4D track prediction method based on improved sparrow algorithm optimized BP neural network

Abstract

The invention relates to the technical field of 4D track prediction, in particular to a 4D track prediction method for optimizing a BP neural network based on an improved sparrow algorithm, and the method comprises the following steps: S1, determining a topological structure of the BP neural network; s2, preprocessing the 4D track data; s3, generating an initial weight and a threshold value by using sine chaotic mapping; s4, calculating population fitness by adopting SSA, and updating individual positions according to foraging and anti-predation behaviors of a population of SSA; s5, judging an algorithm termination condition: iterating to the maximum number of iterations or less than or equal to the set convergence precision, if so, continuing the next step, and if not, returning to the step S4 to continue iteration; and S6, substituting the optimal weight and threshold obtained by algorithm optimization into BP for correction and updating, and performing training and simulation prediction again. By combining the sparrow algorithm and the BP neural network, the complex nonlinear relation in the 4D track data can be more accurately captured, and the precision of 4D track prediction can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of 4D track prediction, and in particular to a 4D track prediction method based on an improved sparrow algorithm to optimize a BP neural network. Background Art

[0002] The 4D track includes the aircraft's motion status in the air in terms of longitude, latitude, altitude and time, and is a classic time-series related data. 4D track prediction technology is the core technology of the future air traffic management automation system, and is also an important part of the civil aviation TBO operation sector. There are currently two main algorithms used in track prediction research. One of them uses related airborne equipment to obtain parameters such as the weight, lift, drag and thrust coefficient of the aircraft during flight to build a flight model for simulation. This algorithm has difficulty in obtaining data and requires huge calculations. The other is a parameter-free method based on estimation algorithms such as Kalman filtering or neural networks, which has a small amount of data and simple calculations. ZhijunWu et al. mainly analyzed the timeliness from the perspective of hierarchical clustering algorithm and k-means clustering algorithm, and combined the design of BP neural network to model the four-dimensional trajectory of aircraft; Harris et al. incorporated the flight plan and meteorological elements during flight into the 4D trajectory prediction model; Verdonk et al. started from the perspective of related trajectories, analyzed interdependent aircraft in pairs, and developed a trajectory prediction model to describe the vertical track profile of aircraft; Kairat et al. considered the prediction timeliness and proposed a method of local linear regression with high effectiveness and can be used for short-term to medium-term trajectory prediction; Li Nan et al. combined with the real-time data of ADS-B, comprehensively considered the latitude and longitude, altitude characteristics, speed characteristics and heading characteristics of the trajectory, and used GA-BP neural network to predict the trajectory of the terminal area; He Miao et al. proposed a method to optimize the terminal area trajectory by combining genetic algorithm; Li Guiyi et al. used BP theory to propose a prediction of the situation of airway traffic network. The traditional BP neural network (Back Propagation Neural Network) model has the problem of low accuracy when performing 4D track prediction, while the swarm intelligence optimization algorithm's characteristic of seeking the global optimal solution can greatly improve the accuracy of track prediction. The present invention proposes to optimize the BP neural network based on the swarm intelligence optimization algorithm to explore the changing rules between the track and the actual time and space. The Sparrow Search Algorithm (SSA) is a newer swarm intelligence algorithm, which is mainly inspired by the feeding behavior of sparrows. It has strong global optimization ability, good parallelism and fast convergence, and is better in convergence accuracy, speed and stability than other swarm intelligence optimization algorithms.

[0003] The existing Chinese patent document CN202310642459.0 discloses a motor rotor system fault diagnosis method based on Sine-SSA-BP, which realizes the fault diagnosis of the motor rotor. 1) Determine the structure and related parameters of the BP neural network and perform feature extraction; 2) Initialize the sparrow population and position with sine chaos mapping; 3) The initial position of the sparrow is used as the weight and bias of the BP neural network; 4) Train the neural network with the data of the training set, and obtain the error value through forward propagation as the fitness value of the individual sparrow population; 5) Update the sparrow position according to the SSA algorithm improved by the sine chaos mapping; 6) Determine whether the algorithm meets the stopping condition. If the stopping condition is met, the optimal weight and bias are output; if not, return to step 4 to continue executing the algorithm; 7) The obtained optimal weight ω and bias b are used as the final weight and bias of the Sine-SSA-BP model, and the optimized Sine-SSA-BP model is used for motor rotor fault diagnosis. The simulation results show that the optimized BP neural network has higher classification accuracy.

[0004] The existing patent also discloses the optimized Sine-SSA-BP model, but the existing patent is for motor rotor fault diagnosis. In the Sine-SSA-BP model used for motor fault diagnosis, the fault is a continuous function of time, but when the motor enters the stable operation period during actual operation, its fault presents the characteristics of randomness. Its fault mode and fault mechanism determine that there is a large difference between the input random sequence of the Sine-SSA-BP algorithm and the characteristics of the track. Therefore, the algorithm model applied to motor rotor fault diagnosis cannot be applied to track prediction;

[0005] The sparrow search algorithm was proposed in 2020. It is a swarm intelligence optimization algorithm derived by simulating the foraging process of sparrow populations. It is currently widely used in fault identification and diagnosis. The SSA-BP algorithm is widely used in trajectory prediction.

