A Fault Diagnosis Method for Rolling Bearings under Variable Speed Conditions

Abstract

A method for diagnosing rolling bearing faults under variable speed conditions, which constructs order spectrum features unaffected by rotational speed through order spectrum analysis of vibration signals in orthogonal directions, extracts effective fault features in the order spectrum features using a multi-layer convolutional neural network, and finally determines the fault type through a fully connected neural network layer, including: measuring the vibration signals in the horizontal direction and the vertical direction of the rolling bearing under different rotational speed conditions using a two-channel acceleration sensor; preprocessing the measured two-channel vibration signals, distinguishing different fault types, setting a certain overlap length, and overlapping and truncating the two-channel vibration signals of each fault type into several segments with the same length; constructing an order spectrum feature matrix; building a one-dimensional convolutional neural network; training the built one-dimensional convolutional neural network; testing the trained one-dimensional convolutional neural network, and calculating the category diagnosis accuracy rate and the total diagnosis accuracy rate. The present invention has significant advantages in fault diagnosis under variable speed conditions.

Description

Technical Field

[0001] The present invention relates to signal analysis and fault diagnosis technologies, and particularly to an intelligent diagnosis method for rolling bearings based on a convolutional neural network. Background Art

[0002] As a key component of rotating mechanical equipment, a rolling bearing plays an important role in support and transmission. Due to the complexity of working conditions, rolling bearings are also components that often fail. Therefore, timely fault diagnosis of them is of great significance for ensuring the safe operation of mechanical equipment. In recent years, data-driven intelligent diagnosis technologies have been rapidly applied in the field of rolling bearing diagnosis, and many successful diagnosis cases have been achieved. However, in practical engineering applications, these intelligent diagnosis technologies still face some challenges, such as: when a rotating device operates under variable-speed conditions, how to efficiently utilize multi-sensor data, how to extract features that accurately represent faults, and how to construct a suitable diagnostic decision network need to be further improved.

[0003] The patent application of invention with the publication number CN112254964A discloses a rolling bearing fault diagnosis method based on a fast multi-scale convolutional neural network, which collects one-dimensional vibration signals at the drive end of a rolling bearing; standardizes each monitored vibration signal collected in the first step; builds a fast multi-scale convolutional neural network model; trains the fast multi-scale convolutional neural network model; collects the acceleration vibration signal of the current rolling bearing and processes it to obtain a test set of samples; and inputs the sample test set in the fifth step into the fast multi-scale convolutional neural network model trained in the fourth step, thereby outputting the fault diagnosis result of the rolling bearing. The patent of invention with the authorization announcement number CN110595775B discloses a rolling bearing fault diagnosis method based on a multi-branch multi-scale convolutional neural network. First, it collects acceleration vibration signals of rolling bearings without faults and with different faults under different operating states, and sets fault state labels according to the fault states corresponding to each acceleration vibration signal. It standardizes each acceleration vibration signal and uses it as a training sample to train the multi-branch multi-scale convolutional neural network model. The multi-branch multi-scale convolutional neural network model includes a low-frequency branch convolutional network, an identity mapping branch convolutional network, a denoising branch convolutional network, a feature fusion layer, a global average pooling layer, and a Softmax layer. Then, it collects the current acceleration vibration signal of the rolling bearing and sends it into the multi-branch multi-scale convolutional neural network model for fault diagnosis.

[0004] The convolutional neural network model for rolling bearing fault detection can effectively improve the fault diagnosis performance of rolling bearings. However, when a rotating device operates under variable-speed conditions, there is still much room for improvement in accurately judging rolling bearing faults in terms of how to extract features that accurately represent faults and how to construct a suitable diagnostic decision network. Summary of the Invention

[0005] In view of the deficiencies of the existing rolling bearing diagnosis methods, the present invention proposes a rolling bearing fault diagnosis method under variable speed conditions. Without relying on the parameters of the bearing to be diagnosed, the convolutional layer and pooling layer of the convolutional neural network are alternately operated to effectively extract the fault feature information in the order spectrum feature matrix, effectively avoiding the influence of speed changes on bearing fault diagnosis.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A rolling bearing fault diagnosis method under variable speed conditions constructs order spectrum features that are not affected by speed through order spectrum analysis of orthogonal direction vibration signals, uses a multi-layer convolutional neural network to extract effective fault features in the order spectrum features, and finally determines the fault type through a fully connected neural network layer. The steps are as follows:

[0008] S1. Use a two-channel acceleration sensor to measure the vibration signals in the horizontal direction and the vertical direction of the rolling bearing under different fault types and at different speed conditions.

[0009] S2. Preprocess the measured two-channel vibration signals under different fault types to distinguish different fault types. The specific method is as follows: Set a certain overlap length, and overlap and truncate the two-channel vibration signals of each fault type into several segments with the same length.

