Aircraft structure crack damage prediction method based on grey neural network under random uncertainty factors

Abstract

The invention provides an aircraft structure crack damage prediction method based on a grey neural network under random uncertainty factors, and the method comprises the steps: firstly obtaining the structural crack historical data of a to-be-analyzed aircraft, and building a grey model for data prediction according to the structural crack historical data; and then utilizing the obtained grey model prediction sequence to output the structure crack prediction data of the next year through the trained neural network. According to the method, the grey theory and the neural network are combined, the damage of the aircraft structure is predicted through the grey theory under the small sample condition, then the neural network is used for conducting deep learning fitting on the predicted value of the grey theory, the neural network topological structure and the initial weight value are determined according to the grey theory, and therefore the prediction precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aircraft structure crack damage prediction, in particular to an aircraft structure crack damage prediction method based on a grey neural network under random uncertainty factors. BACKGROUND

[0002] With the increase of the service life of the aircraft, the failure rate of the aircraft gradually increases, and how to effectively evaluate the cracks in the aircraft structure is an important problem that needs to be solved.

[0003] For an aircraft, it is very difficult to establish a mathematical or physical model for component or system failure prediction, so the historical data of each stage of aircraft component or system design, operation, inspection and maintenance becomes the main means to master the system performance degradation. The existing method directly uses the obtained historical data for prediction, and the prediction result is mostly a specific numerical value. However, the aircraft structure crack data belongs to small sample data, and due to the uncertainty and fuzziness of the aircraft structure crack data, directly using the obtained historical data for prediction also has the problems of insufficient prediction accuracy and stability. SUMMARY

[0004] In view of the problems in the prior art, the present application provides an aircraft structure crack damage prediction method based on a grey neural network under random uncertainty factors, which is aimed at the uncertainty and fuzziness of the crack data, uses quantile sampling method, combines grey theory with neural network, and establishes the probability density function of the crack data in the future time period according to the mean and variance of the prediction value, thereby improving the prediction accuracy and stability.

[0005] The technical scheme of the present application is as follows:

[0006] The aircraft structure crack damage prediction method based on a grey neural network under random uncertainty factors comprises the following steps:

[0007] Step 1: obtaining the structure crack historical data of the aircraft to be analyzed, and establishing a grey model according to the structure crack historical data to predict the data;

[0008] Step 2: using the grey model prediction sequence obtained in step 1 to output the next year's structure crack prediction data through the trained neural network.

[0009] Further, step 1 specifically comprises the following steps:

[0010] Step 1.1: Obtain the structure crack data of each year of the aircraft structure history to be analyzed, and perform fixed quantile sampling on the probability density distribution function of the structure crack data of each year to obtain a crack data vector of each year. The data vectors of each year are combined into a data matrix Y, where Y is an m-row n-column matrix:

[0011]

[0012] wherein represents the structure crack data corresponding to the nth quantile point in the crack data vector of the mth year;

[0013] Step 1.2: Perform grey index test and quasi-smoothness condition judgment on each column of the data matrix Y. If the grey index and quasi-smoothness conditions are met, proceed to step 1.3, otherwise check the abnormal values in the data and repair or remove the abnormal values;

[0014] Step 1.3: Model each column of data in the data matrix Y using grey theory to obtain a grey model prediction sequence of each column of data.

[0015] Further, the specific process of step 1.2 is as follows:

[0016] Take the 0th column data in the data matrix Y as an example, and transpose it into a sequence There are m non-negative original observation values;

[0017] Perform quasi-smoothness test on the sequence y 0 , and set as the level ratio of the original sequence, as the smoothness ratio of the original sequence;

[0018] If the smoothness ratio p(k) of the sequence y 0 satisfies:

[0019] and p(k) ∈ [0, ε], k = 2, 3, …, m; ε < 0.5

[0020] Then y 0 is called a quasi-smooth sequence;

[0021] For any k value, if σ(k) ∈ (0, 1) is satisfied, the sequence y 0 is said to have a negative grey index law;

[0022] For any k value, if σ(k) ∈ (1, b) is satisfied, where b is a real number not less than 1, the sequence y 0 is said to have a positive grey index law;

[0023] For any k value, if σ(k) ∈ (a, b) is satisfied, a-b = Δ, the sequence y 0The gray index law with absolute gray scale Δ.

