Aircraft optimal gravity center position prediction method based on deep neural network
Through the combination of deep neural network classification and regression network, the problem of low efficiency in calculating the optimal center of gravity position of the aircraft is solved, and fast and accurate center of gravity position prediction is achieved, meeting the needs of real-time adjustment of the aircraft.
Patent Information
- Application Number
- CN202411897678.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-23
- Publication Date
- 2025-09-16
AI Technical Summary
The existing technology for calculating the optimal center of gravity position of an aircraft has low efficiency and a long calculation cycle, making it difficult to meet real-time adjustment requirements. In addition, the numerical simulation method has high requirements on the performance of airborne equipment.
A method based on deep neural networks is adopted to screen the flight status of the center of gravity extreme position through the classification network, and combine with the regression network to predict the optimal center of gravity position in the non-extreme position. The combination of the classification network and the regression network is used to achieve rapid prediction of the optimal center of gravity position.
The optimal center of gravity position prediction with small calculation amount, fast prediction speed and good real-time performance is achieved, which avoids the influence of the center of gravity limit position on the prediction result and improves the prediction accuracy.
Smart Images
Figure CN120652965A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of aircraft center of gravity position prediction, and specifically provides a method for predicting the optimal center of gravity position of an aircraft based on a deep neural network. Background Art
[0002] In conventional aerodynamic aircraft, to maintain longitudinal static stability, the center of gravity is positioned forward of the aerodynamic center. The wings are the primary components that provide lift. To balance lift and the moment due to gravity, the horizontal tail generates negative lift, providing a trimming moment. For a given aircraft weight, the greater the distance between the center of gravity and the aerodynamic center, the greater the required trimming moment, meaning the greater the negative lift generated by the horizontal tail. In this case, the wings must generate greater lift to ensure that the combined force of the negative lift generated by the horizontal tail balances gravity. Within a certain range of angles of attack, the greater the lift, the greater the aerodynamic drag experienced by the aircraft. Therefore, by adjusting the position of the aircraft's center of gravity in real time, the trimming moment can be reduced, thereby reducing the aircraft's drag and fuel consumption. However, due to constraints such as aircraft stability and maneuverability, the aircraft's center of gravity cannot be positioned too far forward or aft. In other words, the aircraft's center of gravity has fore-and-aft limits. In a given flight state, an aircraft has an optimal center of gravity position, which minimizes the trimming moment and trimming drag. Based on computational fluid dynamics (CFD) software or other numerical simulation tools, the aerodynamic characteristics of an aircraft under different flight conditions can be simulated, thereby accurately calculating the trim resistance. However, numerical simulation methods have the problems of low computational efficiency and long calculation cycles, making it difficult to meet the needs of real-time adjustment of the aircraft's center of gravity. In addition, accurate numerical simulation requires high-performance computing equipment, which also places high demands on the performance of airborne equipment. In recent years, thanks to the powerful nonlinear fitting capabilities of neural networks, neural networks have been widely used in fields such as data regression prediction and feature classification. However, there is currently no research in the public literature on the application of neural networks in the prediction of the optimal center of gravity position of aircraft. Summary of the Invention
[0003] The purpose of this invention is to propose a method for predicting the optimal center of gravity position of an aircraft based on a deep neural network to solve the problems of low calculation efficiency and long calculation cycle of the optimal center of gravity position of traditional aircraft.
[0004] Technical solution of the present invention: In order to achieve the above-mentioned purpose, according to the first aspect of the present invention, in order to achieve the above-mentioned purpose, the present invention adopts the following technical solution:
[0005] A method for predicting the optimal center of gravity of an aircraft based on a deep neural network is proposed. The specific steps include:
[0006] Step 1: Select N sets of flight status data and the forward and rearward extreme positions of the aircraft's center of gravity within the aircraft envelope. Each set of flight status data includes: aircraft weight, flight altitude, and flight Mach number.
