An unsupervised anomaly detection method for rotating machinery based on KAAE

Abstract

A method for unsupervised anomaly detection in rotating machinery based on Kaplan-Achet Autoencoders (KAAEs) includes the following steps: 1. Data acquisition: Vibration signals of key transmission components in normal and abnormal states of rotating machinery are collected; 2. Data preprocessing: A sample set is obtained through sliding window sampling, normalization, and fast Fourier transform. This is divided into a training set containing only normal samples, a validation set, and a test set containing both normal and abnormal samples; 3. Model construction: A Kolmogorov-Arnold autoencoder (KAAE) is constructed by combining a Kolmogorov-Arnold network (KAN) with an autoencoder (AE); 4. Model training, validation, and testing: The model is trained on the training set, anomaly detection thresholds are obtained on the validation set, and model performance is evaluated on the test set; 5. Anomaly detection: The trained model is used to detect anomalies in rotating machinery. This method fully captures the complex dependencies and latent representations in the data, thereby better fitting the distribution of normal data and enabling unsupervised anomaly detection in rotating machinery.

Description

Technical Field

[0001] The present invention relates to the technical field of rotating machinery anomaly detection, and in particular to a rotating machinery unsupervised anomaly detection method based on KAAE. Background Art

[0002] With the rapid development of modern mechanical systems, rotating machinery has become indispensable in intelligent equipment, and academia and industry have paid great attention to its safety. Under high-intensity operating conditions, various anomalies are inevitable in key transmission components of rotating machinery (such as bearings and gears). Abnormal transmission components directly affect the operational reliability of rotating machinery, potentially leading to serious accidents, economic losses, and even casualties. Therefore, anomaly detection in rotating machinery is of great research value.

[0003] Traditional data-driven anomaly detection methods can be divided into three steps: signal acquisition, feature extraction, and state detection. The acquired signals can be vibration signals, current signals, acoustic signals, and temperature signals. Signal processing methods such as empirical mode decomposition, Hilbert vibration decomposition, atomic decomposition, empirical wavelet transform, variational mode decomposition, and synchro-compression transform are widely used for feature extraction. The extracted features are then used for state detection using machine learning algorithms such as logistic regression, K-nearest neighbor, naive Bayes, decision trees, support vector machines, and artificial neural networks. However, machine learning algorithms are only suitable for small-scale data, and feature extraction through signal processing requires a high reliance on expert prior knowledge and manual feature selection, which limits the generalization ability of these methods.

[0004] In recent years, deep learning technology has attracted widespread attention in the field of rotating machinery anomaly detection due to its adaptive feature extraction capabilities and end-to-end detection characteristics. Deep learning methods such as multi-layer perceptrons, convolutional neural networks, recurrent neural networks, generative adversarial networks, and Transformers have all demonstrated promising results in rotating machinery anomaly detection. However, these methods rely on sufficient labeled data, which limits their application in industrial scenarios. Rotating machinery in industrial settings is mostly in normal conditions, and anomaly labeled data is extremely scarce or even unavailable. Therefore, unsupervised anomaly detection based solely on normal state data can provide greater flexibility and expand the capabilities of these deep learning methods.

[0005] As a classic unsupervised deep learning model, autoencoders are widely used in data dimensionality reduction, feature extraction, and data reconstruction. In recent years, many researchers have explored and improved them to enhance their unsupervised anomaly detection performance in various fields. However, traditional autoencoders are limited by the linear fitting of fully connected layers, making it difficult to effectively reconstruct normal data and extract representative feature representations, resulting in insufficient detection capabilities for anomalous data.

[0006] Compared with the prior art, the differences are as follows:

[0007] Technical comparison with patent CN110132554A "A method for fault diagnosis of rotating machinery based on deep Laplace autoencoder"

[0008] Patent CN110132554A proposes a rotating machinery fault diagnosis method based on deep Laplace autoencoders, which belongs to the field of rotating machinery fault diagnosis technology. This patent proposes an unsupervised anomaly detection method for rotating machinery based on KAAE, which also belongs to the field of rotating machinery anomaly detection technology. The two patents involve fundamentally different technical fields.