[0010] S3. Construct an order spectrum feature matrix.

[0011] S4. Build a one-dimensional convolutional neural network.

[0012] S5. Train the one-dimensional convolutional neural network built in step S4.

[0013] S6. Test the one-dimensional convolutional neural network trained in step S5, and calculate the category diagnosis accuracy rate and the total diagnosis accuracy rate. The specific processes and steps of steps 3-6 are as follows:

[0014] Step 3: Construct an order spectrum feature matrix:

[0015] Step 3.1: Use equation (1) to form a complex signal

[0016] z i = x i + jy i (1)

[0017] Where: i is the serial number of each segment of vibration signal obtained in step 2, z i is the formed complex signal, x i and y iThey are the vibration signals in the horizontal direction and the vertical direction obtained in each segment after Step 2, respectively. j is an imaginary unit and satisfies j 2 = -1;

[0018] Step 3.2: Calculate the order spectrum using Equation (2)

[0019]

[0020] where: k is the order of the order spectrum, O(k) is the spectral value of order k, l and L are the sequence numbers of the data points in the complex signal z i and the total number of data points in the complex signal z i respectively, z il is the l-th data value in the complex signal z i w is the angular frequency, f r and F s are the rotational frequency of the rolling bearing and the sampling frequency of the vibration signal, respectively;

[0021] Step 3.3: Calculate the forward radius and backward radius of each order using Equation (3)

[0022]

[0023] where: R p (k) and R r (k) are the forward radius and backward radius of order k, respectively. |O(k)| and |O(L - k)| represent taking the complex modulus of O(k) and O(L - k), respectively;

[0024] Step 3.4: Calculate the slope of each order using Equation (4)

[0025]

[0026] where: tg(k) is the slope of order k, O R (k) and O I (k) represent taking the real part and imaginary part of O(k), respectively. O R (L - k) and O I (L - k) represent taking the real part and imaginary part of O(L - k), respectively;

[0027] Step 3.5: Combine R p (k), R r (k) and tg(k) into a vector (R p (k) R r (k) tg(k));

[0028] Step 3.6: Starting from k = 1, repeat Steps 3.2 - 3.5 until k = K, where K is the maximum value of the order,

[0029] Set the specific value of K in the application. Combine the vectors obtained for all k = 1, …, K to obtain the matrix

[0030]

[0031] Step 3.7: Normalize each column of the obtained matrix according to formula (5),

[0032]

[0033] where: x(k) and x'(k) represent the k-th data in each column before normalization and the k-th data in each column after normalization respectively, and represent the maximum data and the minimum data in each column respectively.

[0034] The matrix obtained after normalization is the order spectrum feature matrix of this sample (complex signal z i ), and this order spectrum feature matrix will be input into the convolutional neural network in the subsequent steps.

[0035] Repeat Step 3 until all the collected vibration signals are processed and stopped, obtaining a series of order spectrum feature matrix samples of various fault types.

[0036] Step 4: Build a one-dimensional convolutional neural network, and the features of this network are:

[0037] 4.1: The first layer is the input layer, which contains 3 column vector nodes of K×1, and receives the first column, the second column, and the third column of the order spectrum feature matrix from Step 3 respectively;

[0038] 4.2: The second layer to the ninth layer are 4 convolutional layers and 4 pooling layers, and the convolutional layers and pooling layers appear alternately;

[0039] The convolution operations of the 4 convolutional layers are carried out according to formula (6),

[0040]

[0041] In formula (6): q and m are the convolution layer number and the neuron number respectively, and are the output of the m-th neuron in the q-th convolution layer and the bias value of the m-th neuron in the q-th convolution layer respectively, c and C are the channel number and the total number of channels in the (q - 1)-th convolution layer respectively, is the output of the c-th channel in the (q - 1)-th convolution layer, is the connection weight between the c-th channel in the (q - 1)-th convolution layer and the m-th neuron in the q-th convolution layer, and f(·) represents the activation function, taking the ReLU function;

[0042] ReLU (Rectified Linear Unit, the rectified linear unit), also known as the linear rectification function, is a commonly used activation function in artificial neural networks, usually referring to non-linear functions represented by the ramp function and its variants. Its expression is

[0043]

[0044] The pooling operations of the 4 pooling layers are carried out according to equation (8)

[0045]

[0046] In equation (8): q and j are the numbers of the convolutional layer and the pooling block respectively, r, s and i are the data width, the stride of the stride, and the number of the data in the pooling block respectively, c' q,j is the output of the j-th pooling block in the q-th convolutional layer, c q,(j-1)×s+i represents the i-th data value before the pooling operation in the j-th pooling block in the q-th convolutional layer, represents taking the maximum data value in the j-th pooling block in the q-th convolutional layer.

