Aero-engine blade missing data complementation method based on ultrasonic guided wave detection

Abstract

The invention provides an aero-engine blade missing data completion method based on ultrasonic guided wave detection, and the method comprises the steps: firstly, carrying out the projection of a three-dimensional aero-engine blade, and carrying out the grid division of a projection surface; arranging ultrasonic guided wave sensors on the grid points for detection to obtain a detection signal matrix; secondly, setting a missing rate to obtain an incomplete detection signal matrix, and obtaining a mask matrix according to the incomplete detection signal matrix; constructing a missing data completion network / discrimination network, and inputting the incomplete detection signal matrix and the mask matrix into the missing data completion network to obtain an output matrix; inputting the output matrix and the mask matrix into a missing data discrimination network to obtain an output result; and finally, carrying out iterative training on the two networks, and obtaining complemented detection data when the overall loss is kept stable. Based on the optimal network parameters, accurate detection data are complemented at data missing positions, and a reliable data basis is provided for subsequent detection of aero-engine blade defects.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aero-engine blade defect detection, and particularly to an aero-engine blade missing data completion method based on ultrasonic guided wave detection. BACKGROUND

[0002] As a core component of energy conversion, the aero-engine blade is long-term in extreme working conditions of high temperature, high pressure and high speed. In a complex service environment, the blade surface also needs to cope with multiple damage mechanisms such as high-speed sand impact, foreign object impact and thermal coupling effect. The above extreme working conditions are prone to cause the peeling of the thermal barrier coating on the surface of the blade, and induce the initiation of internal micro-cracks or creep deformation and other progressive defects, which may eventually lead to blade fracture failure, engine surge and even catastrophic accidents such as in-flight disintegration. Therefore, it is of great significance to develop aero-engine blade defect detection technology.

[0003] For aero-engine blade detection, the industry usually adopts visual or acoustic detection methods. For example, the invention patent with the application number CN119379623A discloses an aero-engine high-pressure turbine blade full-automatic inspection method, system and equipment. The invention first obtains image data of the blade to be detected, inputs the image data into a trained blade damage recognition model to predict whether there is damage, then calculates the pixel distance of the key feature points on the image data to obtain the actual size of the damage. The invention patent with the application number CN120668776A discloses an in-service electromagnetic acoustic detection system and method for aero-engine blades, which ensures that dangerous cracks exposed outside the blade tenon can be reliably detected by eddy current method, and also ensures that internal fatigue damage can be detected by ultrasonic method. However, the limitation of the ultrasonic method is that it can only detect defects below the sensor.

[0004] To address this limitation, the industry has developed ultrasonic guided wave detection technology, which can detect data across the entire waveguide range. For accurate results, a sufficient number of sensors in a uniform arrangement are typically required. However, due to the complex shape of aero-engine blades, sensor array arrangement is difficult, easily leading to the complete loss of data from individual sensors, which can be considered a non-uniform sensor arrangement. Patent application CN120703216A discloses an aero-engine blade damage detection method based on an improved ultrasonic sparse reconstruction algorithm. However, this invention addresses damage detection under uniform but sparse sensor arrangement, and still cannot solve the problem of decreased detection accuracy caused by data loss under non-uniform sensor arrangement. Patent application CN120724052A discloses an interpolation generation method, device, equipment, and product for industrial data acquisition. This invention uses a generative adversarial network (GAN), but does not specify the network parameter optimization method, and the added noise is mean noise. Therefore, the limitation of this invention is that it cannot utilize optimal network parameters to generate missing data, resulting in a discrepancy between the generated data and the actual data. Summary of the Invention

[0005] To address the shortcomings of the aforementioned background technology, this invention proposes a method for completing missing data in aero-engine blades based on ultrasonic guided wave detection. Based on optimal network parameters, it completes accurate detection data at the missing data points, providing a reliable data foundation for subsequent detection of defects in aero-engine blades.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] A method for completing missing data in aero-engine blades based on ultrasonic guided wave detection, the steps of which are as follows:

[0008] Step 1: Project the three-dimensional aero-engine blade and divide the projection surface into a mesh; place ultrasonic guided wave sensors on the mesh points to detect and obtain a complete detection signal dataset;

[0009] Step 2: Based on the complete detection signal dataset, set the missing rate to obtain the incomplete detection signal dataset;

[0010] Step 3: Obtain the mask matrix based on the incomplete detection signal dataset, and normalize the incomplete detection signal dataset;

[0011] Step 4: Construct a missing data completion network. Input the normalized incomplete detection signal dataset and mask matrix into the missing data completion network to obtain the output matrix.

