Fitting Compensation Method for Missing Data of AIS on Inland River Ships

Abstract

The present invention discloses a method for fitting and compensating missing data of AIS for inland river ships. Based on the existing ship AIS training data set, the present invention constructs an encoder model with mutually orthogonal hidden layer neurons, uses the PSO algorithm to optimize the weights and biases of the neurons, and adds them to the hidden layer of the encoder network model one by one; this method can extract the characteristic variables of AIS historical data to the greatest extent, and further predict the missing AIS data according to the characteristic variables. Compared with the prior art, the present invention has the characteristics of simple model structure and high prediction accuracy.

Description

Technical Field

[0001] The present invention relates to a method for fitting missing data, and particularly to a method for fitting and compensating missing data of AIS of inland river ships, belonging to the field of information technology. Background Art

[0002] Inland river shipping has advantages such as large transportation volume and low cost, and occupies an important position in the economic development of our country. During the navigation of ships, information such as position and ship speed is sent through the Automatic Identification System (AIS). Thus, the purpose of dispatching ships and optimizing shipping can be achieved. However, due to the influence of various external interference factors, data loss occurs in the data transmission and storage links, resulting in the management department being unable to obtain real ship information, and directly affecting the efficiency of inland river shipping. Therefore, the repair of missing data values has become an important research content in the transportation field.

[0003] Currently, for the compensation algorithms of missing data, techniques such as spline interpolation method and support vector machine are mostly applied. However, due to their own limitations, these methods can only process a small number of scattered points, and the fitting accuracy often cannot meet the requirements of engineering technology. Summary of the Invention

[0004] In order to solve the existing deficiencies, the purpose of the present invention is to provide a method for fitting missing data, which can accurately predict missing data, thereby compensating for incomplete databases, improving data integrity, and expanding the application scope of data.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is a method for fitting and compensating missing data of AIS of inland river ships. The implementation process of this method is as follows.

[0006] There is an existing ship AIS training data set {X, Y}, where X ∈ R N*M represents the known AIS historical data, N is the number of samples of AIS historical data, and M is the dimension; Y = {Y j} represents the AIS missing data to be predicted, j = 1, 2,..., Q, and Q is the number of AIS missing data. An encoder network model with an input layer, a hidden layer, and an output layer is constructed. P = P s represents the neurons in the hidden layer, s = 1, 2,..., S, and S is the number of neurons in the hidden layer, that is, the number of feature variables obtained from the AIS historical data. According to the OLS theory, the AIS feature variable Ψ = X · P, where and the corresponding parameter ω = [ω1, ω2,... ω S is calculated by the following formula:

[0007] ω = Ψ · A-1

[0008] Among them is an intermediate parameter. The weights and biases of the neurons are optimized using the PSO algorithm and added to the hidden layer of the encoder network model one by one.

[0009] S1. Add the first neuron to the hidden layer of the encoder network model. First, use the PSO algorithm to randomly generate a set of particles {P i,r}, (1 ≤ i ≤ D, 1 ≤ r ≤ R), where D represents the number of candidate neurons and R represents the maximum number of iterations of the PSO algorithm. P i,r is the i-th particle in the r-th iteration, representing the weights and biases of the neuron. Then, according to the OLS theory, the contribution degree of each particle P i,r is:

[0010]

[0011] Among them

[0012] Select the particle with the maximum contribution degree value and mark it as that is, the i-th particle P i,r in the r-th iteration is selected as the weights and biases of the hidden layer neuron. Therefore, the first feature variable of the AIS data and the corresponding parameter ω1 can be obtained.

[0013] S2. Add the second neuron to the hidden layer. Use the PSO algorithm to randomly generate a new set of particles {P i,r}, (1 ≤ i ≤ D, 1 ≤ r ≤ R). Similarly, P i,r is the i-th particle in the r-th iteration, and each particle represents the weights and biases of the second candidate neuron. Then, according to the OLS theory, the contribution degree of each particle P i,r is:

[0014]

[0015] Among them

[0016] Select the particle with the maximum contribution degree value and mark it as that is, the i-th particle P i,r in the r-th iteration is the weights and biases of the second hidden layer neuron. Therefore, the second feature variable of the AIS data and the corresponding parameter ω2 can be obtained.

