A bearing fault diagnosis method based on group sparse learning algorithm and random forest

Abstract

The application provides a bearing fault diagnosis method based on group sparse learning algorithm and random forest, comprising the following steps: S1, collecting bearing vibration signals by using an acceleration sensor and adding labels to the bearing vibration signals according to the bearing state at the time of collection; S2, reconstructing the bearing vibration signals by using a group sparse learning algorithm; S3, extracting time domain, frequency domain and information entropy features from the reconstructed signals, and constructing a feature set based on the features; S4, classifying and identifying the bearing vibration signals after training by using a random forest model. The application reconstructs the bearing vibration signals by using a group sparse learning algorithm, so as to effectively reduce the noise level and more accurately describe the fault pulse; then, the time domain, frequency domain and information entropy features of the reconstructed signals are extracted, and a feature set is constructed to comprehensively analyze the characteristics of the vibration signals. Finally, the random forest model classifies and identifies the bearing vibration signals.

Description

Technical Field

[0001] This invention relates to a bearing fault diagnosis method based on group sparse learning algorithm and random forest, belonging to the field of bearing fault diagnosis technology. Background Technology

[0002] With the continuous improvement of industrial automation, bearings are widely used in various mechanical equipment. However, due to long-term operation and the influence of external factors, bearings may fail, leading to a decline in equipment performance or even damage. Therefore, timely and accurate diagnosis of bearing faults is crucial for maintaining the normal operation of industrial equipment. However, vibration signals are affected by various interference factors, such as speed fluctuations, rolling element slippage, load distribution in the sensor measurement direction, and periodic changes in impact force, resulting in a non-stationary signal accompanied by strong background noise. These problems lead to relatively low accuracy and efficiency in bearing fault diagnosis, limiting the stability and reliability of equipment operation.

[0003] Traditional signal processing methods such as Fourier transform, wavelet transform, time-frequency analysis, and envelope analysis have limitations when dealing with complex non-stationary vibration signals. Modal analysis requires accurate boundary conditions and sensor placement, making it unsuitable for all vibration systems. Furthermore, methods such as Hilbert-Huang transform, singular spectrum analysis, and maximum correlation kurtosis deconvolution are computationally complex and time-consuming when processing large datasets. To overcome these problems and extract periodic pulses from interference, this method introduces a group sparse learning algorithm. Based on the assumption of group sparsity in the signal, this algorithm effectively separates fault signals, extracts non-zero elements in groups, thereby eliminating redundant information and more accurately capturing data features. This enables more effective processing of complex non-stationary vibration signals, improving the accuracy and efficiency of signal processing.

[0004] Furthermore, despite the progress made by deep learning in fault diagnosis, its "black box" nature limits its practical applications. To overcome this problem, academia has turned to more interpretable algorithms. Among them, random forests have attracted much attention due to their interpretability, resistance to overfitting, adaptability to imbalanced data, and advantages in feature evaluation.

[0005] Therefore, current bearing fault diagnosis methods suffer from low diagnostic accuracy, difficulty in accurately separating fault signals, and poor interpretability. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a bearing fault diagnosis method based on group sparse learning algorithm and random forest. This method can efficiently filter noise, extract multi-dimensional features, and achieve accurate classification and hierarchical diagnosis of bearing fault signals, while maintaining high interpretability and transparency. It effectively solves the problems of low diagnostic accuracy, difficulty in accurately separating fault signals, and poor interpretability in current bearing fault diagnosis methods.

[0007] The present invention is achieved through the following technical solutions.

[0008] This invention provides a bearing fault diagnosis method based on group sparse learning algorithm and random forest, comprising the following steps:

[0009] S1. Use an accelerometer to collect bearing vibration signals and add tags to the bearing vibration signals according to the bearing condition at the time of collection;

[0010] S2. Reconstruct the bearing vibration signal using a group sparse learning algorithm;

[0011] S3. Extract time-domain, frequency-domain, and information entropy features from the reconstructed signal, and construct a feature set based on these features;

[0012] S4. After training with a random forest model, classify and identify the bearing vibration signal.