[0012] Step 5: Construct a missing data discrimination network, and input the output matrix and mask matrix into the missing data discrimination network to obtain the output result;

[0013] Step 6: Calculate the loss of the missing data completion network and the missing data discrimination network separately, and then weight and fuse the two losses to obtain the overall loss;

[0014] Step 7: Divide the inputs of the missing data completion network and the missing data discrimination network into multiple batches and repeat steps 4 to 6 for iterative training. Stop training when the overall loss remains stable to obtain the completed detection data, and then perform inverse normalization on the completed detection data.

[0015] Preferably, the grid size is N1×N2, and ultrasonic guided wave sensors are arranged at the grid points. All sensors emit excitation signals in turn, and all sensors receive detection signals synchronously to form a detection signal matrix. Where N1 represents the transmitting element number, N2 represents the receiving element number, and L represents the detection signal length, i.e., a one-dimensional detection signal vector; M aero-engine blades are detected to form a complete detection signal dataset.

[0016] Preferably, the method for obtaining the incomplete detection signal dataset is as follows: setting a missing rate p, that is, for each detection signal matrix in the complete detection signal dataset, randomly losing some of the detection signal vectors corresponding to the transmit array element index or the receive array element index to form an incomplete detection signal dataset, and setting the data loss part in the incomplete detection signal dataset as NaN.

[0017] Preferably, the method for obtaining the mask matrix based on the incomplete detection signal dataset is as follows:

[0018] Create a mask matrix set with the same size and dimensions as the incomplete detection signal dataset. Positions in the mask matrix set containing data are set to 1, while positions containing missing data are set to 0. For a single aero-engine blade, three three-dimensional matrices can be obtained: the complete detection signal matrix and the... Incomplete detection signal matrix Mask matrix The three three-dimensional matrices are transformed into three two-dimensional matrices, that is, the second and third dimensions are merged into one dimension, which is the complete detection signal matrix. Incomplete detection signal matrix Mask matrix .

[0019] Preferably, for incomplete detection signal matrix After performing min-max normalization, we get:

[0020] (1);

[0021] Where min represents The minimum value, max represents The maximum value, This is a normalized incomplete detection signal matrix.

[0022] Preferably, the missing data completion network is a fully connected network, comprising one input layer, two fully connected layers, and one output layer, which processes the normalized incomplete detection signal matrix. Mask matrix As input The data is fed into the input layer of the missing data completion network, and then passes through a fully connected layer and an output layer:

[0023] (2);

[0024] (3);

[0025] in, For element-wise product, , This represents the number of hidden layer nodes. To complete the weight matrices of the two fully connected layers and the output layer of the network, respectively, using the missing data, To complete the biases of the two fully connected layers and the output layer of the network to fill in the missing data, To complete the outputs of the two fully connected layers and the output layer of the network to fill in the missing data, the ReLU function is used for the activation function of the fully connected layers and the Sigmoid function is used for the activation function of the output layer.

[0026] Replace the values ​​at the locations containing data in the incomplete detection signal matrix with the corresponding values ​​at the output matrix of the output layer to obtain the replaced output matrix. :

[0027] (4).

[0028] Preferably, the missing data discrimination network adopts a fully connected network, comprising one input layer, two fully connected layers, and one output layer; firstly, a reinforcement matrix is ​​created. :

[0029] (5);

[0030] in, ;

[0031] The replaced output matrix Strengthening Matrix Vector concatenation is performed to obtain the input for the missing data discrimination network. ,

[0032] (6);

[0033] Then, through the fully connected layer and the output layer:

[0034] (7);

[0035] in, To determine the weight matrices of the two fully connected layers and the output layer of the network for missing data, To determine the biases of the two fully connected layers and the output layer of the network in case of missing data, The outputs of the two fully connected layers and the output layer of the network are used to determine the missing data.

[0036] Preferably, the method for obtaining the overall loss is as follows:

[0037] Calculate the loss of the missing data discrimination network. :

[0038] (8);

[0039] in, Represents a local minimum value; Expressing expectations;

[0040] Calculate the loss of the network for imputing missing data. :

[0041] (9);

[0042] The two losses are combined to obtain the overall loss. :

[0043] (10);

[0044] in, , All are coefficients.

