CN115809745A - Air traffic flow chaos prediction method and system, storage medium and terminal - Google Patents
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Abstract
The invention discloses an air traffic flow chaos prediction method and system, a storage medium and a terminal. The air traffic flow chaos prediction method comprises the following steps: constructing an air traffic flow chaotic time sequence prediction model; judging whether the air traffic flow has chaotic characteristics or not; if so, carrying out normalization processing on the air traffic flow time sequence; determining phase space reconstruction parameter delay time and embedding dimension according to the air traffic flow time sequence after normalization processing; performing phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the determined delay time and the embedded dimension; inputting the air traffic flow time sequence after the phase space reconstruction into the constructed air traffic flow chaotic time sequence prediction model for prediction. The model is verified through actual traffic flow data, and compared with the traditional method, the method has better prediction precision and prediction speed for the air traffic flow time sequence by utilizing the method.
Description
Technical Field
The invention relates to the technical field of air alternating current flow prediction, in particular to an air traffic flow chaos prediction method and system, a storage medium and a terminal.
Background
The research is carried out on a prediction method based on a nonlinear theory in the industry aiming at the nonlinear chaotic characteristic of the air traffic flow. For example, a scheme for predicting a prediction model of an improved weighted first-order local area method, which is constructed according to the chaotic characteristic of air traffic flow, is disclosed in the prior art; and establishing a time series model by taking 7 days as a time scale, predicting the air traffic flow, and the like. In the aspect of an intelligent prediction method, the prior art discloses a scheme for establishing a gray BP neural network prediction model by combining a gray prediction model and a BP neural network; and (4) a scheme for predicting the air traffic flow by combining a neural network and a regression analysis method and the like.
Many related technical solutions are disclosed in the prior art, but the research on air traffic flow prediction still has at least the following disadvantages:
(1) In the aspect of an intelligent prediction method, although the method has stronger self-learning capability, in the related technical scheme, parameters and the like of the adopted method are not optimized aiming at the characteristics of the air traffic flow, the correlation between the prediction method and the air traffic system is poor, so that the prediction precision and efficiency are poor, the inherent chaotic characteristic of the air traffic system is not considered, and the fitting to a nonlinear system is poor;
(2) In the prediction process based on the chaos theory, a relevant method is not specifically improved but directly applied, for example, a Cao method widely used in research has high subjectivity in parameter selection, cannot completely reflect the inherent characteristics of an air traffic system, and causes the instability of a prediction result.
Disclosure of Invention
In view of the technical problems pointed out in the background art, the present invention aims to provide a method and a system for air traffic flow chaos prediction, a storage medium, and a terminal.
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
first aspect
The invention provides an air traffic flow chaos prediction method, which comprises the following steps:
step 1: constructing an air traffic flow chaotic time sequence prediction model, wherein the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
step 2: calculating Lyapunov indexes of air traffic flow time sequences with different time scales, and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
and step 3: determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest point method;
and 4, step 4: performing phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the delay time and the embedding dimension determined in the step 3, wherein the dimension of the air traffic flow time sequence vector space after the phase space reconstruction is equal to the embedding dimension value determined in the step 3;
and 5: inputting the air traffic flow time sequence after the phase space reconstruction into the air traffic flow chaotic time sequence prediction model constructed in the step 1 for prediction; and determining the number of input layers in the air traffic flow chaotic time sequence prediction model as the embedding dimension value determined in the step 3, and determining the number of output layers as 1.
Second aspect of the invention
Corresponding to the method, the invention also provides an air traffic flow chaos prediction system, which comprises the following units: the device comprises an air traffic flow chaotic time sequence prediction model construction unit, an air traffic flow time sequence normalization processing unit, a phase space reconstruction parameter determination unit, a phase space reconstruction unit and a prediction unit;
the air traffic flow chaotic time sequence prediction model construction unit is used for constructing an air traffic flow chaotic time sequence prediction model, and the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
the air traffic flow time sequence normalization processing unit is used for calculating Lyapunov indexes of air traffic flow time sequences with different time scales and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
the phase space reconstruction parameter determining unit is used for determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest neighbor method;
the phase space reconstruction unit performs phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the delay time and the embedding dimension determined by the phase space reconstruction parameter determination unit, wherein the dimension of the vector space of the air traffic flow time sequence after the phase space reconstruction is equal to the embedding dimension value determined by the phase space reconstruction parameter determination unit;
the prediction unit inputs the air traffic flow time sequence after the phase space reconstruction into an air traffic flow chaotic time sequence prediction model for prediction; the number of input layers in the air traffic flow chaotic time sequence prediction model is determined as an embedded dimension value determined by the phase space reconstruction parameter determination unit, and the number of output layers is determined as 1.