[0047] 4.3: The 10th layer and the 11th layer are the flattening layer and the dropout layer respectively. The specific operation description of the flattening layer is: concatenating the data of each channel output by the 9th layer (i.e., the last pooling layer) end to end to form a column vector; the specific operation description of the dropout layer is: setting the dropout probability to 50%, randomly selecting 50% of the data elements in the column vector output by the 10th layer to be retained, and deleting the other 50% of the elements.

[0048] 4.4: The 12th layer and the 13th layer are both fully connected layers, and the number of neurons they contain is 144 and 5 respectively. The operation of the fully connected layer is carried out according to equation (9)

[0049]

[0050] In equation (9): m is the number of the neuron in the fully connected layer, y m and b m are the output and the bias of the m-th neuron in the fully connected layer respectively, i and I are the number of the input data and the total number of the input data in the fully connected layer respectively, x i is the i-th input data in the fully connected layer, w m,i is the connection weight between the i-th input data and the m-th neuron in the fully connected layer, and f(·) is the activation function.

[0051] The activation function f(·) of the 12th layer takes ReLU (i.e., equation (7)), and the activation function f(·) of the 13th layer takes Softmax, as shown in equation (10)

[0052]

[0053] (10) In the formula, t i is the input of the activation function f(·), i and M are the serial number and the total number of neurons respectively, f(t i ) is the output of the activation function f(·), and e is the natural constant (e = 2.718281828…).

[0054] Step 5: Train the one-dimensional convolutional neural network built in Step 4. The training steps are as follows:

[0055] Step 5.1: Set the training objective function according to formula (11)

[0056]

[0057] In formula (11): i and N are the serial number and the total number of training samples respectively, τ i and t i are the target class vector of the i-th training sample and the class vector output by the convolutional neural network built in Step 4 respectively, c and C are the class serial number and the total number of classes of the training samples respectively, t c is the class vector belonging to the c-th class output by the convolutional neural network built in Step 4, and Θ represents the value of the objective function.

[0058] Step 5.2: Randomly select a certain number from each type of fault in a series of order spectrum feature matrix samples obtained after being processed in Step 3 as training samples.

[0059] Step 5.3: Select the adaptive moment estimation algorithm (Adam) to train the one-dimensional convolutional neural network built in Step 4. The parameters set before training are: batch size, initial learning rate, maximum number of iterations, and the change rate of the objective function value for training to stop. Use the training samples selected in Step 5.2 as the input to train the one-dimensional convolutional neural network built in Step 4. During each iteration, update the convolution kernel coefficients and biases of the 4 convolutional layers and the connection weights and biases between the neurons of the 2 fully connected layers until the change rate of the objective function value < the change rate of the objective function value for training to stop, and the entire training ends.

[0060] Step 6: Test the one-dimensional convolutional neural network trained in Step 5. The implementation steps of the test are as follows:

[0061] Step 6.1 Randomly select a certain number from the remaining order spectrum feature matrix samples of each type of fault selected in Step 5.2 as test samples.

[0062] Step 6.2 Each test sample is sequentially input into the one-dimensional convolutional neural network trained in Step 5, and the output obtained is the diagnostic result of each test sample. When the output class vector is consistent with the target class vector of the test sample, the number of correct test diagnoses for this class is incremented by 1; otherwise, the number of correct test diagnoses for this class remains unchanged. After testing all the test samples, the class diagnostic accuracy rate and the total diagnostic accuracy rate are calculated according to Equations (12) and (13) respectively,

[0063]

[0064]

[0065] where: c and C are respectively the class serial number of the test sample and the total number of classes of the test sample, n c and N c are respectively the number of correct test diagnoses for the test samples of the c-th class and the total number of test samples of the c-th class, η c and η are respectively the diagnostic accuracy rate of the c-th class and the total diagnostic accuracy rate.

[0066] Advantages of the invention:

[0067] 1. For the rolling bearing fault diagnosis method under variable speed conditions of the present invention, the dual-channel vibration signals measured are preprocessed to distinguish different fault types. By setting a certain overlap length, the dual-channel vibration signals of each fault type are overlapped and truncated into several segments with the same length for each segment; the order spectrum feature matrix formed by order spectrum analysis is used as the input of the convolutional neural network to diagnose the rolling bearing faults, effectively avoiding the influence of speed changes.

[0068] 2. For the rolling bearing fault diagnosis method under variable speed conditions of the present invention, without relying on the parameters of the bearing to be diagnosed, when the rolling bearing operates under variable speed conditions, through the alternating operations of the convolutional layer and the pooling layer of the convolutional neural network, the fault feature information in the order spectrum feature matrix is effectively extracted, and the clustering distribution of the main features extracted can be visually observed, providing an effective technical means for the intelligent diagnosis of rolling bearings under variable speed conditions.

