An aircraft end-to-end prediction-distribution robust optimization method

Abstract

The application is suitable for the technical field of air traffic management, and provides an aircraft end-to-end prediction-distribution robust optimization method.The method comprises the following steps: obtaining target airport approach flight data; performing data cleaning and conversion processing; establishing an end-to-end prediction-distribution robust optimization mathematical model with the minimum total flight time and delay time as the target, wherein the prediction module adopts an XGBoost algorithm to perform arrival time prediction, and the optimization module introduces a distribution robust optimization method to process prediction uncertainty; and outputting an optimal flight scheduling scheme and a timetable through parameter initialization, forward solving, backward propagation and multi-round iteration calculation.The application realizes deep cooperation between prediction and optimization, effectively overcomes the problem that prediction errors affect scheduling results in traditional methods, significantly reduces total flight time and total delay time, and improves terminal area operation efficiency and safety.

Description

Technical Field

[0001] This invention belongs to the field of air traffic management technology, and in particular relates to an end-to-end predictive-diversified bar optimization method for aircraft. Background Technology

[0002] With increasingly stringent requirements for terminal area operational efficiency and flight punctuality, aircraft arrival sequencing has become a crucial element in improving the operational effectiveness of a single airport. Traditional terminal area scheduling methods are mostly based on first-come, first-served rules, supplemented by manual adjustments based on experience. While this ensures operational safety to a certain extent, it lacks a systematic optimization of overall airspace resources and struggles to cope with complex operational scenarios under high-density arrival traffic.

[0003] Currently, existing research largely focuses on a single aspect of flight arrival time prediction or scheduling optimization, failing to achieve a high degree of synergy between prediction and scheduling. For example, some methods use machine learning models to predict flight arrival times but do not fully consider the impact of prediction errors on the scheduling results; other studies, while introducing robust optimization to handle uncertainty, rely heavily on classical robust optimization methods, leading to overly conservative scheduling results and limited practical application effectiveness. Furthermore, existing methods generally design prediction and optimization modules separately, neglecting the coupling relationship between them, making it difficult to achieve global optimum in the dynamic operating environment of the terminal area. Summary of the Invention

[0004] The purpose of this invention is to provide an end-to-end prediction-divergent bar optimization method for aircraft, which aims to solve the technical problems existing in the prior art as identified in the background art.

[0005] This invention is implemented as follows: an end-to-end prediction-divider optimization method for aircraft arrival sequencing in a single airport terminal area, comprising the following steps: Step 1: Obtain all arrival flight data for the target airport within the specified time period, including flight trajectory, runway information, waypoints, and arrival route information; Step 2: Perform data cleaning and transformation on all arriving flight data; Step 3: Establish an end-to-end arrival time prediction-partial bar optimization mathematical model with the goal of minimizing the total flight time of arriving flights and flight delay time; Step 4: After initializing the parameters, input the flight trajectory data into the prediction module, and pass the prediction results into the optimization module for multiple rounds of iterative solution. Output the optimal flight scheduling scheme and timetable, and calculate the total delay time and total flight time.

[0006] Preferably, step 1, obtaining all arriving flight data of the target airport within a specified time period, specifically includes: All flights This involves any flight Entry points The time of arrival at the entry point Approach flight path landing runway The time of arrival at the entry point ; All runways assembled Involving any runway All flights ; All entry points gather It involves any entry point. All flights ; Any flight Entry points and landing runway Flight path between and flight time on that path .

[0007] Preferably, in step 2, data preprocessing includes: From flight data, feature data for each trajectory at waypoints in the terminal area are extracted, including: time of passage, altitude, speed, segment distance, track angle, remaining distance to the runway, and approach path, denoted as feature vectors. Simultaneously record tag data, i.e., the actual arrival time of the entry point. ; The feature data and label data are cleaned to remove missing and outlier values; then the feature data is normalized to eliminate dimensional differences. The processed flight trajectory data is divided into training and testing sets according to a preset ratio for subsequent training and evaluation of the prediction model.

[0008] Preferably, in step 3, establishing the end-to-end arrival time prediction-splitting bar optimization mathematical model includes: The prediction module employs the XGBoost algorithm, and the objective function of the XGBoost prediction model is: ; The optimization module includes decision variables, an objective function, and constraints; the decision variables include: , indicating the entry point Flight Whether it is assigned to its runway A flight path between ; , indicating the entry point Flight Delays and postponements; The objective function is: ; The constraints include flight path uniqueness constraint, delay time limit constraint, approach point safety interval constraint, runway arrival time calculation constraint, runway safety interval constraint, prediction result propagation constraint, Bruker optimization uncertainty set constraint, and Bruker expectation constraint.

