Blade natural frequency identification method based on residual neural network

Abstract

A blade natural frequency identification method based on a residual neural network is disclosed. In the method, a frequency identification range of a blade end timing signal is determined based on blade vibration, and the frequency identification range is divided into multiple equal-width frequency bands, and the continuous frequency bands are discretized to obtain multiple random frequency components. A simulation blade end timing signal with the same sensor arrangement mode as the signal to be identified is generated based on the random frequency components. The autocorrelation matrix of the simulation blade end timing signal is calculated and reconstructed into a three-dimensional tensor. The three-dimensional tensor is used as input and the corresponding frequency components are used as labels to generate a data set. A residual neural network model is constructed. Multiple neural network models are trained as frequency estimation models in multiple different frequency bands using multiple data sets in different frequency bands. The measured blade end timing data is segmented in the time domain, and the autocorrelation matrix is calculated. The tensor formed by the autocorrelation matrix is input into the multiple trained frequency estimation models, and the frequency estimation result is finally obtained.

Description

Technical Field

[0001] This invention belongs to the field of non-destructive testing technology for rotor blades of rotating machinery, and in particular, it is a method for identifying the natural frequency of blades based on residual neural networks. Background Technology

[0002] As one of the core components of aero-engines, the stable and reliable performance of aero-engine blades is crucial for ensuring the safety of equipment and personnel. Extreme service environments such as high temperature, high speed, and heavy load can easily cause blade cracks, chipping, and breakage. Statistics show that in my country, blade failures account for 61.7% of all engine-related flight accidents with identified causes. This highlights the importance of monitoring and evaluating the operational status of aero-engine blades for engine safety. Blade tip timing non-contact measurement technology is a promising blade vibration monitoring technology and has been initially applied to experimental research on rotor blade vibration monitoring and component-level testing of related models. However, due to installation limitations, the number of sensors that can be installed is limited. Blade tip timing systems typically sample at frequencies far below the blade's natural frequency. Existing methods for extracting blade tip timing signals suffer severe performance degradation under low signal-to-noise ratios (<5dB) and short sampling lengths (<100). Therefore, a more robust method is needed to address the undersampling reconstruction problem of blade tip timing signals, overcome the frequency folding phenomenon caused by undersampling, and extract blade vibration information from the undersampled blade tip timing signals to support blade condition monitoring.

[0003] The information disclosed in the background section is only intended to enhance the understanding of the background of the present invention, and therefore may contain information that does not constitute prior art known to those skilled in the art in this country. Summary of the Invention

[0004] To address the problems of existing technologies, this invention proposes a blade natural frequency identification method based on a residual neural network. This method extracts the vibration frequency characteristics of non-uniformly undersampled blade tip timing signals, thereby achieving the goal of monitoring blade vibration status. By introducing a deep residual neural network and directly training the network using a large amount of simulation data, this invention obtains a frequency estimation model for non-uniformly undersampled signals in a specific frequency band. While effectively overcoming frequency folding, this method exhibits more stable performance and lower frequency estimation error at low signal-to-noise ratios.

[0005] The objective of this invention is achieved through the following technical solution: a method for identifying the natural frequency of a blade based on a residual neural network includes the following steps:

[0006] In the first step, I blade tip timing sensors are arranged on the blade in such a way that every two blade tip timing sensors are spaced apart by an angle and I blade tip timing sensors are arranged circumferentially. The blade vibration is represented as the superposition of multiple complex frequency signals and Gaussian noise. The frequency recognition range of the blade tip timing signal is determined based on the blade vibration, and the frequency recognition range is divided into multiple frequency bands of equal width. At the same time, the continuous frequency bands are discretized.

[0007] In the second step, discrete frequency values ​​are randomly selected within multiple frequency bands, and a simulated blade tip timing signal with the same blade tip timing sensor arrangement as in the first step is generated based on the random frequency values.

[0008] In the third step, the autocorrelation matrix of the simulated leaf tip timing signal is calculated and reconstructed into a three-dimensional tensor. The three-dimensional tensor and its corresponding frequency components are used as labels to generate multiple training datasets corresponding to each frequency band.

[0009] In the fourth step, a residual neural network model is constructed, which includes an input convolutional layer, residual modules, pooling layers, and an output fully connected layer.