[0009] Patent CN110132554A constructs a deep Laplacian autoencoder; this patent constructs a Kolmogorov-Arnold autoencoder. Both are improvements on traditional autoencoders, but their theoretical foundations are fundamentally different.

[0010] Patent CN110132554A constructs a deep Laplace autoencoder for rotating machinery fault diagnosis, which is a supervised learning algorithm. This patent constructs a Kolmogorov-Arnold autoencoder for unsupervised anomaly detection in rotating machinery, which is an unsupervised learning algorithm. There are essential differences between the two algorithms.

[0011] Technical comparison with patent CN110334764A "Intelligent fault diagnosis method for rotating machinery based on integrated deep autoencoder"

[0012] Patent CN110334764A proposes an intelligent fault diagnosis method for rotating machinery based on an integrated deep autoencoder, which belongs to the field of rotating machinery fault diagnosis technology. This patent proposes an unsupervised anomaly detection method for rotating machinery based on KAAE, which also belongs to the field of rotating machinery anomaly detection technology. The two patents involve fundamentally different technical fields.

[0013] Patent CN110334764A constructs an integrated deep autoencoder; this patent constructs a Kolmogorov-Arnold autoencoder. Both are improvements on traditional autoencoders, but their theoretical foundations are fundamentally different.

[0014] Patent CN110334764A constructs an integrated deep autoencoder for rotating machinery fault diagnosis, which is a supervised learning algorithm. This patent constructs a Kolmogorov-Arnold autoencoder for unsupervised anomaly detection in rotating machinery, which is an unsupervised learning algorithm. There are essential differences between the two algorithms at the algorithm level. Summary of the Invention

[0015] To address the above technical issues, this paper proposes a method for unsupervised anomaly detection in rotating machinery based on Kalmogorov-Arnold (KAAE) networks. This method combines the Kolmogorov-Arnold network (KAN) with an autoencoder (AE) to construct a Kolmogorov-Arnold autoencoder (KAAE). Leveraging the responsiveness and flexibility of KAN, this method fully captures the complex dependencies and latent representations in the data, thereby better fitting the distribution of normal data for unsupervised anomaly detection in rotating machinery.

[0016] To achieve the above object, the technical solution adopted by the present invention is:

[0017] A method for unsupervised anomaly detection of rotating machinery based on KAAE, characterized by comprising the following steps:

[0018] Step 1: Data collection:

[0019] Collect vibration signals of key transmission components of rotating machinery in normal and abnormal conditions;

[0020] Step 2: Data preprocessing:

[0021] The sample set is obtained through sliding window sampling, normalization and fast Fourier transform, and divided into a training set and a validation set containing only normal samples, and a test set containing both normal and abnormal samples;

[0022] Step 3: Model building:

[0023] Combine the Kolmogorov-Arnold network KAN and the autoencoder AE to construct the Kolmogorov-Arnold autoencoder KAAE;

[0024] Step 4: Model training, verification and testing:

[0025] Train the model on the training set, obtain the anomaly detection threshold on the validation set, and evaluate the model performance on the test set;

[0026] Step 5: Anomaly Detection

[0027] Use the trained model to perform anomaly detection on rotating machinery.

[0028] Furthermore, in the step 1 of data collection, one or more sensors are installed at different positions or directions near the rotating mechanical transmission component that needs to be detected for abnormality, and the vibration signals of normal state and abnormal state are collected using data collection equipment.

[0029] Furthermore, in step 2, in order to avoid test leakage, when sliding window sampling, there is no overlap between adjacent windows and a certain interval is maintained; all samples are normalized and fast Fourier transformed.

[0030] Furthermore, in step 3, the overall structure of the KAAE is similar to that of the AE, with the main difference being that the KAAE uses the KAN layer instead of the fully connected layer in the AE. Leveraging the responsiveness and flexibility of the KAN, the complex dependencies and potential representations in the data are fully captured.