[0013] In step S1, the accelerometer is connected to the housing with a magnetic base and placed at the motor drive end for data acquisition.

[0014] Step S2 specifically includes the following steps:

[0015] S2.1. Add a set of sparse, periodic fault pulse signals to the bearing vibration signal within a certain time interval;

[0016] S2.2, Add zero-mean Gaussian distribution assumption weights to the fault pulse signal;

[0017] S2.3. The posterior distribution of the fault pulse signal is approximated by the variational Bayesian inference algorithm;

[0018] S2.4. Iterate the posterior distribution using an alternating update algorithm.

[0019] In step S2.2, the sparsity of the fault pulse signal is further constrained by the Gamma prior.

[0020] In step S2.4, the KL divergence value of the posterior distribution is calculated iteratively.

[0021] The time-domain features include maximum value, minimum value, average value, peak-to-peak value, rectified average value, effective value, variance, standard deviation, kurtosis, root mean square, skewness, waveform factor, peak factor, margin factor, and impulse factor.

[0022] The frequency domain includes centroid frequency, mean square frequency, frequency variance, and frequency band energy.

[0023] In step S3, information entropy includes permutation entropy and fuzzy entropy.

[0024] The permutation entropy is extracted using the following steps:

[0025] S3.1.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector;

[0026] S3.1.2. Perform full permutations on the elements of each m-dimensional vector to obtain all possible permutations;

[0027] S3.1.3 Calculate the permutation entropy using the probability distribution of the permutation in the following manner:

[0028]

[0029] In the formula, p i This represents the probability value of each sorting order occurring.

[0030] The fuzzy entropy is extracted using the following steps:

[0031] S3.2.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector;

[0032] S3.2.2 Calculate the similarity between each pair of m-dimensional vectors;

[0033] S3.2.3, Apply similarity calculation to ambiguity of each m-dimensional vector;

[0034] S3.2.4 Calculate the fuzzy entropy based on the fuzziness and the probability of the fuzziness as follows:

[0035] f 21 =lnφ m (n,r)-lnφ m+1 (n,r),

[0036] In the formula, φ m (n,r) represents the average similarity, where n and r are the gradient and width of the boundary.

[0037] The beneficial effects of this invention are as follows: By reconstructing the bearing vibration signal using a group sparse learning algorithm, the noise level is effectively reduced, and the fault pulse is described more accurately. Subsequently, time-domain, frequency-domain, and information entropy features are extracted from the reconstructed signal to construct a feature set for comprehensive analysis of the vibration signal characteristics. Finally, a random forest model is used to classify and identify the bearing vibration signal. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating at least one embodiment of the present invention;

[0039] Figure 2 These are 10 types of signal time-domain waveforms in one embodiment of the present invention;

[0040] Figure 3 This is the time-domain waveform of the group sparse learning reconstructed signal in one embodiment of the present invention;

[0041] Figure 4 This is a confusion matrix representing the classification results in one embodiment of the present invention;

[0042] Figure 5 This is a histogram of the importance of the evaluated features in one embodiment of the present invention;

[0043] Figure 6 This is a schematic diagram of the first decision tree model in a random forest model according to one embodiment of the present invention. Detailed Implementation

[0044] The technical solution of the present invention is further described below, but the scope of protection is not limited to what is described.

[0045] The first embodiment of the present invention relates to, for example Figure 1 The bearing fault diagnosis method shown includes the following steps: (The method is based on group sparse learning algorithm and random forest.)

[0046] S1. Use an accelerometer to collect bearing vibration signals and add tags to the bearing vibration signals according to the bearing condition at the time of collection;

[0047] S2. Reconstruct the bearing vibration signal using a group sparse learning algorithm;

[0048] S3. Extract time-domain, frequency-domain, and information entropy features from the reconstructed signal, and construct a feature set based on these features;

[0049] S4. After training with a random forest model, classify and identify the bearing vibration signal.