[0069] 3. For the rolling bearing fault diagnosis method under variable speed conditions of the present invention, the vibration signals in the horizontal direction and the vertical direction of the rolling bearing under different rotational speed conditions are measured by using dual-channel acceleration sensors; the vibration data in the orthogonal directions of the rolling bearing are effectively utilized, and high-accuracy intelligent diagnosis is implemented through the built convolutional neural network based on deep learning; it has significant advantages in the aspect of fault diagnosis under variable speed conditions. Description of the drawings

[0070] Figure 1 The figure shows the overall flowchart of the rolling bearing fault diagnosis method under variable speed conditions of the present invention;

[0071] Figure 2 Shown is the structure diagram of the constructed convolutional neural network;

[0072] Figure 3 Shown is the diagnostic confusion matrix of various types of test samples.

[0073] Figure 4 It is the distribution of the first two principal components output by the fully connected layer of the 12th layer in visualization. Detailed implementation manners

[0074] In order to make the technical concept and advantages for the invention to achieve its invention purpose clearer and more understandable, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the following embodiments are only used to explain and illustrate the preferred implementation manners of the present invention, and should not constitute a limitation on the scope of patent protection required by the present invention.

[0075] Embodiment 1

[0076] Refer to Figure 1 , for the rolling bearing fault diagnosis method under variable speed conditions of the present invention, by performing order spectrum analysis on the vibration signals in the orthogonal directions to construct order spectrum features that are not affected by the rotational speed, using a multi-layer convolutional neural network to extract effective fault features in the order spectrum features, and finally making a decision on the fault type through the fully connected neural network layer, the steps are as follows:

[0077] S1. Use a two-channel acceleration sensor to measure the vibration signals in the horizontal direction and the vertical direction of the rolling bearing under different rotational speed conditions;

[0078] S2. Preprocess the measured two-channel vibration signals, distinguish different fault types, set a certain overlap length, and overlap and truncate the two-channel vibration signals of each fault type into several segments with the same length for each segment;

[0079] S3. Construct an order spectrum feature matrix;

[0080] S4. Build a one-dimensional convolutional neural network;

[0081] S5. Train the one-dimensional convolutional neural network built in step S4;

[0082] S6. Test the one-dimensional convolutional neural network trained in step S5, and calculate the category diagnosis accuracy rate and the total diagnosis accuracy rate.

[0083] The intelligent diagnosis method of rolling bearings based on convolutional neural network of the present invention effectively utilizes the vibration data in the orthogonal directions of rolling bearings, constructs order spectrum features that are not affected by rotational speed through order spectrum analysis of orthogonal direction vibration signals, extracts effective fault features in the order spectrum features using a multi-layer convolutional neural network, and finally determines the fault type through a fully connected neural network layer, providing an effective technical solution for the intelligent diagnosis of rolling bearings under variable speed conditions.

[0084] Embodiment 2

[0085] See Figures 1-4 , in this embodiment, a rolling bearing with the model number N205EM is selected as the test object to further specifically describe the implementation solution of the present invention.

[0086] The fault categories in the test include five types: no fault, inner ring wear, outer ring wear, outer ring fracture, and cage fracture. Rolling bearings of each fault category are installed on a QPZZ-II rotary machinery vibration fault test platform and work under two rotational speed conditions: 2100 r / min and 2400 r / min.

[0087] Step 1: Using piezoelectric dual-channel acceleration sensors installed on the outer wall of the ball raceway outer ring of this type of bearing, measure the vibration signals in the horizontal direction and the vertical direction of the rolling bearings under the two rotational speed conditions for these five fault types respectively. The sampling frequency is 12 KHz, and the acquisition duration at each rotational speed is 1 minute.

[0088] Step 2: Preprocess the dual-channel vibration signals of each fault type. The specific method is as follows:

[0089] Set the overlapping length to 300 data points, and overlap and truncate the dual-channel vibration signals of each fault type into several segments so that the length of each segment is the same, which is 2048 data points.

[0090] Step 3: Construct an order spectrum feature matrix. The specific steps are as follows:

[0091] Step 3.1: Use equation (1) to form a complex signal

[0092] z i =x i +jy i (1)

[0093] where: i is the serial number of each segment of vibration signal obtained in Step 2, z i is the formed complex signal, x i and y i are respectively the vibration signals in the horizontal direction and the vertical direction of each segment obtained in Step 2, j is the imaginary unit, and satisfies j 2 =-1;

[0094] Step 3.2: Obtain the order spectrum using Equation (2)

[0095]

[0096] where: k is the order of the order spectrum, O(k) is the spectral value of order k, l and L (in this embodiment, L = 2048) are the data point numbers in the complex signal z i and the total number of data points in the complex signal z i respectively, z il is the complex signal z i the l-th data value in, w is the angular frequency, f r is the rotational frequency of the rolling bearing (in this embodiment, when the rotational speed = 2100 r / min, the rotational frequency is 35 Hz; when the rotational speed = 2400 r / min, the rotational frequency is 40 Hz), F s is the sampling frequency of the vibration signal (in this embodiment, the sampling frequency is 12 KHz);