[0006] The sparrow algorithm takes into account the randomness of individuals in the search process, so it has a strong search ability; secondly, it can adaptively adjust the search parameters during the search process to meet the needs of solving different problems. The rules for updating individual sparrows determine that the update methods of individual sparrow positions can be divided into two types: approaching the origin initial point position and approaching the optimal position of the current iteration population. However, using these two methods will cause the algorithm to easily fall into the local optimum, because it directly jumps to the vicinity of the optimal position, resulting in the algorithm's weak global search ability, and it cannot jump out of the local optimum during the optimization process.

[0007] The sparrow algorithm improved by the present invention based on the sine chaotic mapping is an improvement on the initial population, so that the random sequence generated by it is richer, which is conducive to the optimization and generation of the population. The traditional sparrow algorithm is improved to generate a random population sequence, and the method of discrete chaotic mapping consistent with the algorithm and the problem is used to optimize the initial population of the sparrow algorithm, speed up the algorithm optimization efficiency, reduce the possibility of falling into the local optimum under the same population size and iteration number, and improve the quality of the algorithm solution. Summary of the invention

[0008] The purpose of the present invention is to provide a 4D track prediction method based on an improved sparrow algorithm to optimize the BP neural network. The method is optimized and improved by the sparrow algorithm, combined with the track data set obtained by preprocessing ADS-B data, and the optimal number of hidden layers is traversed by an empirical formula. The ratio of the training set to the test set is determined by the preliminary training of the neural network to achieve the highest expectation.

[0009] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0010] A 4D track prediction method based on an improved sparrow algorithm to optimize BP neural network includes the following steps:

[0011] S1: Determine the topological structure of the BP neural network;

[0012] S2: preprocessing the 4D track data;

[0013] S3: Generate initial weights and thresholds using sinusoidal chaos mapping;

[0014] S4: The population fitness is calculated using the Sparrow Search Algorithm (SSA), and the fitness function is the error of the BP neural network on the training data; the individual positions are updated according to the foraging and anti-predation behaviors of the SSA population;

[0015] S5: Determine the condition for algorithm termination: iterate to the maximum number of iterations or less than or equal to the set convergence accuracy. If it is satisfied, proceed to the next step. If not, return to step S4 to continue iteration.

[0016] S6: Substitute the optimal weights and thresholds obtained by the algorithm into the BP correction update and perform training and simulation prediction again.

[0017] Furthermore, the step S1 specifically includes:

[0018] Before using BP neural network training to predict flight paths, the known parameters must be fixed to prevent multiple training deviations. First, according to the flight path prediction characteristics, the number of input layer nodes is 4, the number of output layer nodes is 4, and the optimal number of hidden layers m of the network structure is found by the minimum mean square error of the training set; after the model parameters are set, the LM algorithm is used to train the BP neural network.

[0019] Furthermore, the LM algorithm in step S1 specifically includes:

[0020] Select the data set. According to the needs of the model, the input features of the training data used in the present invention include: the longitude, latitude and altitude of the aircraft at the current time, and the output features are also time, longitude, latitude and altitude. The selected data must reach a sufficient level, and the range of the training data covers the flight activities of the aircraft during the cruise phase. The data in this phase is relatively smooth to ensure the accuracy of the model training;

[0021] Secondly, the initial data needs to be divided into the total training set and the test set in the data set to determine the appropriate ratio of the training set to the test set.

[0022] Substitute the set network parameters into the network for training and simulation. The optimal number of hidden layer nodes of the network is finally determined by the mean square error of the training set, and used as the number of nodes for later testing. The Sigmoid function with S-shaped single increase and inverse function properties is selected as the transfer function between the input layer and the hidden layer, and the linear purelin function is used as the transfer function between the hidden layer and the output layer.

[0023] Calculate the total error E between the model input and output and compare it with the target error. If the target minimum error is not reached, the weights and thresholds of the network are corrected layer by layer in reverse. Repeat this step until the total error is less than the set minimum target error and output the result.

[0024] Furthermore, the step S2 includes: according to the ADS-B standard signal format, including data cleaning and missing value supplementation:

[0025] Data cleaning removes wrong and garbled codes and retains ADS-B data that conforms to the data format; selects flight data that conforms to the format requirements, including flight phase, altitude change, and heading change data volume;

[0026] Missing value filling: Based on the missing amount in the missing interval, adaptive Lagrange Quadratic Interpolation is used with an interval of 1.0 second to obtain complete flight data within a fixed time interval that can be used as a training set, providing basic data support for subsequent calculations.

[0027] Further, the step S3 includes: improving the initial population by the sparrow algorithm improved based on the sine chaotic map, making the generated random sequence richer, improving the overall fitness value of the population and the initial quality of the population, facilitating the selection and evolution of the population, and improving the global search ability of the SSA algorithm. The expression of the sine chaotic map is:

[0028]

[0029] where μ is the control parameter, and the range is (0, 4]. The sine chaotic map has obvious period-doubling bifurcation characteristics and many period windows. At the same time, its chaotic parameter interval is discontinuous. It is these characteristics that make the pseudo-random sequence generated by the sine chaotic map better meet the random requirements.

[0030] Obtain the sequence X with the best fitness from the chaotic sequence X generated by Equation 4 dim :

[0031] X dim = X fbest (5)

[0032] f best represents the highest fitness value. Using the one obtained by the Sine chaotic map as the initial population of the SSA algorithm enriches the diversity of the population, improves the overall fitness value of the population and the initial quality of the population, and at the same time improves the global search ability of the SSA algorithm.

