Online Measurement and Prediction Method for Slippage Rate of Bearing Cage under Variable Working Conditions Based on Vibration Signals

Abstract

The present invention discloses an online measurement and prediction method for the slip rate of a bearing cage under variable working conditions based on vibration signals, including an offline training stage and an online evaluation stage; in the offline training stage, bearing vibration signals and the slip rate of the bearing cage are collected as an offline training data set, and the obtained offline training data set is denoised by using adaptive VMD to eliminate sample outliers; then, based on RF-LSTM, a slip feature index is constructed for the obtained processed data set, and the feature set is divided into a training set and a test set; finally, an unsupervised diagnosis model for the slip rate based on a convolutional neural network-improved DBSCAN algorithm is constructed, and the diagnosis model is trained and its accuracy is verified by using the training set and the test set respectively; in the online evaluation stage, real-time vibration signals are collected and the diagnosis model is used to measure the slip rate; the slip trend of the bearing is predicted by designing an LSTM-GRU slip rate online prediction model based on an efficient operator; and a slip rate warning value is set for bearing slip warning.

Description

Technical Field

[0001] The present invention relates to the technical field of on-line condition detection of bearings, and mainly relates to an on-line measurement and prediction method for the slip rate of a bearing cage under variable working conditions based on vibration signals. Background Art

[0002] The slip of the bearing cage has always been an important factor restricting the improvement of bearing performance, especially obvious in the aerospace field. The measurement of the slip rate of the bearing cage is greatly affected by the sensor installation conditions and oil stains. Therefore, it is extremely crucial to design a method that can monitor and predict the slip rate in real time online to solve the bearing slip problem.

[0003] Regarding the research related to the measurement of the cage slip rate, the currently mainly adopted strategies are divided into the measurement of the cage rotation speed based on an optical sensor, the measurement of the cage rotation speed based on an eddy current sensor, the measurement of the cage rotation speed based on an acoustic wave signal, and the measurement method of the cage rotation speed based on the modification of the bearing material structure. Among them, the measurement method of the cage rotation speed based on an optical sensor is greatly affected by oil stains and has a very small applicable range; the measurement methods of the cage rotation speed based on an eddy current sensor and based on an acoustic wave signal require a large sensor installation space and are not applicable to equipment with strict space requirements; the measurement method of the cage rotation speed based on the modification of the bearing material structure has a great impact on the bearing performance and cannot be actually applied. Therefore, the measurement of the bearing cage slip rate based on vibration signals is one of the most feasible ideas, and the slip rate can be measured by using the vibration signals of the bearing or the equipment housing.

[0004] Deep learning algorithms can accurately detect the cage slip rate according to the bearing vibration signals, but there are disadvantages such as the need for manual labeling of data, which is relatively complex, large in calculation amount and slow in operation speed, resulting in the inability to achieve real-time detection. With the continuous increase in the amount of data and the complexity of the bearing operating conditions, manual addition of data labels has problems of easy error and low efficiency. At the same time, the occurrence of cage slip has extremely strong timeliness, and it is very necessary to design an online real-time detection and prediction algorithm. Research shows that a large number of multiplication operations in traditional LSTM algorithms will occupy a large amount of memory and increase the operation time, and are not suitable for online data processing. Summary of the Invention

[0005] Object of the Invention: Aiming at the problems existing in the above background art, the present invention provides an on-line measurement and prediction method for the slip rate of a bearing cage under variable working conditions based on vibration signals, aiming to improve the scientificity and effectiveness of traditional measurement algorithms, improve the efficiency of deep learning algorithms, and achieve accurate online prediction of the slip rate based on bearing vibration signals.

[0006] Technical Solution: To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] An online measurement and prediction method for bearing cage slip rate under variable working conditions based on vibration signals includes an offline training phase and an online evaluation phase; the specific steps are as follows:

[0008] Step S1, in an offline training phase, the bearing vibration signal and the bearing cage slip rate are collected simultaneously as an offline training data set;

[0009] Step S2, using adaptive variational mode decomposition to perform noise reduction on the offline training data set obtained in step S1, and remove sample outliers;

[0010] Step S3, constructing a slip feature index for the processed data set obtained in step S2 based on RF-LSTM, and dividing the feature set into a training set and a test set;

[0011] Step S4, constructing an unsupervised diagnosis model for slip rate based on a convolutional neural network-improved DBSCAN algorithm, training the diagnosis model using the training set in step S3, and verifying the accuracy of the diagnosis model using the test set;

[0012] Step S5, in the online evaluation stage, the bearing slip rate is measured by real-time acquisition of the bearing vibration signal and using the unsupervised diagnosis model obtained in step S4;

[0013] Step S6, designing an LSTM-GRU slip rate online prediction model based on an efficient operator; predicting the bearing slip trend based on the bearing cage slip rate output in step S5;

[0014] Step S7, setting a slip rate warning value. When the bearing slip rate prediction value obtained in step S6 is higher than the slip rate warning value, the system alarms.

[0015] Furthermore, the steps of measuring the bearing vibration signal and calculating the cage slip rate in step S1 are as follows:

[0016] Step S1.1: Vibration signal measurement

[0017] Paint the bearing cage evenly black and attach reflective strips. Use a laser speed sensor to measure the actual speed of the cage. c ; Use the speed sensor to measure the inner ring speed of the bearing ω i ; At the same time, the vibration acceleration sensor is used to measure the time domain vibration signal of the bearing;

[0018] Step S1.2: Calculation of bearing cage slip rate

[0019]

[0020] Among them, ω c is the actual speed of the bearing cage, ω cmFor the theoretical speed of the cage, the specific calculation formula is as follows:

[0021]

[0022] Among them, ω i is the rotational speed of the inner ring of the bearing, R w is the radius of the roller; R m is the pitch radius of the bearing.