[0050] The second embodiment of the present invention is largely the same as the first embodiment, except that in step S1, the acceleration sensor is connected to the housing with a magnetic base and placed at the motor drive end position to collect data.

[0051] Step S2 specifically includes the following steps:

[0052] S2.1. Add a set of sparse, periodic fault pulse signals to the bearing vibration signal within a certain time interval;

[0053] S2.2, Add zero-mean Gaussian distribution assumption weights to the fault pulse signal;

[0054] S2.3. The posterior distribution of the fault pulse signal is approximated by the variational Bayesian inference algorithm;

[0055] S2.4. Iterate the posterior distribution using an alternating update algorithm.

[0056] In step S2.2, the sparsity of the fault pulse signal is further constrained by the Gamma prior.

[0057] In step S2.4, the KL divergence value of the posterior distribution is calculated iteratively.

[0058] The third embodiment of the present invention is largely the same as the first embodiment, except that the time-domain features include maximum value, minimum value, average value, peak-to-peak value, rectified average value, effective value, variance, standard deviation, kurtosis, root mean square, skewness, waveform factor, peak factor, margin factor, and impulse factor.

[0059] The frequency domain includes centroid frequency, mean square frequency, frequency variance, and frequency band energy.

[0060] In step S3, information entropy includes permutation entropy and fuzzy entropy.

[0061] The permutation entropy is extracted using the following steps:

[0062] S3.1.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector;

[0063] S3.1.2. Perform full permutations on the elements of each m-dimensional vector to obtain all possible permutations;

[0064] S3.1.3 Calculate the permutation entropy using the probability distribution of the permutation in the following manner:

[0065]

[0066] In the formula, p i This represents the probability value of each sorting order occurring.

[0067] The fuzzy entropy is extracted using the following steps:

[0068] S3.2.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector;

[0069] S3.2.2 Calculate the similarity between each pair of m-dimensional vectors;

[0070] S3.2.3, Apply similarity calculation to ambiguity of each m-dimensional vector;

[0071] S3.2.4 Calculate the fuzzy entropy based on the fuzziness and the probability of the fuzziness as follows:

[0072] f 21 =lnφ m (n,r)-lnφ m+1 (n,r),

[0073] In the formula, φ m (n,r) represents the average similarity, where n and r are the gradient and width of the boundary.

[0074] The fourth embodiment of the present invention, in conjunction with the above embodiments, specifically includes the following steps:

[0075] S1: The accelerometer collects vibration signals and adds tags based on the bearing condition;

[0076] S2: A sparse learning algorithm is used to reconstruct the bearing vibration signal;

[0077] S3: Extract time-domain, frequency-domain, and information entropy features from the reconstructed signal and construct a feature set;

[0078] S4: After training with a random forest model, the bearing vibration signal is classified and identified.

[0079] Preferably, the accelerometer collects vibration signals and adds tags according to the bearing condition, specifically by connecting an accelerometer to a housing with a magnetic substrate and placing the accelerometer at the drive end of the motor housing. As the mechanical equipment operates, the accelerometer continuously collects vibration signals and simultaneously records the bearing condition.

[0080] Preferably, the group sparse learning algorithm reconstructs the bearing vibration signal as follows: (1) Introducing the group sparsity assumption, that is, assuming that the signal has a periodic group sparse distribution within a certain time interval, the vibration frequency changes, and the frequency is zero at other times. (2) Introducing the prior distribution, assuming that the weights of the fault pulse signal conform to a zero-mean Gaussian distribution, and further constraining the sparsity of the weights through the Gamma prior, affecting its distribution accuracy. (3) Using variational Bayesian inference to approximate the difficult-to-compute posterior distribution, transforming the posterior distribution into a problem of minimizing the KL divergence between the approximate distribution and the true distribution. (4) Iterating through an alternating update algorithm to gradually approach the true posterior distribution, ensuring accuracy and precision.

