A bearing residual service life prediction method based on BiLSTM-KAN
Patent Information
- Application Number
- CN202510460783.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-14
- Publication Date
- 2026-10-20
AI Technical Summary
[0004]目前的一些混合模型，如CNN-LSTM、Attention-LSTM等，它们的网络结构冗余，计算成本高，难以在边缘设备实时部署；且未解决轴承多工况下动态特征耦合的建模难题
[0046]本研究采用KAN网络实现振动信号的非线性特征自适应提取，替代人工特征工程并动态适应多工况退化模式；通过双向LSTM同步捕捉正反向时序依赖关系，结合并行-级联轻量化架构使计算效率提升40％以上，在降低15％-30％预测误差的同时支持边缘部署。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of rolling bearing remaining service prediction technology, and specifically to a bearing remaining service prediction method based on BiLSTM-KAN. Background Technology
[0002] Traditional rolling bearing remaining life prediction models rely heavily on manual feature extraction and prior distribution assumptions, exhibiting poor modeling ability and insufficient generalization for nonlinear degradation data. Convolutional Neural Networks (CNNs) perform exceptionally well with graphics, but their ability to capture long-term global information is limited. Recurrent Neural Networks (RNNs) are stronger in this regard. However, compared to traditional RNNs, Long Short-Term Memory (LSTM) networks can learn long-term dependencies. LSTMs incorporate additional storage units that can store historical information and selectively utilize it, enabling the model to handle long-term series. The LSTM structure effectively addresses the gradient vanishing and exploding problems of RNNs. While a single deep learning model like LSTM can capture temporal dependencies, parameter optimization is complex and it struggles to characterize local abrupt changes in bearing degradation. A drawback of LSTMs is their inability to utilize subsequent information, a weakness that BiLSTMs overcome. The BiLSTM model structure consists of two LSTM layers, which learn information in both the forward and backward temporal directions, enabling it to capture information from both the past and the future.
[0003] In terms of fitting, traditional multi-layer perceptrons (MLPs) rely on fixed activation functions. Due to their feature learning, they are less affected by the curse of dimensionality (COD) and cannot optimize univariate functions, thus resulting in inaccuracy in low-dimensional cases. In contrast, spline curves are accurate for low-dimensional functions, easy to adjust locally, and can switch between different resolutions. However, spline curves suffer from severe COD due to their inability to utilize combinatorial structures. The Kolmogorov-Arnold network (KAN), however, combines spline curves and MLPs, simultaneously addressing the problems of both.
[0004] Current hybrid models, such as CNN-LSTM and Attention-LSTM, have redundant network structures, high computational costs, and are difficult to deploy in real time on edge devices; moreover, they have not solved the modeling problem of dynamic feature coupling under multiple operating conditions of bearings. Summary of the Invention
[0005] This invention aims to provide a bearing remaining service life prediction method based on BiLSTM-KAN. This method is scientifically and rationally designed, which can effectively improve the accuracy of motor bearing fault diagnosis and has higher reliability.
[0006] The technical solution of the present invention is as follows:
[0007] The method for predicting the remaining service life of bearings based on BiLSTM-KAN includes the following steps:
[0008] A. Constructing the BiLSTM-KAN fusion network: Using forward and backward LSTM, calculate the final state of the hidden layer of the BiLSTM network, adjust the BiLSTM network, and then replace the last layer of the BiLSTM network with the KAN network to construct the BiLSTM-KAN fusion network.
[0009] B. Train the BiLSTM-KAN fusion network to obtain the trained BiLSTM-KAN fusion network;
[0010] C. Acquire the original vibration signal of the bearing under test in real time, convert the original vibration signal from time domain signal to frequency domain amplitude signal, and then input it into the trained BiLSTM-KAN fusion network to process and obtain a series of trend quantitative health indices of the bearing.
[0011] D. Smooth the trend quantitative health index. Based on the corrected trend quantitative health index, fit it with a cubic polynomial to obtain the trend quantitative health index curve of the bearing. Define the index threshold as 1 when the bearing is damaged, construct the horizontal line of the threshold, and the intersection of the horizontal line of the threshold and the trend quantitative health index curve is the bearing service life.