[0010] In the fifth step, multiple neural network models are trained using training datasets from different frequency bands to serve as frequency estimation models for multiple different frequency bands.

[0011] In the sixth step, the measured blade tip timing data is segmented in the time domain and its autocorrelation matrix is ​​calculated. The tensor formed by the autocorrelation matrix is ​​input into multiple trained frequency estimation models. The frequency estimation of each frequency band is performed using the multiple frequency estimation models trained in the fifth step. The blade tip timing signal is input into the trained neural network model to extract the blade vibration frequency in the blade tip timing signal, and finally the frequency estimation result is obtained.

[0012] In the method described, in the first step,

[0013] Determining the frequency range of the vibration signal to be identified based on blade vibration [f] min f max The frequency band to be identified is discretized and split into X independent frequency vectors of length s by the frequency identification resolution v.

[0014] In the method described, in the second step,

[0015] Step S21: For each independent frequency band vector, randomly select K×N discretized frequencies to generate N continuous complex frequency signals that are superimposed from K frequency components.

[0016] Step S22, based on the leaf tip timing sensor arrangement vector [0, θ1, θ2, ... θ] of the leaf tip timing signal to be identified. I-1 ] T In the formula,

[0017] I represents the number of timing sensors at the blade tip.

[0018] θ1, θ2, ... θ I-1 The included angle between adjacent leaf tip timing sensors;

[0019] A sampling sequence generated by a timing sensor at the blade tip as a single blade rotates:

[0020] In the formula,

[0021] f r R represents the blade rotational speed, and R represents the blade disk radius.

[0022] Based on the sampling sequence, the discretized complex frequency signal is obtained:

[0023] In the formula,

[0024] When i ranges from 1 to K, f i Then we have f1, f2…f K f1, f2…f K These represent the K frequency components contained in the simulated leaf tip timing signal;

[0025] Step S23: Add Gaussian additive white noise with different signal-to-noise ratios to the discretized simulated leaf tip timing signal using the awgn function in MATLAB;

[0026] Step S24, then the energy of the simulated blade tip timing signal with added Gaussian additive white noise is normalized:

[0027]

[0028] In the formula, n represents the length of the simulated leaf tip timing signal y(t), y(t) i ), These represent the i-th value and the conjugate of the i-th value of the signal, respectively.

[0029] In the method described, in the third step,

[0030] Step S31: Rearrange the simulated leaf tip timing signals to form a signal matrix Y. M×Q :

[0031]

[0032] Where Y M×QLet Q be the signal matrix consisting of Q leaf-end timing data sequences of length M.

[0033] [y(t1), y(t2), ..., y(t)] Q By directly extracting from the generated simulated blade tip timing signal y(t), the length n of the simulated blade tip timing signal y(t) should be greater than Q+M, [y(t1), y(t2), ... y(t)]. Q )] represents a signal snapshot, where Q represents the length of the signal snapshot, M represents the number of snapshots, and Q should be greater than M, and M should be much greater than the number of frequency components K contained in the simulated leaf tip timing signal.

[0034] Step S32, calculate the signal matrix Y M×Q Autocorrelation matrix: R YY =YY H The elements of the matrix are all complex numbers. The real part Re{R} of the complex matrix is... YY}、Im{R} YY} and phase ∠{R YY Each of the three real matrices is constructed into a real matrix, and then concatenated to obtain a 3×M×M three-dimensional real tensor T:

[0035] T[1,:,:]=Re{R YY},

[0036] T[2,:,:]=Im{R YY},

[0037] T[3,:,:]=∠{R YY},

[0038] In this way, the tensors T corresponding to the remaining N-1 frequency components are calculated, and these tensors are used to form a training dataset as input to the residual neural network model.

[0039] Step S33: Use the Python toolkit sklearn.preprocessing.StandardScaler module to perform mean normalization on the N three-dimensional real tensors;

[0040] Step S34, based on signal matrix Y M×Q The K frequency components are used to generate a label vector Z with a length of s, where K elements are 1 and the rest are 0. The labels corresponding to the remaining N frequency components are calculated to obtain all the labels corresponding to the training dataset in step S32.

[0041] Step S35: Repeat steps S31 to S34 to calculate the corresponding training datasets and labels for the remaining X-1 frequency bands.