[0024] Further, the process of step 1.3 is:

[0025] Take the sequence y 0 for example, the GM(1,1) model is established as follows:

[0026] y 0 is a non-negative original data sequence, is the 1-AGO first-order accumulation generated sequence of y 0 , z 0 is the adjacent mean value equal weight generated sequence, then

[0027]

[0028] wherein

[0029]

[0030] The gray differential equation is obtained as follows:

[0031]

[0032] is the GM(1,1) model, wherein a is the development coefficient, and b is the gray action amount;

[0033] Let:

[0034] a * = [a, b] T

[0035]

[0036] The matrix form of the GM(1,1) model is obtained as follows:

[0037]

[0038] M = Na *

[0039] The least square estimation of the above equation group is obtained by using the least square method:

[0040] a * = (N T N) -1 N T M

[0041] At this time, the equation:

[0042]

[0043] is the whitening equation of the GM(1,1) model, and the solution of the equation is the time response function, that is​

[0044]

[0045] Thus, the time response sequence of the GM(1,1) model gray differential equation is obtained Each element is:

[0046]

[0047] The cumulative reduction is performed by using the time response sequence, and a gray model prediction sequence of the sequence y 0 is obtained Each element in the formula is:

[0048]

[0049] Further, in step 2, the neural network is trained by taking the prediction sequence of the gray model as input and taking the original data sequence as label; the neural network is a four-layer BP neural network, and the four layers are LA, LB, LC and LD respectively; ω 11 , ω 21 , ω 22 , ω 31 and ω 32 are network weights between layers, and θ is a threshold value of an output node; initial values of the weights and the threshold value are:

[0050] ω 11 =a;

[0051]

[0052] Then, the network error is back-propagated to realize adjustment and optimization of network parameters by the self-learning ability of the BP network; after the neural network is trained, a prediction value of the neural network is output.

[0053] Further, in step 2, the activation function of the LB layer neuron in the network structure is selected as a Sigmoid function, and the activation functions of other layers are linear functions.

[0054] Further, after the structural crack prediction data of the next year is obtained, the mean and the variance are calculated, and then a probability density function of the structural crack data of the next year is obtained, which is used to draw a probability density distribution function image.

[0055] In addition, the application further provides an electronic device and a readable storage medium:

[0056] An electronic device, comprising a processor, a memory, the memory being configured to store one or more programs;

[0057] When the one or more programs are executed by the processor, the above method is implemented.

[0058] A readable storage medium, storing a computer program, when the computer program is executed by a processor, realizes the above method.

[0059] Advantages

[0060] The aircraft structure crack damage prediction method based on the grey neural network under random uncertainty factors provided by the application combines the grey theory and the neural network, firstly predicts the damage of the aircraft structure under small sample conditions through the grey theory, then uses the neural network to perform deep learning fitting on the predicted value of the grey theory, and the neural network topology structure and weight initial value are determined according to the grey theory, so that the prediction accuracy is improved.

[0061] Additional aspects and advantages of the application will be in part apparent and in part pointed out hereinafter. BRIEF DESCRIPTION OF DRAWINGS

[0062] The above and / or additional aspects and advantages of the application will become apparent and be readily understood from the following description, taken in conjunction with the accompanying drawings, in which:

[0063] Figure 1 : Sampling schematic diagram;

[0064] Figure 2 : Neural network structure diagram;

[0065] Figure 3 : Prediction flowchart. DETAILED DESCRIPTION

[0066] The embodiments of the application are described in detail below, which are exemplary and are intended to explain the application, and cannot be understood as a limitation of the application.

[0067] The embodiment combines the grey theory and the neural network, and proposes an aircraft structure crack damage prediction method based on the grey neural network under random uncertainty factors, which specifically includes the following processes:

[0068] Step 1: Obtain the structure crack historical data of the aircraft to be analyzed, and establish a grey model according to the structure crack historical data to perform data prediction;

[0069] Step 1.1: Obtain the structure crack data y of each year of the aircraft structure to be analyzed, for example, crack length data or crack depth data, calculate the mean value mu and the variance sigma of the structure crack data of each year, and obtain the probability density function diagram of the aircraft structure crack data of each year. The structure crack data of each year is normally distributed:

[0070]

[0071] The fixed quantile sampling of the probability density distribution function of the structural crack data of each year is performed to obtain the crack data vector of each year, wherein the crack data vector of the mth year is where n is the number of quantiles. Here, since the crack data is normally distributed, a standardization transformation can be performed The value of each quantile is obtained by looking up the standard normal distribution table and further Here represents the structural crack data corresponding to the nth quantile in the crack data vector of the mth year, μ m and σ m are the mean and variance of the structural crack data of the mth year.

[0072] The obtained crack data is summarized as a data vector The data vectors of each year are combined into a data matrix Y, wherein Y is an m-row and n-column matrix:

[0073]

[0074] where represents the structural crack data corresponding to the nth quantile in the crack data vector of the mth year.

[0075] Step 1.2: Perform grey index test and quasi-smoothness condition judgment on each column in the data matrix Y, if the grey index and quasi-smoothness conditions are met, go to step 1.3, otherwise check the abnormal values in the data and repair or remove the abnormal values.