[0012] In step A, the formula for the BiLSTM network is as follows:
[0013]
[0014] in, and The outputs of the forward and backward LSTMs are y, respectively. t is the final output value of the hidden layer; f(·) and g(·) are the corresponding activation functions.
[0015] The LSTM formula is as follows:
[0016] f t =σ(W xf x t +W hf h t-1 +b f )
[0017] i t =σ(W xi x t +W hi h t-1 +b i )
[0018]
[0019] o t =σ(W xo x t +W ho h t-1 +b o )
[0020]
[0021] in, For element-wise multiplication of vectors, x t h is the input of the LSTM unit at runtime t. t-1 It is the output of the LSTM unit at runtime t-1, h t It is the output of the LSTM unit at runtime t, C t-1 It is the cell state at runtime t-1, C t It is the cell state at runtime t. It is the temporary cell state at runtime t, i t f t and o t These are the output values of the input gate, forget gate, and output gate, respectively, b f b i b c and b o These are the bias terms for the forget gate, input gate, cell state, and output gate, respectively. xf W xi W xc and W xo These are the input layer x t and the hidden layer h of the LSTM unit t The weight values W between runtime t. hf W hi W hc and W hoThese are the hidden layer weights of the LSTM units between runtime t and t-1.
[0022] In step A, the KAN network formula is as follows:
[0023]
[0024] in It is a B-spline function that connects the i-th node in the l-th layer to the j-th node in the (i+1)-th layer.
[0025] In step D, the original vibration signal is converted using a fast Fourier transform, and the formula is as follows:
[0026] X fred =FFT(x) time (4).
[0027] In step D, the formula for smoothing and correcting the trend-based quantitative health index is as follows:
[0028]
[0029] Where ω is the width of the sliding window and t is the running time.
[0030] In step D, the cubic polynomial fitting formula is as follows:
[0031] y = a3t 3 +a2t 2 +a1t+a0 (6)
[0032] Where a3, a2, a1, a0 are the undetermined coefficients of the cubic polynomial, y is the bearing condition value, and t is the running time.
[0033] In step B, the training process of the BiLSTM-KAN fusion network is as follows:
[0034] The training set is composed of raw vibration signal data of some rolling bearings operating under different working conditions selected from the common dataset. Then, the time domain signal of the training set is transformed into the frequency domain signal using fast Fourier transform.
[0035] The Fast Fourier Transform (FFT) is expressed as follows:
[0036] X fred =FFT(x) time (4)
[0037] Then, the frequency domain signal is normalized by range, and a supervised training method is used. The input-output pair is represented as follows: The formula is as follows:
[0038]
[0039] in This represents the N-dimensional input feature vector of a bearing under a certain operating condition at the current moment; while x normalized-t ∈[0,1] represents the percentage of lifespan at the corresponding moment;
[0040] The normalized training set obtained after processing with Formula 7 is then input into the BiLSTM-KAN fusion network for training, resulting in the trained BiLSTM-KAN fusion network.
[0041] The training process is set as follows: the mean squared error (MSE) is used as the loss function, the Adam optimizer updates the network parameters, the learning rate is set to 0.001, and the batch size is 64.
[0042] The algorithm names corresponding to the abbreviations in Chinese and English in this invention are as follows:
[0043] KAN: Kolmogorov-Arnold network;
[0044] BiLSTM: Bidirectional Long Short-Term Memory Network.
[0045] The advantages of this invention compared to existing technologies are:
[0046] This study uses a KAN network to achieve adaptive extraction of nonlinear features from vibration signals, replacing manual feature engineering and dynamically adapting to degradation modes under multiple operating conditions. By synchronously capturing forward and reverse temporal dependencies through bidirectional LSTM and combining it with a parallel-cascaded lightweight architecture, the computational efficiency is improved by more than 40%, and the prediction error is reduced by 15%-30% while supporting edge deployment.
[0047] This invention can extend bearing life, reduce operation and maintenance costs, and reduce equipment energy consumption through maintenance cycle optimization, thus possessing the dual value of industrial reliability and low-carbon economy.
