CN116543204A - Metal plate crack identification method based on 3D convolutional neural network and displacement response - Google Patents
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Abstract
The invention discloses a metal plate crack identification method based on a 3D convolutional neural network and displacement response, which comprises the steps of acquiring surface vibration response displacement data of each metal plate under the action of exciting forces with different frequencies by adopting a displacement sensor for each metal plate with different crack positions; obtaining displacement cloud images of the surface displacement of the metal plate under different frequencies by Fourier transformation aiming at the displacement data; the crack positions of the metal plates are identified and converted into classification problems, and the displacement cloud pictures of the metal plates with different crack positions correspond to different categories; and training by using the displacement cloud picture to obtain a 3D convolutional neural network model, and realizing the position recognition of the metal plate crack in a classification mode by using the trained 3D convolutional neural network model. According to the invention, the sample data contains the spatial information of the vibration response of the surface of the metal plate and the information of the displacement response along with the change of frequency, so that the accurate identification of small cracks can be realized.
Description
Technical Field
The invention relates to the field of crack identification, in particular to a method for identifying cracks at different positions of a metal plate.
Background
In the field of engineering and machine construction, sheet metal is a material that is used in many applications, and is commonly used to manufacture various parts such as car bodies, ship hulls, wings, shells, tanks, and the like. In the actual use process, due to improper manufacturing process or adverse factors such as external load effect, fatigue effect, structural aging and the like, cracks can be slowly generated in the metal plate, and the cracks can gradually expand along with the use of the metal plate, so that fracture and failure accidents can finally occur. Therefore, the crack position identification of the metal plate can not only discover cracks in time and repair or replace the cracks, but also avoid unnecessary accidents or losses; the material selection and the process design can be assisted by a designer.
The manual detection of cracks of the metal plate is difficult to accurately identify local damage and micro cracks of the structure, and the manual field detection workload is large and the labor cost is high. With the development of deep learning, a data-driven manner is widely focused on solving engineering problems; convolutional neural network CNN is one of the most representative deep learning algorithms, and has achieved great success in the field of image processing. In the image processing process, the image is often regarded as a two-dimensional vector, and features are extracted through multiple convolution pooling operations, so that a one-dimensional vector with a specific dimension is finally obtained. The convolutional neural network can integrate the characteristic extraction and classification processes in the traditional damage detection method, and thoroughly avoids information loss caused by manual design and characteristic selection.
However, the 2DCNN cannot capture the correlation between space and frequency, and the 2DCNN ignores the information of the change of the surface displacement of the metal plate along with the frequency of the exciting force, so that the effect of identifying the crack position is poor, and the situation that some small cracks cannot be identified occurs.
Disclosure of Invention
The invention provides a metal plate crack identification method based on a 3D convolutional neural network and displacement response, which is used for processing vibration displacement response data of different frequencies on the plate surface to obtain sample data, training the 3D convolutional neural network by using the sample data, and finally identifying the crack position of the metal plate by using a trained network model; in order to accurately identify the location of the crack on the metal sheet.
The invention adopts the following technical scheme for realizing the purpose:
the metal plate crack identification method based on the 3D convolutional neural network and the displacement response is carried out according to the following process:
for each metal plate with different crack positions, acquiring surface vibration response displacement data of each metal plate under the action of exciting forces with different frequencies by adopting a displacement sensor;
RGB cloud images of the surface displacement of the metal plates under different frequencies are obtained through Fourier transformation according to the surface vibration response displacement data of each metal plate, and the RGB cloud images are cut to obtain displacement cloud images with the same size;
the crack positions of the metal plates are identified and converted into classification problems, and the displacement cloud pictures of the metal plates with different crack positions correspond to different categories; and training the displacement cloud picture to obtain a 3D convolutional neural network model, and realizing the crack position identification of the metal plate in a classification mode by adopting the trained 3D convolutional neural network model.