[0076] Take the 0th column data in the data matrix Y as an example, transpose it into a sequence There are m non-negative original observation values.

[0077] Perform quasi-smoothness test on the sequence y 0 , let be the order ratio of the original sequence, and be the smoothness ratio of the original sequence.

[0078] If the smoothness ratio ρ(k) of the sequence y 0 satisfies:

[0079] and ρ(k) ∈ [0, ε], k = 2, 3, …, m; ε < 0.5

[0080] then y 0 is called a quasi-smooth sequence;

[0081] For any k value, if σ(k) ∈ (0, 1) is satisfied, the sequence y 0 is said to have a negative grey index law;

[0082] For any k value, if σ(k) ∈ (1, b) is satisfied, where b is a real number not less than 1, the sequence y 0 has a positive gray index law;

[0083] For any k value, if σ(k) ∈ (a, b) is satisfied, a-b = Δ, the sequence y 0 has an absolute gray scale Δ of gray index law.

[0084] Step 1.3: After meeting the requirements of gray index and smoothness test, use the data matrix Y to model using gray theory to obtain the gray model prediction sequence;

[0085] Take the sequence y 0 for example, establish the GM(1, 1) model:

[0086] y 0 is a non-negative original data sequence, is the 1-AGO first-order cumulative generation sequence of y 0 , z 0 is the neighbor mean equal weight generation sequence, then

[0087]

[0088] where

[0089]

[0090] The gray differential equation is obtained:

[0091]

[0092] is the GM(1, 1) model, where a is the development coefficient, and b is the gray action amount.

[0093] Let:

[0094] a * = [a, b] T

[0095]

[0096] The matrix form of the GM(1, 1) model is obtained:

[0097]

[0098] M = Na *

[0099] The least square estimation of the above equation group is obtained by using the least square method:

[0100] a *= (N T N) -1 N T M

[0101] The equation at this time is called:

[0102]

[0103] The equation is a whitening equation of the GM(1,1) model, and the solution of the equation is a time response function, that is,

[0104]

[0105] Thus, the time response sequence of the GM(1,1) model gray differential equation is obtained Each element is:

[0106]

[0107] The cumulative reduction is performed using the time response sequence, and the gray model prediction sequence of the sequence y 0 is obtained. Each element in the gray model prediction sequence is:

[0108]

[0109] Step 1.4: For other columns in the data matrix Y, perform steps 1.2 and 1.3 to obtain the corresponding gray model prediction sequence.

[0110] Step 2: Use the gray model prediction sequence obtained in step 1 to output the next year's crack prediction data through the trained neural network.

[0111] For example, the gray model prediction sequence is obtained through step 1. Based on the theory of gray model, the damage of the aircraft structure can be predicted under the condition of small sample, but in the process of approximating complex nonlinear function, a large error will be generated, therefore, the gray theory is further combined with the neural network in this embodiment, the prediction sequence of the gray model is taken as the input, the original data sequence y 0 is taken as the label for neural network training, and the neural network weight is constructed according to the time response function of the gray model.

[0112] In this embodiment, the BP neural network is selected, the transfer function in the BP neural network adopts the S-shaped function, in order to combine the time response function with the BP network topology structure, the time response function of the gray model is changed to obtain

[0113]

[0114] It can be seen that the right side of the equation is basically the same as the forward input operation mode of the BP network, and the mapping modeling can be met by transforming the structure of the network.

[0115] According to the above transformed time response function, the network topology structure is established as shown in Figure 2 The structure is a four-layer BP neural network, which is LA, LB, LC and LD respectively; Δ in the figure is the input value of the network, that is, the prediction value of the grey model ω 11 , ω 21 , ω 22 , ω 31 and ω 32 are the network weights between each layer, and θ is the threshold value of the output node. After the establishment of the network topology structure, the information extracted from the known data by the grey model is used to establish the response function, and the initial values of the parameters (weights, threshold values) in the network are determined as follows:

[0116] ω 11 =a;

[0117]

[0118] Then the network error is back-propagated through the self-learning ability of the BP network to realize the adjustment and optimization of the network parameters. The activation function of the LB layer neurons in the network structure is selected as the Sigmoid function, and the activation functions of the other layers are linear functions f(x)=x, so that the grey model is mapped into the BP network.

[0119] After the neural network is trained through the above process, the prediction value of the neural network is output

[0120] Step 3: For all grey model prediction sequences, the corresponding neural network prediction values are obtained by step 2, and the final prediction data of the structure crack in the future m+1 year is obtained The predicted value conforms to the normal distribution. According to the data vector obtained by prediction, the mean μ m+1 and the variance σ m+1 are calculated, and then the probability density function of the crack data in the future m+1 year is obtained, which is used to draw the probability density distribution function image.