[0033] Further, the step S4 specifically includes: in the SSA, each individual can be divided into discoverers, participants, and alarmists; the discoverers are responsible for finding food and leading the population to search. The participants follow the discoverers to snatch food. The alarmists remain vigilant against environmental threats and warn the sparrow population to move to a safe area;

[0034] When the discoverers do not detect a threat (R2 < ST), they are responsible for guiding the population to forage and conducting extensive searches. When an individual in the population discovers a predator (natural enemy) and issues an alarm (R2 ≥ ST), it will guide the population to the location of the safe area. The position update is described as follows:

[0035]

[0036] where ɑ is a random number belonging to 0 to 1, Q is responsible for controlling the step size, and the step size is random. L is 1×d, d represents the dimension, and all elements are 1. The warning value R2 is in the range of [0, 1], and the safety value ST is in the range of [0.5, 1]. In order to obtain food, the participants follow and supervise the discoverers to grab food (i ≤ N / 2) or search for food alone to eat (i > N / 2). Therefore, the position update of the participants is described as follows:

[0037]

[0038] Among them, X Wp Indicates the worst position of the current population, X p Indicates the best position currently occupied by the current finder. A is a 1×d matrix responsible for controlling the direction, with only 1 or -1 elements, and A + =A T (AA T ) -1 . When aware of danger, the sparrow population will take anti-predator actions. When the current fitness is greater than the fitness of the optimal position, it means that the alerter is aware of the danger at the current position, and they will move closer to other sparrows to reduce the risk of being preyed upon; when the current fitness is equal to the fitness of the optimal position, it means that the sparrow is at the edge of the population and is at high risk of being attacked by predators. In other cases, the joiner will follow the current discoverer's optimal position to forage. The alarm position update formula is as follows:

[0039]

[0040] Among them, β is responsible for controlling the step size, and K is responsible for controlling the direction, ranging between [-1, 1].

[0041] Beneficial effects of the present invention:

[0042] The present invention can effectively improve the accuracy of 4D track prediction by combining the sparrow algorithm with the BP neural network. The sparrow algorithm has a strong global search capability. By simulating the foraging behavior and anti-predation behavior of the sparrow, it can effectively search in the solution space to find the global optimal solution or the point close to the global optimal solution for optimizing the BP network parameters. Compared with the traditional BP neural network, the optimized network can more accurately capture the complex nonlinear relationship in the 4D track data, thereby achieving higher prediction accuracy in different flight stages; it is confirmed by experiments that the sparrow algorithm can effectively improve the BP neural network and then accurately predict the track. Among them, in the departure climb stage, the BP accuracy is 91.2%, SSA-BP is 99.4%, and Sine-SSA-BP is 99.6%; in the cruise stage, BP is 95.1%, SSA-BP is 99.6%, and Sine-SSA-BP is 99.7%; in the descent approach stage, BP is 82.6%, SSA-BP is 97.8%, and Sine-SSA-BP is 99.7%. It can be seen that the Sine-SSA-BP algorithm has higher accuracy in 4D trajectory prediction.

[0043] The present invention improves the initial population of the sparrow algorithm by introducing a sinusoidal chaotic map, thereby increasing the diversity of the population, which helps the algorithm to jump out of the local optimal solution and improve the efficiency and scope of the search. The pseudo-random sequence generated by the sinusoidal chaotic map has stronger randomness and richer diversity, allowing the algorithm to explore a wider solution space during the search process, thereby reducing the risk of falling into the local optimal solution and enhancing the global search capability of the algorithm.

[0044] The Sine-SSA-BP algorithm proposed in this invention not only improves the convergence speed of the algorithm through an improved initialization process and an effective update mechanism, but also enhances the stability and reliability of the algorithm. The algorithm can gradually approach the true optimal solution during the iteration process and can maintain a relatively stable prediction result in multiple runs, which is particularly important for the practical application of 4D track prediction.

[0045] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0047] Figure 1 It is a schematic diagram of the SSA-BP algorithm flow;

[0048] Figure 2 It is a schematic diagram of the Sine-SSA-BP algorithm process;

[0049] Figure 3 This is a schematic diagram of the fractal dimension comparison between the actual value and the predicted value of CSC8843;

[0050] Figure 4 This is a schematic diagram of the comparison of the error fractal dimension of the predicted value of CSC8843;

[0051] Figure 5 This is a schematic diagram of the fractal dimension comparison between the actual value and the predicted value of CSN348;

[0052] Figure 6 This is a schematic diagram of the comparison of the error fractal dimension of the CSN348 prediction value;

[0053] Figure 7 This is a schematic diagram of the fractal dimension comparison between the true value and the predicted value of CSS6975;

[0054] Figure 8 This is a schematic diagram of the comparison of the error fractal dimension of the CSS6975 prediction value. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] Example 1

[0057] The 4D track prediction method based on the improved sparrow algorithm to optimize the BP neural network described in this embodiment includes the following steps:

[0058] S1: Determine the topological structure of the BP neural network;

[0059] Before using BP neural network training to predict flight paths, we must first fix known parameters to prevent multiple training deviations. First, according to the flight path prediction characteristics, the number of nodes in the input layer and output layer is set to 4. Secondly, through experiments, it is found that too many hidden layers drag down the network calculation efficiency, so the number of hidden layer nodes is determined by training traversal and comparing the mean square error of the results to determine the optimal number of hidden layers. Other parameters such as learning rate and maximum number of iterations are finally selected according to the experimental results based on the training effect:

[0060] Table 1 Network parameter settings

[0061]

[0062] After the model parameters are set, the next step is to train the model. The BP neural network is similar in the choice of training methods. The main reference is the problem itself and the number of training samples to select a suitable method such as the steepest descent method or other improved training algorithms. Among them, the LM algorithm has better conditions in all aspects than other methods, with high comprehensive benefits, and is also considered for use in the model of the present invention. In addition, the existing equipment can fully support the large storage space required by this algorithm and achieve the corresponding computing power.