[0042] In the method, in the fourth step, in the residual neural network model,

[0043] The first layer is a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, and a padding parameter of 1.

[0044] The second layer is the batch normalization layer;

[0045] The third layer is the ReLU function activation layer;

[0046] Layers four through seven are residual modules with depths of 64, 128, 256, and 512, respectively.

[0047] The eighth layer is the average pooling layer, with a pooling size of 4×4;

[0048] The ninth layer is a fully connected layer with a weight matrix of 512×s, which maps the data features extracted by the convolutional layer to features of different frequencies.

[0049] The specific structure of the four residual modules in the fourth to seventh layers of the method described is as follows:

[0050] The first layer is a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, a padding parameter of 1, and depths of 64, 128, 256, and 512, respectively.

[0051] The second layer is the batch normalization layer;

[0052] The third layer is a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, a padding parameter of 1, and depths of 64, 128, 256, and 512, respectively.

[0053] The fourth layer is the batch normalization layer;

[0054] The output is the sum of the fourth layer output and the input of the residual module after identity mapping.

[0055] In the method described, in step five,

[0056] When training multiple neural network models using multiple datasets of different frequency bands, the output of the neural network model is activated using the Softmax function, which maps the output to the probability interval of (0, 1).

[0057] In the method described above, in the fifth step, the loss function of the neural network model is the binary cross-entropy function BCELoss, and the formula for calculating the loss of the neural network model is:

[0058] In the formula, Z[i] represents the i-th element in the label vector. Let represent the i-th element of the model's predicted output, and σ represent the activation function.

[0059] In the fifth step of the method, a training dataset is input, and the prediction loss of the neural network model is calculated through forward propagation of the input data. Then, the backward derivative of the neural network model loss is performed, and the neuron parameters in the neural network model are updated using the gradient descent algorithm. This process is repeated until the accuracy or loss of the neural network model converges to a pre-set threshold, thus completing the training of the neural network.

[0060] Beneficial effects

[0061] Compared with existing methods, this method has better performance under low signal-to-noise ratio and short sampling length, lower frequency estimation error, and more sparse extracted frequency components. Attached Figure Description

[0062] The various advantages and benefits of the present invention will become clear to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Obviously, the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0063] In the attached diagram:

[0064] Figure 1 This is a schematic diagram of the basic process of the rotor blade vibration natural frequency identification method based on residual neural network in this invention;

[0065] Figure 2 This is a basic schematic diagram of the blade tip timing signal acquisition in the rotor blade vibration natural frequency identification method based on residual neural network in this invention.

[0066] Figure 3 This is a schematic diagram of the basic structure of the residual network in the rotor blade vibration natural frequency identification method based on residual neural network in this invention.

[0067] Figure 4 This is a schematic diagram of the neural network model training and prediction process of the rotor blade vibration natural frequency identification method based on residual neural network in this invention.

[0068] Figure 5 The figure shows a comparison of Monte Carlo simulation results of the rotor blade vibration natural frequency identification method based on residual neural network in this invention with orthogonal matching pursuit, multiple signal classification and rotating subspace invariant method under different signal-to-noise ratios.

[0069] Figure 6This is a time-domain diagram of the measured blade tip timing signal of the rotor blade vibration natural frequency identification method based on residual neural network in this invention.

[0070] Figure 7(a) shows the frequency domain diagram of the displacement data of blade No. 1 in the measured blade tip timing signal of the rotor blade vibration natural frequency identification method based on residual neural network in this invention, after orthogonal matching tracking, multiple signal classification and residual neural network.

[0071] Figure 7(b) shows the frequency domain diagram of the displacement data of blade No. 2 in the measured blade tip timing signal of the rotor blade vibration natural frequency identification method based on residual neural network in this invention, after orthogonal matching tracking, multiple signal classification and residual neural network.

[0072] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0073] The following is a reference appendix Figures 1 to 7(b) Specific embodiments of the invention will be described in more detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0074] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0075] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0076] like Figures 1 to 7(b) As shown, a method for identifying the natural frequency of rotor blade vibration based on a residual neural network includes,

[0077] Step 1: Divide the frequency range to be identified into several frequency bands;

[0078] Step 2: Generate simulated blade tip timing signals based on the divided frequency bands and sensor arrangement;

[0079] Step 3: Use the autocorrelation matrix of the simulated signal as input and the corresponding frequency components as labels to obtain the dataset;

[0080] Step 4: Construct a residual neural network model. The network structure specifically includes an input convolutional layer, a residual module, a pooling layer, and an output fully connected layer.