[0097] Step 3.3: Calculate the forward radius and reverse radius of each order using Equation (3)

[0098]

[0099] where: R p (k) and R r (k) are the forward radius and reverse radius of order k respectively, |O(k)| and |O(L - k)| represent taking the complex modulus of O(k) and O(L - k);

[0100] Step 3.4: Calculate the slope of each order using Equation (4)

[0101]

[0102] where: tg(k) is the slope of order k, O R (k) and O I (k) represent taking the real part and imaginary part of O(k) respectively, O R (L - k) and O I (L - k) represent taking the real part and imaginary part of O(L - k) respectively;

[0103] Step 3.5: Combine R p (k), R r (k) and tg(k) into a vector (R p (k) R r (k) tg(k));

[0104] Step 3.6: Starting from k = 1, repeat Steps 3.2 - 3.5 until k = K, where K is the maximum order, and the specific value of K can be set in the application. In this embodiment, K = 2000 is set. Combine all the vectors obtained for k = 1, …, K to obtain a matrix

[0105] Step 3.7: Normalize each column of the matrix obtained above according to Equation (5),

[0106]

[0107] where: x(k) and x'(k) respectively represent the k-th data in each column before normalization and the k-th data in each column after normalization, and respectively represent the maximum data and the minimum data in each column.

[0108] The matrix obtained after normalization is the order spectrum feature matrix of this sample (complex signal z i ). In the subsequent steps, this order spectrum feature matrix will be input into the convolutional neural network.

[0109] Repeat Step 3 until all the collected vibration signals are processed and stopped, obtaining a series of order spectrum feature matrix samples of various fault types.

[0110] Step 4: Build a one-dimensional convolutional neural network, and the features of this network are as follows:

[0111] 4.1: The first layer is the input layer, which contains 3 column vector nodes of 2000×1, and respectively receives the first column, the second column, and the third column of the order spectrum feature matrix from Step 3;

[0112] 4.2: The second layer to the ninth layer are 4 convolutional layers and 4 pooling layers, and the convolutional layers and pooling layers appear alternately. Among them: the kernel width and the number of channels of the first convolutional layer are respectively set to 24 and 32; the kernel width and the number of channels of the second convolutional layer are respectively set to 18 and 64; the kernel width and the number of channels of the third convolutional layer are respectively set to 15 and 64; the kernel width and the number of channels of the fourth convolutional layer are respectively set to 12 and 128; the stride of the 4 convolutional layers and the 4 pooling layers are all set to 2.

[0113] The convolution operations of the 4 convolutional layers are carried out according to Equation (6),

[0114]

[0115] In Equation (6): q and m are respectively the convolution layer number and the neuron number, and They are respectively the output of the m-th neuron in the q-th convolutional layer and the bias value of the m-th neuron in the q-th convolutional layer. c and C are respectively the channel number and the total number of channels in the (q - 1)-th convolutional layer. is the output of the c-th channel in the (q - 1)-th convolutional layer. is the connection weight between the c-th channel in the (q - 1)-th convolutional layer and the m-th neuron in the q-th convolutional layer. f(·) represents the activation function, and the ReLU function is taken; the expression of the ReLU function is:

[0116]

[0117] The pooling operations of the 4 pooling layers are carried out according to equation (8).

[0118]

[0119] In equation (8): q and j are respectively the serial number of the convolutional layer and the serial number of the pooling block, r, s and i are respectively the data width of the pooling block, the stride step, and the serial number of the data in the pooling block, c' q,j is the output of the j-th pooling block in the q-th convolutional layer, c q,(j-1)×s+i represents the i-th data value before the pooling operation in the j-th pooling block in the q-th convolutional layer. represents taking the maximum data value in the j-th pooling block in the q-th convolutional layer.

[0120] 4.3: The 10th layer and the 11th layer are respectively the flattening layer and the dropout layer. The specific operation of the flattening layer is: concatenating the data of each channel output by the 9th layer (i.e., the last pooling layer) head to tail to form a column vector; the specific operation of the dropout layer is: setting the dropout probability to 50%, randomly selecting 50% of the data elements in the column vector output by the 10th layer to be retained, and deleting the other 50% of the elements.

[0121] 4.4: The 12th layer and the 13th layer are both fully connected layers, and the number of neurons they contain is 144 and 5 respectively. The operation of the fully connected layer is carried out according to equation (9).

[0122]

[0123] In equation (9): m is the serial number of the neuron in the fully connected layer, y m and b m are respectively the output and the bias value of the m-th neuron in the fully connected layer, i and I are respectively the serial number of the input data of the fully connected layer and the total number of input data, x i is the i-th input data in the fully connected layer, w m,i is the connection weight between the i-th input data and the m-th neuron in the fully connected layer, and f(·) is the activation function.