The metal plate crack identification method based on the 3D convolutional neural network and the displacement response is also characterized in that:
taking a displacement cloud picture at the same crack position and different frequencies as sample data, wherein the sample data is information of the surface vibration displacement of the metal plate along with the change of frequency, is three-dimensional data, comprises vibration displacement information of the surface of the metal plate, and comprises frequency information for exciting to induce the surface displacement of the corresponding metal plate; labeling and classifying the sample data, and classifying the sample data into a training set, a verification set and a test set;
establishing a 3D convolutional neural network model to learn the training set, and adjusting model weights and offsets in iterative training of sample data in the training set by the 3D convolutional neural network model to enable the 3D convolutional neural network model to better fit the sample data in the training set;
the loss function values of the training set and the verification set are compared, the fitting degree of the model is judged according to the loss function values, and the model hyper-parameters are adjusted to achieve better generalization performance;
and performing accuracy rate assessment on the 3D convolutional neural network model which is trained by using the test set, and using the 3D convolutional neural network model with accuracy rate meeting the requirement for identifying the positions of the metal plate cracks.
The metal plate crack identification method based on the 3D convolutional neural network and the displacement response is also characterized in that: the 3D convolutional neural network model comprises 8 parts, namely:
the first part is: a convolution layer, an activation function layer and a pooling layer;
the second part is: a convolution layer, an activation function layer and a pooling layer;
the third part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fourth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fifth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the sixth part is: a full connection layer, an activation function layer and a Dropout layer;
the seventh part is: a full connection layer, an activation function layer and a Dropout layer;
the eighth part is: and (5) a full connection layer.
The metal plate crack identification method based on the 3D convolutional neural network and the displacement response is also characterized in that:
regarding each convolution layer:
in C out Representing the number of output channels, denoted C in Representing the number of input channels;
in D in 、H in And W is in The one-to-one correspondence indicates the depth, height and width of the input sample data;
in D f 、H f And W is f The one-to-one correspondence indicates the size of the convolution kernel in the depth, height and width directions;
then there are:
the input tensor X is (C in ，D in ，H in ，W in ) The output tensor Y is (C out ，D out ，H out ，W out )；
The convolution kernel W has a size (D f ，H f ，W f ) The convolution calculation formula of the convolution layer is shown as formula (1):
in the formula (1):
Y c，d，h，w the value of the output tensor is the value of the output tensor Y at the c-th output channel, the d-th layer depth, the h-th row height and the w-th column width;
b is a bias vector, s 1 、s 2 Sum s 3 Are both the step sizes of the steps,
j＝0,1,2…C in -1；l＝0,1,2…D f -1；i＝0,1,2…H f -1；k＝0,1,2…W f -1；
at the j-th channel (d×s) for the input tensor X 1 +l) depth of layer (h×s) 2 +i) row height and (w×s) 3 k) The value of the output tensor X at the column width;
W l，i，k values at l, i, k for the convolution kernel W;
regarding the activation function layer:
the activation function layer learns a complex mapping relation by introducing an activation function and adding nonlinear transformation, so that better feature extraction and recognition of crack positions of the metal plate are obtained, and a ReLU activation function is adopted by the activation function layer;
regarding the pooling layer:
the pooling calculation of the pooling layer adopts a maximum pooling calculation formula characterized by a formula (2):
in the formula (2):
P c′，d′，h′，w′ values at c 'channel number, d' depth, h 'height, and w' width for the output tensor P;
D. h and W are the depth, height and width of the pooling layer input tensor Q in one-to-one correspondence;
for the input tensor Q, the number of channels at c ', d' x r 1 +t depth, h' ×r 2 +m height and w' ×r 2 A value at +n width;
r 1 、r 2 and r 3 Step sizes are adopted, and c' is the channel number;
t＝0,1,2…D-1；m＝0,1,2…H-1；n＝0,1,2…W-1；
regarding the full connection layer:
the two-dimensional tensor Y' is calculated as shown in formula (3):
Y′＝X′W′+b′ (3)
in the formula (3):
w 'is a weight, b' is a bias vector;
the sixth and seventh full-connection layers have the function of flattening the input tensor X 'into a two-dimensional tensor Y';
the eighth part of the full-connection layer is used for converting the characteristic tensor extracted from the first seven layers of the 3D convolutional neural network into a two-dimensional tensor, wherein one dimension in the two-dimensional tensor is consistent with the number of categories of cracks, the remaining data of the other dimension are the characteristics finally extracted by the 3D convolutional neural network, and the characteristics extracted from the first layer are converted into probability distribution by adopting a Softmax function; the Softmax function is characterized by formula (4):
in the formula (4):
k represents the number of output categories;
z a to input the a-th value of the two-dimensional tensor z f For inputting the f-th value of the two-dimensional tensor z, f=1, 2 … K;
y a is the a-th value of the output two-dimensional tensor y;
when the sample data are three metal plate vibration displacement response cloud charts with different crack positions, the output two-dimensional tensor of the eighth part is (N, 3), wherein N represents the number of input sample data, and 3 represents the probability of cracks at three different positions;
regarding the Dropout layer, the discard rate was set to 0.5.