[0045] Preferably, the method for inverse normalizing the completed detection data is as follows:

[0046] (11);

[0047] in, This represents the detection data after inverse normalization completion.

[0048] Preferably, during training, the parameter vector x includes the batch size m and coefficients. and The set of iteration counts k; during iterative training, global optimization is performed either manually or using the Hippo optimization algorithm. The update rule of the Hippo optimization algorithm consists of five steps: defining the parameter search space, initializing the population, evaluating the fitness of the initial population, iterative optimization, and outputting the results, as detailed below:

[0049] a) Define the parameter search space

[0050] The search space for batch size m is [16, 32, 64, 128, 256, 512, 1024, 2048, 4096], with coefficients... and The search space is 0-1, and the search space for the number of iterations k is [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000].

[0051] b) Initialize the population

[0052] Randomly generate the initial hippopotamus position. For floating-point parameters: coefficients and Use standard random initialization:

[0053] (12);

[0054] in, This is the initial position of the hippopotamus. , These are the lower and upper boundaries of the search space, respectively; A random number in the range [0,1].

[0055] For integer parameters: batch size m and number of iterations k, rounding is required after generation.

[0056] (13);

[0057] Where, round represents the rounding operation;

[0058] c) Assess the fitness of the initial population

[0059] use Train the network in steps four through six, record the network's loss on the validation set, and find the initial global optimum. and the local optimal position of each individual ;

[0060] (14);

[0061] Where MSE represents the mean squared error operation;

[0062] d) Iterative optimization

[0063] For each generation t from 1 to It includes four steps: water patrol stage, land foraging stage, location correction and evaluation, and greedy selection and updating.

[0064] Waterway cruising phase: For each hippo i, calculate its candidate position after the waterway cruising phase according to the formula. :

[0065] (15);

[0066] in, and A random number in the range [0,1]. This is the globally optimal position obtained after t-1 iterations;

[0067] Terrestrial foraging phase: Similarly, for each hippo i, calculate its candidate location after foraging on land. :

[0068] (16);

[0069] in, It was another hippopotamus randomly selected from the population; This represents the local optimal position found by the i-th hippo in the (t-1)th iteration;

[0070] Position correction and evaluation includes three steps: boundary handling, type conversion, and fitness evaluation. The boundary handling process involves checking... and Check if each parameter exceeds its preset range; if so, use a boundary handling strategy to correct it; in type conversion, check if... and The integer parameters in the algorithm are rounded down to obtain the candidate parameter combinations that meet the requirements; in the fitness evaluation, the modified parameters are used respectively. and Train the models and calculate their fitness values. and ;

[0071] Greedy selection and updating: First, compare , and The position with the lowest fitness value is selected as the next generation position for hippo i. Then, update the local optimal position of the individual. ,if ,but Otherwise, leave it unchanged; update the global optimal position. In all In the process, the one with the smallest fitness value is selected as the global optimum for the next generation;

[0072] e) Output results

[0073] The final globally optimal position after iteration. It is the optimal parameter vector x obtained by the Hippo optimization algorithm.

[0074] The beneficial effects of this invention are:

[0075] 1) The array elements in the sensor array of this invention are randomly removed, that is, the detection signal vectors corresponding to the serial numbers of some transmitting array elements or receiving array elements are randomly lost. Therefore, in practice, the sensor array of this invention can be randomly arranged, which can reduce the arrangement difficulty compared to the uniform arrangement of the sensor array.

[0076] 2) The parameter vector x in the missing data completion network / discrimination network of this invention can be obtained not only by manual optimization, but also by the Hippo optimization algorithm. The advantage of the Hippo optimization algorithm is that it can perform global automatic optimization, avoiding manual parameter tuning.

[0077] 3) This invention can complete the missing data at random positions when using ultrasonic guided wave to detect aero-engine blades, and can adaptively optimize parameters during global optimization training. Attached Figure Description

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0079] Figure 1 This is a flowchart from the present invention.

[0080] Figure 2 This is a flowchart of the data completion process in this invention.

[0081] Figure 3 This is the result of completing the missing data for the aero-engine blades in this invention.