[0048] This study constructs a robust bearing life prediction paradigm by integrating bidirectional temporal modeling and interpretable function approximation networks. Its core value lies in two aspects: firstly, the explicit mathematical expression of the KAN network provides a transparent path for degradation mechanism analysis, compensating for the shortcomings of traditional black-box models; secondly, the characteristic interaction mechanism of multi-source signals overcomes the limitations of single-sensor data, providing a solution for equipment health management in industrial scenarios that combines accuracy and practicality. This method has significant engineering implications for reducing operation and maintenance costs and optimizing preventative maintenance strategies. Attached Figure Description
[0049] Figure 1 This is a graph showing the predicted service life of bearing1-3 according to the method of the present invention;
[0050] Figure 2 The graph shows the predicted service life of bearing1-4 according to the method of the present invention. Detailed Implementation
[0051] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0052] Example 1
[0053] The method for predicting the remaining service life of bearings based on BiLSTM-KAN includes the following steps:
[0054] A. Constructing the BiLSTM-KAN fusion network: Using forward and backward LSTM, calculate the final state of the hidden layer of the BiLSTM network, adjust the BiLSTM network, and then replace the last layer of the BiLSTM network with the KAN network to construct the BiLSTM-KAN fusion network.
[0055] In this embodiment, the BiLSTM network adopts a two-layer stacked structure, with each layer containing 128 hidden units and a time step size of 50 to accommodate the long-sequence dependency features during bearing degradation. The KAN network consists of three layers of B-spline functions, with 64 nodes per layer and a spline basis function order of 5. It outputs a trend-based quantitative health indicator (HI) by adaptively learning the nonlinear mapping relationship of frequency domain features. The formula for the BiLSTM network is as follows:
[0056]
[0057] in, and The outputs of the forward and backward LSTMs are y, respectively. t is the final output value of the hidden layer; f(·) and g(·) are the corresponding activation functions.
[0058] The LSTM formula is as follows:
[0059] f t =σ(W xf x t +W hf h t-1 +b f )
[0060] i t =σ(W xi x t +W hi h t-1 +b i )
[0061]
[0062] o t =σ(W xo x t +W ho h t-1 +b o )
[0063]
[0064] in, For element-wise multiplication of vectors, x t h is the input of the LSTM unit at runtime t. t-1 It is the output of the LSTM unit at runtime t-1, h t It is the output of the LSTM unit at runtime t, C t-1 It is the cell state at runtime t-1, C t It is the cell state at runtime t. It is the temporary cell state at runtime t, i t f t and o t These are the output values of the input gate, forget gate, and output gate, respectively, b f b i b c and b o These are the bias terms for the forget gate, input gate, cell state, and output gate, respectively. xf W xi W xc and W xo These are the input layer x t and the hidden layer h of the LSTM unit t The weight values W between runtime t. hf W hi W hc and W ho These are the hidden layer weights of the LSTM units between runtime t and t-1.
[0065] The formula for the KAN network is as follows:
[0066]
[0067] in It is a B-spline function that connects the i-th node in the l-th layer to the j-th node in the (i+1)-th layer.
[0068] In step D, the original vibration signal is converted using a fast Fourier transform, and the formula is as follows:
[0069] X fred =FFT(x) time (4).
[0070] B. Train the BiLSTM-KAN fusion network to obtain the trained BiLSTM-KAN fusion network;
[0071] The training process of the BiLSTM-KAN fusion network is as follows:
[0072] The training set is composed of raw vibration signal data of some rolling bearings operating under different working conditions selected from the common dataset. Then, the time domain signal of the training set is transformed into the frequency domain signal using fast Fourier transform.
[0073] The Fast Fourier Transform (FFT) is expressed as follows:
[0074] X fred =FFT(x) time (4)
[0075] Then, the frequency domain signal is normalized by range, and a supervised training method is used. The input-output pair is represented as follows: The formula is as follows:
[0076]
[0077] in This represents the N-dimensional input feature vector of a bearing under a certain operating condition at the current moment; while x normalized-t ∈[0,1] represents the percentage of lifespan at the corresponding moment;
[0078] The normalized training set obtained after processing with Formula 7 is input into the BiLSTM-KAN fusion network for training, resulting in a trained BiLSTM-KAN fusion network.