[0124] The activation function f(·) of the 12th layer takes ReLU, and the activation function f(·) of the 13th layer takes Softmax, as shown in Equation (10).

[0125]

[0126] In Equation (10), t i is the input of the activation function f(·), i and M are the serial number and total number of neurons respectively, and f(t i ) is the output of the activation function f(·), and e is the natural constant (e = 2.718281828…).

[0127] Through the above steps, a convolutional neural network with the structure as Figure 2 shown is built, and the structure parameters of the convolutional neural network are shown in Table 1.

[0128] Table 1: Structure parameters of the built convolutional neural network

[0129]

[0130] Step 5: Train the one-dimensional convolutional neural network built in Step 4, and the training steps are as follows:

[0131] Step 5.1: Set the training objective function according to Equation (11)

[0132]

[0133] In Equation (11): i and N are the serial number and total number of training samples respectively, τ i and t i are the target category vector of the i-th training sample and the category vector output by the convolutional neural network built in Step 4 respectively, c and C are the category serial number and total number of training samples respectively (in this embodiment, the total number of categories C = 5), t c is the category vector belonging to the c-th category output by the convolutional neural network built in Step 4, and Θ represents the value of the objective function.

[0134] Step 5.2: Randomly select a certain number (in this embodiment, 1330 are randomly selected at each of the two rotational speeds of each fault type, so the number of training samples for each fault type is 2660) from each fault type in a series of order spectrum feature matrix samples obtained after being processed in Step 3 as training samples.

[0135] For the wide applicability of the training samples, the number of selected samples is not less than 1000.

[0136] Step 5.3: Select the Adam (Adaptive Moment Estimation, a first-order gradient-based stochastic objective function optimization algorithm commonly used in the training of convolutional neural networks) to train the one-dimensional convolutional neural network built in Step 4. The parameters set before training are: batch size, initial learning rate, maximum number of iterations, and the change rate of the objective function value for training to stop. In this embodiment, the batch size is 256, the initial learning rate is 0.001, the maximum number of iterations is 50, and the change rate of the objective function value for training to stop is 1%.

[0137] Use the training samples selected in Step 5.2 as the input to train the one-dimensional convolutional neural network built in Step 4. During each iteration, update the convolution kernel coefficients and biases of the 4 convolution layers and the connection weights and biases between the neurons of the 2 fully connected layers until the change rate of the objective function value < the change rate of the objective function value for training to stop, and the entire training ends.

[0138] Step 6: Test the one-dimensional convolutional neural network trained in Step 5. The implementation steps of the test are as follows:

[0139] Step 6.1 Randomly select a certain number from the order spectrum feature matrix samples of various remaining fault types selected in Step 5.2 as test samples. In this embodiment, from the remaining order spectrum feature matrices at two rotational speeds of each fault type, 200 are randomly selected for each, so the number of training samples for each fault type is 400. The specific data is shown in Table 2.

[0140] Table 2: Quantity situation of training samples and test samples in each fault type

[0141]

[0142] Step 6.2 Input each test sample into the one-dimensional convolutional neural network trained in Step 5 in turn. The output obtained is the diagnostic result of each test sample. When the output category vector is the same as the target category vector of this test sample, the number of correct test diagnoses for this category is incremented by one; otherwise, the number of correct test diagnoses for this category remains unchanged.

[0143] After testing all the test samples, calculate the category diagnostic accuracy rate and the total diagnostic accuracy rate according to Equations (12) and (13) respectively.

[0144]

[0145]

[0146] where: c and C are the category serial numbers of the test sample and the total number of categories of the test sample respectively, n c and N cThey are respectively the number of correctly diagnosed test samples of the c-th category and the total number of test samples of the c-th category, η c and η are respectively the diagnostic accuracy rate of the c-th category and the total diagnostic accuracy rate. In this embodiment, C = 5, N c = 400.

[0147] Figure 3 Shows the diagnostic confusion matrix of test samples of each category. Target categories: 1 - no fault, 2 - inner ring wear, 3 - outer ring wear, 4 - outer ring fracture, 5 - cage fracture. From Figure 3 It can be seen that the diagnostic accuracy rate of each category has reached more than 98%. Among them, the diagnostic accuracy rate of the no-fault category is the highest, reaching 100%. The category with the lowest diagnostic accuracy rate is the outer ring fracture fault, which is 395 / 400 = 98.75%. Table 3 lists that the overall diagnostic accuracy rate is 1984 / 2000 = 99.2%.

[0148] Table 3: Diagnostic accuracy rates of test samples of each category and the total diagnostic accuracy rate

[0149]

[0150] From this, it can be seen the effectiveness of the fault diagnosis method of the present invention for rolling bearings under variable speed conditions.