[0081] Step 5: Train the neural network model using simulation data, and verify its accuracy using validation set data;

[0082] Step 6: After preprocessing the timing data of the leaf tip to be identified, input it into the trained neural network for frequency identification.

[0083] In one embodiment, the blade rotation speed corresponding to the intercepted measured blade tip timing data does not change within the time period corresponding to that signal segment, and the measured blade tip timing sensors are circumferentially distributed on the casing. In the method, the output dimension of the neural network should be the same as the number of discretized frequencies in each frequency band, that is, the frequency identification problem is transformed into a multi-label classification problem.

[0084] In the method described, the number of effective frequency components in each frequency band does not exceed K+2.

[0085] Optionally according to the present invention, in step one, the vibration of the blade is regarded as the superposition of multiple complex frequency signals and Gaussian noise. Based on the assumptions of the blade vibration model, the frequency range of the vibration signal to be identified is determined to be 0Hz to 500Hz, the frequency identification resolution is 1Hz, and the frequency band to be identified is discretized and divided into 5 independent frequency vectors of length 100.

[0086] Optionally, in step two, generating the simulation signal based on the characteristics of the signal to be measured includes the following steps:

[0087] S21, For every 5 independent frequency bands, randomly select 20,000 discretized frequency values ​​to generate 10,000 continuous complex frequency signals that are superimposed by 2 frequency components.

[0088] S22, According to the sensor arrangement of the non-contact measurement test bench for blades, there are 5 sensors, and the vector formed by the included angles of the sensors is [0°, 60°, 110°, 120°, 240°]. T ;

[0089] S23. Add Gaussian white noise with five signal-to-noise ratios of -10dB, -5dB, 0dB, 5dB and 10dB to each simulation signal to obtain 50,000 sets of simulation data.

[0090] S24 normalizes the discrete complex frequency signal, resulting in higher prediction accuracy for the neural network model.

[0091] Optionally, in step three, the simulation signal is further processed to obtain the training and testing dataset for the neural network model, specifically including the following steps:

[0092] S31. In order to improve the prediction accuracy of the neural network model under low signal-to-noise ratio, the discrete signals are rearranged and the snapshot length is selected as 32 to form a signal matrix.

[0093] S32, calculate the autocorrelation matrix of the signal matrix, and construct real matrices from the real part, imaginary part and phase of the complex autocorrelation matrix, and concatenate them to obtain a 3×32×32 three-dimensional real tensor. Use this tensor as the input of the residual neural network model.

[0094] S33, normalizes the input data of the neural network model using max-min (linear) normalization;

[0095] S34. Based on the two frequency components contained in the generated signal matrix, generate a tag vector with a length of 100, and two of its elements are 1 (the rest of the elements are 0).

[0096] In one embodiment, S41, preferably, the basic structure of the residual neural network model established in step four is as follows: Figure 3 As shown. The residual network structure includes a data input layer, residual modules, a pooling layer, and an output fully connected layer, as detailed below:

[0097] First layer: conv1, a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, and a padding parameter of 1;

[0098] Second layer: bn1, batch normalization layer;

[0099] The third layer: relu1, the ReLU function activation layer;

[0100] Layers 4 to 7: blocks 1-4, residual modules, with output depths of 64, 128, 256 and 512 respectively;

[0101] Eighth layer: avgpool1, average pooling layer, pooling size is 4×4;

[0102] The ninth layer: fn1, a fully connected layer with a weight matrix of 512×100, maps the data features extracted by the convolutional layer to features of different frequencies.

[0103] S42. Preferably, the residual module is as follows:

[0104] First layer: conv1, a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, and a padding parameter of 1;

[0105] Second layer: bn1, batch normalization layer;

[0106] The third layer: conv2, a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, and a padding parameter of 1;

[0107] Fourth layer: bn2, batch normalization layer;

[0108] The output of the residual module is the sum of the fourth layer output and the result of the residual module input after identity mapping.

[0109] In one embodiment, in step five, the generated dataset is divided into a test set and a training set in a 1:9 ratio.