Third aspect of the invention
Corresponding to the method, the invention also provides a storage medium, wherein at least one instruction, at least one program, a code set or an instruction set is stored in the storage medium, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by a processor to realize the air traffic flow chaos prediction method.
Fourth aspect of the invention
Corresponding to the method, the invention also provides a terminal, which comprises a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to realize the air traffic flow chaos prediction method.
Compared with the prior art, the invention has the beneficial effects that:
the model is verified through actual traffic flow data, and compared with a traditional method, the method has better prediction precision and prediction speed for the air traffic flow time sequence.
Drawings
Fig. 1 is a schematic flow chart of a method provided in an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present embodiment provides an air traffic flow chaos prediction method, which includes the following steps:
step 1: constructing an air traffic flow chaotic time sequence prediction model, wherein the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
the method for constructing the air traffic flow chaotic time sequence prediction model specifically comprises the following steps:
step 1.1: constructing a radial basis function neural network based on the chaotic characteristics;
wherein, the structure of the radial basis function neural network is as follows:
the 1 st layer is an input layer; the input layer transfers the input signal to the radial basis function neural network, wherein the air traffic flow time sequence
As an input vector to the network, a vector is generated,xis an air traffic flow time series value,Nthe time sequence is long for the air traffic flowDegree;
the 2 nd layer is a hidden layer; the radial basis function adopted by the hidden layer is a non-negative nonlinear function with a locally distributed center point radially symmetrical attenuation, and specifically adopts a Gaussian basis function, which is as follows:
in the formula,
；Mthe number of nodes in the hidden layer;Xinputting a vector for the network;
an output that is a hidden layer node;C i is the central vector of the Gaussian function;
is the Euclid norm of the vector;
is as followsiA normalization constant of each hidden node;
the 3 rd layer is an output layer;
is a linear mapping from the hidden layer to the output layer, as follows:
in the formula,yis the output of the output layer;
is the weighting coefficient between the hidden layer and the output layer;
is a hidden layer ofiThe output of each node;bis the threshold of the output layer.
Step 1.2: and optimizing the radial basis function neural network by using a genetic algorithm.
The method comprises the following steps of optimizing a radial basis function neural network by using a genetic algorithm, wherein the method specifically comprises the following steps:
step 1.2.1: by the central vector of the radial basis functionC i And weighting coefficients between the hidden layer and the output layer
And threshold value of output layerbInitializing population individuals in a real number coding mode for network parameters to be optimized;
step 1.2.2: calculating the fitness of the population individuals, taking the mean square error as the fitness function of the population individuals, and training the radial basis function neural network by using the neural network parameters obtained by the population individuals;
step 1.2.3: judging whether the trained radial basis function neural network reaches a preset precision or an evolutionary algebra preset value; if yes, taking the corresponding population individual as an optimal population individual, outputting the neural network parameters of the optimal population individual, and jumping to the step 1.2.5; if not, continuing iteration and jumping to the step 1.2.4;
step 1.2.4: firstly, selecting population individuals by adopting a roulette method, then, carrying out population individual crossing by utilizing an arithmetic crossing method, introducing a mutation operator, and carrying out population individual mutation by taking the mutation probability of 0.05; jumping to step 1.2.3;
step 1.2.5: taking the neural network parameters of the optimal population individuals as the parameters of the radial basis function neural network, and utilizing a new central vector generated by the optimal population individualsC i Weighting factor between hidden layer and output layer
And threshold value of output layerbAnd training to make the radial basis function neural network characteristics accord with the actual sector traffic operation characteristics.