[0023] Furthermore, the specific steps of noise reduction processing and removing sample outliers in step S2 are as follows:

[0024] Step S2.1: Decompose the original time-domain vibration data of the bearing collected in step S1 using VMD to obtain components IMF 1 , IMF 2 ,..., IMF n ;

[0025] Step S2.2: Calculate the correlation coefficients between the high- and low-frequency components and the trend term and the original time-series vibration data, the variance ratios between the high- and low-frequency components and the trend term and the original time-series vibration data, and the permutation entropy respectively based on the components obtained in step S2.1;

[0026] Step S2.3: Use the weighted Softmax loss function to weight the correlation coefficients, variance ratios, and permutation entropy indexes obtained in step S2.2 to balance the contributions of each index to the noise reduction algorithm and obtain a comprehensive noise reduction index;

[0027] Step S2.4: Sort the components obtained in step S2.1 based on the comprehensive noise reduction index obtained in step S2.3, remove the components with noise higher than the preset threshold, and then perform reconstruction to output the time-series vibration data of the bearing after noise reduction;

[0028] Step S2.5: Extract the mean feature of the time-series vibration data of the bearing after noise reduction obtained in step S2.4, screen out the sample points of outliers according to the mean feature, select a segment of sample points without outliers, calculate the standard deviation σ and the mean μ, and use the (μ - 3σ, μ + 3σ) distribution for outlier monitoring and removal.

[0029] Furthermore, the specific steps of constructing the slip feature index in step S3 include:

[0030] Step S3.1: Multi-domain feature extraction;

[0031] Based on the offline training data set after noise reduction processing in step S2, obtain time-domain features, frequency-domain features, and time-frequency domain features respectively to construct a candidate feature set, and use the extracted time-domain features and frequency-domain features to construct relative similarity features;

[0032] The time-domain relative similarity feature is obtained by calculating the similarity of time series at different times;

[0033] The data sequence at a given time t is f t , and the data sequence at the initial time is f 0 , and the similarity feature is expressed as follows:

[0034]

[0035] where k is the data length; and are the means of the data sequences and respectively;

[0036] Calculate the similarity of the time-domain feature sequence, frequency-domain feature sequence, and time-frequency domain feature sequence of the monitored vibration signal and the reference vibration signal respectively through formula (3) to obtain the time-domain relative similarity feature, frequency-domain relative similarity feature, and time-frequency domain relative similarity feature.

[0037] Step S3.2, Feature Evaluation and Selection

[0038] For the feature selection of bearing variable-condition vibration signals, design a correlation evaluation criterion and an importance evaluation criterion to achieve automatic optimization of sensitive features:

[0039] The correlation evaluation criterion is constructed as follows:

[0040]

[0041] where F h and l h represent the eigenvalue of the hth sample and the corresponding time in sequence; and are the sample eigenvalue sequence and the mean of the time sequence respectively; H is the number of samples; the value of the correlation evaluation index ranges from 0 to 1, and the better the correlation between the feature and time, the closer the value is to 1, otherwise the closer it is to 0;

[0042] The importance evaluation criterion is constructed as follows:

[0043] Input the sample data of the bearing vibration signal into the RF model for cross-validation training, and record the mean square error obtained each time; when the mean square error tends to be stable, calculate the importance value of each feature parameter as follows:

[0044]

[0045] where α is the number of decision trees; errB' a is the sample error of the ath tree when the arrangement of the variable changes in the observed values; errB ais the sample error of the a-th tree; is the average sample error; the larger the VI value, the more important the variable;

[0046] When performing feature optimization, considering both correlation and importance, the following comprehensive evaluation criterion is designed:

[0047] Cri = ω 1 Corr + ω 2 VI (6)

[0048] where Cri is the comprehensive evaluation index; ω 1 and ω 2 are the weight coefficients of the correlation and importance evaluation criteria respectively;

[0049] Step S3.3, Health index construction

[0050] According to Equation (6), each candidate feature set extracted in Step S3.1 is evaluated one by one to screen out features sensitive to the degradation of mechanical equipment; the sensitive features are formed into a feature vector and input into the LSTM to fuse the virtual slip index LSTM-HI.

[0051] Furthermore, the method for constructing the unsupervised diagnosis model of the slip rate based on the convolutional neural network-improved DBSCAN algorithm in Step S4 is as follows:

[0052] Using the improved DBSCAN algorithm, the obtained bearing vibration signals, cage slip rate, and virtual slip index LSTM-HI are clustered into two categories; the first category is the data with a bearing slip rate less than 2%, defined as the bearing not slipping; the second category is the data with a bearing slip rate of 3% and above, defined as the bearing significantly slipping; then, according to the clustering results, a convolutional neural network model is trained respectively and the slip rate detection models of the corresponding categories are output; finally, the bearing vibration signals collected online in real time are input into the unsupervised diagnosis model of the slip rate based on the convolutional neural network-improved DBSCAN algorithm for online slip rate detection.