[0079] The training process is set as follows: the mean squared error (MSE) is used as the loss function, the Adam optimizer updates the network parameters, the learning rate is set to 0.001, and the batch size is 64.
[0080] C. Acquire the original vibration signal of the bearing under test in real time, convert the original vibration signal from time domain signal to frequency domain amplitude signal, and then input it into the trained BiLSTM-KAN fusion network to process and obtain a series of trend quantitative health indices of the bearing.
[0081] D. Smooth the trend quantitative health index. Based on the corrected trend quantitative health index, fit it with a cubic polynomial to obtain the trend quantitative health index curve of the bearing. Define the index threshold as 1 when the bearing is damaged. Construct the horizontal line of the threshold. The intersection of the horizontal line of the threshold and the trend quantitative health index curve is the remaining service life of the bearing.
[0082] The formula for smoothing and correcting the trend-based quantitative health index is as follows:
[0083]
[0084] Where ω is the width of the sliding window and t is the running time.
[0085] In step D, the cubic polynomial fitting formula is as follows:
[0086] y = a3t 3 +a2t 2 +a1t+a0 (6)
[0087] Where a3, a2, a1, a0 are the undetermined coefficients of the cubic polynomial, y is the bearing condition value, and t is the running time.
[0088] Example 2
[0089] The method of this invention is as follows: Based on the method of Example 1, the dataset used is IEEE PHM2012, horizontal and vertical vibration signals are selected as key input features, and operating condition 1 (1800 r / m, 4000 N) is used as the benchmark experimental environment; bearing units numbered Bearing1_1 and Bearing1_2 under this operating condition are selected to construct a training set; at the same time, the complete failure sequences of bearings Bearing1_3 and Bearing1_4 under the same operating condition are used as independent test sets; the training set is operated according to the method of Example 1 to complete the training of the BiLSTM-KAN fusion network; then, the training results of the BiLSTM-KAN fusion network are verified by operating according to the method of Example 1 with the independent test set, and the RUL prediction result of the proposed remaining service life prediction model is verified accordingly.
[0090] Comparative Example 1: GWO-CNN-BiLSTM-Attention model;
[0091] Comparative Example 2: PCA-Kmeans-RF.
[0092] Using the mean absolute error (MAE) and root mean square (RMS) eigenvalues as evaluation criteria, the formula is as follows:
[0093]
[0094] The results are shown in Table 1, which compares the prediction results of the three methods.
[0095]
[0096]
[0097] Comparative data shows that the method of this invention significantly outperforms other models in both MAE and RMSE metrics, especially in the comparison between GWO-CNN-BiLSTM and traditional CNN, where error reductions reach 24.2% and 36.1%, respectively. This advantage stems from the collaborative modeling mechanism of dual-modal vibration signals: by dynamically weighting and fusing the time-frequency domain features of horizontal and vertical vibration signals, combined with bidirectional temporal dependency modeling, noise interference is effectively suppressed, while simultaneously capturing multi-scale correlation characteristics during the degradation process. Figure 1 and Figure 2 As can be seen, the regression curve obtained by the method of the present invention further demonstrates that the predicted trajectory of the method of the present invention has a high degree of fit with the actual life curve, and the fluctuation range is significantly converged.
[0098] The innovation of this invention is reflected in three aspects: First, it employs a heterogeneous network architecture to achieve joint mining of spatiotemporal features. The bidirectional recursive units of BiLSTM-KAN are combined with the spline functions of the Kolmogorov-Arnold network, enabling adaptive extraction of nonlinear degradation patterns in signals without manual parameter tuning. Second, it introduces a cross-channel attention gating mechanism, using a dynamic feature weight allocation strategy to enhance the transmission efficiency of key degradation information and weaken the interference of redundant features. Third, it reduces reliance on domain expert experience through an end-to-end deep feature learning framework, addressing the pain points of complex feature engineering and limited generalization ability in traditional methods. Experiments show that the prediction stability of this model under sudden failure scenarios is improved by 19.3% compared to the GWO optimized model, verifying its strong adaptability to complex working conditions.
