Hybrid aeronautical prediction method based on owa operator

Abstract

The application provides a hybrid aviation prediction method based on an OWA operator, acquires an aviation passenger data set, and decomposes the aviation passenger data set into a linear component and a nonlinear residual sequence; the linear component is pretreated to generate a linear component sequence, and a historical sequence in the linear component sequence is defined as an OWA mean of a current sequence in the linear component sequence; a historical random error sequence is calculated based on an ARIMA-OWA model; the historical linear component sequence and the historical random error sequence are substituted into the ARIMA-OWA model to obtain a predicted linear variable; a plurality of data are selected from time sequence data as a first time sequence; a plurality of data are selected from the nonlinear residual sequence as a second time sequence; and the first time sequence, the second time sequence and the predicted linear variable are input into an ANN network to obtain a hybrid prediction result of the time sequence. Compared with an existing time sequence prediction method, the application has better prediction performance.

Description

TECHNICAL FIELD

[0001] The application relates to the field of time series analysis, in particular to a hybrid aviation prediction method based on an OWA operator. BACKGROUND

[0002] An ARIMA (Autoregressive integrated moving average) model has become the most commonly used model tool in the field of time series analysis and is widely used in the fields of environment, health care, finance and the like. In order to improve the accuracy of prediction, researchers have proposed a large number of hybrid time prediction methods in recent years, one of which is a hybrid model of ARIMA and neural network (ANN), which improves the accuracy of ARIMA prediction.

[0003] At present, a hybrid prediction model of time series based on an OWA operator has been widely used in data fusion, risk assessment and intelligent decision-making. The hybrid model adopts an operation method of mean, variance and covariance based on OWA for calculating coefficients in a prediction model equation. However, the accuracy of the ARIMA model prediction still needs to be improved, but there is a lack of effective method, and therefore it is an urgent problem to be solved at present. SUMMARY

[0004] In view of the above situation, the main purpose of the application is to provide a hybrid aviation prediction method based on an OWA operator to solve the above technical problems.

[0005] The application provides a hybrid model of time series based on an OWA operator, which uses an OWA operator to perform weighted processing on time series data and calculates autocorrelation coefficients based on OWA.

[0006] Given an autoregressive order and a moving average order, a corresponding number of autocorrelation coefficients based on OWA are obtained according to the autoregressive order and the moving average order, parameter estimation is performed by using a moment estimation method, autoregressive parameters based on OWA and moving average parameters based on OWA are obtained.

[0007] Based on the ARIMA model, the ARIMA model parameters are replaced by the autoregressive parameters based on OWA and the moving average parameters based on OWA, and an ARIMA-OWA model is obtained.

[0008] The maximum lag order is set, the final autoregressive order, moving average order and difference order of the ARIMA-OWA model are determined by using a loop traversal method, and the autoregressive parameters based on OWA and the moving average parameters based on OWA are dynamically adjusted according to the autoregressive order and the moving average order in each loop traversal process. After the loop traversal is completed, the final ARIMA-OWA model is obtained.

[0009] The application also provides a hybrid aviation prediction method based on an OWA operator, which adopts the hybrid time series model based on the OWA operator, and comprises the following steps:

[0010] Step 1: obtaining an aviation passenger data set, and decomposing the aviation passenger data set by using an MA filter to obtain a linear component and a nonlinear residual sequence;

[0011] Step 2: preprocessing the linear component to generate a linear component sequence, and defining a historical sequence in the linear component sequence as an OWA mean of a current sequence in the linear component sequence;

[0012] Step 3: transforming the ARIMA-OWA model according to the core assumption of the ARIMA model to obtain a transformed model; initializing the historical error of the transformed model, and then substituting the linear component sequence to calculate a historical random error sequence;

[0013] Step 4: substituting the historical linear component sequence and the historical random error sequence into the ARIMA-OWA model to obtain a predicted linear variable;

[0014] Step 5: selecting a plurality of data from the time series data as a first time series;

[0015] selecting a plurality of data from the nonlinear residual sequence as a second time series;

[0016] substituting the first time series, the second time series and the predicted linear variable into an ANN network to obtain a hybrid prediction result of the time series.

[0017] Compared with the prior art, the application has the following beneficial effects:

[0018] 1. Inspired by variance, covariance, autocorrelation coefficient and partial correlation coefficient, ACF-OWA and PACF-OWA coefficients are proposed. The proposed ACF-OWA and PACF-OWA can better capture and extract complex characteristics in time series data, and obtain a more stable time series data that meets the assumption of the ARIMA model.

[0019] 2. On the basis of ACF-OWA and PACF-OWA, an ARIMA model is reconstructed to obtain an ARIMA-OWA model, and the performance of the constructed ARIMA-OWA model is better than that of the ARIMA model. The ARIMA-OWA enhances the dependency between time series data at different time points and improves the ability of the model to process data stability, so that the model can better capture the long-term trend changes and linear relationships between data, thereby improving the accuracy and stability of the model prediction.

[0020] 3. On the basis of ARIMA-OWA, inspired by ARIMA-ANN, a time series prediction method is proposed. The application fully considers the stationarity of data and the strong dependence between data, and solves these problems through innovative methods, creating a model with high universality and flexibility, and having obvious advantages compared with other methods in the field.