[0017] S3. Add the t-th neuron to the hidden layer. Use the PSO algorithm to randomly generate a new set of particles {Pi,r}, (1 ≤ i ≤ D, 1 ≤ r ≤ R), and similarly P i,r is the i-th particle in the r-th iteration. Each particle represents the weights and biases of the t-th candidate neuron. Then, according to the OLS theory, the contribution of each particle P i,r is as follows:

[0018]

[0019] where

[0020] Select the particle that makes the contribution value the largest and label it as i.e., the i-th particle P in the r-th iteration i,r is the weights and biases of the t-th hidden layer neuron. Therefore, the t-th feature variable of the AIS data can be obtained and the corresponding parameter ω t .

[0021] S4. Repeat step 3, and successively add hidden neurons to the neural network until the number of neurons in the hidden layer reaches the maximum value S or the error rate is less than a certain threshold Υ:

[0022]

[0023] Thus, the encoder network model is constructed.

[0024] S5. When the ship is sailing, if the AIS data is missing, the accurate prediction of the missing AIS data can be realized according to the established encoder network model.

[0025] Compared with the prior art, the present invention constructs an encoder model with mutually orthogonal hidden layer neurons, which can extract the feature variables of the AIS historical data to the greatest extent and further predict the missing AIS data based on the feature variables. Compared with the prior art, the present invention has the characteristics of simple model structure and high prediction accuracy. Description of the Drawings

[0026] Figure 1 is the process of adding hidden layer neurons. Detailed Embodiment

[0027] The present invention will be described in detail below with reference to the drawings and embodiments.

[0028] There is an existing ship AIS training data set {X, Y}, where X ∈ R N*M(N = 10, M = 4) represents the known AIS historical data, as shown in Table 1; the three dimensions respectively represent the longitude, latitude, true head, and speed of the ship:

[0029] Table 1

[0030] No. Longitude Latitude Truehead Speed 1 105.716 28.879 229 4.1 2 105.716 28.879 239 4.2 3 105.715 28.878 237 4.2 4 105.715 28.878 235 4.3 5 105.714 28.878 229 4.2 6 105.714 28.877 231 4.1 7 105.713 28.877 236 4 8 105.713 28.877 236 3.7 9 105.712 28.876 238 3.6 10 105.712 28.876 235 3.6

[0031] Y = {Y j} (j = 1, 2, … 10) represents the missing AIS data to be predicted, as shown in Table 2.

[0032] Table 2

[0033]

[0034]

[0035] Construct an encoder network model with an input layer, a hidden layer, and an output layer. P = P s , (s = 1, 2, 3) represents the neurons in the hidden layer, that is, the number of feature variables obtained from the AIS historical data is 3. According to the OLS theory, the AIS feature variable Ψ = X·P, where and the corresponding parameters ω = [ω1, ω2, ω3] of the AIS feature variable are calculated by the following formula:

[0036] ω = Ψ·A -1

[0037] where is an intermediate parameter. Next, use the PSO algorithm to optimize the weights and biases of the neurons and add them to the hidden layer of the encoder network model one by one.

[0038] 1. Add the first neuron to the hidden layer. First, use the PSO algorithm to randomly generate a set of particles {P i,r}, (1 ≤ i ≤ 20, 1 ≤ r ≤ 30), where 20 represents the number of candidate neurons and 30 represents the maximum number of iterations of the PSO algorithm. P i,r is the i-th particle in the r-th iteration, representing the weights and biases of the neuron. Then, according to the OLS theory, the contribution degree of each particle P i,r is:

[0039]

[0040] where

[0041] Select the particle that makes the contribution degree value the largest and mark it as i.e., the i-th particle P in the r-th iteration i,r is selected as the weights and biases of the hidden layer neurons. Thus, the first characteristic variable of the AIS data can be obtained and the corresponding parameter ω1 = [0.087, 0.02, 0.212, -0.318, 0.02, 0.233, 0.045, 0.175, 0.08, 0.184] T .

[0042] 2. Add the second neuron to the hidden layer. Use the PSO algorithm to randomly generate a new set of particles {P i,r}, (1 ≤ i ≤ 20, 1 ≤ r ≤ 30). Similarly, P i,r is the i-th particle in the r-th iteration. Each particle represents the weights and biases of the second candidate neuron. Then, according to the OLS theory, the contribution degree of each particle P i,r is:

[0043]

[0044] where

[0045] Select the particle that makes the contribution degree value the largest and mark it as i.e., the i-th particle P in the r-th iteration i,r is the weights and biases of the second hidden layer neuron. Thus, the second characteristic variable of the AIS data can be obtained and the corresponding parameter ω2 = [0.02,, 0.194, 0.013, -0.015, 0.172, 0.039, 0.08, 0.066, 0.187, 0.075] T .