The decay method is adopted for the super-parameter learning rate in the 3D convolutional neural network training process, and the learning rate is divided by ten every ten training rounds.
Compared with the prior art, the invention has the beneficial effects that:
compared with a general two-dimensional CNN, the convolution kernel of the 3D convolution neural network is one more dimension, and the dimension of the convolution kernel sample is one more dimension; the 3D convolutional neural network can capture the correlation in space and frequency, and the information of the surface displacement of the metal plate along with the frequency change of exciting force is considered, the extracted characteristic information is more abundant, the abundant characteristic information can ensure that crack positions can be accurately identified, and accurate identification can be realized for positions where some smaller cracks appear, and the position identification of the crack with the length of 10mm on the metal plate can be realized at least.
Drawings
FIG. 1 is a schematic view of a sheet metal with cracks;
FIGS. 1a and 1b are schematic views of a metal sheet with different crack locations;
FIG. 2 is a graph of a loss function of a training set and a validation set of a 3D convolutional neural network;
FIG. 3 is a result of visualizing features extracted from a 3D convolutional neural network based on a t-SNE algorithm;
FIG. 4 is a schematic diagram of a method for identifying crack locations in a metal sheet in accordance with an embodiment of the present invention;
FIG. 5 is a sample data of an embodiment of the present invention;
FIG. 6 is a schematic illustration of a convolution calculation of a 2D convolutional neural network;
FIG. 7 is a schematic illustration of a 3D convolutional neural network convolutional calculation;
fig. 8 is a 3D convolutional neural network architecture of the present invention.
Detailed Description
In order that the inventive solution may become more apparent, specific embodiments thereof will be described in more detail below with reference to the accompanying drawings, which illustrate but do not represent the limitation of the invention to the following technical details.
In this embodiment, the metal plate crack recognition method based on the 3D convolutional neural network and the displacement response is performed according to the following procedure:
and for each metal plate with different crack positions, acquiring surface vibration response displacement data of each metal plate under the action of excitation forces with different frequencies by adopting a displacement sensor.
RGB cloud images of the surface displacement of the metal plates under different frequencies are obtained through Fourier transformation according to the surface vibration response displacement data of each metal plate, and the RGB cloud images are cut to obtain 188 multiplied by 188 displacement cloud images with the same size; clipping the cloud picture is a means of data augmentation, and the diversity of training samples is obtained by deforming the cloud picture, so that the model generalization performance is better.
The crack positions of the metal plates are identified and converted into classification problems, and the displacement cloud pictures of the metal plates with different crack positions correspond to different categories; and training by using the displacement cloud picture to obtain a 3D convolutional neural network model, and realizing the position recognition of the metal plate crack in a classification mode by using the trained 3D convolutional neural network model.