[0021] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The construction flow chart of the time series hybrid model based on the OWA operator proposed by the application;

[0023] Figure 2 The algorithm flow chart of the hybrid aviation prediction method based on the OWA operator proposed by the application;

[0024] Figure 3 The autocorrelation and partial autocorrelation coefficient diagram for each data set;

[0025] Figure 4 The time series line graph of the sunspot data set;

[0026] Figure 5 The actual value and predicted value comparison graph of the 8 time series prediction methods on the sunspot data set;

[0027] Figure 6 The time series line graph of the lynx data set;

[0028] Figure 7 The actual value and predicted value comparison graph of the 8 time series prediction methods on the lynx data set;

[0029] Figure 8 The time series line graph of the aviation passenger data set;

[0030] Figure 9 The actual value and predicted value comparison graph of the 8 time series prediction methods on the aviation passenger data set;

[0031] Figure 10 The time series line graph of the star brightness data set;

[0032] Figure 11 The actual value and predicted value comparison graph of the 8 time series prediction methods on the star brightness data set;

[0033] Figure 12 The time series line graph of the exchange rate data set;

[0034] Figure 13 Figure 8 is a bar chart of the average MAE, MSE, MASE of 8 time series prediction methods on 5 data sets.

[0035] Figure 14 Figure 8 is a bar chart of the average MAE, MSE, MASE of 8 time series prediction methods on 5 data sets. DETAILED DESCRIPTION

[0036] Embodiments of the present application are described below by way of example with reference to the accompanying drawings, in which like or similar elements and / or features are identified by the same or similar reference signs, and of which: - Figure 1 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 2 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 3 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 4 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 5 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 6 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 7 shows a schematic diagram of a time series prediction method according to an embodiment of the present application; - Figure 8 shows a bar chart of the average MAE, MSE, MASE of 8 time series prediction methods on 5 data sets.

[0037] These and other aspects of embodiments of the present application will be apparent from and elucidated with reference to the following description and accompanying drawings. In these drawings, show some specific embodiments of embodiments of the present application are specifically disclosed, to represent some ways of implementing principles of embodiments of the present application, but it should be understood that the scope of embodiments of the present application is not limited thereto.

[0038] Referring to Figure 1 The present embodiments provide a time series hybrid model based on an OWA (Ordered Weighted Averaging) operator:

[0039] Step 1, using the OWA operator to weight the time series data, calculating the OWA-based autocorrelation coefficient;

[0040] Step 2, given the autoregressive order and the moving average order, and according to the autoregressive order and the moving average order, a corresponding number of OWA-based autocorrelation coefficients are obtained, and the parameter estimation method is used for parameter estimation, to obtain the OWA-based autoregressive parameter and the OWA-based moving average parameter;

[0041] Step 3, based on the ARIMA model, replacing the ARIMA model parameters with the OWA-based autoregressive parameters and the OWA-based moving average parameters to obtain the ARIMA-OWA model;

[0042] Step 4, setting the maximum lag order, using a loop traversal method to determine the final autoregressive order, moving average order and difference order of the ARIMA-OWA model, and dynamically adjusting the OWA-based autoregressive parameters and the OWA-based moving average parameters according to the autoregressive order and the moving average order in each loop traversal process, and after the loop traversal is completed, the final ARIMA-OWA model is obtained.

[0043] In a preferred embodiment of the present invention, the process of using the OWA operator to weight time series data and calculating the autocorrelation coefficient based on OWA follows the following relationship:

[0044] Equation (14)

[0045] in, This represents the autocorrelation coefficient based on OWA. Represents the first in time series data t The weight vector corresponding to the largest numbers Represents the first in time series data t One element, This indicates the number of elements in the time series. Indicates time interval, This represents the covariance based on OWA. Indicates the variance based on OWA. The OWA mean of time series data. These represent the order of autoregression and the order of moving average, respectively.

[0046] The calculation process for the mean of OWA follows the following formula:

[0047] ;

[0048] in, Represents the first in time series data n One element, Represents the OWA operator. Represents the first in time series data i The weight vector corresponding to the largest numbers Represents the first in time series data i A large number;

[0049] The first in time series data i The calculation process for the weight vectors corresponding to the large numbers follows the following formula:

[0050] ;

[0051] in, Let A and B represent the mean and standard deviation of time series data, respectively. The calculation process for the mean and standard deviation of time series data follows the following relationship:

[0052] .

[0053] In a preferred embodiment of the present invention, given the autoregressive order and the moving average order, and obtaining a corresponding number of OWA-based autocorrelation coefficients based on the autoregressive order and the moving average order, parameter estimation is performed using the method of moments to obtain the OWA-based autoregressive parameters and the OWA-based moving average parameters. Specifically, the process includes the following steps:

[0054] Given the order of the autoregression and the order of the moving average, a corresponding number of OWA-based autocorrelation coefficients are obtained based on the order of the autoregression and the moving average to construct the Yule-Walker equation. The Yule-Walker equation is then used to estimate the OWA-based autoregressive parameters. The corresponding process has the following relationship:

[0055] Equation (15)

[0056] in, This represents the p-th OWA-based autoregressive coefficient. Let represent the (q+p+2)th OWA-based autocorrelation coefficient;

[0057] The moving average parameters based on OWA are calculated based on the obtained autoregressive parameters based on OWA and the moving average order.