[0151] In order to further verify the fault feature extraction ability of the constructed convolutional neural network for rolling bearings under variable speed conditions, Figure 4 Visualizes the distribution of the first 2 principal components output by the fully connected layer of the 12th layer. It can be seen that the clustering effect of the five fault categories is good, thus verifying the effectiveness of the constructed convolutional neural network in extracting the fault features of rolling bearings under variable speed conditions.

Claims

1. A fault diagnosis method for rolling bearings under variable speed conditions, which adopts an intelligent diagnosis method based on a convolutional neural network. By performing order spectrum analysis on the vibration signals in the orthogonal directions, order spectrum features that are not affected by the rotational speed are constructed. A multi-layer convolutional neural network is constructed to extract effective fault features from the order spectrum features. Finally, the fault type is determined through a fully connected neural network layer. It is characterized in that: The steps are as follows: S1. Use a two-channel acceleration sensor to measure the vibration signals in the horizontal direction and the vertical direction of the rolling bearing under different rotational speed conditions. S2. Preprocess the measured two-channel vibration signals, distinguish different fault types, set a certain overlap length, and overlap and truncate the two-channel vibration signals of each fault type into several segments with the same length for each segment. S3. Construct an order spectrum feature matrix, and the process is as follows: Step 3.1: Use equation (1) to form a complex signal z i = x i + j y i (1) Where: i is the serial number of each segment of vibration signal obtained in step S2, and z i is the complex signal formed, x i and y i are respectively the vibration signal in the horizontal direction and the vibration signal in the vertical direction of each segment obtained in step S2, j is the imaginary unit, and satisfies j 2 = -1; Step 3.2: Use equation (2) to calculate the spectral order Where: k is the order of the spectral order, O(k) is the spectral value of order k, l and L are the sequence numbers of the data points in the complex signal z i and the total number of data points in the complex signal z i respectively, z il is the complex signal z i the l-th data value in, w is the angular frequency, f r and F s are the rotational frequency of the rolling bearing and the sampling frequency of the vibration signal respectively; Step 3.3: Use equation (3) to calculate the forward radius and backward radius of each order Where: R p (k) and R r (k) are the positive and negative advance radii of order k respectively, and |O(k)| and |O(L - k)| respectively represent taking the complex moduli of O(k) and O(L - k); Step 3.4: Use equation (4) to calculate the slope of each order where: tg(k) is the slope of order k, O R (k) and O I (k) respectively represent taking the real part and the imaginary part of O(k), O R (L - k) and O I (L - k) respectively represent taking the real part and the imaginary part of O(L - k); Step 3.5: Combine R p (k), R r (k) and tg(k) into a vector (R p (k) R r (k) tg(k)); Step 3.6: Starting from k = 1, repeat steps 3.2 - 3.5 until k = K ends, where K is the maximum value of the order, and the specific value of K is set in the application; merge the vectors obtained for all k = 1,..., K to obtain a matrix Step 3.7: Normalize each column of the obtained matrix according to equation (5). where: x(k) and x'(k) respectively represent the k-th data in each column before normalization processing and the k-th data in each column after normalization processing, and respectively represent the maximum data and the minimum data in each column; The matrix obtained after normalization is this sample, that is, the complex signal z i which is the order spectrum feature matrix. Then, input this order spectrum feature matrix into the convolutional neural network; Repeat the above process until all the collected vibration signals are processed and stopped, and a series of order spectrum feature matrix samples of various fault types are obtained. S4. Build a one-dimensional convolutional neural network. The process of building a one-dimensional convolutional neural network is as follows, and the characteristics of this convolutional neural network are: 4.1: The first layer is the input layer, which contains 3 column vector nodes of K×1, and respectively receives the first column, the second column, and the third column of the order spectrum feature matrix from step S3. 4.2: The second layer to the ninth layer are 4 convolutional layers and 4 pooling layers, and the convolutional layers and pooling layers appear alternately. Among them: the kernel width and the number of channels of the first convolutional layer are respectively set to 24 and 32; the kernel width and the number of channels of the second convolutional layer are respectively set to 18 and 64; the kernel width and the number of channels of the third convolutional layer are respectively set to 15 and 64; the kernel width and the number of channels of the fourth convolutional layer are respectively set to 12 and 128; the stride of the 4 convolutional layers and the 4 pooling layers are all set to 2. The convolution operations of the 4 convolutional layers are carried out according to equation (6). In formula (6): q and m are the serial numbers of the convolutional layer and the neuron respectively, and are the output of the m-th neuron in the q-th convolutional layer and the bias value of the m-th neuron in the q-th convolutional layer respectively. c and C are the serial number of the channel and the total number of channels in the (q - 1)-th convolutional layer respectively, is the output of the c-th channel in the (q - 1)-th convolutional layer, is the connection weight between the c-th channel in the (q - 1)-th convolutional layer and the m-th neuron in the q-th convolutional layer. f(·) represents the activation function, taking the ReLU function, and its expression is: In equation (7): t represents the input value of the activation function, and f(t) is the output value of the activation function. The pooling operations of the 4 pooling layers are carried out according to equation (8). In equation (8): q and j are the numbers of the convolutional layer and the pooling block respectively, r, s, and i are the data width, stride, and the number of the data in the pooling block respectively, and c' q,j is the output of the j-th pooling block in the q-th convolutional layer, and c q,(j-1)×s+i represents the i-th data value before the pooling operation in the j-th pooling block in the q-th convolutional layer, represents taking the maximum data value in the j-th pooling block in the q-th convolutional layer; 4.3: The tenth layer and the eleventh layer are respectively the flattening layer and the dropout layer. 4.4: The twelfth layer and the thirteenth layer are both fully connected layers, and the number of neurons they contain are 144 and 5 respectively; the operations of the fully connected layers are carried out according to equation (9). In equation (9): m is the serial number of neurons in the fully connected layer, y m and b m are respectively the output and bias of the m-th neuron in the fully connected layer. i and I are respectively the serial number and the total number of input data of the fully connected layer. x i is the i-th input data in the fully connected layer, and w m,i is the connection weight between the i-th input data and the m-th neuron in the fully connected layer. f(·) is the activation function; The activation function f(·) of the twelfth layer takes ReLU (i.e., equation (7)), and the activation function f(·) of the thirteenth layer takes Softmax, such as equation (10). In equation (10), t i is the input of the activation function f(·), i and M are the serial number and the total number of neurons respectively, f(t i ) is the output of the activation function f(·), e is the natural constant, e = 2.718281828…; S5. Train the one-dimensional convolutional neural network built in step S4. S6. Test the one-dimensional convolutional neural network trained in step S5, and calculate the category diagnosis accuracy rate and the total diagnosis accuracy rate.