[0053] Furthermore, the improved DBSCAN algorithm is specifically as follows:

[0054] Step S4.1, Calculate the local density of data points

[0055] For the data set composed of the offline bearing vibration data and cage slip rate data obtained in Step S2 Calculate the local density of data points as follows:

[0056]

[0057] where d c represents the truncation distance; η is the number of data sets; I S={1, 2, ..., η} is the index set corresponding to the data set; d ij is the data point γ i and γ j the distance between; ρ i is the number of data points in S whose distance from γ i is less than d c ;

[0058] Design represents a descending order subscript sequence that satisfies ρ q1 ≥ ρ q2 ≥ … ≥ ρ qη ; The distance is calculated as follows:

[0059]

[0060] wherein, represents the data point and the data point the distance between; when has the maximum local density, δ qi represents the data point in the data set that is farthest from the distance between and ; when all local densities are greater than , δ qi represents the data point in the data set that is closest to the distance between and ;

[0061] Step S4.2, Determine the clustering center

[0062] Select the points with both local density and distance higher than the other points as the clustering centers, and assign the remaining points to the corresponding clusters with higher density to the nearest neighbors; Define a boundary region for each cluster, that is, the set of points assigned to this cluster but whose distance from other clusters is less than d c , and then find the point with the highest density in the boundary region of each cluster, and use the density of this point as the threshold to screen the clusters, only retaining the points in the category that are greater than or equal to this density value;

[0063] Step S4.3, Evaluate the clustering result

[0064] Use the traditional Dunn index DVI, Davies-Bouldin index DBI, mutual information MI, purity Purity, and F-value FMeasure clustering evaluation indicators respectively and combine the Renyi entropy to construct an index set to evaluate the clustering result.

[0065] Furthermore, the LSTM-GRU slip rate online prediction model based on the efficient operator in step S6 is specifically as follows:

[0066] S6.1. Based on the obtained time series data of the bearing cage slip rate, for the low-frequency component IMF 1 , IMF 2 ,..., IMF m Construct an LSTM based on an efficient operator for slip rate prediction. For the high-frequency component IMF m+1 , IMF m+2 ,…, IMF n Construct a GRU based on an efficient operator for slip rate prediction;

[0067] S6.2. Construct a GRU based on an efficient operator as follows:

[0068] r t = σ(a r ⊙(ω r ◇x t ) + s r ⊙(R r ◇h t-1 ) + b r ) (9)

[0069] z t = σ(a z ⊙(ω z ◇x t ) + s z ⊙(R z ◇h t-1 ) + b z ) (10)

[0070]

[0071]

[0072] Among them, σ(·) is the Sigmoid function, which changes the data into a value within the range of 0 to 1, thus serving as a gating signal; r t is the update gate; z t is the reset gate; x t is the current input vector; is the current moment reset gate candidate set state; h tg is the current moment hidden state variable; h tg-1 is the previous moment hidden state variable; a r , a z , s r , s z and respectively represent scale coefficients; ω r , R r and b rrespectively represent the update gate weight matrix and the bias term; ω z 、R z 、b z 、 and respectively represent the reset gate weight matrix and the bias term; ⊙ is the Hadamard product; ◇ and ◆ are efficient operators, which respectively satisfy:

[0073]

[0074] E◆K = sign(E)⊙K + sign(K)⊙E (14)

[0075] where the vectors E and K are p-dimensional vectors; e i and k i are respectively the i-th elements of the vectors E and K; sign(·) is the sign function;

[0076] S6.3. The LSTM based on the efficient operator is constructed in step S6.1 as follows:

[0077] f t = σ(a f ⊙(ω f ◇x t ) + s f ⊙(R f ◇h t-1 ) + b f ) (15)

[0078] i t = σ(a i ⊙(ω i ◇x t ) + s i ⊙(R i ◇h t-1 ) + b i ) (16)

[0079]

[0080]

[0081] o t = σ(a o ⊙(ω o ◇x t ) + s o ⊙(R o ◇h tl-1 ) + b o ) (19)

[0082] h tl = o t ◆tanh(c t) (20)

[0083] Among them, f t is the forgetting gate; o t is the output gate; c t is the cell state at the current moment; c t-1 is the cell state at the previous moment; is the candidate set state of the input gate at the current moment; h tl is the hidden state variable at the current moment; h tl-1 is the hidden state variable at the previous moment; i t is the input gate; a f 、a i 、 a o 、s f 、s i 、 and s o respectively represent scale coefficients; ω f 、R f and b f respectively represent the weight matrix and bias term of the forgetting gate; ω i 、R i 、b i 、 and respectively represent the weight matrix and bias term of the input gate; a o 、R o and b o respectively represent the weight matrix and bias term of the output gate;

[0084] S6.4. Weight the prediction results obtained in steps S6.2 and S6.3 as follows, and output the prediction result of the slip rate:

[0085] h z =ω hg h tg +ω hl h tl (21)

[0086] Among them, h z is the prediction result of the slip rate; ω hg and ω hl are respectively the weight coefficients of the slip rate prediction result of the efficient operator GRU and the slip rate prediction result of the efficient operator LSTM.