[0058] When the moving average order is 0, the moving average parameters based on OWA are calculated using the first relational expression, which is as follows:

[0059] ;

[0060] in, This indicates that the moving average coefficient based on OWA is 0;

[0061] When the moving average order is greater than or equal to 1, the moving average parameters based on OWA are calculated using the second relation, which is as follows:

[0062] Equation (16)

[0063] in, Indicates the first i One OWA-based moving average coefficient, This represents the estimated value of the covariance based on OWA. The OWA covariance represents the error vector. The variance of the error is represented as follows: When the autoregression order is 0, the variance of the error is calculated as follows:

[0064] ;

[0065] in, an estimated value of the OWA covariance of the error vector, ;

[0066] The OWA covariance calculation process of the error vector has the following relationship:

[0067] ; equation (17)

[0068] wherein, represents a random error.

[0069] In the preferred embodiment provided by the present application, the second relationship is solved by using a linear iterative method, and specifically includes the following steps:

[0070] Given a set of initial values and , ;

[0071] An iterative condition about the variance of the OWA-based moving average parameter and the error is set, and the iterative condition includes a first precision of a positive real number and a second precision of a positive real number ;

[0072] The initial values , are substituted into the second relationship for iterative solution until is simultaneously satisfied, the iteration is terminated, is the iteration number, and the last output result is taken as the solution of and .

[0073] In the preferred embodiment provided by the present application, based on the ARIMA model, the ARIMA model parameters are replaced by the OWA-based autoregressive parameters and the OWA-based moving average parameters to obtain an ARIMA-OWA model, and the corresponding process has the following relationship:

[0074] ;

[0075] wherein, represents the first OWA-based autoregressive coefficient, represents the time series data with a lag of p order, represents the error value with a lag of q order, represents the q th OWA-based moving average coefficient.

[0076] Please refer to Figure 2 ​This embodiment provides a hybrid aviation forecasting method based on the OWA operator. The method adopts the aforementioned time series hybrid model based on the OWA operator and includes the following steps:

[0077] Step 1: Obtain the airline passenger dataset and decompose it using an MA filter to obtain linear components and nonlinear residual sequences;

[0078] Step 2: Preprocess the linear components to generate a linear component sequence, and define the historical sequence in the linear component sequence as the OWA mean of the current sequence in the linear component sequence;

[0079] Step 3: Transform the ARIMA-OWA model according to the core assumptions of the ARIMA model to obtain the transformed model; initialize the historical error of the transformed model, and then substitute the linear component sequence to calculate the historical random error sequence.

[0080] Step 4: Substitute the historical linear component sequence and the historical random error sequence into the ARIMA-OWA model to obtain the predicted linear variables;

[0081] Step 5: Select several data points from the time series data as the first time series;

[0082] Select some data from the nonlinear residual sequence as a second time series;

[0083] The first time series, the second time series, and the predicted linear variable are fed into the ANN network to obtain the mixed prediction results of the time series.

[0084] In a preferred embodiment of the present invention, the process of decomposing time series data using an MA filter to obtain linear components and nonlinear residual sequences has the following relationship:

[0085] ;

[0086] ;

[0087] in, Indicates the first t The linear components of each element, Indicates the filter length. Represents a nonlinear residual sequence. Represents the first in time series data i One element, Indicates the first t Each element.

[0088] In the preferred embodiments provided by the present application, the ARIMA-OWA model is transformed according to the core assumption of the ARIMA model to obtain a transformed model; the historical error of the transformed model is initialized, and then the linear component sequence is substituted to calculate the corresponding process of the historical random error sequence, and the following relationship exists:

[0089] ;

[0090] wherein, represents the normalized linear component of the lag p order, represents the normalized linear component of the t element.

[0091] In the preferred embodiments provided by the present application, the historical linear component sequence and the historical random error sequence are substituted into the ARIMA-OWA model to obtain the corresponding process of the predicted linear variable, and the following relationship exists:

[0092] ;

[0093] wherein, represents the predicted linear variable, represents the ARIMA-OWA model.

[0094] In the preferred embodiments provided by the present application, the first time sequence, the second time sequence and the predicted linear variable are input into the ANN network to obtain the corresponding process of the hybrid prediction result of the time sequence, and the following relationship exists:

[0095] ;

[0096] wherein, respectively represent the length of the selected data in the second time sequence data and the nonlinear residual sequence, represents the first time sequence, represents the second time sequence, represents the nonlinear function of the neural network, represents the time sequence data, represents the nonlinear residual sequence.

[0097] The model of Example 1 below is denoted as ARIMA-OWA, and the method of Example 2 is denoted as ARIMA-OWA-ANN. In order to verify the performance of the present application, the mean absolute error (MAE), the root mean square error (MSE) and the mean absolute percentage error (MASE) indexes are used to evaluate the advantages and disadvantages of different models, and the evaluation indexes are shown in the following formula:

[0098] ;

[0099] ;

[0100] ;

[0101] where, denotes the mean absolute error, denotes the root mean square error, denotes the mean absolute percentage error.

[0102] The following will use five time series datasets as the basis for experiments, among which the Wolf Sunspot Dataset and the Canadian Lynx Dataset are widely used in statistical and neural network literature. The other three are: Airline Passengers Dataset and Stellar Brightness Dataset and USD / MXN exchange rate dataset, which are from different application fields and are also commonly used as basic datasets for time series prediction. A brief overview of the five datasets is given below:

[0103] (1) The Wolf Sunspot Dataset records the number of sunspots observed each month from 1700 to 1987, with a total of 288 observations (as shown in Figure 4 Researchers often use the sunspot dataset to study the relationship between solar activity and various phenomena on Earth, such as climate relationships, Earth disturbances, and radio wave propagation.