[0009] Preferably, in step 4, outputting the optimal flight scheduling scheme and timetable includes: Initialize the parameters of the prediction module and the optimization module respectively; Input flight trajectory data and extract data features and data tags Input prediction module The data is passed to the prediction module, and then the prediction results are passed to the module. Pass it to the optimization module; The optimal solution for flight scheduling and flight timetable is obtained through multiple rounds of iteration. The iterative process includes forward solving, backpropagation, and iterative convergence steps.

[0010] The beneficial effects of this invention are: This invention achieves deep collaboration between flight arrival time prediction and approach sequencing scheduling through an end-to-end prediction-partial bar optimization framework, effectively overcoming the shortcomings of traditional methods that separate prediction and optimization. By introducing the partial bar optimization method, it ensures the robustness of the solution while avoiding the over-conservatism of traditional methods when dealing with prediction uncertainties. This invention can dynamically allocate the optimal approach path and precise over-time for each flight, significantly reducing total flight delays and total flight time, effectively avoiding conflicts between aircraft at waypoints and runways, and improving the overall operational efficiency and safety level of the terminal area. Attached Figure Description

[0011] Figure 1 A flowchart illustrating an end-to-end prediction-divergent bar optimization method for aircraft provided in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the implementation process of an end-to-end prediction-divider optimization method for aircraft, provided in an embodiment of the present invention. Figure 3 The flowchart of the prediction module of an end-to-end prediction-divergent bar optimization method for aircraft provided in this embodiment of the invention is shown. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0013] like Figure 1 and Figure 2 The diagram shows a flowchart of an end-to-end prediction-divider optimization method for aircraft, the method comprising: Step 1: Obtain all arriving flight data for the target airport within a specified time period, including flight trajectory data, runway information data, waypoint data, and arrival route information, specifically including: All flights This involves any flight Entry points The time of arrival at the entry point Approach flight path landing runway The time of arrival at the entry point ; All runways assembled Involving any runway All flights ; All entry points gather It involves any entry point. All flights ; Any flight Entry points and landing runway Flight path between and flight time on that path .

[0014] Step 2: Process all arriving flight data, including data cleaning and data transformation, specifically as follows: From flight data, feature data for each trajectory at waypoints in the terminal area are extracted, including: time of passage, altitude, speed, segment distance, track angle, remaining distance to the runway, and approach path, denoted as feature vectors. Simultaneously record tag data, i.e., the actual arrival time of the entry point. ; The feature data and label data are cleaned to remove missing and outlier values; then the feature data is normalized to eliminate dimensional differences. The processed flight trajectory data is divided into training and testing sets according to a preset ratio for subsequent training and evaluation of the prediction model.

[0015] Step 3: Establish an end-to-end arrival time prediction-minimum Brubar bar optimization mathematical model with the goal of minimizing the total flight time of arriving flights and flight delay time. The end-to-end arrival time prediction-minimum Brubar bar optimization mathematical model includes a prediction module and an optimization module. Prediction module: Employs the XGBoost algorithm with the SPO decision loss function. As a training objective, the predicted arrival time is improved through multiple iterations. The decision perception capability, and its objective function are as follows; ; in: ; ; ; in, For loss function, This is the actual arrival time. To predict the arrival time, For the predicted time The optimal decision under the given circumstances For real time The optimal decision under the given circumstances For decision-making objectives, For the t-th tree model, For the data characteristics of flight i, This is a regularization term used to control model complexity and avoid overfitting. To control the complexity penalty of trees, It is the number of leaves on the tree. for The weights of the regularization terms, for The weights of the regularization terms, It is the predicted score of the j-th leaf.

[0016] like Figure 3 The diagram illustrates an XGBoost-based flight arrival time prediction method according to an embodiment of the present invention, along with an algorithm flowchart. The main processes and steps include: 1. Model initialization and parameter settings, specifically including: Set initial prediction values Initialize XGBoost hyperparameters including the learning rate. Maximum depth (max-deep), regularization parameter , , The number of iterations n and the minimum split gain wait.

[0017] 2. The end-to-end iterative training process specifically includes: For each iteration Calculate the predicted value of the current model. The result is then fed into the optimization module to solve for the optimal decision. ; Calculate SPO decision loss Simultaneously, its gradient information is calculated, and a new regression tree is constructed based on this gradient. And the split point is selected by maximizing the gain; Update prediction model Tree model set and prediction results .