[0087] Beneficial effects:

[0088] The present invention proposes an efficient online accurate prediction algorithm for the slip rate of the bearing cage under variable working conditions aiming at the problem of online measurement of the slip rate of the bearing cage. Compared with the prior art, the advantages are as follows:

[0089] (1) The bearing vibration data set is denoised by using adaptive variational mode decomposition. The weighted Softmax loss function is used to balance the contributions of various indicators to the denoising algorithm to obtain a comprehensive denoising index, significantly improving the denoising effect;

[0090] (2) The LSTM-HI for the slipping index is constructed based on RF-LSTM, realizing the transformation from manually designed features to data-centric, and automatically optimizing the feature indicators sensitive to slipping by using machine learning algorithms;

[0091] (3) A convolutional neural network-improved DBSCAN algorithm is designed to classify data by using a clustering algorithm, realizing unsupervised detection and diagnosis of the slipping rate, and improving the efficiency and accuracy of the algorithm;

[0092] (4) An online prediction model of the slipping rate based on LSTM-GRU with efficient operators is designed. The traditional multiplication operation is replaced by addition operation and sign function multiplication operation, significantly improving the calculation speed and reducing the memory occupancy. Description of the Drawings

[0093] Figure 1 It is the flow chart of the online measurement method for the slipping rate of the bearing cage provided by the present invention;

[0094] Figure 2 It is the bearing condition monitoring diagram in the embodiment of the present invention;

[0095] Figure 3 It is the flow chart of the adaptive variational mode decomposition denoising provided by the present invention;

[0096] Figure 4 It is the outlier rejection result in the embodiment of the present invention;

[0097] Figure 5 It is the flow chart of constructing the slipping feature index based on RF-LSTM provided by the present invention;

[0098] Figure 6 It is the flow chart of the unsupervised diagnosis algorithm for the slipping rate based on convolutional neural network-improved DBSCAN provided by the present invention;

[0099] Figure 7 It is the model clustering result based on the improved DBSCAN in the embodiment of the present invention;

[0100] Figure 8 It is the online monitoring result of the slipping rate in the embodiment of the present invention;

[0101] Figure 9 It is the flow chart of the online prediction algorithm for the slipping rate based on LSTM-GRU with efficient operators provided by the present invention;

[0102] Figure 10This is the online prediction result of the slip rate in the embodiment of the present invention. Specific embodiments

[0103] The present invention will be further described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0104] The online measurement and prediction method of the bearing cage slip rate under variable working conditions based on vibration signals provided by the present invention is as Figure 1 shown, including an offline training stage and an online evaluation stage. The specific steps are as follows:

[0105] Step S1, offline training stage, collect the bearing vibration signal and the bearing cage slip rate simultaneously as the offline training data set;

[0106] In this embodiment, on the bearing test platform, a vibration acceleration sensor is used to measure the bearing vibration signal, and the sampling frequency is 51.2KHz. At the same time, the bearing speed is continuously increased to change the slip state of the bearing. The vibration signal and the cage speed corresponding to the collected vibration signal are as Figure 2 shown. Since the amount of data is large, the data in the 200s - 500s segment is selected for the experiment. The speed and slip rate changes corresponding to this segment of data are as Figure 3 shown. It can be seen from the figure that in this segment of data, the inner ring speed of the bearing changes from 2500 to 4500, passing through five segments of changes: 2500, 3000, 3500, 4000, and 4500. The slip rate changes approximately from 0% to 10%. The slip rate is small in the first 222s, rises sharply from 222s to 230s, and is about 10% after 230s.

[0107] For the measurement of the bearing cage slip rate and the vibration signal, the following specific measurement steps are adopted in this embodiment:

[0108] Step S1.1, vibration signal measurement

[0109] The bearing cage is evenly blackened and reflective strips are pasted on it. The actual speed ω of the cage is measured by a laser speed sensor c ; the inner ring speed ω of the bearing is measured by a speed sensor i ; at the same time, the bearing time-domain vibration signal is measured by a vibration acceleration sensor;

[0110] Step S1.2, calculation of the bearing cage slip rate

[0111]

[0112] Among them, ω c is the actual speed of the bearing cage, ω cm is the theoretical speed of the cage, the specific calculation formula is as follows:

[0113]

[0114] Among them, ω i is the bearing inner ring speed, R w is the roller radius; R m is the bearing pitch circle radius.

[0115] Step S2: Use adaptive variational mode decomposition to perform noise reduction on the offline training data set obtained in step S1, and remove sample outliers. Figure 3-4 As shown,

[0116] Step S2.1: Decompose the original time domain vibration data of the bearing collected in step S1 using VMD to obtain component IMFs 1 ,IMF 2 ,...,IMF n ;

[0117] Step S2.2, based on the components obtained in step S2.1, respectively calculate the correlation coefficients of the high and low frequency components and trend items with the original time series vibration data, the variance ratios of the high and low frequency components and trend items with the original time series vibration data, and the permutation entropy;

[0118] Step S2.3, using the weighted Softmax loss function to weight the correlation coefficient, variance ratio and permutation entropy indicators obtained in step S2.2, applying a larger weight to the indicators with smaller changes between the components, and applying a smaller weight to the indicators with larger changes between the components, balancing the contribution of each indicator to the denoising algorithm, and obtaining a comprehensive denoising indicator;

[0119] Step S2.4, sorting the components obtained in step S2.1 based on the comprehensive noise reduction index obtained in step S2.3, removing the components with noise higher than a preset threshold, and then reconstructing to output the time series vibration data of the bearing after noise reduction;

[0120] Step S2.5, extract the mean characteristics of the time series vibration data of the bearing after noise reduction obtained in step S2.4, and filter out the sample points of outliers based on the mean characteristics, select a section of sample points without outliers, calculate the standard deviation σ and mean μ, and use the (μ-3σ, μ+3σ) distribution to monitor and eliminate outliers.