[0104] (2) The Canadian Lynx Dataset contains the number of lynx captured each year in the Mackenzie River region of northern Canada. The observation data from 1821 to 1934 is recorded, with a period of about 10 years, and a total of 114 observations (as shown in Figure 6 ).

[0105] (3) The Airline Passengers Dataset corresponds to the number of international airline passengers per month (in thousands), including data from January 1949 to December 1960 (as shown in Figure 8 ), with a data size of 144 months.

[0106] (4) The Stellar Brightness Dataset (as shown in Figure 10 ) contains daily stellar brightness observation data at the same location and at the same time (possibly the same time every day), with a total of 600 observations.

[0107] (5) The exchange rate dataset contains daily fixed exchange rate data of US Dollar against Mexican Peso (USD / MXN) from August 2017 to October 2019, and is presented in the form of monthly arithmetic mean, with a total of 27 monthly arithmetic means as observation data (as shown in Figure 12 ).

[0108] During the experiment, in order to evaluate the performance of different time series prediction models, each dataset is divided into training set and test set. The training data is used to train the model, and the test data is used to evaluate the performance of the trained model. In order to adjust the hyperparameters, 20% of the training data is selected as the validation set, so as to adjust and evaluate in real time during the model training process.

[0109] The ACF-OWA and PACF-OWA coefficients of the given 5 datasets are shown in Figure 3 , and it can be seen from Figure 3 that: after joining the OWA operator, most of the positive values in the autocorrelation and partial autocorrelation coefficients of each dataset are larger, the positive correlation is enhanced, and the negative values are smaller, the negative correlation is weakened, and compared with the ARIMA model, the ARIMA-OWA model has stronger dependence between different time points on the 5 time series datasets.

[0110] The variances of the error terms of ARIMA and ARIMA-OWA on the 5 datasets can be calculated, and the calculation results are shown in Table 1.

[0111] Table 1, Error Variance Table of Each Dataset

[0112]

[0113] From Table 1, it can be seen that the error variance of ARIMA-OWA method is smaller than that of ARIMA method on the given 5 datasets, which shows that using ARIMA-OWA to calculate time series data, the result is more relatively stable than ARIMA, so that more favorable linear part data prediction can be obtained. The ARIMA-OWA-ANN proposed in the present application uses the ARIMA-OWA method to obtain prediction data, compared with the ARIMA-ANN prediction model proposed by Buyuksahin and Ertekin, the ARIMA-OWA-ANN proposed in the present application improves the stability of ARIMA.

[0114] On the five data sets given above, ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, Buyuksahin-Ertekin and ARIMA-OWA-ANN time series prediction models are used for experiments respectively. In the experiment process, when solving the most suitable ARIMA model parameters, the maximum lag order is set to 20, and then the simplest ARIMA model parameters are solved by circulation. In addition, since there is no universally accepted ANN network parameter selection method, the ANN network parameters are adjusted by experience method in the embodiment. Then the Adam optimization algorithm is used to train the neural network, and a suitable learning rate (lr) is initialized, which determines the update speed when the model is initialized. In the ANN learning process, the weight will be modified in the iteration process until the value of the L1 loss function is minimum. In order to prevent the iteration from entering a dead loop and acceptable time efficiency, the number of iterations is set to 500 in the implementation process, that is, the number of epochs is 500. The transfer function used in the hidden layer of the ANN network is LeakReLU. In the implementation process, the MAE, MSE and MASE index performances of them are compared and analyzed, and it can be seen from Table 2 that the MAE, MSE and MASE index performances of ARIMA-OWA are better than those of ARIMA, and the MAE, MSE and MASE index performances of ARIMA-OWA-ANN are better than those of ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, Buyuksahin-Ertekin, so the ARIMA-OWA-ANN proposed in the embodiment has the optimal performance. The performance comparison of all data sets is shown in Table 2.

[0115] Table 2, performance comparison of all data sets

[0116]

[0117] The sunspot data set has 288 observation data (as shown in Figure 4 , which is considered to be nonlinear and non-Gaussian, and is often used to evaluate many linear and nonlinear models. In order to evaluate the prediction performance of the proposed hybrid model, the sunspot data set is divided into two samples of training set and test set. The training data set of 221 observations from 1700 to 1920 is used to establish and train the model, and then the test data set of the last 67 observations from 1921 to 1987 is used to evaluate the performance of the model.

[0118] In the sunspot dataset, the same as other studies: when the model is a single ARIMA, the ARIMA model parameters are set to 9 (AR(9)), and when the model is a single ANN, a 4x4x1 neural network architecture is used, consisting of 4 input nodes, 4 hidden nodes, and 1 output node.

[0119] In the method proposed in the present application, the linear component can be extracted using a MA filter with a length of 15. At this time, the ADF test of the time series data of sunspots can be solved to be 0.003. Since 0.003 is much smaller than the threshold value 0.05, the time series of sunspots is stationary. When the ARIMA-OWA model is used, the same order 9 (AR(9)) as the ARIMA model is used. In the experimental process, the network architecture of the hybrid method is 8x6x1, and the best fitting neural network model is obtained. The neural network model has 8 nodes in the input layer, of which 4 are past observations, 1 node is used for the prediction result of the linear component, and 3 are residual series. The network architecture of other hybrid methods corresponds to Buyuksahin-Ertekin's method.