[0031] The KAAE has a symmetrical structure, consisting of an encoding network and a decoding network, both of which have the same number of layers. The number of layers can be adjusted according to different task requirements.

[0032] In the KAAE, the encoding network compresses high-dimensional input data into low-dimensional feature representations using KAN, gradually reducing the dimensionality of the data with each layer. The decoding network converts the low-dimensional feature representations into a reconstructed form of the input data using KAN, gradually increasing the dimensionality of the data with each layer. The goal is to reconstruct the input data to obtain a low-dimensional representation that best expresses the essential characteristics of the data, as shown in the following formula:

[0033] h=f(x)=KAN(x) (1)

[0034] z=g(h)=KAN′(h) (2)

[0035]

[0036] in, represents the input data, f(·) represents the encoding network, represents the low-dimensional features obtained after encoding, g(·) represents the decoding network, Represents the reconstructed data obtained after decoding, L MSE Represents the mean square error reconstruction loss function, and the training goal of the model is to minimize it;

[0037] In the KAN, each layer is structured as a learnable activation function matrix, which is parameterized and optimized during training, as shown in the following formula:

[0038] Φ={φ q,p},p=1,...,n in ,q=1,...,n out (4)

[0039] Among them, n in and n out Represent the input feature dimension and output feature dimension respectively;

[0040] The KAN is implemented by stacking layers. The mapping transformation of each layer acts on the output of the previous layer to produce the input of the next layer. An L-layer KAN is shown as follows:

[0041] φ l,j,i ,l=0,...,L-1,j=1,...,nl+1 ,i=1,...,n l (5)

[0042]

[0043] Among them, φ l,j,i represents the learnable activation function connecting the i-th neuron in layer l and the j-th neuron in layer l+1, x l+1,j represents the activation value of the jth neuron in the l+1th layer, Φ l Represents the function matrix of the lth layer, containing n l ×n l+1 A learnable activation function;

[0044] The learnable activation function is a weighted sum of a spline function and a bias function, as shown in the following formula:

[0045] φ(x)=w s spline(x)+w b b(x) (9)

[0046]

[0047] Where spline(·) represents the linear combination of B-spline functions, c i represents the learnable combination coefficient, b(·) represents the bias function, and w s and w b Represents a learnable weight factor to better control the overall magnitude of the learnable activation function.

[0048] Furthermore, in step 4, the model training uses a training set containing only normal samples to train KAAE, and the Adam optimization algorithm is used to update the model parameters;

[0049] For model verification, a validation set containing only normal samples is input into the trained KAAE to obtain the reconstruction loss value of each validation sample. In order to avoid the difficulty of manually adjusting the threshold and selecting the percentage interval, the maximum value of the reconstruction loss value of all validation samples is selected as the threshold for detecting abnormal samples;

[0050] The model test inputs a test set containing normal samples and abnormal samples into the trained KAAE, obtains the reconstruction loss value of each test sample, determines it as normal or abnormal based on the threshold, and evaluates the model performance through multiple indicators.

[0051] Compared with the prior art, the advantages of the present invention are:

[0052] By combining the Kolmogorov-Arnold network (KAN) with an autoencoder (AE), a Kolmogorov-Arnold autoencoder (KAAE) was constructed. Leveraging the responsiveness and flexibility of KAN, the KAN fully captures the complex dependencies and latent representations in the data, thereby better fitting the distribution of normal data for unsupervised anomaly detection in rotating machinery. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of the method of the present invention;

[0054] Figure 2 Schematic diagram of the structure of KAAE of the method of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0056] In this embodiment, if Figure 1 As shown, a KAAE-based unsupervised anomaly detection method for rotating machinery includes the following steps: Step 1, data acquisition: collecting vibration signals of normal and abnormal states of key transmission components of rotating machinery (such as bearings and gears); Step 2, data preprocessing: obtaining a sample set through sliding window sampling, normalization and fast Fourier transform, and dividing it into a training set and a validation set containing only normal samples, and a test set containing normal samples and abnormal samples; Step 3, model construction: combining the Kolmogorov-Arnold network KAN and the autoencoder AE to construct the Kolmogorov-Arnold autoencoder KAAE; Step 4, model training, verification and testing: training the model on the training set, obtaining the anomaly detection threshold on the verification set, and evaluating the model performance on the test set; Step 5, anomaly detection: using the trained model to perform anomaly detection on rotating machinery.