[0121] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and modifications to the above embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A method for predicting crack damage in aircraft structures under random uncertainty factors based on grey neural network, characterized by: The following steps are involved: Step 1: Obtain the historical data of structural cracks of the aircraft to be analyzed, and establish a grey model for data prediction based on the historical data of structural cracks; Step 2: Use the grey model prediction sequence obtained in step 1 to output the structural crack prediction data for the next year through the trained neural network.

2. The method for predicting aircraft structural crack damage based on a grey neural network under random uncertainty factors according to claim 1 is characterized by: Step 1 specifically includes the following steps: Step 1.1: Obtain the structural crack data for each year of the aircraft structure to be analyzed. Perform fixed quantile sampling on the probability density distribution function of the structural crack data for each year to obtain the crack data vector for each year. Combine the data vectors for each year into a data matrix Y, where Y is a matrix with m rows and n columns: in Represents the structural crack data corresponding to the nth quantile in the crack data vector of the mth year; Step 1.2: Perform a gray index test and quasi-smoothness condition check on each column in the data matrix Y. If the gray index and quasi-smoothness conditions are met, proceed to step 1.

3. Otherwise, check for outliers in the data and repair or remove them. Step 1.3: Use grey theory to model each column of data in the data matrix Y and obtain the grey model prediction sequence of each column of data.

3. The method for predicting crack damage in aircraft structures based on a grey neural network under random uncertainty factors according to claim 2 is characterized by: The specific process of step 1.2 is as follows: Take the data in column 0 of the data matrix Y as an example and transpose it into a sequence There are m non-negative original observations; For sequence y 0 To conduct quasi-smoothness test, is the original sequence level ratio, is the smoothness ratio of the original sequence; If the sequence y 0 The smoothness ratio ρ(k) satisfies: Moreover, p(k)∈[0,ε],k=2,3,…,m; ε<0.5 Then it is called y 0 is a quasi-smooth sequence; For any value of k, if σ(k)∈(0,1) is satisfied, then the sequence y is called 0 It has a negative gray index law; For any value of k, if σ(k)∈(1,b) is satisfied, where b is a real number not less than 1, then the sequence y is called 0 Positive gray index law; For any value of k, if σ(k)∈(a,b), ab=Δ, then the sequence y is called 0 It has a gray index law with an absolute grayscale of Δ.

4. The method for predicting crack damage in aircraft structures based on a grey neural network under random uncertainty factors according to claim 3 is characterized by: The process of step 1.3 is: With sequence y 0 For example, establish the GM(1,1) model: y 0 is a non-negative original data sequence, y 0 The 1-AGO first-order cumulative generation sequence, z 0 for The neighboring mean equal weights generate a sequence, then in Then we get the grayscale differential equation: is the GM(1,1) model, where a is the development coefficient and b is the gray action; make: a * =[a,b] T Then the matrix form of the GM(1,1) model is: I = In * For the above system of equations, the least squares method is used to obtain the least squares estimate: a * =(N T N) -1 N T M Now the equation is called: is the whitening equation of the GM(1,1) model, and the solution of this equation is the time response function, that is, Thus, the time response sequence of the GM(1,1) model grey differential equation is obtained The elements are: Using the time response sequence to perform cumulative reduction, we can get the sequence y 0 Grey model prediction sequence The elements are:

5. The method for predicting aircraft structural crack damage based on a grey neural network under random uncertainty factors according to claim 2 is characterized by: In step 2, the prediction sequence of the grey model is used as input and the original data sequence is used as label for neural network training; the neural network is a four-layer BP neural network, namely LA, LB, LC and LD; ω 11 ,ω 21 ,ω 22 ,ω 31 and ω 32 are the network weights between each layer, θ is the threshold of the output node, and the initial values ​​of the weights and thresholds are: oh 11 =a; Then, the network error is back-propagated through the self-learning ability of the BP network to adjust and optimize the network parameters; after the neural network training is completed, the predicted value of the neural network is output.

6. The method for predicting crack damage in aircraft structures based on grey neural networks under random uncertainty factors according to claim 5 is characterized by: In step 2, the activation function of the LB layer neurons in the network structure is selected as the Sigmoid function, and the activation functions of other layers are all linear functions.

7. The method for predicting aircraft structural crack damage based on a grey neural network under random uncertainty factors according to claim 1 is characterized by: After obtaining the structural crack prediction data for the next year, the mean and variance are calculated, and then the probability density function of the structural crack data for the next year is obtained, which is used to draw the probability density distribution function image.

8. An electronic device comprising a processor and a memory, wherein the memory is used to store one or more programs; characterized in that: When the one or more programs are executed by the processor, the method according to any one of claims 1 to 7 is implemented.

9. A readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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