0038] where represents the value of the index x i at the k-th sample point, is the mean value of the index x i ; ​

[0039] b. First, standardize the covariance to obtain the standardized covariance matrix H ij :

[0040]

[0041] where σ i and σ j are the standard deviations of the indicators x i and x j respectively;

[0042] c. Add a regularization term to improve numerical stability to obtain the final covariance matrix:

[0043]

[0044] where is a small regularization coefficient set for empirical values, and the typical value adopted in the present invention is 10 -2 , δ ij is the Kronecker delta function, and when i = j, δ ij = 1, otherwise δ ij = 0.

[0045] Preferably, in step D, the specific method for optimizing the weight constraint is as follows,

[0046] Define the Lagrangian function L as:

[0047]

[0048] where λ is the Lagrange multiplier used for the constraint of the sum of weights,

[0049] To ensure that the sum of weights is 1, the Lagrange multiplier method is introduced to optimize the scoring function. By taking the partial derivative of L and setting it to zero, the optimal weights W * and the value of the Lagrange multiplier λ can be obtained, so as to achieve the purpose of optimizing the weights.

[0050] Preferably, the Lagrange multiplier λ optimizes the environmental scoring model in the following way,

[0051] Method 1, through the feedback mechanism of the Lagrange multiplier λ to constrain the weight adjustment,

[0052] a. Use the derivative information of the objective function provided by each constraint condition of the Lagrange multiplier λ to adjust each weight so that it conforms to the optimization objective; through the magnitude of λ, it can be determined whether a certain constraint needs to be strengthened or relaxed to achieve the feedback in the optimization process;

[0053] b. Optimize the weight allocation of each environmental indicator in practical applications through a weight adjustment strategy combined with the Lagrange multiplier λ, and adjust the weight configuration to achieve the optimal performance of the comprehensive score;

[0054] In the second method, balance the constraint and the objective function through the Lagrange multiplier λ to ensure that the finally optimized weight can satisfy the constraint and maximize the scoring function;

[0055] In the third method, setting the value of the Lagrange multiplier λ reasonably can avoid over - bias towards a certain indicator.

[0056] Preferably, in step E, the optimal weight W * The formula for iterative update is:

[0057]

[0058] where is the first - order gradient of the scoring function, H·W is the product of the Hessian matrix and the weight vector, reflecting the second - order gradient information, η is the learning rate in the gradient descent method, which is a positive number and determines the step size of weight adjustment in each iteration. Usually, it is between 10 -4 and 10 -1 and is set according to factors such as problem complexity, data volume, and gradient magnitude. In the present invention, a fixed learning rate η = 0.005 is adopted.

[0059] Preferably, in step E, the specific scoring method is as follows:

[0060] First, determine the optimal weight W * ;

[0061] Then, introduce the optimal weight W * into the scoring calculation formula;

[0062] Finally, the green operation score is calculated based on the optimized optimal weight W * The scoring function is as follows:

[0063]

[0064] where: S green is the final green operation score, is the optimal weight after dynamic optimization, x′ i is the normalized index data, and H ij is the element in the covariance matrix, representing the correlation between indicators.

[0065] Compared with the prior art, the advantages of the present invention are:

[0066] 1. The present invention combines multi-dimensional indicators and complex optimization algorithms to propose a comprehensive and adaptable airport green operation evaluation model, which can provide a comprehensive analysis tool for airport environmental management and decision-making. Its features are as follows:

[0067] 2. High-precision evaluation: By introducing a multi-dimensional gradient optimization algorithm and a Hessian matrix to capture the complex relationships between different environmental indicators, high-precision evaluation of the green operation status of the airport apron is achieved under limited data volume, making the evaluation results more in line with the actual environmental conditions.

[0068] 3. Strong dynamic adaptability: The present invention uses the Lagrange multiplier method and the gradient descent method to dynamically adjust the weights, enabling the model to automatically optimize the weight allocation according to real-time environmental changes, ensuring the applicability and flexibility of the evaluation system at different airports and different times.