[0057] In step 1, one or more sensors are installed at different positions or directions near the rotating mechanical transmission components (such as bearings and gears) that need to be detected for abnormalities, and a data acquisition device is used to collect vibration signals in normal and abnormal states.

[0058] In this example, two triaxial accelerometers were installed at strategic locations near a high-speed aircraft bearing. Data acquisition equipment was used to synchronously collect vibration signals from six channels. During the acquisition process, the operating conditions were varied by varying the bearing's speed and load. At a sampling frequency of 51,200 Hz, vibration signals were collected for the bearing's normal state and six different abnormal conditions.

[0059] In this embodiment, in step 2, in order to avoid test leakage, when the sliding window is sampled, there is no overlap between adjacent windows and a certain interval is maintained. After sampling, each sample contains 1024 signal points; all samples are normalized and fast Fourier transformed, and each sample contains 512 signal points after data processing.

[0060] In this embodiment, the data collection process includes three different operating conditions, all of which have different bearing speeds and loads. Data preprocessing yields 500 normal samples for each operating condition, of which 200 are used for training, 100 for validation, and 200 for testing. Data preprocessing also yields 50 samples for each abnormal state for each operating condition, and all 300 abnormal samples are used for testing, as shown in Table 1 below:

[0061]

[0062]

[0063] In step 3, the overall structure of the KAAE is similar to that of the AE, with the main difference being that the KAAE uses the KAN layer instead of the fully connected layer in the AE. Leveraging the responsiveness and flexibility of the KAN, the complex dependencies and potential representations in the data are fully captured.

[0064] The KAAE has a symmetrical structure, consisting of an encoding network and a decoding network, both of which have the same number of layers. The number of layers can be adjusted according to different task requirements.

[0065] In this embodiment, if Figure 2 As shown in the KAAE, the encoding network compresses high-dimensional input data into low-dimensional feature representations using KAN, gradually reducing the dimensionality of the data with each layer; the decoding network converts the low-dimensional feature representations into a reconstructed form of the input data using KAN, gradually increasing the dimensionality of the data with each layer. The goal is to reconstruct the input data to obtain a low-dimensional representation that best expresses the essential characteristics of the data, as shown in the following formula:

[0066] h=f(x)=KAN(x) (1)

[0067] z=g(h)=KAN′(h) (2)

[0068]

[0069] in, represents the input data, f(·) represents the encoding network, represents the low-dimensional features obtained after encoding, g(·) represents the decoding network, Represents the reconstructed data obtained after decoding, L MSERepresents the mean square error reconstruction loss function, and the training goal of the model is to minimize it;

[0070] In the KAN, each layer is structured as a learnable activation function matrix, which is parameterized and optimized during training, as shown in the following formula:

[0071] Φ={φ q,p},p=1,...,n in ,q=1,...,n out (4)

[0072] Among them, n in and n out Represent the input feature dimension and output feature dimension respectively;

[0073] The KAN is implemented by stacking layers, where each layer's mapping transformation acts on the output of the previous layer to produce the input of the next layer. A KAN with L layers is shown below:

[0074] φ l,j,i ,l=0,...,L-1,j=1,...,n l+1 ,i=1,...,n l (5)

[0075]

[0076] Among them, φ l,j,i represents the learnable activation function connecting the i-th neuron in layer l and the j-th neuron in layer l+1, x l+1,j represents the activation value of the jth neuron in the l+1th layer, Φ l Represents the function matrix of the lth layer, containing n l ×n l+1 A learnable activation function;