[0007] Step 2: Obtain the optimal center of gravity position corresponding to each set of flight conditions in step 1 based on experimental testing or computational fluid dynamics methods;
[0008] In one possible embodiment, in step 2, the method for determining the optimal center of gravity position is: in experimental testing or computational fluid dynamics calculations, a set of flight conditions are set, the aircraft's trim resistance is tested or calculated, and then the aircraft's center of gravity position is adjusted along the aircraft's body axis until the aircraft's trim resistance reaches a minimum. The center of gravity position at this time is the optimal center of gravity position.
[0009] Step 3: Based on the forward and rearward extreme positions of the aircraft's center of gravity, perform normalization preprocessing on the optimal center of gravity position corresponding to each set of flight states obtained in step 2;
[0010] In a possible embodiment, in step 3, the specific process of normalization preprocessing includes:
[0011]
[0012] in is the normalized optimal center of gravity position; G is the unnormalized optimal center of gravity position; G min is the front limit position of the center of gravity; G max is the extreme position behind the center of gravity; The range of the value is [-1,1], the limit position before the center of gravity Limit position behind the center of gravity
[0013] Step 4: Create a classification network. The network is a serial structure, which consists of input layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, fully connected layer, softmax layer, and classification output layer.
[0014] In one possible embodiment, the input sample dimension of the input layer is 3; the output dimension of the classification output layer is 3; and the mathematical expressions of the other layers are:
[0015] The mathematical expression of the fully connected layer is:
[0016]
[0017] Among them, x i is the input value of the i-th neuron; w ji is the weight connecting the i-th input neuron and the j-th output neuron; b j is the bias of the jth output neuron.
[0018] The mathematical expression of the tanh activation layer is:
[0019]
[0020] Among them, y i is the i-th output of the tanh activation layer, x i is the i-th input to the tanh activation layer.
[0021] The mathematical expression of the softmax activation layer is:
[0022]
[0023] Among them, y j is the j-th output of the softmax activation layer, x j is the j-th input to the softmax activation layer.
[0024] Step 5: Create a regression network. The network is a serial structure, which is input layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, and regression output layer.
[0025] In one possible embodiment, the input sample dimension of the input layer is 3; the output result dimension of the regression output layer is 1; and the mathematical expressions of the other layers are:
[0026] The mathematical expression of the fully connected layer is:
[0027]
[0028] Among them, x i is the input value of the i-th neuron; w ji is the weight connecting the i-th input neuron and the j-th output neuron; b j is the bias of the jth output neuron.
[0029] The mathematical expression of the tanh activation layer is:
[0030]
[0031] Among them, y i is the i-th output of the tanh activation layer, x i is the i-th input to the tanh activation layer.
[0032] Step 6: Create the input dataset X for the classification network CI , X CI It is a matrix with N rows and 3 columns. Each row of data is a set of samples, representing a set of flight status data in step 1. Create the output label dataset X of the classification networkCO , X CO is a vector of N rows and 1 column; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row (i=1,2,…N) is -1, X CO The i-th row element of is set to -1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is 1, X CO The i-th row element of is set to 1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is greater than -1 and less than 1, X CO The i-th row element of is set to 0;
[0033] Step 7: Place the X CO The set of row numbers whose elements are 0 is denoted as R0. CI Extract the data corresponding to the row number in the set R0 as the regression network input data set X RI , X RI N R Matrix with 3 rows and 3 columns, N R is the number of data samples in set R0, each row of data is a set of samples, representing a set of flight status data. Create a regression network output dataset X RO , X RO N R Row 1 column vector. X RO Each row element value is X RI The optimal center of gravity position corresponding to each row of flight status data.
[0034] Step 8: X CI As the input data of the classification network, X CO As the output data of the classification network, it is used for training and testing of the classification network. RI As the input data of the regression network, X RO As the output data of the regression network, it is used for training and testing of the regression network.
[0035] In one possible embodiment, the classification network model loss function is defined as the cross entropy loss CEL, where CEL is defined as:
[0036]
[0037] Where n is the number of data samples; C is the number of classification categories; y ij is the true label (0 or 1) of the jth category for the i-th data sample; is the predicted probability that the i-th data sample belongs to the j-th category.