In the implementation, the displacement cloud images at different frequencies of the same crack position are used as sample data, wherein the sample data is information of the vibration displacement of the surface of the metal plate along with the change of frequency, is three-dimensional data, comprises the vibration displacement information of the surface of the metal plate, and comprises frequency information for exciting to induce the surface displacement of the corresponding metal plate; labeling and classifying the sample data, and classifying the sample data into a training set, a verification set and a test set;
FIGS. 1, 1a and 1b are schematic views of a metal sheet with different crack locations; the length and the width of the metal plates are 450mm, and the thickness is 3mm; the sheet metal crack in fig. 1 is located in the very middle of the sheet, 50mm from the very middle of the sheet metal crack in fig. 1a, 100mm from the very middle of the sheet metal crack in fig. 1 b; the lengths of the cracks are 10mm; the square area S in the right center of the metal plate is the approximate location where the excitation force is randomly applied. Sheet metal data for a total of 3 different crack locations were collected, 170 sample data for each crack location, with 100 sample data for the training set, 30 sample data for the validation set, and 40 sample data for the test set.
Establishing a 3D convolutional neural network model to learn a training set, and adjusting model weights and offsets in iterative training of sample data in the training set by the 3D convolutional neural network model to enable the 3D convolutional neural network model to better fit the sample data in the training set;
the loss function values of the training set and the verification set are compared, the fitting degree of the model is judged according to the loss function values, and the model hyper-parameters are adjusted to achieve better generalization performance;
FIG. 2 is a graph showing the loss function of the 3D convolutional neural network training in this embodiment, in which both the training error (the error of the neural network model on the training data set) and the generalization error (the error of the neural network model on the verification data set) are reduced to less than 0.1, and the difference between the generalization error and the training error is very small, so that the model is said to have no over-fitting and under-fitting conditions; the 3D convolutional neural network model in this embodiment was constructed very successfully.
FIG. 3 is a result of visualizing the extracted features of the 3D convolutional neural network based on the t-SNE algorithm, and the data features of 3 cracks at different positions are obviously divided into three parts, which illustrates that the invention has good effect on identifying crack positions by adopting the displacement data of the surface of the metal plate with different frequencies.
Performing accuracy evaluation on the 3D convolutional neural network model after training by using a test set, and using the 3D convolutional neural network model with accuracy meeting the requirement for identifying the positions of the metal plate cracks, wherein FIG. 4 is a schematic diagram for identifying the positions of the metal plate cracks in the embodiment; and acquiring a A, B, C metal plate surface displacement cloud picture, inputting the obtained metal plate surface displacement cloud picture into a trained 3D convolutional neural network, and identifying that the positions of cracks are respectively in the middle of the metal plate, 50mm away from the middle and 100mm away from the middle.
Setting excitation frequencies of excitation forces with different frequencies as follows:to->The interval is->And analogy with video information which is three-dimensional data, wherein each displacement cloud picture is regarded as a frame of picture, and the corresponding excitation frequency is regarded as time dimension information in the video information.
FIG. 5 is a sample data in the present embodiment;
the (1) diagram, (2) diagram, (3) diagram, … diagram and (20) diagram in FIG. 5 are in one-to-one correspondenceTo->And at intervals of20 of (2) frequency information. Fig. 6 is a schematic diagram of convolution calculation of 2DCNN, where the size of sample picture data is h×w, k is the size of convolution kernel, the direction of arrow represents the moving direction of convolution kernel during convolution calculation, and the output is the data size after convolution calculation. FIG. 7 is a 3D convolutional neural network convolutionThe size of the sample picture data is H multiplied by W multiplied by L, the convolution kernel is k multiplied by D, the arrow direction represents the moving direction of the convolution kernel in the convolution calculation, and obviously, the dimension of the convolution kernel sample in the convolution calculation of the 3D convolution neural network is one more than 2DCNN, and the data size after the convolution calculation is output. Compared with a general two-dimensional CNN, the 3D convolution neural network in the embodiment has one more convolution kernel and one more convolution kernel sampling dimension; the 3D convolutional neural network can capture the correlation between space and frequency, and the information of the surface displacement of the metal plate along with the frequency change of exciting force is considered, the extracted characteristic information is more abundant, the abundant characteristic information can ensure more accurate identification of crack positions, and the accurate identification of positions where some smaller cracks appear can also be realized.