[0120] The performance metrics of the proposed sunspot dataset model are shown in Table 2. Table 2 shows that: (1) ARIMA and ANN have the lowest performance compared to other hybrid methods, indicating that a single model cannot fully handle all features in the time series; (2) The ARIMA-OWA method significantly improves the performance of the ARIMA model, indicating that the linear model has a better ability to handle linear components; (3) The hybrid methods of Zhang, Khashei-Bijari, Babu-Reddy, and Buyuksahin-Ertekin do indeed produce better results. However, their predictive performance is lower than that of the ARIMA-OWA-ANN method. Specifically, in terms of the MAE metric, ARIMA-OWA-ANN improves upon ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, and Buyuksahin-Ertekin methods by 25.6%, 18.4%, 16.6%, 22.0%, 4.1%, 11.7%, and 2.8%, respectively. In terms of MSE (Mean Sequence Equation), ARIMA-OWA-ANN improved upon the methods ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, and Buyuksahin-Ertekin by 40.3%, 36.7%, 33.4%, 30.3%, 7.8%, 19.8%, and 3.9%, respectively. In terms of MASE (Mean Sequence Equation), ARIMA-OWA-ANN improved upon the methods ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, and Buyuksahin-Ertekin by 24.8%, 18.4%, 16.6%, 22.0%, 4.1%, 11.7%, and 2.8%, respectively. Figure 5 The actual and predicted values ​​of eight time series forecasting methods on a sunspot dataset are compared.

[0121] The lynx dataset contains 114 observations (e.g.) Figure 6 As shown), the first 100 observations from 1821 to 1920 were used to train the model as the training set, and the last 14 observations from 1921 to 1934 were used to evaluate the model's performance as the test set. As with other studies, the logarithm of the data (base 10) was used in the analysis. When the ARIMA model was used as a single model, the parameters of the ARIMA model were set to 12 (AR(12)), similar to Khashei-Bijari and Khashei-Bijari. When the ANN model was used alone, a 7x5x1 neural network architecture was adopted.

[0122] In the proposed method, the linear component is extracted when the length of the fixed MA filter is 5. The ADF test value of the lynx time series data is 0.0019, which is much smaller than the threshold value 0.05, indicating that the data set is stationary. The ARIMA-OWA model has an order of 12 (AR(12)), and the architecture of the ANN is 9x9x1, which is: the input layer has 9 nodes, of which 5 are past observations, 1 node is used for the prediction result of the linear component, and 3 are residual series.

[0123] The performance indicators of the lynx data set model are shown in Table 2. From Table 2, it can be seen that: (1) the performance of the ARIMA-ANN hybrid method is higher than that of the single model ARIMA and ANN; (2) the ARIMA-OWA method significantly improves the performance of the traditional ARIMA model; (3) the performance indicators of the ARIMA-OWA-ANN method are the best. In terms of MAE indicators, ARIMA-OWA-ANN improves 27.2%, 24.4%, 15.1%, 16.9%, 12.5%, 16.3% and 6.3% compared with ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively. In terms of MSE indicators, ARIMA-OWA-ANN improves 34.3%, 33.2%, 21.9%, 13.5%, 9.7%, 15.0% and 5.4% compared with ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively. In terms of MASE indicators, ARIMA-OWA-ANN improves 27.2%, 24.4%, 15.1%, 16.9%, 12.5%, 16.3% and 6.3% compared with ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively. Figure 7 The comparison between the actual values and the predicted values of the eight time series prediction methods on the lynx data set is given.

[0124] The air passenger data set has a size of 144 months of observation data (as shown in Figure 8 ). The data from January 1948 to July 1958 for 114 months is used as training data, and the last 29 months from August 1958 to December 1960 are used as test data to test the performance of the model. When analyzing the data, natural logarithmic processing is used.

[0125] When the linear model is a single ARIMA model, it is found that using an order of AR(13) is the most parsimonious of all ARIMA models. Meanwhile, through the repeated process of tuning, when the nonlinear model is a single ANN, the ANN in ARIMA-ANN adopts 40x20x1 as the most fitted neural network architecture.

[0126] In the proposed method, the linear component is extracted when the length of the fixed MA filter is 27. The ADF test value of the air passenger dataset is 0.002, which is far less than 0.05, and the dataset is stationary. The order of the ARIMA-OWA model is 13 (AR(13)). According to the experiment: the network architecture in the ARIMA-OWA-ANN model is 40x40x1, the best fitted neural network model is obtained. The neural network model in the input layer has 40 nodes, of which 39 are past observations, and 1 node is used for the prediction result of the linear component. The residual series becomes 0 in the tuning process. In addition, the network architecture and component allocation of the Khashei-Bijari and Buyuksahin-Ertekin method are the same as those of the ARIMA-OWA-ANN method, the network structure of the Zhang method is 40x20x1, and the architecture of the Babu-Reddy method is 18x18x1.