[0082] Figure 4 Error analysis for completing missing data of aero-engine blades in this invention. Detailed Implementation

[0083] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0084] like Figure 1 As shown, this embodiment of the invention provides a method for missing data completion of aero-engine blades based on ultrasonic guided wave detection. The method involves projecting a three-dimensional aero-engine blade and dividing the projection surface into a mesh; arranging ultrasonic guided wave sensors at the mesh points to acquire a detection signal matrix; setting a missing rate to obtain an incomplete detection signal matrix; obtaining a mask matrix based on the incomplete detection signal matrix; performing dimensionality transformation on the above matrix; and inputting the matrix into a missing data completion network for missing data completion. During training, the network parameter vector is adaptively optimized globally using the Hippo optimization algorithm or manually optimized to minimize the overall loss, i.e., to ensure that the completed data closely approximates the actual data. The specific steps are as follows:

[0085] Step 1: Project the 3D aero-engine blade and divide the projection surface into an N1×N2 mesh; deploy ultrasonic guided wave sensors at the mesh points to acquire a complete detection signal dataset; all sensors emit excitation signals in turn, and all sensors synchronously receive detection signals to form a detection signal matrix. Where N1 represents the transmitting element number, N2 represents the receiving element number, and L represents the detection signal length, i.e., a one-dimensional detection signal vector; M aero-engine blades are detected to form a complete detection signal dataset.

[0086] Step 2: Based on the complete detection signal dataset, set the missing rate to obtain the incomplete detection signal dataset;

[0087] A missing rate p is set. For each detection signal matrix in a complete detection signal dataset, the detection signal vector corresponding to the missing transmit or receive element indices is deleting, forming an incomplete detection signal dataset. The missing data in the incomplete detection signal dataset is set to NaN. The missing rate p is typically a value between 0 and 1, and the missing transmit or receive element indices are randomly dropped.

[0088] Step 3: Obtain the mask matrix from the incomplete detection signal dataset and normalize the incomplete detection signal dataset; create a mask matrix set with the same size and dimensions as the incomplete detection signal dataset. For positions in the incomplete detection signal dataset containing data, set the corresponding position in the mask matrix set to 1; for missing data in the incomplete detection signal dataset, set the corresponding position in the mask matrix set to 0. For a single aero-engine blade, three three-dimensional matrices can be obtained: the complete detection signal matrix... Incomplete detection signal matrix Mask matrix The three three-dimensional matrices are transformed into three two-dimensional matrices, that is, the second and third dimensions are merged into one dimension, which is the complete detection signal matrix. Incomplete detection signal matrix Mask matrix .

[0089] For incomplete detection signal matrix After performing min-max normalization, we get:

[0090] (1);

[0091] Where min represents The minimum value, max represents The maximum value, This is a normalized incomplete detection signal matrix.

[0092] Step 4: Construct a missing data completion network. Input the normalized incomplete detection signal dataset and mask matrix into the missing data completion network to obtain the output matrix.

[0093] The missing data completion network uses a fully connected network, consisting of one input layer, two fully connected layers, and one output layer, to process the normalized incomplete detection signal matrix. Mask matrix As input The data is fed into the input layer of the missing data completion network, and then passes through a fully connected layer and an output layer:

[0094] (2);

[0095] (3);

[0096] in, For element-wise product, , This represents the number of hidden layer nodes. To complete the weight matrices of the two fully connected layers and the output layer of the network, respectively, using the missing data, To complete the biases of the two fully connected layers and the output layer of the network to fill in the missing data, To complete the outputs of the two fully connected layers and the output layer of the network to fill in the missing data, the ReLU function is used for the activation function of the fully connected layers and the Sigmoid function is used for the activation function of the output layer.

[0097] Replace the values ​​at the locations containing data in the incomplete detection signal matrix with the corresponding values ​​at the output matrix of the output layer to obtain the replaced output matrix. :

[0098] (4).

[0099] Step 5: Construct a missing data discrimination network, and input the output matrix and mask matrix into the missing data discrimination network to obtain the output result;

[0100] The missing data discrimination network adopts a fully connected network, consisting of one input layer, two fully connected layers, and one output layer; firstly, a reinforcement matrix is ​​created. :

[0101] (5);

[0102] in, ;

[0103] The replaced output matrix Strengthening Matrix Vector concatenation is performed to obtain the input for the missing data discrimination network. ,

[0104] (6);

[0105] Then, through the fully connected layer and the output layer:

[0106] (7);

[0107] in, To determine the weight matrices of the two fully connected layers and the output layer of the network for missing data, To determine the biases of the two fully connected layers and the output layer of the network in case of missing data, The outputs of the two fully connected layers and the output layer of the network are used to determine the missing data.