[0081] Preferably, the extraction of time-domain, frequency-domain, and information entropy features from the reconstructed signal and the construction of a feature set are as follows: This study selected nineteen feature parameters, including time-domain and frequency-domain statistical properties, to describe information such as the waveform, amplitude, and frequency distribution of the vibration signal. Furthermore, the study also introduced permutation entropy and fuzzy entropy as features to more accurately capture the complex dynamic characteristics of the signal.

[0082] Preferably, the classification and identification of bearing vibration signals after training with a random forest model involves the random forest model learning from labeled bearing vibration signal data and building multiple decision trees to identify different bearing states. After model training, an unknown vibration signal is input, and the random forest automatically classifies it.

[0083] Example 1

[0084] Based on the above implementation method, taking a certain bearing as an example, the specific steps are as follows:

[0085] Step S1: The accelerometer collects vibration signals and adds tags according to the bearing condition;

[0086] A 16-channel DAT recorder was used to acquire digital data at a rate of 12,000 samples per second. The acquired data was transferred to a Matlab environment for further processing, recording bearing condition information and labeling the data. All acquired data files were saved in Matlab (*.Mat) format. Finally, a file containing data and labels was created, and training and test sets were created. Using the Western Reserve University public bearing dataset as an example, the dataset contains three different types and degrees of damage: damage to the rolling element (B), inner ring (IR), and outer ring (OR), with damage diameters of 7, 14, and 21 mils, respectively. A total of nine different damage states and one normal state are included. Table 1 lists the labels for different fault types and degrees in this example. 200 sets of acceleration vibration signals were acquired from bearings in 10 different operating states, totaling 2000 samples. 70% of the samples were used as the training set, and the remaining 30% as the test set. The time-domain waveforms of the acquired bearing vibration signals are shown below. Figure 2 As shown.

[0087] Table 1 Labels for different fault types and fault severity

[0088]

[0089] Step S2: Reconstruct the bearing vibration signal using a group sparse learning algorithm;

[0090] Assume the acquired signal can be represented as:

[0091] y = x + w (1)

[0092] In the formula: This represents the bearing vibration signal measured under background noise. It is a local fault pulse signal with a periodic group sparse structure; Let represent independent and identically distributed Gaussian noise, with each element having a mean of zero and a variance of σ. 2 Through a sparse Bayesian learning model, each element of x is modeled with a different precision γ. n The zero-mean Gaussian prior distribution is:

[0093]

[0094] Where γ=[γ1,γ2,...,γ N ] T This controls the sparsity precision of x. γ is further modeled as a Gamma distribution with independent and identically distributed characteristics, i.e.:

[0095]

[0096] To capture the sparse structure of the group, let x n Not only affected by γ n It is also controlled by its neighboring γ n-1 and γ n+1 Control. In this case, equation (3) can be rewritten as:

[0097]

[0098] In the formula: z n =[z n,1 ,z n,2 ,z n,3 ] T This is called an assignment vector, where all elements except one are 0. Because Z n It is unknown, so we model it as non-information prior:

[0099]

[0100] Based on the hierarchical model described above, the joint probability density function of x, α, γ, and Z can be written as:

[0101] p(y,Ω)=p(y|x,α)p(α)p(x|γ,Z)p(γ)p(Z) (6)

[0102] Here, Ω = {x, α, γ, Z} contains all hidden variables.

[0103] An approximation is obtained using variational Bayesian inference, i.e., the approximate factorization of p(Ω|y) is:

[0104] p(Ω|y)≈q(Ω)=q(x)q(α)q(γ)q(Z) (7)

[0105] The KL (Kullback-Leibler) divergence is a method used to measure the similarity between two probability distributions. It approximates the optimal solution by minimizing the KL divergence between the approximate distribution and the actual distribution. To obtain the best approximation, an alternating update algorithm is usually used to calculate the KL divergence value.

[0106]

[0107]

[0108]

[0109]

[0110] An iterative update algorithm is used to progressively infer the fault pulse signal x with a group sparse structure from the observed data. The time-domain waveform of the reconstructed signal from the group sparse learning is shown below. Figure 3 As shown.