[0069] 4. Low data requirements: Compared with traditional neural network or data-driven models, this method has lower dependence on data volume, is applicable to scenarios with limited data in the airport apron, and has strong generality and practicality.

[0070] 5. Support for multi-dimensional decision-making: The comprehensive score of this evaluation method can not only provide a global judgment for airport green operation management, but also identify the influence degree of each environmental factor on green operation, provide a quantitative basis for environmental protection decision-making, and help the airport achieve more scientific environmental protection management. Description of the Drawings

[0071] Figure 1 is the method flow chart of the present invention. Detailed Embodiment

[0072] An airport apron green operation evaluation method based on multi-dimensional gradient optimization, see Figure 1 , and the method flow is as follows. Step A, perform data collection and standardization processing

[0073] Collect the green operation index data of the airport apron, such as air quality, noise level, carbon emissions, water quality, etc., and perform standardization processing on each index to convert it into data with the same dimension for unified analysis;

[0074] Among them, define the standardized index matrix as follows:

[0075] X = [x 1 , x 2 ,..., x n

[0076] Among them, x i represents the standardized value of the i-th index.

[0077] ​Preferably, in step B, the green operation scoring function is f(X, W), and the introduced weight vector is W = [w 1 , w 2 ,..., w n . The formula of the constructed green operation scoring function is as follows.

[0078]

[0079] Among them, g(x i ) is a monotonically increasing function for the non-linear transformation of index data. Common choices include logarithmic functions or exponential functions; H ij represents the elements in the Hessian matrix, which is used to characterize the second-order non-linear relationship between indicators.

[0080] The function expression of the monotonically increasing function g(x) is as follows.

[0081] g(x) = ln(x + 1)

[0082] According to the above definition, g(x) can be sensitive at low values and weaken the growth rate at high values, which is suitable for environmental indicators with large data fluctuations.

[0083] Therefore, the green scoring function f(X, W) can be expressed as:

[0084]

[0085] Step B, constructing a multi-dimensional green scoring function

[0086] According to the collected index data, construct a green operation scoring function, and in this scoring function, introduce a weight vector to reflect the influence of each indicator.

[0087] The green operation scoring function constructed by the present invention constructs a scoring function that can accurately reflect the interaction between various environmental factors, and uses a non-linear transformation function (such as logarithmic or exponential function) to process the index data, thereby improving the accuracy and scientificity of the evaluation results.

[0088] Step C, calculating the elements of the Hessian matrix

[0089] Calculate the covariance matrix based on the normalized data, and perform standardization processing to obtain the standardized covariance matrix. Add a regularization term to improve numerical stability to obtain the final covariance matrix.

[0090] The specific calculation method of step C is as follows.

[0091] a. For the elements of the covariance matrix of m observation samples (i.e., environmental data at m time points), it can be expressed as:

[0092]

[0093] Among them, represents the index x of the k-th sample point i value, is the mean of the index x i mean value;

[0094] b. First, standardize the covariance to obtain the standardized covariance matrix H ij :

[0095]

[0096] Among them, σ i and σ j are the standard deviations of the indices x i and x j respectively;

[0097] c. Add a regularization term to improve numerical stability to obtain the final covariance matrix:

[0098]

[0099] Among them, is a small regularization coefficient set for empirical values, and the typical value adopted in the present invention is 10 -2 , δ ij is the Kronecker delta function, and when i = j, δ ij = 1, otherwise δ ij = 0.

[0100] Step D, use the Lagrange multiplier method to perform weight constraint optimization

[0101] Introduce the Lagrange multiplier method to optimize the scoring function to obtain the optimal weights W * and the value of the Lagrange multiplier λ. The Lagrange multiplier λ provides the specific direction and amplitude of how to adjust the weights during the optimization process, so that while satisfying the constraints, the scoring function is maximized;

[0102] The Lagrange multiplier method is used to solve optimization problems under certain constraints. In the scoring model of the present invention, while maximizing the environmental score, we hope to satisfy some constraints, such as the sum of the weights of each environmental indicator must meet certain norms or constraint relationships. These constraints are introduced through the Lagrange multiplier λ, and they provide feedback on the weight adjustment during the optimization process. During the optimization process, the Lagrange multiplier λ is actually a measure of the influence of the constraint conditions on the objective function. Specifically, the value of the Lagrange multiplier reflects the degree of influence of each constraint condition on the objective function during the optimization process. If the Lagrange multiplier λ is large, it means that the constraint condition has a great influence on the objective function, and vice versa, the influence is small.