[0046] 3. Add the 3rd neuron to the hidden layer. Use the PSO algorithm to randomly generate a new set of particles {P i,r}, (1 ≤ i ≤ 20, 1 ≤ r ≤ 30). Similarly, P i,r is the i-th particle in the r-th iteration. Each particle represents the weights and biases of the 3rd candidate neuron. Then, according to the OLS theory, the contribution degree of each particle P i,r is:

[0047]

[0048] where

[0049] Select the particle that makes the contribution degree value the largest and mark it as i.e., the i-th particle P in the r-th iteration i,rThey are the weights and biases of the neurons in the third hidden layer. Therefore, the third feature variable of the AIS data can be obtained and the corresponding parameter ω3 = [0.102, 0.072, 0.087, 0.033, -0.151, 0.106, 0.244, 0.117, 0.094, 0.155] T .

[0050] 4. Repeat step 3, and successively add hidden neurons to the neural network until the number of neurons in the hidden layer reaches the maximum value of 3 or the error rate is less than a certain threshold of 0.1:

[0051]

[0052] So far, the encoder network model is constructed.

[0053] 5. When the ship is sailing, if the AIS data is missing, the accurately predicted AIS missing data can be realized according to the established encoder network model.

Claims

1. An interpolation compensation method for missing AIS data of inland river ships. The implementation process of this method is as follows: Existing ship AIS training data set {X, Y}, where X ∈ R N*M To represent the known AIS historical data, N is the number of samples of AIS historical data, and M is the dimension; Y = {Y j} represents the missing AIS data to be predicted, j = 1, 2, … Q, and Q is the number of missing AIS data; construct an encoder network model with an input layer, a hidden layer, and an output layer, P = P s represents the neurons in the hidden layer, s = 1, 2, …, S, and S is the number of neurons in the hidden layer, that is, the number of feature variables obtained from the AIS historical data; according to the OLS theory, the AIS feature variable Ψ = X · P, where and the corresponding parameter ω of the AIS feature variable = [ω1, ω2, … ω S is calculated by the following formula: ω = Ψ·A -1 Among them is an intermediate parameter; the weights and biases of the neurons are optimized using the PSO algorithm and added to the hidden layer of the encoder network model one by one; S1. Add the first neuron to the hidden layer of the encoder network model; first, use the PSO algorithm to randomly generate a set of particles {P i,r}, where D represents the number of candidate neurons, 1 ≤ i ≤ D, 1 ≤ r ≤ R, and R represents the maximum number of iterations of the PSO algorithm,; P i,r is the i-th particle in the r-th iteration, representing the weight and bias of the neuron. Then, according to the OLS theory, the contribution of each particle P i,r is: Among them Select the particle with the largest contribution value and mark it as the i-th particle P in the r-th iteration i,r to be the weights and biases of the hidden layer neurons; obtain the first feature variable of the AIS data and the corresponding parameter ω1; S2. Add a second neuron to the hidden layer; randomly generate a new set of particles {P i,r}, P i,r is the i-th particle in the r-th iteration, and each particle represents the weights and biases of the second candidate neuron; then according to the OLS theory, the contribution degree of each particle P i,r is: Among them Select the particle with the largest contribution value and mark it as i.e., the i-th particle P in the r-th iteration i,r is the weight and bias of the second hidden layer neuron; obtain the second feature variable of the AIS data and the corresponding parameter ω2; S3. Add the t-th neuron to the hidden layer; randomly generate a new set of particles {P i,r} using the PSO algorithm, where P i,r is the i-th particle in the r-th iteration, and each particle represents the weights and biases of the t-th candidate neuron; then according to the OLS theory, the contribution of each particle P i,r is: Among them Select the particle with the largest contribution value and label it as i.e., the i-th particle P in the r-th iteration i,r is the weight and bias of the t-th hidden layer neuron; obtain the t-th feature variable of the AIS data and the corresponding parameter ω t ; S4. Repeat S3, and gradually add hidden neurons to the neural network until the number of neurons in the hidden layer reaches the maximum value S or the error rate is less than a certain threshold Υ. So far, the encoder network model is constructed. S5. When the ship is sailing, if AIS data is missing, the accurate prediction of the missing AIS data can be realized according to the established encoder network model.

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