[0121] The 3σ criterion is adopted here. Assume that a set of monitoring data only contains random data. After processing it to obtain the standard deviation, the data containing this error should be excluded. The 3σ criterion holds that the probability that the numerical distribution is in (μ - σ, μ + σ) is 68.27%; the probability that the numerical distribution is in (μ - 2σ, μ + 2σ) is 95.45%; the probability that the numerical distribution is in (μ - 3σ, μ + 3σ) is 99.73%.

[0122] Step S3. Based on RF-LSTM, construct the skidding feature index for the processed data set obtained in step S2, and divide the feature set into two parts: a training set and a test set. Specifically, as Figure 5 shown, divide the original vibration signal according to a fixed time window. The segmentation window is 5120, that is, every 5120 sampling points are segmented into a sample. After segmentation, calculate the time-domain features, frequency-domain features, and time-frequency domain features of each segment of the signal.

[0123] Step S3.1. Multi-domain feature extraction

[0124] Based on the offline training data set after noise reduction processing in step S2, extract 14 time-domain features including mean value, effective value, average power, root mean square value, kurtosis, margin, peak value, variance, standard deviation, entropy, peak index, waveform index, pulse index, and margin index 14. Extract 5 frequency-domain features and time-frequency domain features including center frequency, mean square frequency, root mean square frequency, mean frequency, and frequency standard deviation. Use the extracted time-domain features and frequency-domain features to construct relative similarity features to eliminate the problem of different value ranges of traditional feature values.

[0125] The time-domain relative similarity feature is obtained by calculating the similarity of time series at different times;

[0126] The data sequence at a given time t is f t , and the data sequence at the initial time is f 0 . The similarity feature is expressed as follows:

[0127]

[0128] where k is the data length; and are the mean values of the data sequences and respectively;

[0129] respectively calculate the similarity of the time-domain feature sequence, frequency-domain feature sequence, and time-frequency domain feature sequence of the monitored vibration signal and the reference vibration signal through formula (3) to obtain the time-domain relative similarity feature, frequency-domain relative similarity feature, and time-frequency domain relative similarity feature.

[0130] Step S3.2. Feature evaluation and selection

[0131] For the selection of bearing variable working condition vibration signal characteristics, design the correlation evaluation criterion and the importance evaluation criterion to realize the automatic optimization of sensitive characteristics:

[0132] The correlation evaluation criterion is constructed as follows:

[0133]

[0134] Among them, F h and l h respectively represent the eigenvalue of the h-th sample and the corresponding moment; and are the mean values of the sample eigenvalue sequence and the time sequence respectively; H is the number of samples; the value of the correlation evaluation index ranges from 0 to 1, and the better the correlation between the feature and time, the closer the value is to 1, otherwise the closer it is to 0;

[0135] The importance evaluation criterion is constructed as follows:

[0136] Input the bearing vibration signal sample data into the RF model for cross-validation training, and record the mean square error obtained each time; when the mean square error tends to be stable, calculate the importance value of each feature parameter as follows:

[0137]

[0138] Among them, α is the number of decision trees; errB' a is the sample error of the a-th tree when the arrangement of variables in the observed values changes; errB a is the sample error of the a-th tree; is the average sample error; the larger the VI value, the more important the variable;

[0139] When performing feature optimization, considering both correlation and importance, design the following comprehensive evaluation criterion:

[0140] Cri = ω 1 Corr + ω 2 VI (6)

[0141] Among them, Cri is the comprehensive evaluation index; ω 1 and ω 2 are the weight coefficients of the correlation and importance evaluation criteria respectively;

[0142] Step S3.3, Construction of health index

[0143] According to formula (6), evaluate each candidate feature set extracted in step S3.1 one by one, and screen out the features sensitive to the degradation of mechanical equipment; form a feature vector with the sensitive features and input it into LSTM to fuse the virtual slip index LSTM-HI.

[0144] Step S4. Construct an unsupervised diagnosis model for slip rate based on a convolutional neural network - improved DBSCAN algorithm, train the diagnosis model using the training set in Step S3, and verify the accuracy of the diagnosis model using the test set. Specifically, as Figure 6 shown,

[0145] First, use the improved DBSCAN algorithm to cluster the acquired bearing vibration signals, cage slip rate, and virtual slip index LSTM - HI into two categories; the first category is the data with a bearing slip rate less than 2%, defined as the bearing not slipping; the second category is the data with a bearing slip rate of 3% or more, defined as the bearing significantly slipping. The clustering results are as Figure 7 shown. Then, train a convolutional neural network model according to the clustering results and output a slip rate detection model for the corresponding category; finally, input the online - collected bearing vibration signals into the unsupervised diagnosis model for slip rate based on the convolutional neural network - improved DBSCAN algorithm for online slip rate detection, as Figure 8 shown.

[0146] The specific process of constructing the improved DBSCAN algorithm is as follows:

[0147] Step S4.1. Calculate the local density of data points

[0148] For the data set composed of the offline bearing vibration data and cage slip rate data obtained in Step S2 calculate the local density of data points as follows:

[0149]

[0150] where d c represents the truncation distance; η is the number of data sets; I S ={1, 2,..., η} is the index set corresponding to the data set; d ij is the distance between data points γ i and γ j ; ρ i is the number of data points in S whose distance from γ i is less than d c ;

[0151] Design to represent a descending - order permutation subscript sequence that satisfies ρ q1 ≥ρ q2 ≥…≥ρ qη ; calculate the distance as follows:

[0152]

[0153] where, represents the data point The distance to the data point ; when has the maximum local density, δ qi represents the distance between the data point in the dataset with the largest distance to ; when all local densities are greater than , δ qi represents the distance between the data point in the dataset with the smallest distance to ;

[0154] Step S4.2, Determine the clustering centers

[0155] Select the points with significantly higher local density and distance than the remaining points as the clustering centers, and assign the remaining points to the clusters of the nearest neighbors with higher density; Define a boundary region for each cluster, that is, the set of points assigned to this cluster but with a distance less than d c to the points of other clusters, and then find the point with the highest density in the boundary region of each cluster, and use the density of this point as the threshold to screen the clusters, only retaining the points in the category that are greater than or equal to this density value.