And 2, step: calculating Lyapunov indexes of air traffic flow time sequences with different time scales, and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
and step 3: determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest point method;
the method for determining the value of the embedding dimension based on the improved Cao method of the false nearest neighbor method comprises the following steps:
step 3.1: for the
The amount of the backward reconstruction is as follows:
in the formula,
，jphase point number of backward vector space for phase space reconstruction;
taking values for the delay time;min order to find the embedding dimension value,mis an integer and
，
taking the value of embedded dimension after phase space reconstructionmOf vector space ofjA vector number;
step 3.2: definition of
For embedding the dimension value equal tomTime of flight
The nearest neighbor of the phase point in vector space is given by:
in the formula,
is corresponding to
The nearest neighbor of (a);
step 3.3: the following formula is defined:
wherein,
a maximum vector norm representing a metric of euclidean distance;
is composed ofmThe second of + 1-dimensional reconstruction phase spacejA vector number;
is that
In thatmThe first of + 1-dimensional reconstruction phase spacejThe nearest neighbor of the phase points;
is used for judging atmAny two points in the vicinity of the dimension reconstruction phase space aremWhether the +1 dimension reconstruction phase space is still adjacent or not, if so, the pair of points is a true adjacent point, otherwise, the pair of points is a false adjacent point, and the observation is made that
Judging whether the virtual adjacent point is larger than a limit value;
step 3.4: for the different points of the phase, it is,
have different limit values and different air traffic flow time series have different limit values, thereby giving an embedded dimension value which is not correlated with the air traffic flow time series datamMethod of determination, determiningDefined by the following equation:
wherein,
for all that is
Is determined by the average value of (a),
sum delay time value only
And embedding dimension valuem(ii) related;
represents from
To
Namely frommTomA degree of change of + 1;
step 3.5: adding a criterion for distinguishing between deterministic and stochastic signals, defining the following equation:
wherein,
the average value of the distances of all adjacent points;
to represent
To
Degree of change of (2) when always
When =1, the air traffic flow time sequence is a random signal, correspondingmThe embedded dimension value which is not an air traffic flow time sequence can be continuously iterated; since there is a correlation between data of deterministic air traffic flow time series, there must be
Is not equal to 1, therefore, when
While corresponding tomEmbedding dimension values of the air traffic flow time series;
step 3.6: increase stepwisemAnd repeatedly executing step 3.1, step 3.2, step 3.3, step 3.4 and step 3.5 when
When no longer changedmEmbedding dimension values of the air traffic flow time series;
step 3.7: introduction of
A step of determining whether no change is present, the iterative determination being dependent onmIncrease of (2)
Whether to stop changing, according to calculation in step 3.4
Is selected to an acceptable deviation levele；eThe value of (b) is determined according to the required accuracy,
；
step 3.8 calculation
Mean value of
Absolute value of sum deviation
As shown in the following formula;
wherein,kfor all in the cumulative calculation in step 3.4mThe value of (a) is,
；
i.e. eachkCorresponding tomIs/are as follows
A value of (i) iskAndmwhen corresponding to
；
Step 3.9: comparing absolute values of dispersion
Level of deviation from acceptableeSize; if it is
，
Is composed of
Is the first one satisfied
Corresponding tokDetermining the embedding dimension value; if it is not
，
Is composed of
Is the minimum value of
In
Corresponding subscriptuFor a new starting point, updatekIn the range of
；
Step 3.10: repeating the steps 3.7, 3.8 and 3.9 until the stepkSatisfy the acceptable deviation leveleAnd is made of
Is not equal to 1, and the ratio of the total weight of the components,
for each onekCorresponding to
At this timekI.e. the finally obtained embedding dimension valuem。
And 4, step 4: performing phase space reconstruction on the air traffic flow time sequence subjected to the normalization processing by using the delay time and the embedding dimension determined in the step 3, wherein the dimension of the air traffic flow time sequence vector space after the phase space reconstruction is equal to the embedding dimension value determined in the step 3;
and 5: inputting the air traffic flow time sequence after the phase space reconstruction into the air traffic flow chaotic time sequence prediction model constructed in the step 1 for prediction; and determining the number of input layers in the air traffic flow chaotic time sequence prediction model as the embedding dimension value determined in the step 3, and determining the number of output layers as 1.