[0063] (1) Selecting a data set. According to the needs of the model, the input features of the training data used in the present invention include: the longitude, latitude and altitude of the aircraft at the current time, and the output features are also time, longitude, latitude and altitude. The selected data should reach a sufficient level. The range of the training data covers the flight activities of the aircraft during the cruising phase. The data in this phase is relatively smooth, ensuring the accuracy of the model training.

[0064] (2) Secondly, the initial data needs to be divided into the total training set and the test set, and the appropriate ratio of the training set to the test set is determined. The setting of the ratio of the training set to the test set is discussed in detail in Chapter 5.

[0065] (3) Substitute the set network parameters into the network for training and simulation. The optimal number of hidden layer nodes of the network is finally determined by the mean square error of the training set, and used as the number of nodes for subsequent testing. The Sigmoid function with S-shaped monotonically increasing and inverse function properties is selected as the transfer function between the input layer and the hidden layer, and the linear purelin function is used as the transfer function between the hidden layer and the output layer. First, based on the experimental data, the prediction accuracy of the model is calculated, and then the degree of fit of the model is calculated. Finally, the mean square error of the model is calculated to evaluate the prediction performance of the model. Through these evaluation indicators, the accuracy and precision of the model can be obtained to determine the prediction effect of the model.

[0066] (4) Calculate the total error E between the model input and output and compare it with the target error. If the target minimum error is not reached, the weights and thresholds of the network are corrected layer by layer in reverse. Repeat this step until the total error is less than the set minimum target error and output the result.

[0067] S2: preprocessing the 4D track data;

[0068] According to the ADS-B standard signal format, it mainly includes data cleaning and missing value supplementation:

[0069] Data cleaning mainly removes some wrong codes and garbled codes, retains ADS-B data that conforms to the data format; selects flight data that conforms to the format requirements, such as flight stage, altitude change, heading change data volume, etc. The results after cleaning are as follows:

[0070] Table 2 Data cleaning results

[0071]

[0072]

[0073] Filling missing values. Due to the influence of factors such as signal shielding and channel interference, the collected data has certain missing values. According to the missing value of the missing interval, adaptive Lagrange Quadratic Interpolation is used with an interval of 1.0 second to obtain complete flight data within a fixed time interval that can be used as a training set, providing basic data support for subsequent calculations.

[0074] S3: Generate initial weights and thresholds using sinusoidal chaos mapping;

[0075] S4: Use the sparrow search algorithm (SSA) to calculate the fitness of the population. The fitness function is usually the error of the BP neural network on the training data; according to the foraging and anti-predation behavior of the SSA population, the individual position is updated; in the SSA rule, the position of the individual will change continuously due to the different roles played by the individual, and the individual position is updated as formula (1) to (3);

[0076] The parameters of the sparrow algorithm are determined by referring to the parameter ranges and solution efficiency recommended by professionals from all walks of life and combining them with the actual situation of the present invention. The main parameters include the size of the population, which is an N×N matrix; the maximum evolutionary algebra, also known as the number of iterations; the safety value, such as formula (1), which is the judgment value of whether the finder position is updated;

[0077]

[0078] Where ɑ is a random number between 0 and 1, Q is responsible for controlling the step length, which is random. L is 1×d, d represents the size, and all elements are 1. The warning value R2 is in the range of [0,1], and the safety value ST is in the range of [0.5,1]. In order to obtain food, the participant follows and supervises the finder to grab food (i≤N / 2) or finds food alone and eats it alone (i>N / 2). Therefore, the position update of the participant is described as follows:

[0079]

[0080] Among them, X Wp Indicates the worst position of the current population, X p Indicates the best position currently occupied by the current finder. A is a 1×d matrix responsible for controlling the direction, with only 1 or -1 elements, and A + =A T (AA T ) -1 When aware of danger, the sparrow population will take anti-predator actions. When the current fitness is greater than the fitness of the optimal position, it means that the alerters are aware of the danger in the current position, and they will move closer to other sparrows to reduce the risk of being preyed upon; when the current fitness is equal to the fitness of the optimal position, it means that the sparrows are at the edge of the population and are at high risk of being attacked by predators.

[0081] The proportion of discoverers; the alert value, i.e., the value of formula (2) to determine whether the position of the alerter is updated;

[0082]

[0083] The upper and lower limits of variables are essential for the implementation of the algorithm; the number of variables is determined by the number of input layers, hidden layers, and output layers of the trained BP neural network, and mainly determines the number of iterations within the algorithm; reasonable setting of algorithm parameters will not only maximize the algorithm, but also achieve comprehensive results in efficiency, for example, the population size and number of iterations are directly linked to the overall efficiency and operation time of the algorithm. The main parameter settings of the algorithm implemented in the present invention are as follows:

[0084] Table 3 Main parameter settings of (improved) sparrow algorithm

[0085]

[0086] S5: Determine the condition for algorithm termination: iterate to the maximum number of iterations or less than or equal to the set convergence accuracy. If it is satisfied, proceed to the next step. If not, return to step S4 to continue iteration.