[0111] Step S3: Extract time-domain, frequency-domain, and information entropy features from the reconstructed signal and construct a feature set;

[0112] Nineteen different feature parameters were selected to analyze different state characteristics in the vibration signal. These nineteen features are f1 to f15 in the time-domain feature parameter list shown in Table 2, representing time-domain statistical characteristics, mainly used to describe information such as the waveform, amplitude, and amplitude distribution of the signal; and f16 to f19 in the frequency-domain feature parameter list shown in Table 3, representing frequency-domain statistical characteristics, used to identify changes in frequency distribution. In addition, the concept of information entropy was introduced to quantify the uncertainty and complexity of the data and better capture the complex dynamic characteristics of the signal. Specifically, permutation entropy and fuzzy entropy were used as features to more accurately extract the state characteristics of the bearing.

[0113] Table 2 List of Time-Domain Feature Parameters

[0114]

[0115]

[0116] Table 3 List of frequency domain characteristic parameters

[0117]

[0118] Permutation entropy is a nonlinear characteristic used to measure the complexity of a time series. It is based on the permutation of a signal, that is, rearranging the data points of the signal into a new sequence. The calculation steps for permutation entropy are as follows:

[0119] (1) Select the embedding dimension m: Vectorize the original signal according to the embedding dimension m to obtain a series of m-dimensional vectors.

[0120] (2) Generate permutations: Perform full permutations on the elements of each m-dimensional vector to obtain all possible permutations.

[0121] (3) Calculate the probability distribution: count the number of occurrences of each permutation and calculate its probability.

[0122] (4) Calculate the permutation entropy: The permutation entropy is calculated using the probability distribution of the permutation, usually expressed in the form of Shannon entropy, as shown in equation (12):

[0123]

[0124] In the formula, p i This represents the probability value of each sorting order occurring.

[0125] Fuzzy entropy is a characteristic used to describe the randomness and complexity of time series data. Similar to permutation entropy, fuzzy entropy is also a measure based on probability distribution, but it introduces the concept of "fuzziness," taking into account the similarity of signals. The calculation steps for fuzzy entropy are as follows:

[0126] (1) Select the embedding dimension m: Vectorize the original signal according to the embedding dimension m to obtain a series of m-dimensional vectors.

[0127] (2) Calculate similarity: Calculate the similarity between each pair of m-dimensional vectors, usually using Euclidean distance or other similarity measurement methods.

[0128] (3) Define ambiguity: Use similarity to calculate the ambiguity of each vector. The higher the ambiguity, the more random the signal.

[0129] (4) Calculate the fuzzy entropy: Substitute the probability distribution of fuzziness into the Shannon entropy formula to calculate the fuzzy entropy, as shown in equation (13):

[0130] f 21 =lnφ m (n,r)-lnφ m+1 (n,r) (13)

[0131] Where, φ m (n,r) represents the average similarity, where n and r are the gradient and width of the boundary.

[0132] Step S4: After training with a random forest model, classify and identify the bearing vibration signal.

[0133] A random forest classifier is constructed using feature data and corresponding labels from the training set. Random forest is an ensemble learning algorithm consisting of multiple decision trees. During training, each decision tree is trained based on different features, introducing randomness to increase the model's diversity and generalization ability. By learning from the training set, the random forest model can learn the complex relationships between features of different fault categories.

[0134] For a classification task, there are N decision trees, and the classification results of each tree are C1, C2, ..., Cn. N These represent the categories chosen by the N trees, and the random forest selects the final classification result through a voting mechanism:

[0135]

[0136] Wherein, δ(C i C k ) is an indicator function, when C i =C k The value is 1 if the condition is met, and 0 otherwise. This formula indicates that the final classification result is category C among all decision trees. k The category that received the most votes.