According to the inherent chaotic characteristics of the air traffic flow time sequence, an air traffic flow chaotic time sequence prediction model with a genetic algorithm coupled with a radial basis function neural network is established. The method adopts an improved Cao method based on iterative optimization of false nearest point dispersion and acceptable deviation, corrects the problem of subjective errors in the Cao method by introducing an embedding dimension stability criterion, and obtains a more accurate embedding dimension of a traffic time sequence, so that the reconstructed phase space can better reflect the internal characteristics of an air traffic system. On the basis of reconstructing a phase space of a time sequence, aiming at the defects of unstable prediction effect and parameter error of a radial basis function neural network, a method for predicting a chaotic time sequence by the radial basis function neural network of a coupled genetic algorithm is provided. The central vector, the weighting coefficient and the output layer threshold value of the radial basis function neural network are optimized by using a genetic algorithm, the defect that the neural network is sensitive to an initial value is overcome, then the neural network is trained by using the optimal coefficient searched by a solution space, chaos is combined with the neural network, and the fitting performance of a prediction model to a nonlinear system is improved. Taking 5min time interval as an example, compared with a long-short term memory neural network and a traditional radial basis function neural network, the average absolute error, the symmetric average absolute percentage error and the root mean square error of the provided prediction model are respectively reduced by 17.88%, 6.25% and 21.47% and the running speed is improved by 14.46%.
Corresponding to the method, the embodiment also provides an air traffic flow chaos prediction system, which comprises the following units: the device comprises an air traffic flow chaotic time sequence prediction model construction unit, an air traffic flow time sequence normalization processing unit, a phase space reconstruction parameter determination unit, a phase space reconstruction unit and a prediction unit;
the air traffic flow chaotic time sequence prediction model construction unit is used for constructing an air traffic flow chaotic time sequence prediction model, and the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
the method for constructing the air traffic flow chaotic time sequence prediction model specifically comprises the following steps:
step 1.1: constructing a radial basis function neural network based on the chaotic characteristic;
the structure of the radial basis function neural network is as follows:
the 1 st layer is an input layer; the input layer transfers the input signal to the radial basis function neural network, wherein the air traffic flow time sequence
As an input vector to the network, a vector is generated,xis an air traffic flow time series value,Nis the length of the air traffic flow time series;
the 2 nd layer is a hidden layer; the radial basis function adopted by the hidden layer is a non-negative nonlinear function with a locally distributed center point radially symmetrical attenuation, and specifically adopts a Gaussian basis function, which is as follows:
in the formula,
；Mthe number of nodes of the hidden layer is shown;Xinputting a vector for the network;
an output that is a hidden layer node;C i is the central vector of the Gaussian function;
is the Euclid norm of the vector;
is a firstiNormalized constants of the hidden nodes;
the 3 rd layer is an output layer;
is a linear mapping from the hidden layer to the output layer as follows:
in the formula,yis the output of the output layer;
is the weighting factor between the hidden layer and the output layer;
is a hidden layer ofiThe output of each node;bis the threshold of the output layer.
Step 1.2: and optimizing the radial basis function neural network by using a genetic algorithm. The method comprises the following specific steps:
step 1.2.1: by the central vector of the radial basis functionC i And weighting coefficients between the hidden layer and the output layer
And threshold value of output layerbInitializing population individuals in a real number coding mode for network parameters to be optimized;
step 1.2.2: calculating population individual fitness, taking the mean square error as a fitness function of the population individuals, and training a radial basis function neural network by using neural network parameters obtained by the population individuals;
step 1.2.3: judging whether the trained radial basis function neural network reaches a preset precision or an evolutionary algebra preset value; if yes, taking the corresponding population individual as an optimal population individual, outputting the neural network parameters of the optimal population individual, and jumping to the step 1.2.5; if not, continuing iteration and jumping to the step 1.2.4;
step 1.2.4: firstly, selecting population individuals by adopting a roulette method, then, carrying out population individual crossing by utilizing an arithmetic crossing method, introducing a mutation operator, and carrying out population individual mutation, wherein the mutation probability is 0.05; jumping to step 1.2.3;
step 1.2.5: taking the neural network parameters of the optimal population individuals as the parameters of the radial basis function neural network, and utilizing a new central vector generated by the optimal population individualsC i Between the hidden layer and the output layerWeighting factor
And threshold value of output layerbAnd training to make the radial basis function neural network characteristics accord with the actual sector traffic operation characteristics.