The 3D convolutional neural network model in this embodiment includes 8 parts, which are respectively:
the first part is: a convolution layer, an activation function layer and a pooling layer;
the second part is: a convolution layer, an activation function layer and a pooling layer;
the third part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fourth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fifth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the sixth part is: a full connection layer, an activation function layer and a Dropout layer;
the seventh part is: a full connection layer, an activation function layer and a Dropout layer;
the eighth part is: and (5) a full connection layer.
Regarding each convolution layer:
in C out Representing the number of output channels, denoted C in Representing the number of input channels;
in D in 、H in And W is in The one-to-one correspondence indicates the depth, height and width of the input sample data;
in D f 、H f And W is f The one-to-one correspondence indicates the size of the convolution kernel in the depth, height and width directions;
then there are:
the input tensor X is (C in ，D in ，H in ，W in ) The output tensor Y is (C out ，D out ，H out ，W out )；
The convolution kernel W has a size (D f ，H f ，W f ) The convolution calculation formula of the convolution layer is shown as formula (1):
in the formula (1):
Y c，d，h，w the value of the output tensor is the value of the output tensor Y at the c-th output channel, the d-th layer depth, the h-th row height and the w-th column width;
b is a bias vector, s 1 、s 2 Sum s 3 Are both the step sizes of the steps,
j＝0,1,2…C in -1；l＝0,1,2…D f -1；i＝0,1,2…H f -1；k＝0,1,2…W f -1；
at the j-th channel (d×s) for the input tensor X 1 +l) depth of layer (h×s) 2 +i) row height and (w×s) 3 +k) the value of the output tensor X at the column width;
W l，i，k the values of the convolution kernels W at l, i and k are 3 multiplied by 3;
regarding the activation function layer:
the activation function layer is a ReLU activation function by introducing an activation function and adding nonlinear transformation, so that a 3D convolutional neural network model is learned to a complex mapping relation, better feature extraction and recognition of crack positions of a metal plate are obtained;
regarding the pooling layer:
the size of the pooling window of the first part pooling layer is 1 multiplied by 2, and the rest parts are 2 multiplied by 2; the pooling calculation of the pooling layer uses a maximum pooling calculation formula characterized by formula (2):
in the formula (2):
P c′，d′，h′，w′ values at c 'channel number, d' depth, h 'height, and w' width for the output tensor P;
D. h and W are the depth, height and width of the pooling layer input tensor Q in one-to-one correspondence;
for the input tensor Q, the number of channels at c ', d' x r 1 +t depth, h' ×r 2 +m height and w' ×r 2 A value at +n width;
r 1 、r 2 and r 3 Step sizes are adopted, and c' is the channel number;
t＝0,1,2…D-1；m＝0,1,2…H-1；n＝0,1,2…W-1；
regarding the full connection layer:
the two-dimensional tensor Y' is calculated as shown in formula (3):
Y′＝X′W′+b′ (3)
in the formula (3):
w 'is a weight, b' is a bias vector;
the sixth and seventh full-connection layers have the function of flattening the input tensor X 'into a two-dimensional tensor Y';
the eighth part of the full-connection layer is used for converting the characteristic tensor extracted from the first seven layers of the 3D convolutional neural network into a two-dimensional tensor, wherein one dimension in the two-dimensional tensor is consistent with the number of categories of cracks, the remaining data of the other dimension are the characteristics finally extracted by the 3D convolutional neural network, and the characteristics extracted from the first layer are converted into probability distribution by adopting a Softmax function; the Softmax function is characterized by equation (4):
in the formula (4):
k represents the number of output categories;
z a to input the a-th value of the two-dimensional tensor z f For inputting the f-th value of the two-dimensional tensor z, f=1, 2 … K;
y a is the a-th value of the output two-dimensional tensor y;
when the sample data are three metal plate vibration displacement response cloud charts with different crack positions, the output two-dimensional tensor of the eighth part is (N, 3), wherein N represents the number of input sample data, and 3 represents the probability of cracks at three different positions;
regarding the Dropout layer, the discarding rate is set to 0.5, and the Dropout layer can reduce the overfitting phenomenon of the model in the 3D convolutional neural network model; with the Dropout layer, each neuron has a certain probability to be abandoned in the training process, so that the number of neurons in the training process is reduced, which is equivalent to the reduction of the model scale, and the over-fitting phenomenon of the model is reduced.