[0127] The performance indicators of the proposed air passenger dataset model are shown in Table 2. As can be seen from Table 2, (1) in the dataset, among the methods used alone, ANN has better accuracy compared with ARIMA compared with the sunspot dataset and the lynx dataset. This may be because the air passenger dataset is more stable compared with the sunspot dataset and the lynx dataset; (2) the ARIMA-ANN hybrid method has lower performance than the ANN model, for example, the Zhang and Babu-Reddy method; (3) the ARIMA-OWA method improves the performance of the traditional ARIMA model; (4) the ARIMA-OWA-ANN has the best performance, which is specifically shown as follows: in the MAE indicator, the ARIMA-OWA-ANN is improved by 26.8%, 65.5%, 43.1%, 33.3%, 6.7%, 59.3% and 5.9% compared with the ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods respectively. In the MSE indicator, the ARIMA-OWA-ANN is improved by 42.3%, 87.3%, 64.2%, 56.5%, 12.4%, 83.5% and 10.0% compared with the ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods respectively. In the MASE, the ARIMA-OWA-ANN is improved by 26.8%, 65.5%, 43.1%, 33.3%, 6.7%, 59.3% and 5.9% compared with the ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods respectively. Figure 9 The comparison effect of actual values and predicted values of the eight decision methods on the air passenger dataset is given.

[0128] The star brightness dataset has 600 observation data (as shown in Figure 10 The first 480 data are used as training data, and the last 120 data are used as test data for testing the performance of the model. When the linear model is an ARIMA model alone, it is found through experiments that using the order AR(7) is the simplest one among all ARIMA models. At the same time, through repeated experimental tuning process, when the nonlinear model is an ANN alone, using 8x15x1 is the most fitting neural network architecture.

[0129] In the method proposed in the application, when the length of the fixed MA filter is 5, the linear component is extracted. The ADF test value of the given star brightness dataset is , which is much less than 0.05, the data set is stationary. The order of ARIMA-OWA is 7 (AR(7)). According to the experiment, the best fitting neural network model is obtained when the network architecture of ARIMA-OWA-ANN is 19x19x1, the input layer has 19 nodes, of which 18 are past observations and 1 node is used for the prediction result of the linear component, and the residual series becomes 0 in the tuning process. In addition, the network architecture and component allocation of the Khashei-Bijari and Buyuksahin-Ertekin methods are the same as ARIMA-OWA-ANN, the ANN network structure of the Zhang method is 8x15x1, and the ANN network architecture of the Babu-Reddy method is 4x7x1.

[0130] The performance indicators of the star brightness data set are shown in Table 2. From Table 2, it can be seen that: (1) except for the Babu-Reddy hybrid method, the performance of the hybrid method is better than that of the single ARIMA and ANN method; (2) the ARIMA-OWA method improves the performance of the traditional ARIMA model; (3) the ARIMA-OWA-ANN has the best performance. Specifically, in terms of MAE indicators, ARIMA-OWA-ANN improves 27.1%, 25.2% and 23.0% compared with ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively, 19.1%, 3.3%, 37.5% and 2.6%. In terms of MSE indicators, ARIMA-OWA-ANN improves 47.5%, 48.2%, 43.3%, 40.8%, 6.2%, 59.2% and 3.4% compared with ANN, ARIMA and ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively. In terms of MASE, ARIMA-OWA-ANN improves 27.1%, 25.1% and 23.0% compared with ANN, ARIMA and ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, respectively, 19.1%, 3.2%, 37.5% and 2.6%. Figure 11 The comparative analysis of the actual values and predicted values of the eight methods on the star brightness data set is given.

[0131] The exchange rate data set has a total of 27 monthly arithmetic means as observation data (as shown in Figure 12 , the observation values from August 2017 to July 2019 are used as training models, which are the training set, and the last 3 months of observation values are used to evaluate the performance of the model, which is the test set.

[0132] When the linear model is a single ARIMA model, it is found through experiments that using order AR(4) is the best among all ARIMA models. Meanwhile, when the nonlinear model is a single ANN, using 10x2x1 is the best neural network architecture.

[0133] In the method proposed in the present application, the linear component is extracted when the length of the MA filter is 10. The ADF test of the given exchange rate dataset is 0.042, which is much smaller than 0.05, and the data is stationary. The order of ARIMA-OWA is: 4(AR(4)). According to experiments, the best fitting neural network model is obtained when the network architecture of ARIMA-OWA-ANN is 7x2x1, the input layer has 7 nodes, of which 4 are past observations, 1 node is used for the prediction result of the linear component, and 2 are residual sequences. In addition, the network architecture and component allocation of the Khashei-Bijari and Buyuksahin-Ertekin methods are the same as those of the ARIMA-OWA-ANN method, the network structure of the Zhang method is 10x2x1, and the architecture of the Babu-Reddy method is 4x6x1.