[0137] A trained random forest model can be used to classify and identify vibration signals with unknown fault states. When new vibration signal features require fault diagnosis, these features are input into the trained random forest model. In this embodiment, the fault diagnosis results are as follows: Figure 4 As shown, the diagnostic accuracy rate is as high as 99.83%, such as... Figure 5 The following is a histogram showing the importance of each random forest evaluation feature: Figure 6 The first decision tree model shown in this embodiment can be understood by analyzing the structure of a single decision tree in a random forest. The reasoning process and influencing factors of the prediction results can be gained in depth.

[0138] Therefore, the present invention:

[0139] (1) By reconstructing the vibration signal through a group sparse learning algorithm, noise components can be filtered out, thereby improving the signal quality and impact characteristics. Such preprocessing steps help reduce the interference of background noise on the fault signal and improve the identification of the fault signal.

[0140] (2) Not only are features extracted in the time domain, but also in the frequency domain and information entropy domain. Multi-dimensional feature extraction can more comprehensively reflect the operating status of the bearing, enhancing the accuracy and stability of fault diagnosis.

[0141] (3) Introducing random forest as a classifier, this algorithm has strong interpretability. Random forest can evaluate the importance of features, help engineers understand the basis of diagnostic results, and thus increase the credibility of diagnostic results.

[0142] (4) Random forest is an efficient ensemble learning algorithm that can handle large-scale data and has a fast training speed. This enables the present invention to quickly and efficiently classify and diagnose bearing faults in practical applications.

Claims

1. A bearing fault diagnosis method based on group sparse learning algorithm and random forest, characterized in that, Includes the following steps: S1. Use an accelerometer to collect bearing vibration signals and add tags to the bearing vibration signals according to the bearing condition at the time of collection; S2. Reconstruct the bearing vibration signal using a group sparse learning algorithm; Step S2 specifically includes the following steps: S2.

1. Add a set of sparse, periodic fault pulse signals to the bearing vibration signal within a certain time interval; S2.2, Add zero-mean Gaussian distribution assumption weights to the fault pulse signal; S2.

3. The posterior distribution of the fault pulse signal is approximated by the variational Bayesian inference algorithm; S2.

4. Iterate the posterior distribution using an alternating update algorithm; S3. Extract time-domain, frequency-domain, and information entropy features from the reconstructed signal, and construct a feature set based on these features; S4. After training with a random forest model, classify and identify the bearing vibration signal.

2. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, In step S1, the accelerometer is connected to the housing with a magnetic base and placed at the motor drive end for data acquisition.

3. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, In step S2.2, the sparsity of the fault pulse signal is further constrained by the Gamma prior.

4. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, In step S2.4, the KL divergence value of the posterior distribution is calculated iteratively.

5. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, The time-domain features include maximum value, minimum value, average value, peak-to-peak value, rectified average value, effective value, variance, standard deviation, kurtosis, root mean square, skewness, waveform factor, peak factor, margin factor, and impulse factor.

6. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, The frequency domain includes centroid frequency, mean square frequency, frequency variance, and frequency band energy.

7. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 1, characterized in that, In step S3, information entropy includes permutation entropy and fuzzy entropy.

8. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 7, characterized in that, The permutation entropy is extracted using the following steps: S3.1.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector; S3.1.

2. Perform full permutations on the elements of each m-dimensional vector to obtain all possible permutations; S3.1.3 Calculate the permutation entropy using the probability distribution of the permutation in the following manner: ， In the formula, This represents the probability value of each sorting order occurring.

9. The bearing fault diagnosis method based on group sparse learning algorithm and random forest as described in claim 7, characterized in that, The fuzzy entropy is extracted using the following steps: S3.2.1 Embed the reconstructed signal into an m-dimensional vector to obtain an m-dimensional vector; S3.2.2 Calculate the similarity between each pair of m-dimensional vectors; S3.2.3, Apply similarity calculation to ambiguity of each m-dimensional vector; S3.2.4 Calculate the fuzzy entropy based on the fuzziness and the probability of the fuzziness as follows: ， In the formula, The average similarity is represented by , where n and r are the gradient and width of the boundary.

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