[0087] S6: Substitute the optimal weights and thresholds obtained by the algorithm into the BP correction update and perform training and simulation prediction again.

[0088] Furthermore, the step S1 specifically includes: wherein the number of input layer nodes is 4, the number of output layer nodes is 4, and the optimal number of hidden layers m of the network structure is found by the minimum mean square error of the training set;

[0089] Furthermore, step S3 includes: improving the initial population based on the sparrow algorithm improved by the sine chaos map, so that the random sequence generated by it is richer, improving the overall fitness value of the population and the initial quality of the population, which is beneficial to the selection and generation of the population, and improving the global search ability of the SSA algorithm. The expression of the sine chaos map is:

[0090]

[0091] Where μ is the control parameter, ranging from (0, 4]. The sinusoidal chaotic mapping has obvious period-doubling bifurcation characteristics, more period windows, and its chaotic parameter interval is discontinuous. It is these characteristics that make the pseudo-random sequence generated by the sinusoidal chaotic mapping more in line with the random requirements.

[0092] Obtain the sequence X with the best fitness from the chaotic sequence X generated by formula 4 dim :

[0093] X dim =X fbest (5)

[0094] f bestIndicates the highest fitness value. Using the Sine chaotic map as the initial population of the SSA algorithm enriches the diversity of the population, improves the overall fitness value of the population and the initial quality of the population, and at the same time improves the global search ability of the SSA algorithm.

[0095] Example 2

[0096] SSA-BP algorithm

[0097] The sparrow search algorithm is a swarm intelligence optimization algorithm obtained by simulating the foraging process of a sparrow population. In SSA, each individual can be divided into discoverers, participants, and alarmists. Discoverers are responsible for finding food and leading the population to search. Participants follow the discoverers to snatch food. Alarmists remain vigilant against environmental threats and warn the sparrow population to move to a safe area.

[0098] When the discoverers do not detect a threat (R2 < ST), they are responsible for guiding the population to forage and conducting extensive searches. When an individual in the population discovers a predator (natural enemy) and issues an alarm (R2 ≥ ST), it will guide the population to the location of a safe area. The position update is described as follows:

[0099]

[0100] where ɑ is a random number belonging to 0 to 1, Q is responsible for controlling the step size, and the step size is random. L is 1×d, d represents the dimension, and all elements are 1. The warning value R2 is in the range of [0, 1], and the safety value ST is in the range of [0.5, 1]. To obtain food, participants follow and supervise the discoverers to grab food (i ≤ N / 2) or search for food alone to eat alone (i > N / 2). Therefore, the position update of the participants is described as follows:

[0101]

[0102] where, X Wp represents the worst position of the current population, and X p represents the best position currently occupied by the current discoverer. A is a 1×d matrix responsible for controlling the direction, and the elements are only 1 or -1, and A+ = AT(AAT)-1. When aware of danger, the sparrow population will perform anti-predation behaviors. When the current fitness is greater than the fitness of the optimal position, it indicates that the alarmists perceive the danger of the current position, and they will approach other sparrows to reduce the risk of being preyed upon; when the current fitness is equal to the fitness of the optimal position, it means that the sparrows are on the edge of the population and the risk of being attacked by predators is very high. In other cases, the joiners will forage in the vicinity of the optimal position of the current discoverer. The position update formula for the alarmists is as follows:

[0103]

[0104] Among them, β is responsible for controlling the step length, and K is responsible for controlling the direction, ranging between [-1, 1]. It is not difficult to see from the above mathematical expressions that with the change of the sparrow's fitness value and the generation and update of the population, the same sparrow may play three roles. The sparrow as the discoverer has high energy. After the alerter detects the danger, the three sparrows may evacuate to other safe areas due to different flight trajectories. The followers with lower energy values ​​will evacuate to the safe area first to forage for food and replenish energy to a certain value, and then play the role of the discoverer to continue looking for food. Therefore, each sparrow will change its role due to the warning signal. Finally, after continuous cyclic iterative updates, the global optimal value and the best fitness value are obtained.

[0105] Sine-SSA-BP algorithm

[0106] BP neural network has adaptive and nonlinear characteristics, can solve some complex nonlinear problems and adapt to complex input-output relationships, so it has been widely used in fields such as track prediction. However, the gradient correction of BP neural network will change greatly due to the choice of learning rate, resulting in slow convergence or oscillation problems. Unknown disturbances and model selection will affect the prediction effect of neural network. Sparrow algorithm is an algorithm that adjusts search parameters adaptively. It can automatically adjust neural network parameters to improve the performance of neural network. The core idea of ​​the algorithm is: according to the output result of the current neural network, through appropriate parameter adjustment, the output result is closer to the expected result. It can regard the process of adjusting neural network parameters as a kind of "search", that is, in the space of neural network parameters, according to the adjustment results, continuously search for the optimal parameter combination. The SSA-BP algorithm process is shown in the figure.

[0107] S1: Determine the topological structure of the BP neural network. The number of input layer nodes is 4, the number of output layer nodes is 4, and the optimal number of hidden layers m of the network structure is found by minimizing the mean square error of the training set;

[0108] S2: Preprocess the 4D track data.