[0077] The learnable activation function is a weighted sum of a spline function and a bias function, as shown in the following formula:

[0078] φ(x)=w s spline(x)+w b b(x) (9)

[0079]

[0080] Where spline(·) represents the linear combination of B-spline functions, c i represents the learnable combination coefficient, b(·) represents the bias function, and w s and w b represents a learnable weight factor to better control the overall magnitude of the learnable activation function;

[0081] In this embodiment, the encoding network and decoding network of the KAAE are both two-layer structures. Batch normalization BN is added to reduce the change of data distribution and stabilize the network training process. The linear rectifier unit ReLU is used as the activation function to improve the nonlinear expression ability of the network, alleviate the gradient disappearance and accelerate the network convergence. The detailed parameter configuration of the KAAE is as follows

[0082] As shown in Table 2:

[0083]

[0084] In step 4, the model is trained using a training set containing only normal samples to train KAAE, and the Adam optimization algorithm is used to update the model parameters.

[0085] In this embodiment, the model training and hyperparameter configurations are as follows: batch size is 128, number of iterations is 300, initial learning rate is 0.01, and decays by 0.1 times at iterations 20 and 200, respectively.

[0086] In step 4, the model is validated by feeding a validation set containing only normal samples into the trained Kafka Autoencoder (KAAE) to obtain the reconstruction loss for each validation sample. To avoid the difficulty of manually adjusting the threshold and selecting the percentage interval, the maximum reconstruction loss value of all validation samples is selected as the threshold for detecting abnormal samples.

[0087] In step 4, the model is tested by inputting a test set containing normal samples and abnormal samples into the trained KAAE to obtain the reconstruction loss value of each test sample, determining whether it is normal or abnormal based on the threshold, and evaluating the model performance through multiple indicators.

[0088] In this embodiment, the calculation formulas for the four evaluation indicators (accuracy, precision, recall and F1 score) are:

[0089]

[0090] Among them, TP represents the number of correctly detected abnormal samples; TN represents the number of correctly detected normal samples; FP represents the number of incorrectly detected abnormal samples; FN represents the number of incorrectly detected normal samples;

[0091] In this example, in addition to comparing KAAE with traditional autoencoders, we also selected popular improved autoencoders, including the memory-augmented autoencoder (MAE), the variational autoencoder (VAE), the sparse autoencoder (SAE), and the denoising autoencoder (DAE). It is worth noting that, for a fair comparison, all of these models used the same input signal form, training strategy, and hyperparameter configuration. To reduce the impact of randomness, each experiment was repeated five times, and the evaluation metrics were averaged as the final experimental results.

[0092] In this embodiment, the unsupervised anomaly detection results of all models are shown in Table 3 below:

[0093]

[0094] As can be seen from the table, KaaS's accuracy, precision, recall, and F1 score all exceeded 96%, reaching 97.84%, 99.77%, 96.62%, and 98.13%, respectively. Compared to traditional autoencoders, these evaluation metrics improved by 14.71%, 0.02%, 24.53%, and 15.41%, respectively. Accuracy, recall, and F1 score achieved the best performance among all models. SAE's precision was 0.08% higher than KaaS, but the remaining three evaluation metrics lagged significantly behind KaaS.

[0095] As can be seen from the above examples, the present invention is a method for unsupervised anomaly detection in rotating machinery based on a Kalmogorov-Arnold (KAAE) architecture. Compared to existing technologies, the present invention offers the advantage of combining a Kolmogorov-Arnold network (KAN) with an autoencoder (AE) to construct a Kolmogorov-Arnold autoencoder (KAAE). Leveraging the responsiveness and flexibility of KAN, the method fully captures the complex dependencies and latent representations in the data, thereby better fitting the distribution of normal data for unsupervised anomaly detection in rotating machinery.