[0156] Step S4.3, Evaluate the clustering results

[0157] Use traditional clustering evaluation indicators such as the Dunn index DVI, the Davies-Bouldin index DBI, the mutual information MI, the purity Purity, and the F-measure FMeasure, and combine them with the Renyi entropy to construct an indicator set to evaluate the clustering results.

[0158] Step S5, In the online evaluation stage, measure the bearing slip rate by collecting bearing vibration signals in real time and using the unsupervised diagnosis model obtained in step S4;

[0159] Step S6, In the online evaluation stage, design an LSTM-GRU slip rate online prediction model based on efficient operators, as shown in Figure 9 ; Predict the bearing slip trend based on the bearing cage slip rate output in step S5. Specifically,

[0160] S6.1, Based on the obtained bearing cage slip rate time series data, construct an LSTM based on efficient operators for slip rate prediction for the low-frequency components IMF 1 , IMF 2 ,..., IMF m , and construct a GRU based on efficient operators for slip rate prediction for the high-frequency components IMF m+1 , IMF m+2 ,…, IMF n ;

[0161] S6.2. Construct the GRU based on efficient operators as follows:

[0162] r t = σ(a r ⊙ (ω r ◇ x t ) + s r ⊙ (R r ◇ h t-1 ) + b r ) (9)

[0163] z t = σ(a z ⊙ (ω z ◇ x t ) + s z ⊙ (R z ◇ h t-1 ) + b z ) (10)

[0164]

[0165]

[0166] where σ(·) is the Sigmoid function, which changes the data to a value in the range of 0 to 1 and serves as the gating signal; r t is the update gate; z t is the reset gate; x t is the current input vector; is the state of the reset gate candidate set at the current moment; h tg is the hidden state variable at the current moment; h tg-1 is the hidden state variable at the previous moment; a r , a z , s r , s z and respectively represent the scaling coefficients; ω r , R r and b r respectively represent the update gate weight matrix and the bias term; ω z , R z , b z , and respectively represent the reset gate weight matrix and the bias term; ⊙ is the Hadamard product; ◇ and ◆ are efficient operators, which respectively satisfy:

[0167]

[0168] E ◆ K = sign(E) ⊙ K + sign(K) ⊙ E (14)

[0169] Among them, vectors E and K are p-dimensional vectors; e i and k i are the i-th elements of vectors E and K respectively; sign(·) is the sign function;

[0170] S6.3. In step S6.1, construct the LSTM based on the efficient operator as follows:

[0171] f t = σ(a f ⊙ (ω f ◇ x t ) + s f ⊙ (R f ◇ h t-1 ) + b f ) (15)

[0172] i t = σ(a i ⊙ (ω i ◇ x t ) + s i ⊙ (R i ◇ h t-1 ) + b i ) (16)

[0173]

[0174]

[0175] o t = σ(a o ⊙ (ω o ◇ x t ) + s o ⊙ (R o ◇ h tl-1 ) + b o ) (19)

[0176] h tl = o t ◆ tanh(c t ) (20)

[0177] Among them, f t is the forget gate; o t is the output gate; c t is the cell state at the current moment; c t-1 is the cell state at the previous moment; is the candidate set state of the input gate at the current moment; h tl is the hidden state variable at the current moment; h tl-1 is the hidden state variable at the previous moment; i t is the input gate; af and a i 、 a o 、s f 、s i 、 and s o respectively represent the scale factor; ω f 、R f and b f respectively represent the forget gate weight matrix and the bias term; ω i 、R i 、b i 、 and respectively represent the input gate weight matrix and the bias term; a o 、R o and b o respectively represent the output gate weight matrix and the bias term;

[0178] S6.4. Weight the prediction results obtained in steps S6.2 and S6.3 as follows and output the slip rate prediction result:

[0179] h z = ω hg h tg + ω hl h tl (21)

[0180] where h z is the slip rate prediction result; ω hg and ω hl are the weight coefficients of the slip rate prediction result of the efficient operator GRU and the slip rate prediction result of the efficient operator LSTM respectively.

[0181] Step S7. Set the slip rate warning value. When the bearing slip rate prediction value obtained in step S6 is higher than the slip rate warning value, the system alarms.

[0182] In this embodiment, the slip rate warning value is set to 2%. When the on-line predicted bearing slip rate prediction value is higher than 2%, the system alarms in time.