[0103] In step D, the specific method for performing weight constraint optimization is as follows.

[0104] Define the Lagrangian function L as:

[0105]

[0106] where λ is the Lagrange multiplier for the constraints on the total sum of weights.

[0107] To ensure that the sum of the weights is 1, the Lagrange multiplier method is introduced to optimize the scoring function. By taking the partial derivative of L and setting it to zero, the optimal weights W * and the value of the Lagrange multiplier λ can be obtained, thus achieving the purpose of optimizing the weights.

[0108] The Lagrange multiplier λ optimizes the environmental scoring model in the following way.

[0109] Method 1: Through the feedback mechanism of the Lagrange multiplier λ to constrain the weight adjustment.

[0110] a. Utilize the derivative information of each constraint condition provided by the Lagrange multiplier λ to adjust each weight so that it conforms to the optimization objective; through the magnitude of λ, it can be determined whether a certain constraint needs to be strengthened or relaxed to achieve feedback during the optimization process; for example, if the multiplier value of a certain constraint condition is large, it means that we need to satisfy this condition more strictly, and if the value is small, this condition can be relaxed.

[0111] b. Through the weight adjustment strategy combined with the Lagrange multiplier λ, optimize the weight allocation of each environmental indicator in practical applications, and adjust the weight configuration to achieve the optimal performance of the comprehensive score; because the magnitude of the Lagrange multiplier directly affects the final weight allocation, enabling us to maximize the comprehensive score on the premise of satisfying various constraints.

[0112] Method 2: By using the Lagrange multiplier λ to balance the constraints and the objective function, ensuring that the finally optimized weights can not only meet the constraints but also maximize the scoring function. In the weight optimization problem, there may be cases where some constraints are relatively strong and these requirements may conflict with maximizing the objective function. The Lagrange multiplier λ can be used to measure and adjust the degree of these conflicts to help balance the conflicts between various constraint conditions and the objective function during the optimization process.

[0113] Method 3: By reasonably setting the value of the Lagrange multiplier λ, overemphasis on a certain index can be avoided.

[0114] To avoid overemphasis on a certain index, by reasonably setting the value of the Lagrange multiplier λ, the over-optimization of the weight of a certain environmental index can be avoided, thus making the scoring function more balanced. Especially when multiple environmental indexes are involved, the Lagrange multiplier ensures that the influence of each index is properly reflected during the optimization process.

[0115] The Lagrange multiplier λ can optimize the environmental scoring model in the following way: The specific method is as follows.

[0116] Suppose we have a constraint condition, such as the sum of the total weights must be equal to 1, that is: W 1 +W 2 +W 3 = 1. Under this constraint, we hope to optimize the objective function (comprehensive score). By introducing the Lagrange multiplier λ, our objective function becomes:

[0117] L(W 1 ,W 2 ,W 3 ,λ) = f(X, W) - λ(W 1 +W 2 +W 3 - 1)

[0118] The Lagrange multiplier λ will provide the specific direction and amplitude of how to adjust the weights W 1 ,W 2 ,W 3 during this optimization process, so as to maximize the scoring function while meeting the constraints.

[0119] Step E: Dynamic weight update and scoring

[0120] During each scoring, first calculate the optimal weights W * ,and then substitute them into the scoring function to calculate the final green operation score. For the optimal weights W * ,use the gradient descent method for iterative update. By dynamically updating the weights, the evaluation model can adapt to different environmental changes;

[0121] In the present invention, the comprehensive score of environmental quality depends on the weighted calculation of multiple indicators. However, since environmental conditions may change over time, location, or other factors, we introduce a dynamic weight update mechanism to ensure that the scoring process can adapt to environmental changes in real time, thereby improving the accuracy of evaluation.