[0096] The above description is merely a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent variation based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A KAAE-based unsupervised anomaly detection method for rotating machinery, characterized in that: The following steps are involved: Step 1: Data collection: Collect vibration signals of key transmission components of rotating machinery in normal and abnormal conditions; Step 2: Data preprocessing: The sample set is obtained through sliding window sampling, normalization and fast Fourier transform, and divided into a training set and a validation set containing only normal samples, and a test set containing both normal and abnormal samples; Step 3: Model building: Combine the Kolmogorov-Arnold network KAN and the autoencoder AE to construct the Kolmogorov-Arnold autoencoder KAAE; KAAE uses KAN layer to replace the fully connected layer in AE; The KAAE is a symmetrical structure consisting of an encoding network and a decoding network, both of which have the same number of layers. The number of layers is adjusted according to the needs of different tasks. In the KAAE, the encoding network compresses high-dimensional input data into low-dimensional feature representations through KAN, gradually reducing the dimension of the data at each layer; the decoding network converts the low-dimensional feature representation into a reconstructed form of the input data through KAN, gradually increasing the dimension of the data at each layer. The goal is to reconstruct the input data to obtain a low-dimensional representation that best expresses the essential characteristics of the data, as shown in the following formula: （1） （2） （3） Where x∈ℝ N represents the input data, f(·) represents the encoding network, h∈ℝ M represents the low-dimensional features obtained after encoding, g(·) represents the decoding network, z∈ℝ N Represents the reconstructed data obtained after decoding, L MSE Represents the mean square error reconstruction loss function, and the training goal of the model is to minimize it; In the KAN, each layer is structured as a learnable activation function matrix, which is parameterized and optimized during training, as shown in the following formula: （4） Among them, n in and n out Represent the input feature dimension and output feature dimension respectively; The KAN is implemented by stacking layers. The mapping transformation of each layer acts on the output of the previous layer to produce the input of the next layer. An L-layer KAN is shown as follows: （5） （6） （7） （8） Among them, φ l,j,i represents the learnable activation function connecting the i-th neuron in layer l and the j-th neuron in layer l+1, x l+1,j represents the activation value of the jth neuron in the l+1th layer, Φ l Represents the function matrix of the lth layer, containing n l ×n l+1 A learnable activation function; The learnable activation function is a weighted sum of a spline function and a bias function, as shown in the following formula: （9） （10） （11） Where spline(·) represents the linear combination of B-spline functions, c i represents the learnable combination coefficient, b(·) represents the bias function, and w s and w b represents a learnable weight factor to better control the overall magnitude of the learnable activation function; Step 4: Model training, verification and testing: Train the model on the training set, obtain the anomaly detection threshold on the validation set, and evaluate the model performance on the test set; Step 5: Anomaly Detection Use the trained model to perform anomaly detection on rotating machinery.

2. The unsupervised anomaly detection method for rotating machinery based on KAAE according to claim 1 is characterized in that: In the step 1 of data collection, one or more sensors are installed at different positions or directions near the rotating mechanical transmission component that needs to be detected for abnormality, and the vibration signals of normal state and abnormal state are collected using data collection equipment.

3. The unsupervised anomaly detection method for rotating machinery based on KAAE according to claim 1 is characterized in that: In step 2, to avoid test leakage, when sliding window sampling, there is no overlap between adjacent windows and a certain interval is maintained; all samples are normalized and fast Fourier transformed.

4. The unsupervised anomaly detection method for rotating machinery based on KAAE according to claim 1 is characterized in that: In step 4, the model training uses a training set containing only normal samples to train KAAE, and the Adam optimization algorithm is used to update the model parameters; For model verification, a validation set containing only normal samples is input into the trained KAAE to obtain the reconstruction loss value of each validation sample. In order to avoid the difficulty of manually adjusting the threshold and selecting the percentage interval, the maximum value of the reconstruction loss value of all validation samples is selected as the threshold for detecting abnormal samples; The model test inputs a test set containing normal samples and abnormal samples into the trained KAAE, obtains the reconstruction loss value of each test sample, determines it as normal or abnormal based on the threshold, and evaluates the model performance through multiple indicators.

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