[0183] The above is only the preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. An online measurement and prediction method for the slip rate of a bearing cage under variable working conditions based on vibration signals, characterized in that, it includes an offline training stage and an online evaluation stage; the specific steps are as follows: Step S1, in the offline training stage, simultaneously collect the bearing vibration signals and the slip rate of the bearing cage as the offline training data set; Step S2, use the adaptive variational mode decomposition (VMD) to perform noise reduction processing on the offline training data set obtained in Step S1, and eliminate sample outliers; Step S3, based on the random forest (RF)-long short-term memory network (LSTM), construct slip feature indicators for the processed data set obtained in Step S2, and divide the feature set into two parts: a training set and a test set; Step S4, construct an unsupervised diagnosis model for the slip rate based on the convolutional neural network-improved density-based spatial clustering of applications with noise (DBSCAN) algorithm, use the training set in Step S3 to train the diagnosis model, and use the test set to verify the accuracy of the diagnosis model; Step S5, in the online evaluation stage, achieve the measurement of the bearing slip rate by collecting the bearing vibration signals in real time and using the unsupervised diagnosis model obtained in Step S4; Step S6, design an LSTM-gated recurrent unit (GRU) slip rate online prediction model based on an efficient operator; predict the bearing slip trend based on the slip rate of the bearing cage output in Step S5; Step S7, set a slip rate warning value, and when the predicted value of the bearing slip rate obtained in Step S6 is higher than the slip rate warning value, the system alarms; The specific steps of the noise reduction processing and elimination of sample outliers in Step S2 are as follows: Step S2.1: Use VMD to decompose the original bearing time-domain vibration data collected in Step S1 to obtain components IMF 1 , IMF 2 , IMF n ; Step S2.2, calculate the correlation coefficients of the high- and low-frequency components, the trend term and the original time-series vibration data, the variance ratios of the high- and low-frequency components, the trend term and the original time-series vibration data, and the permutation entropy respectively based on the components obtained in Step S2.1; Step S2.3, use the weighted Softmax loss function to weight the correlation coefficients, variance ratios, and permutation entropy indicators obtained in Step S2.2 to balance the contributions of each indicator to the noise reduction algorithm and obtain a comprehensive noise reduction indicator; Step S2.4, sort the components obtained in Step S2.1 based on the comprehensive noise reduction indicator obtained in Step S2.3, remove the components with noise higher than the preset threshold, and then perform reconstruction to output the time-series vibration data of the bearing after noise reduction; Step S2.5, extract the mean feature of the time-series vibration data of the bearing after noise reduction obtained in Step S2.4, screen out the sample points of outliers according to the mean feature, select a segment of sample points without outliers, calculate the standard deviation σ and the mean μ, and use the (μ - 3σ, μ + 3σ) distribution for outlier monitoring and elimination; The specific steps of constructing the slip feature indicators in Step S3 include: Step S3.1, multi-domain feature extraction; Based on the offline training data set after noise reduction processing in Step S2, obtain time-domain features, frequency-domain features, and time-frequency domain features respectively to construct a candidate feature set, and use the extracted time-domain features and frequency-domain features to construct relative similarity features; The time-domain relative similarity features are obtained by calculating the similarity of time series at different moments; The data sequence at a given time t is f t , and the data sequence at the initial time is f 0 . The similarity feature is represented as follows: where k is the data length; and are the mean values of the data sequences and respectively; Calculate the similarities of the time-domain feature sequences, frequency-domain feature sequences, and time-frequency domain feature sequences between the monitored vibration signal and the reference vibration signal through Equation (3) respectively, and obtain the time-domain relative similarity feature, frequency-domain relative similarity feature, and time-frequency domain relative similarity feature; Step S3.2, Feature Evaluation and Selection For the feature selection of the bearing vibration signal under variable working conditions, design the correlation evaluation criterion and importance evaluation criterion to realize the automatic optimization of sensitive features: The correlation evaluation criterion is constructed as follows: Among them, F h and l h respectively represent the eigenvalue and the corresponding time of the h-th sample; and are the sample eigenvalue sequence and the time series mean respectively; H is the number of samples; the value of the correlation evaluation index is The better the correlation between the feature and the time, the closer the value is to 1, otherwise it is closer to 0; The importance evaluation criterion is constructed as follows: Input the bearing vibration signal sample data into the RF model for cross-validation training, and record the mean square error obtained each time; when the mean square error tends to be stable, calculate the importance value of each feature parameter as follows: where α is the number of decision trees; errB' a is the sample error of the ath tree when the arrangement of variables changes in the observed values; errB a is the sample error of the ath tree; is the average sample error; the larger the VI value, the more important the variable; When performing feature optimization, comprehensively consider the correlation and importance, and design the following comprehensive evaluation criterion: Cri = ω 1 Corr + ω 2 VI (6) Among them, Cri is the comprehensive evaluation index; ω 1 and ω 2 are the weight coefficients of the correlation and importance evaluation criteria, respectively; Step S3.3, Health Index Construction Evaluate each candidate feature set extracted in Step S3.1 according to Equation (6), and screen the features sensitive to the degradation of mechanical equipment; form a feature vector with the sensitive features and input it into the LSTM to fuse the virtual slip index LSTM-HI; The method for constructing the unsupervised diagnosis model of the slip rate based on the convolutional neural network-improved DBSCAN algorithm in Step S4 is as follows: Use the improved DBSCAN algorithm to cluster the obtained bearing vibration signal, cage slip rate, and virtual slip index LSTM-HI into two categories; the first category is the data with a bearing slip rate less than 2%, which is defined as the bearing not slipping; the second category is the data with a bearing slip rate of 3% or more, which is defined as the bearing slipping significantly; then train the convolutional neural network model according to the clustering results and output the slip rate detection models corresponding to the categories; finally, input the bearing vibration signal collected online in real time into the unsupervised diagnosis model of the slip rate based on the convolutional neural network-improved DBSCAN algorithm for online slip rate detection; The specific improved DBSCAN algorithm is as follows: Step S4.1, Calculate the local density of data points For the data set composed of the offline bearing vibration data and the cage slip rate data obtained in step S2 Calculate the local density of the data points as follows: where d c represents the truncation distance; η is the number of datasets; is the index set corresponding to the dataset; d ij is the distance between the data points γ i and γ j ; ρ i is the number of data points in S whose distance from γ i is less than d c . Design representation in a descending order subscript sequence that satisfies The distance is calculated as follows: Among them, d qiqj represents the distance between the data point and the data point ; when qi has the maximum local density, δ represents the distance between the data point with the maximum distance from in the data set and ; when all local densities are greater than qi δ represents the distance between the data point with the minimum distance from in the data set and ; Step S4.2, Determine the clustering center Select points whose local density and distance are both higher than the rest of the points as the clustering centers, and assign the remaining points to the clusters of their nearest neighbors with higher density; define a boundary region for each cluster, i.e., the set of points that are assigned to this cluster but whose distance to other clusters is less than d c Then, find the point with the highest density in the boundary region of each cluster, and use the density of this point as a threshold to screen the clusters, only retaining the points in the category that are greater than or equal to this density value; Step S4.3, Evaluate the clustering results Use the traditional Dunn index DVI, Davies-Bouldin index DBI, mutual information MI, purity Purity, and F-value FMeasure clustering evaluation indicators respectively and combine them with Renyi entropy to construct an index set to evaluate the clustering results.