[0038] In a possible embodiment, the optimization training method is the Adam algorithm.
[0039] In one possible embodiment, the regression network model uses mean square error (MSE) as the loss function, where MSE is defined as:
[0040]
[0041] Where n is the number of data samples; y i is the true value of the i-th data sample; is the predicted value of the ith data sample.
[0042] In a possible embodiment, the optimization training method is the Adam algorithm.
[0043] Step 9: Select several sets of flight status data within the aircraft envelope to predict the corresponding optimal center of gravity position. Input each set of flight status data into the trained classification network in turn. If the output of the classification network is -1, the optimal center of gravity position corresponding to the flight status data is predicted to be -1; if the output of the classification network is 1, the optimal center of gravity position corresponding to the flight status data is predicted to be 1;
[0044] If the output of the classification network is 0, the flight status data is fed into the trained regression network. The output of the regression network is the predicted optimal center of gravity position corresponding to the flight status data. This completes the prediction of the aircraft's optimal center of gravity position.
[0045] The advantages of the present invention are: 1. The method of the present invention realizes the prediction of the optimal center of gravity position by combining a classification network and a regression network, which has the advantages of small calculation amount, fast prediction speed and good real-time performance;
[0046] 2. In the method described in this invention, a classification network is used to classify flight state data, screening out flight states with extreme center of gravity positions; a regression network is used for flight states with non-extreme center of gravity positions, accurately predicting the optimal center of gravity position. Compared to methods that directly use regression networks for center of gravity position prediction, this method avoids the influence of a large number of extreme center of gravity position conditions on the regression prediction results, achieving higher prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] Figure 1 A schematic diagram of the prediction process of a method for predicting the optimal center of gravity position of an aircraft based on a deep neural network according to the method described in this application;
[0048] Figure 2 The prediction effect of the regression network of the method described in this application, in which the true value is recorded as Test, the data is represented by a straight line, the predicted value is recorded as Prediction, and the data is represented by a hollow circle;
[0049] Figure 3In order to compare the prediction effect of the comparison method, the comparison method directly uses the regression network to predict the center of gravity position. In the figure, the true value is recorded as Test, the data is represented by a straight line, and the predicted value is recorded as Prediction, and the data is represented by a hollow circle. DETAILED DESCRIPTION
[0050] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative work are within the scope of protection of the present invention.
[0051] The features and illustrative embodiments of various aspects of the present invention will be described in detail below. In the detailed description below, many specific details are proposed in order to provide a comprehensive understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention can be implemented without the need for some of these specific details. The following description of the embodiments is merely intended to provide a better understanding of the present invention by illustrating examples of the present invention. The present invention is in no way limited to any specific arrangement and method proposed below, but rather encompasses any improvements, replacements, and modifications to structures, methods, and devices without departing from the spirit of the present invention. In the accompanying drawings and the following description, well-known structures and techniques are not shown to avoid unnecessary ambiguity in the present invention.
[0052] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other, and the embodiments can refer to and quote each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0053] Example 1
[0054] like Figure 1 As shown in FIG, a method for predicting the optimal center of gravity position of an aircraft based on a deep neural network includes the following steps:
[0055] Step 1: Select 6216 sets of flight status data and the forward and aft extreme positions of the aircraft's center of gravity within the aircraft envelope. Each set of flight status data includes: aircraft weight, flight altitude, and flight Mach number.
[0056] Step 2: Obtain the optimal center of gravity position corresponding to each set of flight conditions in step 1 using a computational fluid dynamics method. The optimal center of gravity position is determined by setting a set of flight conditions in a computational fluid dynamics calculation, calculating the aircraft's trim drag, and then adjusting the aircraft's center of gravity position along the aircraft's body axis until the aircraft's trim drag is minimized. The center of gravity position at this point is the optimal center of gravity position.