The air traffic flow time sequence normalization processing unit is used for calculating Lyapunov indexes of air traffic flow time sequences with different time scales and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
the phase space reconstruction parameter determining unit is used for determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest neighbor method;
the method for determining the value of the embedding dimension based on the improved Cao method of the false nearest neighbor method comprises the following steps:
step 3.1: for the
The amount of the backward reconstruction is as follows:
in the formula,
，jphase point number of the backward vector space for phase space reconstruction;
taking values for the delay time;min order to find the embedding dimension value,mis an integer and
，
taking the value of embedded dimension after phase space reconstructionmOf vector space ofjA vector number;
step 3.2: definition of
For embedding the dimension value equal tomTime of flight
The nearest neighbor of the phase point in vector space is given by:
in the formula,
is corresponding to
The nearest neighbor of (a);
step 3.3: the following formula is defined:
wherein,
a maximum vector norm representing a metric of euclidean distance;
is composed ofmOf + 1D reconstruction phase spacejA vector number;
is that
In thatmThe second of + 1-dimensional reconstruction phase spacejThe nearest neighbor of the phase points;
is used for judging atmAny two points adjacent in the dimension reconstruction phase space aremWhether the + 1-dimensional reconstruction phase space is still adjacent, if so, thisA pair of points is a true neighbor, otherwise a false neighbor, by observing
Judging whether the virtual adjacent point is larger than a limit value;
step 3.4: for the different points of the phase, it is,
have different limit values and different air traffic flow time series have different limit values, thereby giving an embedded dimension value which is not correlated with the air traffic flow time series datamThe following formula is defined:
wherein,
for all that is
Is determined by the average value of (a),
sum delay time value only
And embedding dimension valuemRelated to;
represents from
To
Namely frommTomA degree of change of + 1;
step 3.5: adding a criterion for distinguishing between deterministic and stochastic signals, defining the following equation:
wherein,
the average value of the distances of all adjacent points;
to represent
To
Degree of change of (2) when always
When =1, the air traffic flow time sequence is a random signal, correspondingmThe embedded dimension value which is not the air traffic flow time sequence can be continuously iterated; since there is a correlation between data of deterministic air traffic flow time series, there must be
Is not equal to 1, therefore, when
While corresponding tomEmbedding dimension values for the air traffic flow time series;
step 3.6: increase stepwisemAnd repeatedly executing step 3.1, step 3.2, step 3.3, step 3.4 and step 3.5 when
When no longer changedmEmbedding dimension values of the air traffic flow time series;
step 3.7: introduction of
A step of determining whether no change is detected, the iterative determination being based onmIncrease in
Whether to stop changing, according to calculation in step 3.4
Is selected to an acceptable deviation levele；eThe value of (b) is determined according to the required accuracy,
；
step 3.8 calculation
Mean value of
Absolute value of sum deviation
As shown in the following formula;
wherein,kfor all in the cumulative calculation in step 3.4mThe value of (a) is,
；
i.e. eachkCorresponding tomIs/are as follows
A value of (a), i.e. whenkAnd withmWhen corresponding to
；
Step 3.9: comparing absolute values of dispersion
Level of deviation from acceptableeSize; if it is
，
Is composed of
Is the first one satisfied
Corresponding tokDetermining the embedding dimension value; if it is used
，
Is composed of
Is the minimum value of
In
Corresponding subscriptuFor a new starting point, updatekIn the range of
；
Step 3.10: step 3.7, step 3.8 and step 3.9 are repeatedly executed until the stepkSatisfy the acceptable deviation leveleAnd is and
is not equal to 1, and is,
for each onekCorresponding to
At this time ofkI.e. the finally obtained embedding dimension valuem。
The phase space reconstruction unit performs phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the delay time and the embedding dimension determined by the phase space reconstruction parameter determination unit, wherein the dimension of the vector space of the air traffic flow time sequence after the phase space reconstruction is equal to the embedding dimension value determined by the phase space reconstruction parameter determination unit;
the prediction unit inputs the air traffic flow time sequence after the phase space reconstruction into an air traffic flow chaotic time sequence prediction model for prediction; the number of input layers in the air traffic flow chaotic time sequence prediction model is determined as an embedded dimension value determined by the phase space reconstruction parameter determination unit, and the number of output layers is determined as 1.
In addition, the present embodiment also provides a storage medium, where at least one instruction, at least one program, a code set, or an instruction set is stored in the storage medium, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the air traffic flow chaos prediction method as described above.
In addition, the present embodiment also provides a terminal, which includes a processor and a memory, where the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the air traffic flow chaos prediction method as described above.