[0134] The performance indicators of the proposed exchange rate dataset model are shown in Table 2. From Table 2, it can be seen that: (1) the dataset appears to limit the model performance of the Babu-Reddy method, with lower performance than single models, but the performance of other hybrid methods is still higher than that of ARIMA or ANN models; (2) the ARIMA-OWA method also improves the performance of the traditional ARIMA model; (3) the ARIMA-OWA-ANN performance indicator is better than the GARCH-OWA. The best MAE and MSE results of the GARCH-OWA model are 0.0149 and 0.0006, respectively. The ARIMA-OWA-ANN method has much higher performance than the GARCH-OWA; (4) the ARIMA-OWA-ANN method has certain advantages compared with existing time series prediction methods, which are reflected in: in the MAE indicator, the ARIMA-OWA-ANN is improved by 30.0%, 35.7%, 29.2%, 21.7%, 70.6%, and 6.2% compared with the ANN, ARIMA, ARIMA-OWA, Zhang, Babu-Reddy, and Buyuksahin-Ertekin methods, respectively. In the MSE indicator, it is improved by 61.2%, 51.7%, 61.4%, 47.6%, 18.3%, 91.7%, and 6.1% compared with the ANN, ARIMA, and ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy, and Buyuksahin-Ertekin methods, respectively. In the MASE, the ARIMA-OWA-ANN is improved by 30.0%, 35.7%, 29.2%, 21.7%, 70.6%, and 6.2% compared with the ANN, ARIMA, and ARIMA-OWA, Zhang, Babu-Reddy, and Buyuksahin-Ertekin methods, respectively.

[0135] For these evaluation methods, the present application will use the random function in Python programming language to randomly generate 100 data, and construct a data set with the value range of 0-1. In the case of one-step prediction, the prediction range is 10. According to the experiment, the order of the ARIMA model is set to AR(3, 0, 0), in addition, the network structure of the nonlinear model ANN is 3x3x1, and the ANN network structure of the hybrid model is set to 4x9x1. The obtained data is modeled by using the ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods, and the MAE, MSE and MASE evaluation values of the proposed ARIMA-OWA-ANN method are calculated respectively. The filter length is fixed to 16 during the experiment, and the stationarity test (ADF) result of the data set is 0.0015, which is much smaller than the threshold value 0.05. For the Khashei-Bijari method, the Buyuksahin-Ertekin method and the proposed ARIMA-OWA-ANN method, the number of input nodes is 4, of which 3 are original data values and one is the prediction result of the linear component, and the number of nonlinear residual series becomes 0 in the tuning process. The performance measurement results obtained by using the data are shown in Table 3, and the one-step prediction results are shown in Table 4. Figure 13

[0136] Table 3, Performance comparison of different methods under randomly generated data

[0137]

[0138] From Table 3 and Figure 13 It can be seen that: the MAE, MSE and MASE performance of ARIMA-OWA is better than that of ARIMA. The MAE, MSE and MASE performance of ARIMA-OWA-ANN is better than that of ANN, ARIMA, ARIMA-OWA, Zhang, Khashei-Bijari, Babu-Reddy and Buyuksahin-Ertekin methods. Therefore, the ARIMA-OWA-ANN hybrid model developed by the present application can obtain better performance on random time series.

[0139] In the experiment of the present application, several important results are obtained: (1) when using a single model, the prediction performance of the ARIMA model is better than that of the ANN model in the sunspot data set and the lynx data set, but the opposite is true in the aviation passenger data set and the star brightness data set; (2) on all data sets, the ARIMA-OWA model proposed by the present application significantly improves the prediction performance of the ARIMA model (as Figure 14 ​(1) ARIMA-OWA-ANN model can better capture long-term trend changes and linear relationships between data, thus improving the accuracy and stability of model prediction; (2) When data fluctuation is large, the hybrid method can have better performance than a single method. When special data values appear in the data, the assumptions made by other hybrid methods will reduce the prediction performance. For example, Zhang and Babu-Reddy method assumes that the relationship between linear and nonlinear components is additive, which reduces the prediction performance compared with ANN model in the air passenger data set and the star brightness data set. In addition, Buyuksahin-Ertekin method combines Khashei-Bijari and Babu-Reddy methods, which overcomes the risk of performance reduction caused by some assumptions, but more or less is subject to some conditions in time series data, such as data stationarity, data dependence, etc., thereby affecting the prediction result; (3) ARIMA-OWA-ANN model has obvious advantages compared with other methods in this field.

[0140] In order to further analyze the ARIMA-OWA-ANN hybrid time series prediction method, the average values of MAE, MSE and MASE of the eight time series prediction methods in Table 2 on the five data sets given above are statistically analyzed, and the results are shown in Figure 14

[0141] From Figure 14 it can be seen that: the average MAE, MSE and MASE of ARIMA-OWA-ANN model on the five data sets are the smallest, so it is optimal. At the same time, the average MAE, MSE and MASE of ARIMA-OWA model on the five data sets are smaller than those of ARIMA, so ARIMA-OWA is superior to ARIMA. At the same time, compared with ARIMA, the data sequence processed by OWA operator is relatively stable, which is more conducive to the establishment of hybrid model. ARIMA model has good adaptability to fixed order and high frequency data, but poor adaptability to non-stationary and sensitive data. The ARIMA-OWA-ANN model proposed in the present application eliminates these limitations, uses OWA to process linear components, improves the stability of time series data, and the use of ANN improves the adaptability of the model to data and the accuracy of prediction.

[0142] ​It should be understood that, although the steps in the flowcharts of the embodiments of the present application are shown in sequence according to the arrows, the steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in the present application, the execution of the steps is not strictly limited in sequence, and the steps can be executed in other sequences. Moreover, at least some of the steps in the embodiments can include a plurality of sub-steps or stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence of the sub-steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least part of other steps or sub-steps or stages of other steps.