[0057] Step 3: Based on the forward and rearward extreme positions of the aircraft's center of gravity, the optimal center of gravity position corresponding to each set of flight states obtained in step 2 is normalized and preprocessed. In step 3, the specific process of normalization preprocessing includes:
[0058]
[0059] in is the normalized optimal center of gravity position; G is the unnormalized optimal center of gravity position; G min is the front limit position of the center of gravity; G max is the extreme position behind the center of gravity; The range of the value is [-1,1], the limit position before the center of gravity Limit position behind the center of gravity
[0060] Step 4: Create a classification network. The network is a series structure, which consists of input layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, fully connected layer, softmax layer, and classification output layer. The input layer has an input sample dimension of 3; the classification output layer has an output result dimension of 3; the mathematical expressions of the other layers are:
[0061] The mathematical expression of the fully connected layer is:
[0062]
[0063] Among them, x i is the input value of the i-th neuron; w ji is the weight connecting the i-th input neuron and the j-th output neuron; b j is the bias of the jth output neuron.
[0064] The mathematical expression of the tanh activation layer is:
[0065]
[0066] Among them, y i is the i-th output of the tanh activation layer, x i is the i-th input to the tanh activation layer.
[0067] The mathematical expression of the softmax activation layer is:
[0068]
[0069] Among them, y j is the j-th output of the softmax activation layer, x j is the j-th input of the softmax activation layer;
[0070] Step 5: Create a regression network. The network is a series structure, which consists of input layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, and regression output layer. The input layer has an input sample dimension of 3; the regression output layer has an output result dimension of 1; the mathematical expressions of the other layers are:
[0071] The mathematical expression of the fully connected layer is:
[0072]
[0073] Among them, x i is the input value of the i-th neuron; w ji is the weight connecting the i-th input neuron and the j-th output neuron; b j is the bias of the jth output neuron.
[0074] The mathematical expression of the tanh activation layer is:
[0075]
[0076] Among them, y i is the i-th output of the tanh activation layer, x i is the i-th input to the tanh activation layer.
[0077] Step 6: Create the input dataset X for the classification network CI , X CI It is a 6216-row 3-column matrix, where each row of data is a set of samples, representing a set of flight status data in step 1; create the output label dataset X of the classification network CO , X CO is a 6216-row, 1-column vector; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row (i=1,2,…N) is -1, X CO The i-th row element of is set to -1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is 1, X CO The i-th row element of is set to 1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is greater than -1 and less than 1, X CO The i-th row element of is set to 0;
[0078] Step 7: Place the X CO The set of row numbers whose elements are 0 is denoted as R0. CI Extract the data corresponding to the row number in the set R0 as the regression network input data set X RI , X RI N RMatrix with 3 rows and 3 columns, N R is the number of data samples in set R0, N R =822, each row of data is a set of samples, representing a set of flight status data. Create a regression network output data set X RO , X RO It is a vector with 822 rows and 1 column. RO Each row element value is X RI The optimal center of gravity position corresponding to each row of flight status data.
[0079] Step 8: X CI As the input data of the classification network, X CO As the output data of the classification network, it is used for training and testing of the classification network. RI As the input data of the regression network, X RO As the output data of the regression network, it is used for training and testing of the regression network.
[0080] The classification network model loss function is defined as the cross entropy loss CEL, and CEL is defined as:
[0081]
[0082] Where n is the number of data samples; C is the number of classification categories, C = 3; y ij is the true label (0 or 1) of the jth category for the i-th data sample; is the predicted probability that the i-th data sample belongs to the j-th category. The optimization training method is the Adam algorithm.
[0083] The regression network model uses mean square error (MSE) as the loss function, and MSE is defined as:
[0084]
[0085] Where n is the number of data samples; y i is the true value of the i-th data sample; is the predicted value of the i-th data sample. The optimization training method is the Adam algorithm.
[0086] Step 9: Select 1243 sets of flight status data within the aircraft envelope to predict the corresponding optimal center of gravity position. The prediction process is as follows: Figure 1 Each set of flight status data is sequentially input into the trained classification network. If the output of the classification network is -1, the optimal center of gravity position corresponding to the flight status data is predicted to be -1; if the output of the classification network is 1, the optimal center of gravity position corresponding to the flight status data is predicted to be 1.