The terminal is a PC and other terminal equipment with a data processing function.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. The air traffic flow chaos prediction method is characterized by comprising the following steps of:
step 1: constructing an air traffic flow chaotic time sequence prediction model, wherein the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
and 2, step: calculating Lyapunov indexes of air traffic flow time sequences with different time scales, and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
and 3, step 3: determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after the normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest neighbor method;
and 4, step 4: performing phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the delay time and the embedding dimension determined in the step 3, wherein the dimension of the air traffic flow time sequence vector space after the phase space reconstruction is equal to the embedding dimension value determined in the step 3;
and 5: inputting the air traffic flow time sequence after the phase space reconstruction into the air traffic flow chaotic time sequence prediction model constructed in the step 1 for prediction; and determining the number of input layers in the air traffic flow chaotic time sequence prediction model as the embedding dimension value determined in the step 3, and determining the number of output layers as 1.
2. The air traffic flow chaos prediction method according to claim 1, wherein in step 1, the air traffic flow chaos time sequence prediction model is constructed as follows:
step 1.1: constructing a radial basis function neural network based on the chaotic characteristic;
step 1.2: and optimizing the radial basis function neural network by using a genetic algorithm.
3. The air traffic flow chaos prediction method according to claim 2, wherein in step 1.1, the radial basis function neural network has the following structure:
the 1 st layer is an input layer; the input layer transfers the input signal to the radial basis function neural network, wherein the air traffic flow time sequence
As an input vector to the network, a vector is generated,xis an air traffic flow time series value,Nis the length of the air traffic flow time series;
the 2 nd layer is a hidden layer; the radial basis function adopted by the hidden layer is a non-negative nonlinear function with a locally distributed center point radially symmetrical attenuation, and specifically adopts a Gaussian basis function, which is as follows:
in the formula,
；Mthe number of nodes of the hidden layer is shown;Xinputting a vector for the network;
an output that is a hidden layer node;C i is the central vector of the Gaussian function;
is the Euclid norm of the vector;
is as followsiNormalized constants of the hidden nodes;
the 3 rd layer is an output layer;
is a linear mapping from the hidden layer to the output layer as follows:
in the formula,yis the output of the output layer;
is the weighting coefficient between the hidden layer and the output layer;
is a hidden layer ofiThe output of each node;bis the threshold of the output layer.
4. The air traffic flow chaos prediction method according to claim 3, characterized in that in step 1.2, the radial basis function neural network is optimized by using a genetic algorithm, specifically as follows:
step 1.2.1: by the central vector of the radial basis functionC i And weighting coefficients between the hidden layer and the output layer
And threshold value of output layerbInitializing population individuals in a real number coding mode for network parameters to be optimized;
step 1.2.2: calculating the fitness of the population individuals, taking the mean square error as the fitness function of the population individuals, and training the radial basis function neural network by using the neural network parameters obtained by the population individuals;
step 1.2.3: judging whether the trained radial basis function neural network reaches a preset precision or an evolution algebra preset value; if yes, taking the corresponding population individual as an optimal population individual, outputting the neural network parameters of the optimal population individual, and jumping to the step 1.2.5; if not, continuing iteration and jumping to the step 1.2.4;
step 1.2.4: firstly, selecting population individuals by adopting a roulette method, then, carrying out population individual crossing by utilizing an arithmetic crossing method, introducing a mutation operator, and carrying out population individual mutation by taking the mutation probability of 0.05; jumping to step 1.2.3;
step 1.2.5: taking the neural network parameters of the optimal population individuals as the parameters of the radial basis function neural network, and utilizing a new central vector generated by the optimal population individualsC i Weighting factor between hidden layer and output layer
And threshold value of output layerbAnd training to enable the radial basis function neural network characteristics to accord with the actual sector traffic operation characteristics.