Claims
1. A method for predicting the remaining service life of bearings based on BiLSTM-KAN, characterized in that, Includes the following steps: A. Constructing the BiLSTM-KAN fusion network: Using forward and backward LSTM, calculate the final state of the hidden layer of the BiLSTM network, adjust the BiLSTM network, and then replace the last layer of the BiLSTM network with the KAN network to construct the BiLSTM-KAN fusion network. B. Train the BiLSTM-KAN fusion network to obtain the trained BiLSTM-KAN fusion network; C. Acquire the original vibration signal of the bearing under test in real time, convert the original vibration signal from time domain signal to frequency domain amplitude signal, and then input it into the trained BiLSTM-KAN fusion network to process and obtain a series of trend quantitative health indices of the bearing. D. Smooth the trend quantitative health index. Based on the corrected trend quantitative health index, fit it with a cubic polynomial to obtain the trend quantitative health index curve of the bearing. Define the index threshold as 1 when the bearing is damaged. Construct the horizontal line of the threshold. The intersection of the horizontal line of the threshold and the trend quantitative health index curve is the remaining service life of the bearing.
2. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step A, the formula for the BiLSTM network is as follows: in, and The outputs of the forward and backward LSTMs are y, respectively. t is the final output value of the hidden layer; f(·) and g(·) are the corresponding activation functions.
3. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1 or 2, characterized in that: The LSTM formula is as follows: f t =σ(W xf x t +W hf h t-1 +b f ) i t =σ(W xi x t +W hi h t-1 +b i ) o t =σ(W xo x t +W ho h t-1 +b o ) in, For element-wise multiplication of vectors, x t h is the input of the LSTM unit at runtime t. t-1 It is the output of the LSTM unit at runtime t-1, h t It is the output of the LSTM unit at runtime t, C t-1 It is the cell state at runtime t-1, C t It is the cell state at runtime t. It is the temporary cell state at runtime t, i t f t and o t These are the output values of the input gate, forget gate, and output gate, respectively, b f b i b c and b o These are the bias terms for the forget gate, input gate, cell state, and output gate, respectively. xf W xi W xc and W xo These are the input layer x t and the hidden layer h of the LSTM unit t The weight values W between runtime t. hf W hi W hc and W ho These are the hidden layer weights of the LSTM units between runtime t and t-1.
4. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step A, the KAN network formula is as follows: in It is a B-spline function that connects the i-th node in the l-th layer to the j-th node in the (i+1)-th layer.
5. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step D, the original vibration signal is converted using a fast Fourier transform, and the formula is as follows: X fred =FFT(x time ) (4)。 6. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step D, the formula for smoothing and correcting the trend-based quantitative health index is as follows: Where ω is the width of the sliding window and t is the running time.
7. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step D, the cubic polynomial fitting formula is as follows: y=a3t 3 +a2t 2 +a1t+a0 (6) Where a3, a2, a1, a0 are the undetermined coefficients of the cubic polynomial, y is the bearing condition value, and t is the running time.
8. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 1, characterized in that: In step B, the training process of the BiLSTM-KAN fusion network is as follows: The training set is composed of raw vibration signal data of some rolling bearings operating under different working conditions selected from the common dataset. Then, the time domain signal of the training set is transformed into the frequency domain signal using fast Fourier transform. The Fast Fourier Transform (FFT) is expressed as follows: X fred =FFT(x time ) (4) Then, the frequency domain signal is normalized by range, and a supervised training method is used. The input-output pair is represented as follows: The formula is as follows: in This represents the N-dimensional input feature vector of a bearing under a certain operating condition at the current moment; while x normalized-t ∈[0,1] represents the percentage of lifespan at the corresponding moment; The normalized training set obtained after processing with Formula 7 is then input into the BiLSTM-KAN fusion network for training, resulting in the trained BiLSTM-KAN fusion network.
9. The bearing remaining service prediction method based on BiLSTM-KAN as described in claim 8, characterized in that: The training process is set as follows: the mean squared error (MSE) is used as the loss function, the Adam optimizer updates the network parameters, the learning rate is set to 0.001, and the batch size is 64.