[0087] If the output of the classification network is 0, the flight status data is fed into the trained regression network. The output of the regression network is the predicted optimal center of gravity position corresponding to the flight status data. This completes the prediction of the aircraft's optimal center of gravity position.
[0088] Use MATLAB to simulate the above steps and get Figure 2 The prediction results are shown in Figure 1. The true value is denoted as Test, the data is represented by a straight line, and the predicted value is denoted as Prediction, and the data is represented by hollow circles. It can be seen that the network's prediction of the center of gravity position is very close to the true value.
[0089] Comparative Example
[0090] The difference between the comparative example and Example 1 is that the classification network model is not constructed, and the regression network model is directly used to predict the center of gravity position, which specifically includes the following steps:
[0091] Step 1: Select 6216 sets of flight status data and the forward and aft extreme positions of the aircraft's center of gravity within the aircraft envelope. Each set of flight status data includes: aircraft weight, flight altitude, and flight Mach number.
[0092] Step 2: Obtain the optimal center of gravity position corresponding to each set of flight conditions in step 1 using a computational fluid dynamics method. The optimal center of gravity position is determined by setting a set of flight conditions in a computational fluid dynamics calculation, calculating the aircraft's trim drag, and then adjusting the aircraft's center of gravity position along the aircraft's body axis until the aircraft's trim drag is minimized. The center of gravity position at this point is the optimal center of gravity position.
[0093] Step 3: Based on the forward and rearward extreme positions of the aircraft's center of gravity, the optimal center of gravity position corresponding to each set of flight states obtained in step 2 is normalized and preprocessed. In step 3, the specific process of normalization preprocessing includes:
[0094]
[0095] in is the normalized optimal center of gravity position; G is the unnormalized optimal center of gravity position; G min is the front limit position of the center of gravity; G max is the extreme position behind the center of gravity; The range of the value is [-1,1], the limit position before the center of gravity Limit position behind the center of gravity
[0096] Step 4: Create a regression network. The network is a series structure, which consists of input layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, fully connected layer, tanh activation layer, and regression output layer. The input layer has an input sample dimension of 3; the regression output layer has an output result dimension of 1; the mathematical expressions of the other layers are:
[0097] The mathematical expression of the fully connected layer is:
[0098]
[0099] Among them, x i is the input value of the i-th neuron; w ji is the weight connecting the i-th input neuron and the j-th output neuron; b j is the bias of the jth output neuron.
[0100] The mathematical expression of the tanh activation layer is:
[0101]
[0102] Among them, y i is the i-th output of the tanh activation layer, x i is the i-th input to the tanh activation layer.
[0103] Step 5: Create the input dataset X for the regression network CI , X CI It is a 6216-row 3-column matrix, where each row of data is a set of samples, representing a set of flight status data in step 1; create the output dataset X of the regression network RO , X RO is a 6216-row, 1-column vector, X RO Each row element value is X RI The optimal center of gravity position corresponding to each row of flight status data.
[0104] Step 6: X RI As the input data of the regression network, X RO As the output data of the regression network, it is used for training and testing of the regression network.
[0105] The regression network model uses mean square error (MSE) as the loss function, and MSE is defined as:
[0106]
[0107] Where n is the number of data samples; y i is the true value of the i-th data sample; is the predicted value of the i-th data sample. The optimization training method is the Adam algorithm.
[0108] Step 7: Select 1,243 sets of flight status data within the aircraft's envelope to predict the corresponding optimal center of gravity position. Each set of flight status data is sequentially input into the trained regression network. The output of the regression network is the predicted optimal center of gravity position for that flight status data. This completes the aircraft's optimal center of gravity prediction.
[0109] Use MATLAB to simulate the above steps and get Figure 3 The prediction results are shown in the figure. The true value is marked as Test, the data is represented by a straight line, and the predicted value is marked as Prediction, and the data is represented by hollow circles. It can be seen that the network's prediction of the center of gravity position deviates significantly from the true value, and the prediction accuracy is lower than the method described in the present invention.