[0108] Step 6: Calculate the loss of the missing data completion network and the missing data discrimination network separately, and then weight and fuse the two losses to obtain the overall loss;

[0109] Calculate the loss of the missing data discrimination network. :

[0110] (8);

[0111] in, To represent a minimum value, avoid the occurrence of log(0), and It is a value close to 0; Expressing expectations;

[0112] Calculate the loss of the network for imputing missing data. :

[0113] (9);

[0114] The two losses are combined to obtain the overall loss. :

[0115] (10);

[0116] in, , All are coefficients.

[0117] Step 7: Divide the inputs of the missing data completion network and the missing data discrimination network into multiple batches and repeat steps 4 to 6 for iterative training. The training algorithm uses the SGD algorithm to minimize the overall loss, thus obtaining the completed detection data. Then, perform inverse normalization on the completed detection data.

[0118] (11);

[0119] in, This represents the detection data after inverse normalization completion.

[0120] Figure 2 The diagram illustrates the process of using ultrasonic guided waves to complete missing data in aero-engine blade detection. An incomplete detection signal dataset is obtained by setting a missing rate from a complete detection signal dataset. A mask matrix set is then derived from the incomplete detection signal dataset. This matrix undergoes dimensionality transformation and is input into a fully connected layer and a normalization layer to obtain the output matrix. The error between the output matrix and the incomplete detection signal matrix set is calculated as loss 1. The output matrix and the enhancement matrix are input into a fully connected layer and a logical output layer to obtain the prediction mask matrix. The error between the prediction mask matrix and the mask matrix set is calculated as loss 2. Loss 1 and loss 2 are combined as the overall loss. During training, the parameter vectors are adaptively optimized globally using manual tuning or the Hippo optimization algorithm to minimize the overall loss.

[0121] During training, the parameter vector x includes the batch size m and coefficients. and The set of iteration counts k; the update rule of the Hippo optimization algorithm consists of five steps: defining the parameter search space, initializing the population, evaluating the fitness of the initial population, iterative optimization, and outputting the results, as follows:

[0122] a) Define the parameter search space

[0123] The search space for batch size m is [16, 32, 64, 128, 256, 512, 1024, 2048, 4096], with coefficients... and The search space is 0-1, and the search space for the number of iterations k is [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000].

[0124] b) Initialize the population

[0125] Randomly generate the initial hippopotamus position. For floating-point parameters: coefficients and Use standard random initialization:

[0126] (12);

[0127] in, This is the initial position of the hippopotamus. , These are the lower and upper boundaries of the search space, respectively; A random number in the range [0,1].

[0128] For integer parameters: batch size m and number of iterations k, rounding is required after generation.

[0129] (13);

[0130] Where, round represents the rounding operation;

[0131] c) Assess the fitness of the initial population

[0132] use Train the network in steps four through six, record the network's loss on the validation set, and find the initial global optimum. and the local optimal position of each individual ;

[0133] (14);

[0134] Where MSE represents the mean squared error operation;

[0135] d) Iterative optimization

[0136] For each generation t from 1 to It includes four steps: water patrol stage, land foraging stage, location correction and evaluation, and greedy selection and updating.

[0137] Waterway cruising phase: For each hippo i, calculate its candidate position after the waterway cruising phase according to the formula. :

[0138] (15);

[0139] in, and A random number in the range [0,1]. This is the globally optimal position obtained after t-1 iterations;

[0140] Terrestrial foraging phase: Similarly, for each hippo i, calculate its candidate location after foraging on land. :

[0141] (16);

[0142] in, It was another hippopotamus randomly selected from the population; This represents the local optimal position found by the i-th hippo in the (t-1)th iteration;

[0143] Position correction and evaluation includes three steps: boundary handling, type conversion, and fitness evaluation. The boundary handling process involves checking... and Check if each parameter exceeds its preset range; if so, use a boundary handling strategy to correct it; in type conversion, check if... and The integer parameters in the algorithm are rounded down to obtain the candidate parameter combinations that meet the requirements; in the fitness evaluation, the modified parameters are used respectively. and Train the models and calculate their fitness values. and ;

[0144] Greedy selection and updating: First, compare , and The position with the lowest fitness value is selected as the next generation position for hippo i. Then, update the local optimal position of the individual. ,if ,but Otherwise, leave it unchanged; update the global optimal position. In all In the process, the one with the smallest fitness value is selected as the global optimum for the next generation;

[0145] e) Output results

[0146] The final globally optimal position after iteration. It is the optimal parameter vector x obtained by the Hippo optimization algorithm.