[0143] It should be understood that the parts of the present application can be realized by hardware, software, firmware or a combination thereof. In the above-described embodiments, a plurality of steps or methods can be realized by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if realized by hardware, as in another embodiment, any one or a combination of the following technologies known in the art can be used: discrete logic circuit with logic gate circuit for implementing logic functions on data signals, application specific integrated circuit with suitable combination logic gate circuit, programmable gate array (PGA), field programmable gate array (FPGA), etc.

[0144] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example" or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0145] The above-described embodiments only express several embodiments of the present application, which are described in detail and in detail, but cannot be understood as limiting the scope of the patent of the present application. It should be noted that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the scope of protection of the patent of the present application should be subject to the appended claims.

Claims

1. A hybrid aeronautical prediction method based on OWA operator, characterized in that, The method comprises the following steps: Step 1, obtaining an air passenger data set corresponding to the number of international flight passengers per month, decomposing the air passenger data set by using an MA filter to obtain a linear component and a nonlinear residual sequence; Step 2, preprocessing the linear component to generate a linear component sequence, and defining a historical sequence in the linear component sequence as an OWA mean of a current sequence in the linear component sequence; Step 3, transforming the ARIMA-OWA model according to the core assumptions of the ARIMA model to obtain a transformed model; initializing the historical error of the transformed model, and then substituting the linear component sequence to calculate a historical random error sequence, and the corresponding process exists the following relationship: ； wherein, represents the normalized lag p linear component of the order represents the normalized linear component of the t element; Step 4, substituting the historical linear component sequence and the historical random error sequence into the ARIMA-OWA model to obtain a predicted linear variable; Step 5, selecting a plurality of data from the time series data as a first time series; selecting a plurality of data from the nonlinear residual sequence as a second time series; sending the first time series, the second time series and the predicted linear variable into an ANN network to obtain a hybrid prediction result of the time series, and the corresponding process exists the following relationship: ； wherein, represents a predicted linear variable, respectively represent the length of selected data in the time series data and the nonlinear residual series, represents a first time series, represents a second time series, represents a nonlinear function of a neural network, represents a first time series data, represents a first nonlinear residual series; The construction process of the ARIMA-OWA model is as follows: using an OWA operator to perform weighted processing on time series data to calculate an OWA-based autocorrelation coefficient; given the autoregressive order and the moving average order, and according to the autoregressive order and the moving average order, a corresponding number of OWA-based autocorrelation coefficients are obtained, and parameter estimation is performed by using a moment estimation method to obtain OWA-based autoregressive parameters and OWA-based moving average parameters; based on the ARIMA model, the ARIMA model parameters are replaced by the OWA-based autoregressive parameters and the OWA-based moving average parameters to obtain an ARIMA-OWA model, and the corresponding process exists the following relationship: ； in, This represents the first OWA-based autoregressive coefficient. Indicates lag p Time series data of order 1 Indicates lag q Order error value, Indicates the first q One OWA-based moving average coefficient; setting a maximum lag order, using a loop traversal method to determine the final autoregressive order, moving average order and difference order of the ARIMA-OWA model, and dynamically adjusting the OWA-based autoregressive parameters and the OWA-based moving average parameters according to the autoregressive order and the moving average order in each loop traversal process, and after the loop traversal is completed, the final ARIMA-OWA model is obtained; given the autoregressive order and the moving average order, and according to the autoregressive order and the moving average order, a corresponding number of OWA-based autocorrelation coefficients are obtained, and parameter estimation is performed by using a moment estimation method to obtain OWA-based autoregressive parameters and OWA-based moving average parameters, which specifically comprises the following steps: given the autoregressive order and the moving average order, and according to the autoregressive order and the moving average order, a corresponding number of OWA-based autocorrelation coefficients are obtained, and the Yule-Walker equation is constructed to estimate the OWA-based autoregressive parameters, and the corresponding process exists the following relationship: ； wherein, represents the pth OWA-based autoregressive coefficient, represents the q+p+2th OWA-based autocorrelation coefficient, respectively represent the autoregressive order and the moving average order; according to the obtained OWA-based autoregressive parameters and the moving average order, the OWA-based moving average parameters are calculated; When the moving average order is 0, the OWA-based moving average parameter is calculated using a first relationship as follows: ； wherein, denotes the OWA mean of the time series data, denotes that the moving average coefficient based on OWA is 0; When the moving average order is greater than or equal to 1, the OWA-based moving average parameter is calculated using a second relationship as follows: ； wherein, denotes an estimate of the OWA-based covariance, denotes the OWA covariance of the error vector, denotes the variance of the error, which is calculated as follows when the autoregressive order is 0: ； wherein denotes an estimate of the OWA-based covariance, ; The OWA covariance calculation process of the error vector has the following relationship: ； wherein represents a random error.

2. The hybrid aviation prediction method based on OWA operator according to claim 1, characterized in that, The time series data is decomposed using an MA filter to obtain a linear component and a nonlinear residual sequence, and the corresponding process has the following relationship: ； ； wherein, represents a linear component of the t th element, represents a filter length, represents a nonlinear residual sequence, represents the i th element of the time series data, represents the t th element.

3. The hybrid aviation prediction method based on OWA operator according to claim 1 or 2, characterized in that, The historical linear component sequence and the historical random error sequence are substituted into the ARIMA-OWA model to obtain the corresponding process of the predicted linear variable as follows: ； wherein, denotes the ARIMA-OWA model.

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