The super parameter learning rate in the training process of the 3D convolutional neural network adopts an attenuation method, the learning rate is divided by ten in every training round, and the learning rate is a very important super parameter in the training of the 3D convolutional neural network, and guides the step length of parameter updating of each step in the training process of the neural network. The larger the learning rate is, the larger the amplitude representing the parameter update of the neural network at each iteration is; otherwise, it will be smaller. The learning rate adopts an attenuation method, so that the learning rate is high in the initial training stage, the parameters of the 3D convolutional neural network model are updated faster, the learning rate is small in the later training stage, and the stability and the precision of the model are ensured.
Fig. 8 is a 3D convolutional neural network architecture in this embodiment, one sample data is 20 RGB cloud images, and in order to improve the generalization capability of the network in the 3D convolutional neural network training process, 17 samples are taken from 20 samples each time as training samples. 17 in 3×17@188×188 represents 17 samples, 3 represents 3 channels per image, the cloud image in this embodiment is an RGB three-channel image, and 188×188 represents the size of each sample. C is an abbreviation for convolution, P is an abbreviation for pooling, and F is an abbreviation for full concatenation; then C3a is the calculation of the first convolution layer of the third portion.
According to the method, frequency information is introduced by considering the information that the surface displacement of the metal plate changes along with the frequency of the exciting force, so that the characteristic information which can be extracted for identifying the crack is more abundant; the abundant characteristic information effectively ensures that the 3D convolutional neural network can identify crack positions more accurately, and can also realize accurate identification on positions where some smaller cracks appear.
Claims (4)
1. A metal plate crack identification method based on a 3D convolutional neural network and displacement response is characterized by comprising the following steps of:
for each metal plate with different crack positions, acquiring surface vibration response displacement data of each metal plate under the action of exciting forces with different frequencies by adopting a displacement sensor;
RGB cloud images of the surface displacement of the metal plates under different frequencies are obtained through Fourier transformation according to the surface vibration response displacement data of each metal plate, and the RGB cloud images are cut to obtain displacement cloud images with the same size;
the crack positions of the metal plates are identified and converted into classification problems, and the displacement cloud pictures of the metal plates with different crack positions correspond to different categories; and training the displacement cloud picture to obtain a 3D convolutional neural network model, and realizing the crack position identification of the metal plate in a classification mode by adopting the trained 3D convolutional neural network model.
2. The method for identifying metal plate cracks based on the 3D convolutional neural network and displacement response according to claim 1,
the method is characterized in that:
taking a displacement cloud picture at the same crack position and different frequencies as sample data, wherein the sample data is information of the surface vibration displacement of the metal plate along with the change of frequency, is three-dimensional data, comprises vibration displacement information of the surface of the metal plate, and comprises frequency information for exciting to induce the surface displacement of the corresponding metal plate; labeling and classifying the sample data, and classifying the sample data into a training set, a verification set and a test set;
establishing a 3D convolutional neural network model to learn the training set, and adjusting model weights and offsets in iterative training of sample data in the training set by the 3D convolutional neural network model to enable the 3D convolutional neural network model to better fit the sample data in the training set;
the loss function values of the training set and the verification set are compared, the fitting degree of the model is judged according to the loss function values, and the model hyper-parameters are adjusted to achieve better generalization performance;
and performing accuracy rate assessment on the 3D convolutional neural network model which is trained by using the test set, and using the 3D convolutional neural network model with accuracy rate meeting the requirement for identifying the positions of the metal plate cracks.