5. The air traffic flow chaos prediction system is characterized by comprising the following units: the device comprises an air traffic flow chaotic time sequence prediction model construction unit, an air traffic flow time sequence normalization processing unit, a phase space reconstruction parameter determination unit, a phase space reconstruction unit and a prediction unit;
the air traffic flow chaotic time sequence prediction model construction unit is used for constructing an air traffic flow chaotic time sequence prediction model, and the air traffic flow chaotic time sequence prediction model is a radial basis function neural network optimized by utilizing a genetic algorithm;
the air traffic flow time sequence normalization processing unit is used for calculating Lyapunov indexes of air traffic flow time sequences with different time scales and judging whether the air traffic flow has chaotic characteristics or not according to the Lyapunov indexes; if so, carrying out normalization processing on the air traffic flow time sequence;
the phase space reconstruction parameter determining unit is used for determining phase space reconstruction parameter delay time and an embedding dimension according to the air traffic flow time sequence after normalization processing, wherein the value of the embedding dimension is determined by using an improved Cao method based on a false nearest neighbor method;
the phase space reconstruction unit performs phase space reconstruction on the air traffic flow time sequence after the normalization processing by using the delay time and the embedding dimension determined by the phase space reconstruction parameter determination unit, wherein the dimension of the vector space of the air traffic flow time sequence after the phase space reconstruction is equal to the embedding dimension value determined by the phase space reconstruction parameter determination unit;
the prediction unit inputs the air traffic flow time sequence after the phase space reconstruction into an air traffic flow chaotic time sequence prediction model for prediction; the number of input layers in the air traffic flow chaotic time sequence prediction model is determined as an embedded dimension value determined by the phase space reconstruction parameter determination unit, and the number of output layers is determined as 1.
6. The chaotic prediction system for air traffic flow according to claim 5, wherein the chaotic time series prediction model for air traffic flow is constructed as follows:
step 1.1: constructing a radial basis function neural network based on the chaotic characteristics;
step 1.2: and optimizing the radial basis function neural network by using a genetic algorithm.
7. The chaotic air traffic flow prediction system according to claim 6, wherein the radial basis function neural network has a structure as follows:
the 1 st layer is an input layer; the input layer transfers the input signal to the radial basis function neural network, wherein the air traffic flow time sequence
As an input vector to the network, a vector is generated,xis an air traffic flow time series value,Nis the length of the air traffic flow time series;
the 2 nd layer is a hidden layer; the radial basis function adopted by the hidden layer is a non-negative nonlinear function with a locally distributed center point radially symmetrical attenuation, and specifically adopts a Gaussian basis function, which is as follows:
in the formula,
；Mthe number of nodes in the hidden layer;Xinputting a vector for the network;
an output that is a hidden layer node;C i is the central vector of the Gaussian function;
is the Euclid norm of the vector;
is as followsiNormalized constants of the hidden nodes;
the 3 rd layer is an output layer;
is a linear mapping from the hidden layer to the output layer, as follows:
in the formula,yis the output of the output layer;
is the weighting factor between the hidden layer and the output layer;
is a hidden layer ofiThe output of each node;bis the threshold of the output layer.
8. The chaotic prediction system for air traffic flow according to claim 6, wherein a genetic algorithm is used to optimize the neural network of radial basis functions, specifically as follows:
step 1.2.1: by radial basis functionsCentral vector of (2)C i And weighting coefficients between the hidden layer and the output layer
And threshold value of output layerbInitializing population individuals for network parameters to be optimized by adopting a real number coding mode;
step 1.2.2: calculating the fitness of the population individuals, taking the mean square error as the fitness function of the population individuals, and training the radial basis function neural network by using the neural network parameters obtained by the population individuals;
step 1.2.3: judging whether the trained radial basis function neural network reaches a preset precision or an evolutionary algebra preset value; if so, taking the corresponding population individual as an optimal population individual, outputting the neural network parameter of the optimal population individual, and jumping to the step 1.2.5; if not, continuing iteration and jumping to the step 1.2.4;
step 1.2.4: firstly, selecting population individuals by adopting a roulette method, then, carrying out population individual crossing by utilizing an arithmetic crossing method, introducing a mutation operator, and carrying out population individual mutation by taking the mutation probability of 0.05; jumping to step 1.2.3;
step 1.2.5: taking the neural network parameters of the optimal population individuals as the parameters of the radial basis function neural network, and utilizing a new central vector generated by the optimal population individualsC i Weighting factor between the hidden layer and the output layer
And threshold value of output layerbAnd training to enable the radial basis function neural network characteristics to accord with the actual sector traffic operation characteristics.
9. A storage medium having stored therein at least one instruction, at least one program, set of codes, or set of instructions, which is loaded and executed by a processor to implement the air traffic flow chaos prediction method according to any one of claims 1-4.
10. A terminal, comprising a processor and a memory having stored therein at least one instruction, at least one program, set of codes, or set of instructions, which is loaded and executed by the processor to implement the method of chaotic prediction of air traffic flow according to any one of claims 1 to 4.
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