[0122] Optimal weight W * The formula for iterative update is as follows:

[0123]

[0124] where is the first-order gradient of the scoring function, H·W is the product of the Hessian matrix and the weight vector, reflecting the second-order gradient information, η is the learning rate in the gradient descent method, which is a positive number that determines the step size of weight adjustment in each iteration. Usually, it is between 10 -4 and 10 -1 , and is set according to factors such as problem complexity, data volume, and gradient magnitude. In the present invention, a fixed learning rate η = 0.005 is adopted.

[0125] The specific scoring method is as follows:

[0126] First, determine the optimal weight W * ;

[0127] Use to represent the optimal weight vector, which can be determined through adaptive optimization, historical data training, or real-time adjustment mechanisms to maximize the rationality of the scoring model;

[0128] The methods for determining the optimal weight include but are not limited to: optimization based on historical data (such as minimum variance estimation), adjustment based on real-time feedback (such as dynamic weighted average), regression analysis based on machine learning (such as gradient descent optimization); once the optimal weight W * is determined, it can be used for the final scoring calculation.

[0129] Then, introduce the optimal weight W * into the scoring calculation formula;

[0130] Finally, the green operation score is calculated based on the optimized optimal weight W * , and the scoring function is as follows:

[0131]

[0132] where: S green is the final green operation score, is the dynamically optimized optimal weight, x′ i is the normalized index data, Hij It represents an element in the covariance matrix and indicates the correlation between indicators.

[0133] To more intuitively understand the scoring process after dynamic weight update, we list the calculation steps:

[0134] Data preprocessing: Normalize all environmental indicator data to eliminate the influence of dimensions and obtain x'. i ;

[0135] Calculate the optimal weight W * : Use dynamic optimization methods (such as weighted regression, adaptive update) to solve and obtain the optimal weight vector W * ;

[0136] Scoring calculation:

[0137] Calculate the logarithmic transformation term:

[0138] Calculate the covariance weighted term:

[0139] Combine the two parts to obtain the final score S green .

[0140] Application of scoring results: According to the scoring results, perform green operation optimization or adjustment and enter the next round of iterative evaluation.

[0141] Step F, output of green operation score,

[0142] The final green operation score is the calculation result of f(X, W). This score is used to evaluate the overall performance of the airport flight area in various green operation indicators and provide a decision-making basis for airport management.

[0143] The application of the multi-dimensional gradient optimization algorithm in the present invention: Based on the first-order and second-order gradient information (including the Hessian matrix), an accurate model is established for the complex relationship between the green operation indicators of the airport flight area, breaking through the limitations of the existing simple weighted average method. Its dynamic weight adjustment mechanism: Through the Lagrange multiplier method and the gradient descent method, the dynamic optimization and adjustment of weights are realized, enabling the green operation score to be adaptively adjusted according to real-time data changes, and solving the problem of fixed weights in traditional evaluation methods.

[0144] The following will further illustrate the present invention in combination with implementation cases. In the implementation cases of the present invention, the data is from an airport environment with a small amount of data, and there is no large-scale historical database support for the green operation evaluation of this environment. The characteristics of this scenario include: Limited data volume: Since the data collection related to airport green operation evaluation is still in the early stage and long-term monitoring data has not been accumulated, this implementation case is calculated based on the observed data within a limited time window.

[0145] Insufficient historical data; little historical data.

[0146] Indicator selection: In this implementation case, representative environmental variables (such as carbon emissions, energy consumption, noise level, etc.) are selected as key indicators.