3. The metal plate crack identification method based on the 3D convolutional neural network and the displacement response, which is characterized in that: the 3D convolutional neural network model comprises 8 parts, namely:
the first part is: a convolution layer, an activation function layer and a pooling layer;
the second part is: a convolution layer, an activation function layer and a pooling layer;
the third part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fourth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the fifth part is: the system comprises a convolution layer, an activation function layer, a convolution layer, an activation function layer and a pooling layer;
the sixth part is: a full connection layer, an activation function layer and a Dropout layer;
the seventh part is: a full connection layer, an activation function layer and a Dropout layer;
the eighth part is: and (5) a full connection layer.
4. The metal plate crack identification method based on the 3D convolutional neural network and displacement response, according to claim 3, is characterized in that:
regarding each convolution layer:
in C out Representing the number of output channels, denoted C in Representing the number of input channels;
in D in 、H in And W is in The one-to-one correspondence indicates the depth, height and width of the input sample data;
in D f 、H f And W is f The one-to-one correspondence indicates the size of the convolution kernel in the depth, height and width directions;
then there are:
the input tensor X is (C in ，D in ，H in ，W in ) The output tensor Y is (C out ，D out ，H out ，W out )；
The convolution kernel W has a size (D f ，H f ，W f ) The convolution calculation formula of the convolution layer is shown as formula (1):
in the formula (1):
Y c，d，h，w the value of the output tensor is the value of the output tensor Y at the c-th output channel, the d-th layer depth, the h-th row height and the w-th column width;
b is a bias vector, s 1 、s 2 Sum s 3 Are both the step sizes of the steps,
j＝0,1,2…C in -1；l＝0,1,2…D f -1；i＝0,1,2…H f -1；k＝0,1,2…W f -1；
at the j-th channel (d×s) for the input tensor X 1 +l)Depth of layer (h×s) 2 +i) row height and (w×s) 3 +k) the value of the output tensor X at the column width;
W l，i，k values at l, i, k for the convolution kernel W;
regarding the activation function layer:
the activation function layer learns a complex mapping relation by introducing an activation function and adding nonlinear transformation, so that better feature extraction and recognition of crack positions of the metal plate are obtained, and a ReLU activation function is adopted by the activation function layer;
regarding the pooling layer:
the pooling calculation of the pooling layer adopts a maximum pooling calculation formula characterized by a formula (2):
in the formula (2):
P c′，d′，h′，w′ values at c 'channel number, d' depth, h 'height, and w' width for the output tensor P;
D. h and W are the depth, height and width of the pooling layer input tensor Q in one-to-one correspondence;
for the input tensor Q, the number of channels at c ', d' x r 1 +t depth, h' ×r 2 +m height and w' ×r 2 A value at +n width;
r 1 、r 2 and r 3 Step sizes are adopted, and c' is the channel number;
t＝0,1,2…D-1；m＝0,1,2…H-1；n＝0,1,2…W-1；
regarding the full connection layer:
the two-dimensional tensor Y' is calculated as shown in formula (3):
Y′＝X′W′+b′ (3)
in the formula (3):
w 'is a weight, b' is a bias vector;
the sixth and seventh full-connection layers have the function of flattening the input tensor X 'into a two-dimensional tensor Y';
the eighth part of the full-connection layer is used for converting the characteristic tensor extracted from the first seven layers of the 3D convolutional neural network into a two-dimensional tensor, wherein one dimension in the two-dimensional tensor is consistent with the number of categories of cracks, the remaining data of the other dimension are the characteristics finally extracted by the 3D convolutional neural network, and the characteristics extracted from the first layer are converted into probability distribution by adopting a Softmax function; the Softmax function is characterized by formula (4):
in the formula (4):
k represents the number of output categories;
z a to input the a-th value of the two-dimensional tensor z f For inputting the f-th value of the two-dimensional tensor z, f=1, 2 … K;
y a is the a-th value of the output two-dimensional tensor y;
when the sample data are three metal plate vibration displacement response cloud charts with different crack positions, the output two-dimensional tensor of the eighth part is (N, 3), wherein N represents the number of input sample data, and 3 represents the probability of cracks at three different positions;
regarding the Dropout layer, the discard rate was set to 0.5; the decay method is adopted for the super-parameter learning rate in the 3D convolutional neural network training process, and the learning rate is divided by ten every ten training rounds.
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