[0018] 3. Convergence judgment and model output, specifically including: Check if the improvement in the objective function value is less than a preset threshold. If it has not converged, return to S2 to continue iterating. If it has converged, output the trained XGBoost ensemble model. Output the final predicted arrival time. This is used for scheduling decisions in subsequent optimization modules.

[0019] Optimization Module: Considering the uncertainty of the prediction error distribution, a partial bar optimization model is established with the objective of minimizing the total delay time and total path flight time. Decision variables include: 1. Indicates the entry point Flight Whether it is assigned to its runway A flight path between , , , ; 2. Indicates the entry point Flight Delays and postponements , .

[0020] The objective function is: The constraints include flight path uniqueness constraints, delay time limit constraints, approach point safety interval constraints, runway arrival time calculation constraints, runway safety interval constraints, prediction result propagation constraints, and a robust expectation constraint introduced to address the uncertainty of prediction errors, ensuring the robust feasibility of the sequencing scheme under uncertain environments.

[0021] Flight route uniqueness constraint: , ; Delay time limit constraint: , ; Safety interval constraints at the approach point: , ; Runway arrival time calculation constraints: , ; Runway safety separation constraints: ; Prediction result propagation constraints: ; Uncertainty set constraints in Brussels bar optimization: ; Expected constraints A and B for the blue bar: A: ; B: ; Because the original sub-Bruker expectation constraints contain absolute value operations and the expectation form of random variables, direct solution is difficult and not conducive to practical engineering applications. To improve the solvability of the model, this invention further transforms the above sub-Bruker expectation constraints into an equivalent semidefinite programming form, so as to utilize existing commercial solvers for efficient solution.

[0022] Specifically, for the expected value constraint A of the split-blob bar, by introducing auxiliary variables and Lagrange duality theory, it is transformed into the following tractable semidefinite programming constraint set: ; ; ; in and Let be a coefficient vector, whose construction satisfies: ; Where the auxiliary variable is a scalar. Representing the Lagrange multipliers, used to control the size of the uncertain fuzzy set in the dual transformation, and as a conservative adjustment parameter in the split-bar optimization. , Related; Represents an n-order positive semi-definite matrix, used to construct a quadratic form and capture the covariance structure of the prediction error; an n-dimensional real vector. Represents the Lagrange multiplier vector, used to handle linear terms in uncertainty sets; scalar The constant term on the right side of the inequality constraint used to balance the duality transformation; an n-dimensional coefficient vector. and It is used to transform nonlinear absolute value constraints into linear combinations of random variables, thereby facilitating the application of bibru bar optimization theory.

[0023] Similarly, the expected value constraint B of the partial blue bar can also be transformed into the following set of semidefinite programming constraints using a similar method: ; ; ; in and The coefficient vector is constructed to satisfy: ; Where the auxiliary variable is a scalar. Representing the Lagrange multipliers, used to control the size of the uncertain fuzzy set in the dual transformation, and as a conservative adjustment parameter in the split-bar optimization. , Related; Represents an n-order positive semi-definite matrix, used to construct a quadratic form and capture the covariance structure of the prediction error; an n-dimensional real vector. Represents the Lagrange multiplier vector, used to handle linear terms in uncertainty sets; scalar The constant term on the right side of the inequality constraint used to balance the duality transformation; an n-dimensional coefficient vector. and It is used to transform nonlinear absolute value constraints into linear combinations of random variables, thereby facilitating the application of bibru bar optimization theory.

[0024] Step 4: Input the flight trajectory data into the prediction module, and pass the prediction results into the optimization module for multiple rounds of iterative solution. Output the optimal flight scheduling plan and timetable, and calculate the total delay time and total flight time, including: Parameter initialization: Set the learning rate, tree depth, regularization parameters, etc. of the prediction module, as well as the flight information, safety interval, maximum delay time, and split bar parameters of the optimization module. Forward solution: The optimization module solves for the ranking scheme based on the current predicted arrival time and calculates the objective function value and SPO loss; Backpropagation: Feeds the SPO loss back to the prediction module to update the XGBoost model parameters; Iterative convergence: Repeat the forward solution and backpropagation steps until the objective function is improved below a preset threshold, and output the final optimal sorting scheme, timetable and corresponding total delay time and total flight time.

[0025] The aircraft end-to-end prediction-split bar optimization method also includes: Step 5: Visualize and evaluate the sequencing scheme to verify the effectiveness of the method in reducing total delays and total flight time, and in avoiding waypoint and runway conflicts.