[0110] S51. Preferably, the output of the neural network model is activated using the Sigmoid function, and the output is mapped to the probability interval (0, 1).

[0111] S52. Preferably, the loss function used by the network is the binary cross-entropy function BCELoss, and the final formula for calculating the loss of the neural network model prediction result is as follows: In the formula Z [i] This represents the i-th element in the label vector. Let represent the i-th element of the predicted output of the neural network model, and σ represent the activation function.

[0112] S53. Preferably, the prediction loss of the neural network model is calculated by forward propagation of the input data, and then the loss of the neural network model is back-derived. The neuron parameters in the network model are updated using the ADAM algorithm. This process is repeated until the accuracy or loss of the neural network model converges to a preset threshold, thus completing the training of the neural network model.

[0113] In step six, the experimentally measured blade tip timing signal is preprocessed according to S31 to S33 to obtain a three-dimensional tensor with a dimension of 3×32×32, which is then input into five trained neural network models. The five trained neural network models are used to estimate the frequency of each frequency band, thereby extracting the blade vibration frequency characteristics from the blade tip timing signal.

[0114] I. Acquiring timing signals from the leaf tip

[0115] like Figure 2 As shown, the vibration displacement of the blade tip was collected using a blade tip timing non-contact measurement experimental platform, and the selected blade tip timing sensor was an optical fiber sensor.

[0116] In this step, the initial parameters of the experimental setup are as follows: the angles of the five sensors mounted along the circumference of the impeller are 0°, 60°, 110°, 120°, and 240°. The initial motor speed is set to 60Hz, the speed acceleration is 0.5Hz / s, the speed is uniformly increased to 92Hz, and the motor speed is maintained at 92Hz for 40s. The impeller is an integral aluminum alloy impeller with 8 blades, a impeller radius of R = 68mm, a blade thickness of d = 1mm, and a blade width of w = 20mm.

[0117] In this step, the experimental data is collected as follows: When the bladed disk rotates, a timing sensor at the blade tip causes a change in the intensity of emitted light, further generating a rectangular pulse. The rising or falling edge of this pulse is taken as the arrival time of the blade. When the bladed disk rotates at low speed, the blade does not vibrate, and the arrival time of the blade at this time is the theoretical arrival time. As the rotational speed increases, the blade vibrates, and the arrival time of the blade becomes advanced or delayed. The arrival time of the blade at this time is the actual arrival time. By calculating the difference between the actual and theoretical arrival times of the blade, the vibration displacement of the blade can be calculated.

[0118] The experimentally collected data on the relationship between blade tip vibration displacement and rotational speed and time are as follows: Figure 6 As shown in the figure, it can be seen that as the rotational speed of the bladed disk increases and decreases, assuming that the rotational speed remains constant within the sampled vibration displacement segment, resonance occurs in the blade at a disk rotational speed of approximately 85Hz, where the blade's vibration displacement is at its maximum. According to the finite element analysis results, the first-order natural frequency of the aluminum alloy bladed disk used in the experiment is around 380Hz, while the sampling frequency of the blade tip timing sensor is equal to the disk's rotational frequency, which is far lower than the blade's first-order natural frequency, indicating a serious undersampling problem.

[0119] II. Generating Simulation Signals and Datasets

[0120] Based on undersampled signal analysis methods such as blade finite element analysis and multiple signal classification, the blade frequency identification range is determined to be 0Hz to 500Hz, with a frequency identification resolution of 1Hz. The frequency identification problem is transformed into a multi-label classification problem. Since classifying the complete spectrum directly would greatly increase the difficulty of the network, it would require a deeper network structure, a larger training dataset, and higher computational complexity. At the same time, each input data would cover more class labels, all of which would lead to a decrease in the performance of the neural network model. Therefore, the frequency band to be identified is discretized and divided into 5 independent frequency vectors of length 100. Five residual neural networks with the same structure are used to identify the frequency features of the signal to be identified in the corresponding frequency band.