[0147] Figure 3 The image shows the results of data completion using ultrasonic guided waves to detect missing data in aero-engine blades. The horizontal axis represents the sensor number, and the vertical axis represents the sampling points. Figure 3 (a) is the detection signal matrix. Figure 3 (b) is an incomplete detection signal matrix. Figure 3 (c) is the prediction mask matrix. After missing data completion, the missing data for sensor 2 was completed.

[0148] Figure 4 The diagram shows the error analysis for data completion using ultrasonic guided waves to detect missing data in aero-engine blades. The horizontal axis represents the missing rate, ranging from 0.2 to 0.9, and the vertical axis represents the mean square error. After data completion, the mean square error is significantly lower than before completion.

[0149] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for completing missing data in aero-engine blades based on ultrasonic guided wave detection, characterized in that, The steps are as follows: Step 1: Project the three-dimensional aero-engine blade and divide the projection surface into a mesh; place ultrasonic guided wave sensors on the mesh points to detect and obtain a complete detection signal dataset; Step 2: Based on the complete detection signal dataset, set the missing rate to obtain the incomplete detection signal dataset; Step 3: Obtain the mask matrix based on the incomplete detection signal dataset, and normalize the incomplete detection signal dataset; Step 4: Construct a missing data completion network. Input the normalized incomplete detection signal dataset and mask matrix into the missing data completion network to obtain the output matrix. Step 5: Construct a missing data discrimination network, and input the output matrix and mask matrix into the missing data discrimination network to obtain the output result; Step 6: Calculate the loss of the missing data completion network and the missing data discrimination network separately, and then weight and fuse the two losses to obtain the overall loss; Step 7: Divide the inputs of the missing data completion network and the missing data discrimination network into multiple batches and repeat steps 4 to 6 for iterative training. Stop training when the overall loss remains stable to obtain the completed detection data, and then perform inverse normalization on the completed detection data.

2. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 1, characterized in that, The grid size is N1×N2, and ultrasonic guided wave sensors are arranged at the grid points. All sensors emit excitation signals in turn, and all sensors receive detection signals synchronously, forming a detection signal matrix. Where N1 represents the transmitting element number, N2 represents the receiving element number, and L represents the detection signal length, i.e., a one-dimensional detection signal vector; M aero-engine blades are detected to form a complete detection signal dataset.

3. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 2, characterized in that, The method for obtaining the incomplete detection signal dataset is as follows: set a missing rate p, that is, for each detection signal matrix in the complete detection signal dataset, randomly lose some of the detection signal vectors corresponding to the transmit array element index or the receive array element index to form an incomplete detection signal dataset, and set the missing data part in the incomplete detection signal dataset as NaN.

4. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 2 or 3, characterized in that, The method for obtaining the mask matrix based on the incomplete detection signal dataset is as follows: Create a mask matrix set with the same size and dimensions as the incomplete detection signal dataset. For positions in the incomplete detection signal dataset where data is present, set the corresponding position in the mask matrix set to 1; for missing data in the incomplete detection signal dataset, set the corresponding position in the mask matrix set to 0. For a single aero-engine blade, three three-dimensional matrices can be obtained: a complete detection signal matrix. Incomplete detection signal matrix Mask matrix The three three-dimensional matrices are transformed into three two-dimensional matrices, that is, the second and third dimensions are merged into one dimension, which is the complete detection signal matrix. Incomplete detection signal matrix Mask matrix .

5. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 4, characterized in that, For incomplete detection signal matrix After performing min-max normalization, we get: （1）； Where min represents The minimum value, max represents The maximum value, This is a normalized incomplete detection signal matrix.

6. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 5, characterized in that, The missing data completion network is a fully connected network, consisting of one input layer, two fully connected layers, and one output layer, which processes the normalized incomplete detection signal matrix. Mask matrix As input The data is fed into the input layer of the missing data completion network, and then passes through a fully connected layer and an output layer: （2）； （3）； in, For element-wise product, , This represents the number of hidden layer nodes. To complete the weight matrices of the two fully connected layers and the output layer of the network, respectively, using the missing data, To complete the biases of the two fully connected layers and the output layer of the network to fill in the missing data, To complete the outputs of the two fully connected layers and the output layer of the network to fill in the missing data, the ReLU function is used for the activation function of the fully connected layers and the Sigmoid function is used for the activation function of the output layer. Replace the values ​​at the locations containing data in the incomplete detection signal matrix with the corresponding values ​​at the output matrix of the output layer to obtain the replaced output matrix. : （4）。 7. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 6, characterized in that, The missing data discrimination network adopts a fully connected network, consisting of one input layer, two fully connected layers, and one output layer; firstly, a reinforcement matrix is ​​created. : （5）； in, ; The replaced output matrix Strengthening Matrix Vector concatenation is performed to obtain the input for the missing data discrimination network. , （6）； Then, through the fully connected layer and the output layer: （7）； in, To determine the weight matrices of the two fully connected layers and the output layer of the network for missing data, To determine the biases of the two fully connected layers and the output layer of the network in case of missing data, The outputs of the two fully connected layers and the output layer of the network are used to determine the missing data.

8. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 7, characterized in that, The method for obtaining the overall loss is as follows: Calculate the loss of the missing data discrimination network. : （8）； in, Represents a local minimum value; Expressing expectations; Calculate the loss of the network for imputing missing data. : （9）； The two losses are combined to obtain the overall loss. : （10）； in, , All are coefficients.

9. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 7, characterized in that, The method for inverse normalization of the completed detection data is as follows: （11）； in, This represents the detection data after inverse normalization completion.

10. The method for completing missing data of aero-engine blades based on ultrasonic guided wave detection according to claim 8, characterized in that, During training, the parameter vector x includes the batch size m and coefficients. and A set of iteration counts k; In iterative training, global optimization is performed either manually or using the Hippo Optimization Algorithm. The update rules of the Hippo Optimization Algorithm consist of five steps: defining the parameter search space, initializing the population, evaluating the fitness of the initial population, iterative optimization, and outputting the results, as detailed below: a) Define the parameter search space The search space for batch size m is [16, 32, 64, 128, 256, 512, 1024, 2048, 4096], with coefficients... and The search space is 0-1, and the search space for the number of iterations k is [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]. b) Initialize the population Randomly generate the initial hippopotamus position. For floating-point parameters: coefficients and Use standard random initialization: （12）； in, This is the initial position of the hippopotamus. , These are the lower and upper boundaries of the search space, respectively; A random number in the range [0,1]. For integer parameters: batch size m and number of iterations k, rounding is required after generation. （13）； Where, round represents the rounding operation; c) Assess the fitness of the initial population use Train the network in steps four through six, record the network's loss on the validation set, and find the initial global optimum. and the local optimal position of each individual ; （14）； Where MSE represents the mean squared error operation; d) Iterative optimization For each generation t from 1 to It includes four steps: water patrol stage, land foraging stage, location correction and evaluation, and greedy selection and updating. Waterway cruising phase: For each hippo i, calculate its candidate position after the waterway cruising phase according to the formula. : （15）； in, and A random number in the range [0,1]. This is the globally optimal position obtained after t-1 iterations; Terrestrial foraging phase: Similarly, for each hippo i, calculate its candidate location after foraging on land. : （16）； in, It was another hippopotamus randomly selected from the population; This represents the local optimal position found by the i-th hippo in the (t-1)th iteration; Position correction and evaluation includes three steps: boundary handling, type conversion, and fitness evaluation. The boundary handling process involves checking... and Check if each parameter exceeds its preset range; if so, use a boundary handling strategy to correct it; in type conversion, check if... and The integer parameters in the algorithm are rounded down to obtain the candidate parameter combinations that meet the requirements; in the fitness evaluation, the modified parameters are used respectively. and Train the models and calculate their fitness values. and ; Greedy selection and updating: First, compare , and The position with the lowest fitness value is selected as the next generation position for hippo i. Then, update the local optimal position of the individual. ,if ,but Otherwise, leave it unchanged; update the global optimal position. In all In the process, the one with the smallest fitness value is selected as the global optimum for the next generation; e) Output results The final globally optimal position after iteration. It is the optimal parameter vector x obtained by the Hippo optimization algorithm.

Images