2. The rolling bearing fault diagnosis method under variable speed conditions according to claim 1, characterized in that: In the aforementioned step 4.3, the specific operation of the flattening layer is: concatenate the data of each channel output by the last pooling layer, that is, the 9th layer, head to tail to form a column vector; the specific operation of the dropout layer is: set the dropout probability to 50%, and randomly select 50% of the data elements in the column vector output by the 10th layer to be retained, and delete the other 50% of the elements.

3. The rolling bearing fault diagnosis method under variable speed conditions according to claim 1 or 2, characterized in that: Step S5: The steps for training the one-dimensional convolutional neural network built in step S4 are as follows: Step 5.1: Set the training objective function according to equation (11) In formula (11): i and N are respectively the serial number and the total number of training samples, and τ i and t i are respectively the target class vector of the i-th training sample and the class vector output by the convolutional neural network built in step S4, c and C are respectively the class serial number of the training sample and the total number of classes of the training samples, and t c is the class vector belonging to the c-th class output by the convolutional neural network built in step S4, and Θ represents the value of the objective function; Step 5.2: Randomly select a certain number from each fault type in a series of order spectrum feature matrix samples obtained after being processed by step S3 as training samples; Step 5.3: Use the training samples selected in step 5.2 as the input, and select the adaptive moment estimation algorithm to train the one-dimensional convolutional neural network built in step S4. In each iteration process, update the convolution kernel coefficients and biases of the 4 convolutional layers, and the connection weights and biases between the neurons of the 2 fully connected layers until the change rate of the objective function value < the change rate of the objective function value for training to stop, and the entire training ends; the parameters set before training are: batch size, initial learning rate, maximum number of iterations, change rate of the objective function value for training to stop.

4. The rolling bearing fault diagnosis method under variable speed conditions according to claim 3, characterized in that: Step S6, the steps for testing the one-dimensional convolutional neural network trained in step S5 are: Step 6.1 Randomly select a certain number from the order spectrum feature matrix samples of the remaining various fault types selected in step 5.2 as test samples; Step 6.2 Input each test sample into the one-dimensional convolutional neural network trained in step S5 in turn, and the output obtained is the diagnosis result of each test sample; When the output category vector is consistent with the target category vector of the test sample, the number of correct test diagnoses of this category is incremented by 1, otherwise, the number of correct test diagnoses of this category remains unchanged; after testing all the test samples, calculate the category diagnosis accuracy rate and the total diagnosis accuracy rate according to equations (12) and (13) respectively. Where: c and C are respectively the class serial number of the test sample and the total number of classes of the test sample, n c and N c are respectively the number of correctly diagnosed test samples of the c-th class and the total number of test samples of the c-th class, η c and η are respectively the diagnostic accuracy rate of the c-th class and the total diagnostic accuracy rate.

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