2. According to the method for online measurement and prediction of the cage slip rate of a bearing under variable working conditions based on vibration signals described in claim 1, wherein, The steps of measuring the bearing vibration signal and calculating the cage slip rate in Step S1 are as follows: Step S1.1, Vibration signal measurement Paint the bearing cage evenly black and attach reflective strips, and use a laser speed sensor to measure the actual speed ω of the cage c ; Use a speed sensor to measure the speed ω of the inner ring of the bearing i ; At the same time, use a vibration acceleration sensor to measure the bearing time-domain vibration signal; Step S1.2, Calculate the cage slip rate of the bearing where ω c is the actual rotational speed of the bearing cage, and ω cm is the theoretical rotational speed of the cage. The specific calculation formula is as follows: Among them, ω i is the rotational speed of the inner ring of the bearing, and R w is the roller radius; R m is the pitch radius of the bearing.

3. According to the method for online measurement and prediction of the cage slip rate of a bearing under variable working conditions based on vibration signals described in claim 1, wherein, The specific LSTM-GRU slip rate online prediction model based on efficient operators in Step S6 is as follows: S6.

1. Based on the obtained time series data of the bearing cage slip rate, for the low-frequency component IMF 1 , IMF 2 , IMF m Construct an LSTM based on an efficient operator for slip rate prediction. For the high-frequency component IMF m+1 , IMF m+2 ,..., IMF n Construct a GRU based on an efficient operator for slip rate prediction; S6.2, Construct the GRU based on efficient operators as follows: r t = σ(a r e(ω r ◇x t ) + s r e(R r ◇h t-1 ) + b r ) (9) z t = σ(a z e(ω z ◇x t ) + s z e(R z ◇h t-1 ) + b z ) (10) Among them, σ(·) is the Sigmoid function, which changes the data into a value in the range of 0 to 1, thereby serving as a gating signal; r t is the update gate; z t is the reset gate; x t is the current input vector; is the state of the reset gate candidate set at the current moment; h tg is the hidden state variable at the current moment; h tg-1 is the hidden state variable at the previous moment; a r and a z and s r and s z and respectively represent scaling factors; ω r and R r and b r respectively represent the weight matrix and bias term of the update gate; ω z and R z and b z and and respectively represent the weight matrix and bias term of the reset gate; is the Hadamard product; ◇ and ◆ are efficient operators, which respectively satisfy: where vectors E and K are p-dimensional vectors; e i and k i are the i-th elements of vectors E and K respectively; sign(·) is the sign function; S6.3, In Step S6.1, construct the LSTM based on efficient operators as follows: f t = σ(a f e(ω f ◇x t ) + s f e(R f ◇h t-1 ) + b f ) (15) i t = σ(a i e(ω i ◇x t ) + s i e(R i ◇h t-1 ) + b i ) (16) o t = σ(a o e(ω o ◇x t ) + s o e(R o ◇h tl-1 ) + b o ) (19) h tl = o t ◆tanh(c t ) (20) where, f t is the forget gate; o t is the output gate; c t is the cell state at the current time; c t-1 is the cell state at the previous time; is the candidate set state of the input gate at the current time; h tl is the hidden state variable at the current time; h tl-1 is the hidden state variable at the previous time; i t is the input gate; a f 、a i 、 a o 、s f 、s i 、 and s o respectively represent scaling coefficients; ω f 、R f and b f respectively represent the weight matrix and bias term of the forget gate; ω i 、R i 、b i 、 and respectively represent the weight matrix and bias term of the input gate; a o 、R o and b o respectively represent the weight matrix and bias term of the output gate; S6.

4. Weight the prediction results obtained in steps S6.2 and S6.3 as follows and output the prediction result of the slip rate: h z = ω hg h tg + ω hl h tl (21) where h z is the prediction result of the slip ratio; ω hg and ω hl are the weight coefficients of the prediction results of the slip ratio by the efficient operator GRU and the prediction results of the slip ratio by the efficient operator LSTM, respectively.

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