[0121] In this step, 20,000 repeatable frequency values ​​are randomly generated in each frequency band, and further, 10,000 complex sinusoidal signals containing two complex frequency components are generated. These signals should have the same amplitude and phase. Simultaneously, to further improve the performance of the neural network model at low signal-to-noise ratios, complex Gaussian white noise with different signal-to-noise ratios is added to the original noise-free signal. Energy normalization is performed to avoid overfitting of the neural network due to energy variations in the simulated signal caused by the introduction of white noise with different signal-to-noise ratios, thus reducing the estimation accuracy of the neural network under real data. Based on information such as the sensor installation angle and rotational speed of the blade tip timing non-contact measurement experimental platform, these simulated signals are downsampled into non-uniform undersampled signals.

[0122] In this step, the one-dimensional simulated signal is rearranged into a signal matrix, and the autocorrelation matrix of the signal is calculated. Since the original simulated signal is a complex sinusoidal signal, the resulting autocorrelation matrix is ​​also complex. However, most neural networks cannot handle complex numbers because existing activation functions will exhibit non-differentiable singularities in the complex plane, preventing the neural network parameters from being updated. Therefore, the complex matrix is ​​transformed into a three-dimensional tensor, which is then used as the network input.

[0123] In this step, a label vector is generated. The length of the label vector is 100. The index of the vector corresponds to the magnitude of the frequency value. For a simulated signal containing two frequency components, the corresponding label vector has two elements that are 1 (and the rest of the elements are 0).

[0124] Furthermore, the three-dimensional tensor is reshaped into a one-dimensional vector, and after mean normalization or linear normalization, it is reshaped again into a high-dimensional tensor. The complex matrix is ​​used as data_x, and the label vector is used as data_y, forming the dataset.

[0125] III. Construction and Training of Residual Neural Networks

[0126] The established residual neural network structure is as follows: Figure 3 As shown in the diagram. Conv represents a 2D convolutional layer, bn represents a batch normalization layer, relu represents the ReLU activation function, avgpool represents an average pooling layer, and fn1 represents a fully connected layer. The convolutional layer is used for initial feature extraction, the batch normalization layer accelerates the training of the neural network model, the activation function layer introduces non-linearity into the network, making deeper layers meaningful, the pooling layer reduces feature dimensionality and improves the generalization ability of the neural network model to some extent, and the fully connected layer maps the data features extracted by the convolutional layer to features of different frequencies. The residual network structure includes one data input layer, 18 residual modules, one pooling layer, and one fully connected output layer, as detailed below:

[0127] First layer: conv1, a two-dimensional convolutional layer with a kernel size of 3×3, a stride of 1, and a padding parameter of 1;

[0128] Second layer: bn1, batch normalization layer;

[0129] The third layer: relu1, the ReLU function activation layer;

[0130] Layers 4 to 7: blocks 1-4, residual modules, with output depths of 64, 128, 256 and 512 respectively;

[0131] Eighth layer: avgpooll, average pooling layer, pooling size is 4×4;

[0132] Ninth layer: fn1, a fully connected layer with a weight matrix of 512×100.

[0133] Through data preprocessing in the second step, simulated undersampled signals under different signal-to-noise ratios are obtained. The dataset is divided into a validation set and a training set in a ratio of 1:9. Since the data volume is relatively large (>10000), the original training dataset is further split into multiple batches.

[0134] Based on the above residual deep network model, the model is trained using the training dataset, and then the estimation accuracy and loss of the neural network model are verified using the validation set after each epoch. Specifically, the following steps are included: Step (1), create the constants and hyperparameters required for training the neural network model, including: batch size, learning rate, maximum training epoch, initialization of network weights, optimizer for neural network model parameters, loss function type, etc.; Step (2), load the neural network model, initialize the neural network model parameters and training hyperparameters, loss function and optimizer; Step (3), convert the generated simulation data from Ndarray format to tensor format for easier calculation and faster processing, reshape the three-dimensional tensor and perform linear normalization, and save the normalization parameter Scalar_01. Step (4): Load data into the neural network model input. When the data is input into the neural network, an output result is obtained. Step (5): Calculate the output loss of the neural network model based on the output result vector and the true label vector of the input data, and save the loss result. Step (6): Calculate the derivative of the neural network model loss with respect to the weight parameters from the output layer to the input layer, i.e., the backpropagation of the gradient. Update the parameters of the neural network model according to the updater and save the model parameters. Step (7): Output the training information, including training batch, learning rate, loss value, and accuracy. Repeat steps (4)-(7) until a batch ends. Step (8): Update the weight parameters of the network model and save the weight parameters of the model with the smallest error. Repeat steps (4)-(8) until all batches have passed the neural network model and an epoch ends. Step (9): Use the validation set data to validate the model obtained by the current training. If the validation set loss is less than the validation loss of the previous cycle, save the result of the current epoch. Repeat steps (4)-(9) until the number of training steps of the neural network model reaches the preset max_epoch.