[0026] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0027] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0028] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An end-to-end prediction-divider optimization method for aircraft, characterized in that, The method includes: Step 1: Obtain all arrival flight data for the target airport within the specified time period, including flight trajectory data, runway information data, waypoint data, and arrival route information; Step 2: Process all incoming flight data, including data cleaning and data transformation; Step 3: Establish an end-to-end arrival time prediction-minimum Brubar bar optimization mathematical model with the goal of minimizing the total flight time of arriving flights and flight delay time. The end-to-end arrival time prediction-minimum Brubar bar optimization mathematical model includes a prediction module and an optimization module. Step 4: Input the flight trajectory data into the prediction module, and input the prediction results into the optimization module for multiple rounds of iterative solution, output the optimal flight scheduling plan and timetable, and calculate the total delay time and total flight time.

2. The method according to claim 1, characterized in that, The target airport's data on all arriving flights within the specified time period includes: All flights This involves any flight Entry points The time of arrival at the entry point Approach flight path landing runway The time of arrival at the entry point ; All runways assembled Involving any runway All flights ; All entry points gather Involves any entry point All flights ; Any flight Entry points and landing runway Flight path between and flight time on that path .

3. The method according to claim 2, characterized in that, The processing of all arriving flight data includes: From flight data, feature data for each trajectory at waypoints in the terminal area are extracted, including: time of passage, altitude, speed, segment distance, track angle, remaining distance to the runway, and approach path, denoted as feature vectors. Simultaneously record tag data, i.e., the actual arrival time of the entry point. ; The feature data and label data are cleaned to remove missing and outlier values; then the feature data is normalized to eliminate dimensional differences. The processed flight trajectory data is divided into training and testing sets according to a preset ratio for subsequent training and evaluation of the prediction model.

4. The method according to claim 3, characterized in that, The established end-to-end arrival time prediction-partial Brussels bar optimization mathematical model aims to minimize the total flight time of arriving flights and flight delay time, wherein: The end-to-end arrival time prediction-minimum bar optimization mathematical model includes a prediction module and an optimization module; ； ； ； ； in, For loss function, This is the actual arrival time. To predict the arrival time, For the predicted time The optimal decision under the given circumstances For real time The optimal decision under the given circumstances For decision-making objectives, For the t-th tree model, For data features, This is a regularization term used to control model complexity and avoid overfitting. To control the complexity penalty of trees, It is the number of leaves on the tree. for The weights of the regularization terms, for The weights of the regularization terms, It is the predicted score of the j-th leaf; The optimization module includes decision variables, objective function, and constraints; The decision variables include: , indicating the entry point Flight Whether it is assigned to its runway A flight path between , , , ; , indicating the entry point Flight Delays and postponements , ; The objective function is: The constraints include: Flight route uniqueness constraint: , ; Delay time limit constraint: , ; Safety interval constraints at the approach point: , ; Runway arrival time calculation constraints: , ; Runway safety separation constraints: ; Prediction result propagation constraints: ; Uncertainty set constraints in Brussels bar optimization: ； Expected Constraints of the Brodler Bar: ； 。 5. The method according to claim 4, characterized in that, Step 4, which involves outputting the optimal flight scheduling plan and timetable, and calculating the total delay time and total flight time, specifically includes: Initialize the parameters of the prediction module and the optimization module separately. The parameters of the prediction module include the learning rate. Number of iteration rounds Maximum tree depth (max-deep) and minimum split gain Regularization parameters and ; The optimization module parameters include flight volume, number of approach points and runways, and flight arrival times. Flight route arrival points Maximum delay time Safety interval and Path flight time Parameters of the blue bar and ; Input flight trajectory data and extract data features and data tags Input prediction module Then, the prediction results from the prediction module are... Pass it to the optimization module; The optimal flight scheduling scheme and flight timetable are obtained through multiple rounds of iteration, and the total delay time and route flight time are calculated. The iterative process includes: The forward solving module optimizes the predicted arrival time based on the current round. Solve for the scheduling scheme, and calculate the objective function value and decision loss. ; Backpropagation will reduce decision loss. Feedback is sent to the prediction module as a basis for adjusting the XGBoost model parameters; The iteration converges, and the forward and backward propagation are repeated. The iteration terminates when the improvement of the objective function value is less than a preset threshold. The final optimal flight scheduling scheme, timetable, and corresponding total delay time and path flight time are output.

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