Claims
1. A method for predicting the optimal center of gravity of an aircraft based on a deep neural network, characterized in that: The specific steps include: Step 1: Select N sets of flight state data and the forward and rearward extreme positions of the aircraft's center of gravity within the aircraft envelope; Step 2: Obtain the optimal center of gravity position corresponding to each set of flight states in Step 1 based on experimental tests or computational fluid dynamics methods; Step 3: Perform normalization preprocessing on the optimal center of gravity position corresponding to each set of flight states obtained in Step 2 according to the forward and rearward extreme positions of the aircraft's center of gravity; Step 4: Create a classification network; Step 5: Create a regression network; Step 6: Create an input data set X for the classification network CI , and output label dataset X CO If X CI The optimal center of gravity position corresponding to the flight status data of the i-th row (i=1,2,…N) is -1, X CO The i-th row element of is set to -1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is 1, X CO The i-th row element of is set to 1; if X CI The optimal center of gravity position corresponding to the flight status data of the i-th row is greater than -1 and less than 1, X CO Set the i-th row element of to 0; Step 7: Set X CO The set of row numbers whose elements are 0 is denoted as R0. CI Extract the data corresponding to the row number in the set R0 as the regression network input data set X RI ; Create regression network output dataset X RO , X RO Each row element value is X RI The optimal center of gravity position corresponding to each row of flight status data; Step 8: Take X CI As the input data of the classification network, X CO As the output data of the classification network, it is used for training and testing of the classification network; RI As the input data of the regression network, X RO As the output data of the regression network, it is used for training and testing the regression network; Step 9: Select several sets of flight status data within the aircraft envelope to predict the corresponding optimal center of gravity position.
2. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, characterized in that: In step 2, the method for determining the optimal center of gravity position is: in experimental testing or computational fluid dynamics calculations, a set of flight conditions are set, the aircraft's trim resistance is tested or calculated, and then the aircraft's center of gravity position is adjusted along the aircraft's body axis until the aircraft's trim resistance reaches a minimum. The center of gravity position at this time is the optimal center of gravity position.
3. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: In step 3, the specific process of normalization preprocessing includes: in is the normalized optimal center of gravity position; is the unnormalized optimal center of gravity position; is the front limit position of the center of gravity; is the extreme position behind the center of gravity; The range of the value is [-1,1], the limit position before the center of gravity =-1, extreme position behind the center of gravity =1.
4. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: In step 4, the input sample dimension of the input layer is 3; the output dimension of the classification output layer is 3; the mathematical expressions of the other layers are: The mathematical expression of the fully connected layer is: (1) in, is the input value of the i-th neuron; is the weight connecting the i-th input neuron and the j-th output neuron; is the bias of the jth output neuron; The mathematical expression of the tanh activation layer is: (2) in, is the i-th output of the tanh activation layer, is the i-th input of the tanh activation layer; The mathematical expression of the softmax activation layer is: (3) in, is the j-th output of the softmax activation layer, is the j-th input to the softmax activation layer.
5. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: In step 5, the input sample dimension of the input layer is 3; the output result dimension of the regression output layer is 1; the mathematical expressions of the other layers are: The mathematical expression of the fully connected layer is: (4) in, is the input value of the i-th neuron; is the weight connecting the i-th input neuron and the j-th output neuron; is the bias of the jth output neuron; The mathematical expression of the tanh activation layer is: (5) in, is the i-th output of the tanh activation layer, is the i-th input to the tanh activation layer.
6. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: The classification network model loss function is defined as the cross entropy loss CEL, and CEL is defined as: (6) Where n is the number of data samples; C is the number of classification categories; is the true label (0 or 1) of the jth category for the i-th data sample; is the predicted probability that the i-th data sample belongs to the j-th category.
7. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: The regression network model uses mean square error (MSE) as the loss function, and MSE is defined as: (7) Where n is the number of data samples; is the true value of the i-th data sample; is the predicted value of the ith data sample.
8. The method for predicting the optimal center of gravity of an aircraft based on a deep neural network according to claim 1, wherein: In step 8, the optimization training method is the Adam algorithm.