[0135] IV. Frequency Feature Extraction

[0136] To further compare the frequency estimation accuracy of the proposed method with existing uniformly undersampled signal analysis methods under low signal-to-noise ratio and short snapshot lengths, multiple signal classification, orthogonal matched pursuit, and subspace rotation invariance methods will be introduced for comparison with residual neural network methods. Monte Carlo simulations will be performed using simulation data, and the simulation results are as follows: Figure 6As shown, the residual neural network method has a lower frequency estimation error at low signal-to-noise ratios of -15dB to 15dB, which indicates that the residual neural network has strong robustness in processing non-uniform undersampled leaf tip timing signals.

[0137] Furthermore, the trained neural network model is used to extract frequency features from the blade tip timing data measured on the non-contact blade tip timing measurement experimental platform in step one. The original data is segmented in the time domain to ensure that the rotational speed can be considered constant within a single snapshot. A three-dimensional tensor is obtained using the data preprocessing method from step two. This three-dimensional tensor is input into the trained neural network model. The one-dimensional vector output by the network is directly used as the pseudo-spectral amplitude representing the frequency of the truncated signal after softmax, as shown in Figures 7(a) and 7(b). Taking blades 1 and 2 of the bladed disk as examples, the estimation results of the residual neural network are compared with the spectra obtained by methods such as orthogonal matching pursuit. It can be seen that the residual neural network, while correctly indicating the frequency features contained in the undersampled blade tip timing signal, produces sparser predictions. Frequency leakage caused by short snapshots is also suppressed, and noise and other factors have less interference with the estimation results, proving the feasibility of the frequency estimation method based on the residual neural network in practical applications.

[0138] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for identifying the natural frequency of a blade based on a residual neural network, the method comprising the following steps: In the first step (S1), I blade tip timing sensors are arranged on the blade in such a way that every two blade tip timing sensors are spaced apart by an angle and I blade tip timing sensors are arranged circumferentially. The blade vibration is represented as the superposition of multiple complex frequency signals and Gaussian noise. The frequency recognition range of the blade tip timing signal is determined based on the blade vibration, and the frequency recognition range is divided into multiple frequency bands of equal width. At the same time, the continuous frequency bands are discretized. In the second step (S2), discrete frequency values ​​are randomly selected within multiple frequency bands, and a simulated leaf tip timing signal with the same leaf tip timing sensor arrangement as in the first step is generated based on the random frequency values. In the third step (S3), the autocorrelation matrix of the simulated leaf tip timing signal is calculated and reconstructed into a three-dimensional tensor. The three-dimensional tensor is used as input and its corresponding frequency components are used as labels to generate multiple training datasets corresponding to each frequency band. In the fourth step (S4), a residual neural network model is constructed, which includes an input convolutional layer, residual modules, pooling layers, and an output fully connected layer. In the fifth step (S5), multiple neural network models are trained using training datasets of different frequency bands to serve as frequency estimation models for multiple different frequency bands. In the sixth step (S6), the measured blade tip timing data is segmented in the time domain and its autocorrelation matrix is ​​calculated. The tensor formed by the autocorrelation matrix is ​​input into multiple trained frequency estimation models. The frequency estimation of each frequency band is performed using the multiple frequency estimation models trained in the fifth step. The blade tip timing signal is input into the trained neural network model to extract the blade vibration frequency in the blade tip timing signal, and finally the frequency estimation result is obtained. In the second step (S2), Step S21: For each independent frequency band vector, randomly select... A discrete frequency, generating One reason A continuous complex frequency signal with superimposed frequency components; Step S22, based on the blade tip timing signal to be identified, the arrangement vector of the blade tip timing sensors. In the formula, The number of timing sensors at the blade tip. The included angle between adjacent leaf tip timing sensors; A sampling sequence generated by a timing sensor at the blade tip as a single blade rotates: In the formula, For blade rotation speed, Indicates the bladed disk radius. Based on the sampling sequence, the discretized complex frequency signal is obtained: In the formula, When i ranges from 1 to K, Then there is , These respectively represent the components contained in the simulated leaf tip timing signal. One frequency component; Step S23: Add Gaussian additive white noise with different signal-to-noise ratios to the discretized simulated leaf tip timing signal using the awgn function in MATLAB; Step S24, then the energy of the simulated blade tip timing signal with added Gaussian additive white noise is normalized: ， In the formula, Represents the simulated blade tip timing signal Length, , These represent the signal's first and second parts, respectively. The value and the first The conjugate of each value; In the third step (S3), Step S31: Rearrange the simulated leaf tip timing signals to form a signal matrix. : ， in for A length of The signal matrix is ​​composed of the timing data sequence at the leaf tip. By directly from the generated simulated blade tip timing signal Extracting and simulating the timing signal at the leaf tip. length It should be greater than , This represents a segment of signal snapshots, in which Indicates the length of the signal snapshot. Indicates the number of snapshots, and Greater than ; Step S32, calculate the signal matrix Autocorrelation matrix: The elements of the matrix are all complex numbers. The real part of the complex matrix is... virtual part With phase Each of the three real number matrices is constructed separately, and then the three real number matrices are concatenated to obtain a... Three-dimensional real tensor : ， ， ， Calculate the rest in this way Tensor corresponding to each frequency component These tensors are used to form a training dataset, which is then used as input to the residual neural network model. Step S33, use the Python toolkit sklearn.preprocessing.StandardScaler module to... The three-dimensional real tensor is subjected to mean normalization. Step S34, based on the signal matrix Contains Each frequency component generates a label vector. The length of the label vector is And among them are One element is 1, and the rest are 0; calculate the labels corresponding to the remaining N frequency components to obtain all the labels corresponding to the training dataset in step S32. Step S35, repeat steps S31 to S34 to calculate the remaining... The training dataset and labels corresponding to each frequency band.