[0109] S3: Initialization of the weight threshold of BP. The initial weight experience value is between (-2.4 / F, 2.4 / F) or (√-9 / F, √9 / F), where F is the number of neurons connected to the weight input end.

[0110] S4: SSA calculates the population fitness and updates the optimal individual, and selects the population fitness function;

[0111] S5: Foraging and anti-predation behavior of the population, updating individual positions. In the SSA rule, the positions of individuals will constantly change due to their different roles, and the individual positions are updated as formula 1-3;

[0112] S6: Determine the condition for algorithm termination - the maximum number of iterations or the convergence precision less than or equal to the set number. If the condition is satisfied, proceed to the next step. If not, return to step S4.

[0113] S7: Substitute the optimal weights and thresholds obtained by the algorithm into the BP correction update and perform training and simulation prediction again.

[0114] The randomness of the individual search process of the Sparrow Algorithm gives it a strong search capability; secondly, it can adaptively adjust the search parameters during the search process to meet the solution requirements of different problems. However, the limitation of the convergence mechanism of the Sparrow Algorithm is that in the optimization process, if the location of the optimal solution is far away from the origin, the algorithm may fall into the local optimum, resulting in weak global search capability. The present invention improves the traditional Sparrow Algorithm to generate a random population sequence, and uses a discrete chaotic mapping method that is consistent with the algorithm and the problem, referred to as Sine-SSA, to optimize the initial population of the Sparrow Algorithm, speed up the optimization efficiency of the algorithm, reduce the possibility of falling into the local optimum under the same population size and number of iterations, and improve the quality of the algorithm solution. The improvement of the initialization population by the improved Sparrow Algorithm based on the sinusoidal chaotic mapping makes the generated random sequence richer, improves the overall fitness value of the population and the initial quality of the population, is conducive to the selection and advancement of the population, and improves the global search capability of the SSA algorithm. The expression of the sinusoidal chaotic mapping is:

[0115]

[0116] Where μ is the control parameter, ranging from (0, 4]. The sinusoidal chaotic mapping has obvious period-doubling bifurcation characteristics, more period windows, and its chaotic parameter interval is discontinuous. It is these characteristics that make the pseudo-random sequence generated by the sinusoidal chaotic mapping more in line with the random requirements.

[0117] Obtain the sequence X with the best fitness from the chaotic sequence X generated by equation (4) dim :

[0118] X dim =X fbest (5)

[0119] fbest indicates the highest fitness value. The initial population obtained by Sine chaotic mapping is used as the SSA algorithm, which enriches the diversity of the population, improves the overall fitness value of the population and the initial quality of the population, and improves the global search ability of the SSA algorithm. Therefore, the present invention calls this algorithm an improved sparrow algorithm optimized BP neural network, referred to as Sine-SSA-BP.

[0120] Example 3

[0121] The data of the present invention comes from an ADS-B ground station of the Communication, Navigation and Monitoring Laboratory of the Civil Aviation Flight Academy of China. The ADS-B system can provide real-time and accurate monitoring information such as aircraft position, and has a wide range of application prospects in air traffic services in high-density flight areas. This data set mainly includes the aircraft arriving and departing from Chengdu Shuangliu and some aircraft passing through routes such as W230, G212, W233, and W81. The time span is large and the trajectory volume is large. The ground station ADS-B standard signal format, each data contains information such as longitude (LON), latitude (LAT), time (TIME), GPS altitude (HEIGHT), pressure altitude (ALTITUDE), heading (HEADING), ground speed (GS), flight number (CALLSIGN), etc., which can be used as a data set for 4D track prediction after decoding. The data collected initially is cleaned and interpolated, and 11 flight data that meet the requirements are screened out.

[0122] Table 1 Data cleaning results

[0123]

[0124] In order to more objectively and comprehensively evaluate the prediction performance of SSA and Sine-SSA after optimizing the BP neural network, the present invention selects the data sets of five characteristic stages of aircraft departure climb, cruise climb, cruise, cruise descent and descent approach for experiment and evaluation. The specific flights are CSC8843, CHB6335, CSN348, CSZ9238 and CSS6975.

[0125] Departure climb and cruise climb

[0126] Since the ADS-B signal will be blocked by obstacles, the ADS-B in the laboratory is generally unable to receive aircraft data below about 4700ft above Shuangliu Airport. Therefore, the process of the aircraft climbing from 4700ft to an altitude below 26240ft (8000m) is defined as the aircraft departure climb phase; the process of climbing from 8000m to the designated cruising altitude is regarded as the cruise climb process. Although the aircraft has altitude changes in the cruise climb phase, it is slower than the departure climb phase due to its faster speed. The aircraft altitude changes frequently in the departure climb phase, so the accuracy of the altitude prediction results may be affected. The aircraft that meets the requirements in this range is CSC8843, and the amount of data that meets the requirements is 825. The training set is divided into 495 pieces with a duration of 8.25 minutes; the test set is divided into 330 pieces with a duration of 5.5 minutes.