[0147] The evaluation method is as follows:

[0148] 1. Data collection

[0149] Collect data on 3 green operation indicators:

[0150] X 1 : Energy consumption level (kWh)

[0151] X 2 : Carbon emission intensity (kg CO 2 / unit area)

[0152] X 3 : Noise intensity (dB)

[0153] The original data collected is as follows:

[0154]

[0155] 2. Data preprocessing

[0156] 2.1 Normalization

[0157] Adopt the normalization formula:

[0158]

[0159] The calculated normalized data is as follows:

[0160]

[0161] 3. Parameter definition

[0162] 3.1 Weight vector

[0163] Define the weight vector:

[0164] W = [w 1 ,w 2 ,w 3 = [0.4, 0.3, 0.3] (2)

[0165] 3.2 Offset parameter ∈

[0166] ∈ = 0.01

[0167] 3.3 H ij Calculation formula

[0168]

[0169] 3.4 Calculate the covariance matrix

[0170] Based on the normalized data, calculate the covariance matrix:

[0171]

[0172] 3.5 Calculate the standard deviation

[0173] The standard deviation is;

[0174] σ 1 = 0.3624, σ 2 = 0.3873, σ 3 = 0.4153 (5)

[0175] 3.6 Calculate H ij matrix

[0176] Substitute the covariance and standard deviation to calculate H ij :

[0177]

[0178] The calculation result is:

[0179]

[0180] 4. Green operation score calculation

[0181] Scoring formula:

[0182]

[0183] 4.1 Calculate item by item

[0184] Taking sample 1 (X 1 ′ = 0.25, X 2 ′ = 0.40, X 3 ′ = 0.50) as an example:

[0185] The first part: logarithmic part

[0186] log_part = 0.4 · ln(0.25 + 1) + 0.3 · ln(0.40 + 1) + 0.3 · ln(0.50 + 1) (9)

[0187] = 0.4 · 0.2231 + 0.3 · 0.3365 + 0.3 · 0.4055 (10)

[0188] = 0.0892 + 0.1009 + 0.1217 = 0.3118 (11)

[0189] Second part: Quadratic weight term

[0190]

[0191] Calculate matrix multiplication:

[0192]

[0193] Then calculate:

[0194]

[0195] Total score

[0196] f(X, W) = 0.3118 + 0.4102 = 0.7220 (17)

[0197] 5. Calculate the scores of the remaining samples

[0198] Calculate the scores of the remaining samples according to the same steps:

[0199]

[0200] It can be seen from the above embodiments that the present invention can also obtain reasonable evaluation results through a scientific modeling method in the case of limited data volume. Moreover, the scoring method does not need to rely on long-term historical data. By constructing a scoring function based on partial derivatives, gradients, and matrix calculations, the weights can be dynamically adjusted under a small-scale data set, and a stable green operation scoring result can be obtained.

[0201] In summary, compared with the traditional big data-driven methods (such as deep learning), the method of the present invention is more suitable for the case of limited data volume and can effectively evaluate the green operation of the airport in a small-sample environment. This embodiment evaluates the airport environment with a small data volume and insufficient historical data. The mathematical modeling method adopted can effectively complete the green operation scoring with limited data support and has good promotion applicability.

[0202] The above has introduced in detail a method for evaluating the green operation of an airport flight area based on multi-dimensional gradient optimization provided by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. It is possible to make changes and improvements to the present invention without exceeding the concept and scope defined by the appended claims. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for evaluating green operation of airport flight areas based on multi-dimensional gradient optimization, characterized in that: The method flow is as follows: Step A: Data collection and standardization Collect green operation index data of airport flight areas, standardize various indicators and convert them into data of the same dimension; Step B: Constructing a multidimensional green scoring function Based on the collected indicator data, a green operation scoring function is constructed, and a weight vector is introduced into the scoring function to reflect the influence of each indicator; Step C, calculate the Hessian matrix elements The covariance matrix is ​​calculated based on the normalized data, and the standardized covariance matrix is ​​obtained by standardization. Regularization terms are added to improve numerical stability to obtain the final covariance matrix. Step D: Weight Constrained Optimization Using Lagrange Multiplier Method The Lagrange multiplier method is introduced to optimize the scoring function and obtain the optimal weight W that satisfies the weight and constraints. * and the value of the Lagrange multiplier λ, which provides the specific direction and magnitude of how to adjust the weights during the optimization process so as to maximize the scoring function while satisfying the constraints; Step E: Dynamic weight update and scoring At each scoring, the optimal weight W is first calculated * , and then substitute it into the scoring function to calculate the final green running score. For the optimal weight W * , using the gradient descent method for iterative updates, and dynamically updating the weights to enable the evaluation model to adapt to different models and to different environmental changes; Step F, green run scoring output.

2. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: In step A, the standardized indicator matrix is ​​defined as follows: X=[x1,x2,...,x n ] Among them, x i Represents the standardized value of the i-th indicator.

3. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: In step B, the green running scoring function is f(X, W), and the introduced weight vector is W = [w1, w2, ..., w n ], the constructed green running scoring function formula is as follows, Among them, g(x i ) is a monotonically increasing function, which is used for nonlinear transformation of index data. Common choices include logarithmic function or exponential function; H ij Represents the elements in the Hessian matrix, which is used to characterize the second-order nonlinear relationship between indicators.

4. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 3 is characterized by: The function expression of the monotonically increasing function g(x) is as follows: g(x)=ln(x+1) According to the above definition, g(x) can remain sensitive at low values ​​and reduce the growth rate at high values, which is suitable for environmental indicators with large data fluctuations; Therefore, the green score function f(X, W) can be expressed as:

5. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: The specific calculation method of step C is as follows: a. For m observation samples (i.e. environmental data at m time points), the elements of the covariance matrix can be expressed as: in, Indicates the index x of the kth sample point i The value of is the indicator x i The mean of b. First standardize the covariance to obtain the standardized covariance matrix H ij : Among them, σ i and σ j They are respectively i and x j The standard deviation of c. Add regularization terms to improve numerical stability and obtain the final covariance matrix: Wherein, is a small regularization coefficient set by empirical value, and the typical value used in the present invention is 10 -2 , δ ij is the Kroneckerdelta function, when i=j,δ ij =1, otherwise δ ij =0.

6. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: In step D, the specific method for weight constraint optimization is as follows: Define the Lagrangian function L as: Among them, λ is the Lagrange multiplier, which is used to constrain the sum of weights. To ensure that the sum of the weights is 1, the Lagrange multiplier method is introduced to optimize the scoring function. By taking the partial derivative of L and setting it to zero, the optimal weight W* and the value of the Lagrange multiplier λ that meet the weights and constraints can be obtained, thereby achieving the purpose of optimizing the weights.

7. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 6 is characterized by: The Lagrange multiplier λ optimizes the environmental scoring model in the following way, Method 1: Feedback mechanism of weight adjustment through Lagrange multiplier λ constraint. a. Use the derivative information of each constraint condition to the objective function provided by the Lagrange multiplier λ to adjust the weights of each item to make it meet the optimization goal; through the size of λ, it can be determined whether a constraint needs to be strengthened or relaxed, so as to achieve feedback in the optimization process; b. Through the weight adjustment strategy combined with the Lagrange multiplier λ, the weight distribution of each environmental indicator is optimized in practical applications, and the weight configuration is adjusted to achieve the best performance of the comprehensive score; Method 2: Balance the constraints and the objective function through the Lagrange multiplier λ to ensure that the final optimized weights can both satisfy the constraints and maximize the scoring function; Method three: By reasonably setting the value of the Lagrange multiplier λ, excessive bias towards a certain indicator can be avoided.

8. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: In step E, the optimal weight W * The formula for iterative update is: in is the first-order gradient of the scoring function, H·W is the product of the Hessian matrix and the weight vector, reflecting the second-order gradient information, and η is the learning rate in the gradient descent method, which is a positive number that determines the step size of the weight adjustment at each iteration, usually around 10 -4 to 10 -1 The learning rate η is set according to the complexity of the problem, the amount of data, the size of the gradient, and other factors. In the present invention, a fixed learning rate η = 0.005 is used.

9. The airport flight zone green operation evaluation method based on multi-dimensional gradient optimization according to claim 1 is characterized by: In step E, the specific scoring method is as follows: First, determine the optimal weight W * ; Then, the optimal weight W * Introducing the scoring calculation formula; Finally, the green operation score is based on the optimized optimal weight W * Calculate and the scoring function is as follows: Where: S green Score the final green run, is the optimal weight after dynamic optimization, x′ i is the normalized index data, H ij is an element in the covariance matrix, indicating the correlation between indicators.

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