2. The method according to claim 1, wherein, In the first step (S1), Determining the frequency range of the vibration signal to be identified based on blade vibration. and frequency recognition resolution The frequency band to be identified is discretized and then divided into... A length of . Independent frequency vectors.

3. The method according to claim 1, wherein, In the fourth step (S4), in the residual neural network model, The first layer is a two-dimensional convolutional layer, with a kernel size of [size missing]. The step size is 1, and the fill parameter is 1. The second layer is the batch normalization layer; The third layer is the ReLU function activation layer; Layers four through seven are residual modules with depths of 64, 128, 256, and 512, respectively. The eighth layer is the average pooling layer, with a pooling size of... ; The ninth layer is a fully connected layer, and its weight matrix is... The data features extracted by the convolutional layer are mapped to features of different frequencies.

4. The method according to claim 3, wherein, The four residual modules from the fourth to the seventh layers have the following specific structures: The first layer is a two-dimensional convolutional layer, with a kernel size of [size missing]. The step size is 1, the fill parameter is 1, and the depths are 64, 128, 256 and 512 respectively; The second layer is the batch normalization layer; The third layer is a two-dimensional convolutional layer, with a kernel size of [missing value]. The step size is 1, the fill parameter is 1, and the depths are 64, 128, 256 and 512 respectively; The fourth layer is the batch normalization layer; The output is the sum of the fourth layer output and the input of the residual module after identity mapping.

5. The method according to claim 1, wherein, In the fifth step (S5), When training multiple neural network models using multiple datasets from different frequency bands, the output of the neural network models is activated using the Softmax function, and the output is mapped to... Within the probability range.

6. The method according to claim 5, wherein, In step five (S5), the loss function of the neural network model is the binary cross-entropy function BCELoss, and the formula for calculating the loss of the neural network model is: ， In the formula Represents the first element in the label vector. One element, The first element of the model's predicted output One element, This represents the activation function.

7. The method according to claim 6, wherein, In the fifth step (S5), the training dataset is input, and the prediction loss of the neural network model is calculated through forward propagation of the input data. Then, the backward derivative of the neural network model loss is performed, and the neuron parameters in the neural network model are updated using the gradient descent algorithm. This process is repeated until the accuracy or loss of the neural network model converges to a pre-set threshold, thus completing the training of the neural network.

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