[0127] Table 2 Summary of CSC8843 track prediction errors

[0128]

[0129] Figure 1 The results show that the BP, SSA-BP and Sine-SSA-BP algorithms have high prediction accuracy in the early stage of the prediction sequence, but as the prediction sequence increases, the prediction value of BP gradually moves away from the true value and approaches the curve of the training function LM method, reflecting the limitation of the amount of BP prediction data. The prediction value of SSA deviates less from the true value, but the deviation gradually increases as the prediction sequence increases. The characteristics of departure climb and cruise climb are frequent changes in altitude sequence, and from the prediction results of the Sparrow algorithm for altitude, the deviations of SSA and Sine-SSA from the true value are almost the same, reflecting the applicability of the Sparrow algorithm in predicting the altitude of the track. Figure 2 The error of each algorithm is much smaller than that of BP. The prediction accuracy of longitude and latitude is at least 10 times higher, and the prediction accuracy of altitude is even increased by nearly 100 times. The prediction accuracy of Sine-SSA-BP in latitude is increased by nearly 20 times. The various errors of flight CSC8843 are summarized in the following table. The prediction accuracy is calculated by MAPE, and the prediction accurate segment (the first ten points) is selected for calculation. Finally, the prediction accuracy of the BP prediction model in the departure climb and cruise climb stages is 91.2%, SSA-BP is 99.4%, and Sine-SSA-BP is 99.6%.

[0130] Cruise phase

[0131] When the aircraft reaches a height of 8000m or more, it can enter the cruising stage. However, since cruising at a lower cruising altitude is not economical, the cruising altitude set by airlines is usually within the RVSM airspace (8900m-12500m Lv Xiaoping. Analysis of the impact of implementing RVSM on my country's airspace capacity and flow. China Civil Aviation, 2008 (06): 58-59.). The aircraft point set at this stage is large and the data is relatively complete. Generally, more than 20 minutes of data can be obtained. The altitude of the aircraft entering the cruising altitude changes slightly. The altitude change is mainly due to the influence of wind. Therefore, the present invention defines the aircraft that meets the requirements in this interval as CSN348, and the amount of data that meets the requirements is 2000. The training set is divided into 1200 pieces with a duration of 20 minutes; the test set is divided into 800 pieces with a duration of 13.3 minutes.

[0132] The data in the cruise phase is very stable, so generally speaking the prediction results are better than in other situations. Figure 3This is the prediction of each dimension of flight CSN348. It can be seen that the prediction accuracy of BP, SSA-BP and Sine-SSA-BP has been significantly improved compared with the departure climb stage, but from the perspective of longitude and altitude prediction, BP prediction is still close to the curve of the training function LM method. The deviation between the prediction of the Sparrow Algorithm and the true value is small, and longitude is still the prediction dimension with the largest deviation. From the prediction results of the Sparrow Algorithm for altitude, SSA-BP does not fit the altitude well, and Sine-SSA-BP happens to improve this point, and can discover changes as small as 10ft, making the altitude prediction more refined. Figure 4 This is the prediction error of the three methods of CSN348. The error of the optimized BP is still significantly reduced, and the improved sparrow algorithm can still further reduce the error.

[0133] Table 3 Summary of CSN348 track prediction errors

[0134]

[0135] In summary, the prediction accuracy of the BP prediction model in the cruise phase is 95.1%, SSA-BP is 99.6%, and Sine-SSA-BP is 99.7%.

[0136] Descent approach and cruise descent phase

[0137] Since ADS-B signals may be blocked by obstacles, the present invention defines the process of an aircraft descending from 26240ft (8000m) to an altitude below 4700ft as the process of an aircraft descending approach; and defines the process of descending to 8000m as the process of a cruise descent. In contrast to the cruise climb phase, the altitude of an aircraft in a cruise descent changes gently, while the altitude of an aircraft in a descending approach phase changes frequently, so the accuracy of the altitude prediction results may be affected. The aircraft that meets the requirements in this interval is CSS6975, and the amount of data that meets the requirements is 1079. The training set is divided into 648 items with a length of 10.8 minutes; the test set is divided into 431 items with a length of 7.18 minutes.

[0138] Figure 5The figure shows the prediction of each dimension during the descent and approach phase of flight CSS6975. The same as the previous two phases is that the prediction accuracy of BP, SSA-BP and Sine-SSA-BP is very high in the early stage of the prediction sequence, but as the time series increases, the error of BP prediction becomes larger and larger, approaching the curve of the training function LM method. In contrast, the deviation between the prediction of the Sparrow algorithm and the true value is small, which intuitively shows the improvement after BP optimization, but the offset becomes larger as the prediction sequence increases. The characteristics of departure climb and cruise climb are frequent changes in altitude sequence. From the prediction results of the Sparrow algorithm for altitude, the deviation between SSA and Sine-SSA and the true value is small, reflecting the applicability of the Sparrow algorithm in predicting the altitude of the flight path. Figure 6 It reflects the prediction error of each method. It can be clearly seen that the error of the sparrow algorithm after optimizing BP is much smaller than that of BP. At the same time, the improved sparrow algorithm is also improved compared with the original one.

[0139] Table 4 Summary of CSS6975 track prediction errors

[0140]

[0141] In summary, the prediction accuracy of the BP prediction model in the cruise phase is 82.6%, SSA-BP is 97.8%, and Sine-SSA-BP is 99.7%.

[0142] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A 4D track prediction method based on an improved sparrow algorithm to optimize BP neural network, characterized in that: The following steps are involved: S1: Determine the topological structure of the BP neural network; S2: preprocessing the 4D track data; S3: Generate initial weights and thresholds using sinusoidal chaos mapping; S4: The fitness of the population is calculated using the sparrow search algorithm, and the fitness function is the error of the BP neural network on the training data; the individual positions are updated according to the foraging and anti-predation behaviors of the SSA population; S5: Determine the condition for algorithm termination: iterate to the maximum number of iterations or less than or equal to the set convergence accuracy. If it is satisfied, proceed to the next step. If not, return to step S4 to continue iteration. S6: Substitute the optimal weights and thresholds obtained by the algorithm into the BP correction update and perform training and simulation prediction again.

2. The 4D track prediction method based on the improved sparrow algorithm and BP neural network optimization as claimed in claim 1, characterized in that: The step S1 specifically includes: before using the BP neural network to train and predict the track, firstly, the known parameters must be fixed to prevent multiple training deviations; firstly, according to the track prediction characteristics, where the number of input layer nodes is 4 and the number of output layer nodes is 4, the optimal number of hidden layers m of the network structure is found by the minimum value of the mean square error of the training set; after the model parameters are set, the LM algorithm is used to train the BP neural network.

3. The 4D track prediction method based on the improved sparrow algorithm and BP neural network optimization as claimed in claim 2, characterized in that: The LM algorithm in step S1 specifically includes: Select a dataset. The input features of the training data include: the longitude, latitude and altitude of the aircraft at the current time. The output features are also time, longitude, latitude and altitude. Secondly, the initial data needs to be divided into the total training set and the test set, and the ratio of the training set to the test set needs to be determined; Substitute the set network parameters into the network for training and simulation; finally determine the optimal number of hidden layer nodes of the network through the mean square error of the training set, and use it as the number of nodes for subsequent testing; select the S-shaped single-increase and inverse function Sigmoid function as the transfer function between the input layer and the hidden layer, and use the linear purelin function as the transfer function between the hidden layer and the output layer; Calculate the total error E between the model input and output and compare it with the target error. If the target minimum error is not reached, the weights and thresholds of the network are corrected layer by layer in reverse. Repeat this step until the total error is less than the set minimum target error and output the result.

4. The 4D track prediction method based on the improved sparrow algorithm and BP neural network optimization as claimed in claim 1, characterized in that: The step S2 includes: according to the ADS-B standard signal format, including data cleaning and missing value supplementation: Data cleaning removes wrong and garbled codes and retains ADS-B data that conforms to the data format; selects flight data that conforms to the format requirements, including flight phase, altitude change, and heading change data volume; Missing value filling: According to the missing amount in the missing interval, adaptive Lagrange quadratic interpolation is used with an interval of 1.0 second to obtain complete flight data within a fixed time interval that can be used as the training set requirement, providing basic data support for subsequent calculations.

5. The 4D track prediction method based on the improved sparrow algorithm and BP neural network optimization as claimed in claim 1, characterized in that: The step S3 includes: improving the initialization population based on the sparrow algorithm improved by the sine chaos map, so that the generated random sequence is richer, the overall fitness value of the population and the initial quality of the population are improved, which is beneficial to the selection and generation of the population and improves the global search ability of the SSA algorithm; the expression of the sine chaos map is: Among them, μ is a control parameter with a range of (0, 4]; the sine chaotic map has obvious period-doubling bifurcation characteristics and many period windows, and at the same time its chaotic parameter interval is discontinuous; it is these characteristics that make the pseudo-random sequence generated by the sine chaotic map better meet the random requirements; Obtain the sequence X with the best fitness from the chaotic sequence X generated by formula 4 dim : X dim =X fbest (5) f best Indicates that the fitness value is the highest; using the Sine chaotic map as the initial population of the SSA algorithm enriches the diversity of the population, improves the overall fitness value of the population and the initial quality of the population, and at the same time improves the global search capability of the SSA algorithm.

6. The 4D track prediction method based on the improved sparrow algorithm and BP neural network optimization as claimed in claim 1, characterized in that: The specific steps of step S4 include: in SSA, each individual can be divided into a discoverer, a participant, and an alarmist; the discoverer is responsible for finding food and leading the population to search; the participant follows the discoverer to snatch food; the alarmist remains vigilant against environmental threats and warns the sparrow population to move to a safe area; When the discoverer does not detect a threat, that is, R2 < ST, they are responsible for guiding the population to forage and conducting extensive searches; when an individual in the population discovers a predator and issues an alarm, that is, R2 ≥ ST, it will guide the population to the location of the safe area; the position update is described as follows: Among them, ɑ is a random number belonging to 0 to 1, Q is responsible for controlling the step size, and the step size is random; L is 1×d, where d represents the size and all elements are 1; the warning value R2 is in the range of [0, 1], and the safety value ST is in the range of [0.5, 1]; in order to obtain food, the participant follows and supervises the discoverer to grab food (i ≤ N / 2) or searches for food alone to eat (i > N / 2); therefore, the position update of the participant is described as follows: Among them, X Wp Indicates the worst position of the current population, X p Indicates the best position currently occupied by the current finder; A is a 1×d matrix responsible for controlling the direction, with only 1 or -1 elements, and A + =A T (AA T ) -1 ; When aware of danger, the sparrow population will take anti-predator actions; the current fitness is greater than the fitness of the optimal position, indicating that the alerter is aware of the danger at the current position, and they will move closer to other sparrows to reduce the risk of being preyed upon; when the current fitness is equal to the fitness of the optimal position, it means that the sparrow is at the edge of the population and is at high risk of being attacked by predators; in other cases, the joiner will follow the current discoverer's optimal position to forage; the alarm position update formula is as follows: Among them, β is responsible for controlling the step size, and K is responsible for controlling the direction, with a range between [-1, 1].

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