Bearing life prediction method based on adaptive physical information and kan network
By combining adaptive physical information and KAN network, a hybrid prediction model is constructed, which solves the model defects and spectral bias problems in bearing remaining life prediction and achieves high-precision and robust life prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHENYANG UNIV
- Filing Date
- 2026-03-30
- Publication Date
- 2026-06-30
AI Technical Summary
Existing technologies for predicting the remaining life of bearings suffer from model defects and spectral bias. Traditional deep learning models struggle to capture high-frequency fault impacts, and physical models cannot adapt to time-varying material properties, resulting in insufficient prediction accuracy and interpretability.
By combining adaptive physical information with KAN networks, a hybrid prediction model is constructed by identifying time-varying physical parameters in real time and capturing high-frequency random fluctuations using Kolmogorov-Arnold networks. This model includes parameter estimation, physical mechanisms, and residual correction branches, which addresses model defects and spectral biases.
It achieves high-precision remaining life prediction with uncertainty quantification, improves prediction accuracy and robustness, and adapts to bearing degradation processes under complex working conditions.
Smart Images
Figure CN122309985A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical fault diagnosis and predictive maintenance technology, specifically relating to a bearing life prediction method based on adaptive physical information and KAN network. Background Technology
[0002] As the joints of rotating machinery, the operating condition of rolling bearings directly affects the reliability and safety of the entire mechanical system. Predicting the remaining life (RUL) of bearings using condition monitoring data has become a key technology for ensuring industrial safety and shifting from "reactive maintenance" to "predictive maintenance." Because bearings primarily bear alternating loads, they are highly susceptible to fatigue failure; therefore, accurately predicting their remaining life is crucial for avoiding catastrophic accidents and reducing total life-cycle costs.
[0003] In recent years, data-driven methods, represented by deep learning, have made significant progress in the field of Prognostics and Health Management (PHM). While models such as Long Short-Term Memory (LSTM) networks and Transformers excel at capturing time dependencies, they are typically based on Multilayer Perceptron (MLP) architectures, which inherently suffer from spectral bias. Mathematically, MLPs tend to preferentially fit low-frequency functions, making it difficult to capture high-frequency random fluctuations. Since bearing degradation signals are often a superposition of low-frequency trends and high-frequency fault impacts, traditional deep learning models are prone to "oversmoothing," resulting in the loss of residual details containing rich fault information. Furthermore, these "black box" models lack intermediate inference processes, making it difficult to meet the high-reliability decision-making requirements of industrial settings.
[0004] On the other hand, while physical model-based methods (such as the Paris-Erdogan crack propagation law) offer good interpretability, they often suffer from model deficiency. Traditional physical models typically assume that material constants, such as the fracture coefficient and geometric parameters, remain constant throughout the entire lifespan. However, in real-world industrial scenarios, material properties dynamically degrade with the accumulation of fatigue damage. Static physical equations cannot track this time-varying characteristic, leading to significant discrepancies between predicted results and actual values during accelerated failure stages, and making them unsuitable for adapting to complex degradation processes under varying operating conditions. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention proposes a bearing life prediction method based on adaptive physical information and KAN networks. This method uses an adaptive evolution mechanism of physical parameters to identify time-varying physical parameters in real time, thus solving the model defects of traditional fatigue crack propagation models. In addition, a Kolmogorov-Arnold network is used to model the local residuals in the degradation process, and a learnable spline activation function on the edge is used to capture high-frequency random fluctuations, overcoming the spectral bias problem of traditional deep learning models. This achieves high-precision remaining life prediction with uncertainty quantification.
[0006] In a first aspect, the present invention provides a bearing life prediction method based on adaptive physical information and KAN network, comprising the following steps:
[0007] The full life cycle vibration signal of the rolling bearing was obtained, and the time series samples were extracted using the sliding window method. The sample data was then normalized to obtain normalized time series sample data.
[0008] A prediction model is constructed, including a parameter estimation branch, a physical mechanism branch, and a residual correction branch. Time-varying physical parameters are extracted from normalized time-series sample data through the parameter estimation branch, and global physical trend components are calculated based on the time-varying physical parameters through the physical mechanism branch. Local residual components are calculated based on normalized time-series sample data through the residual correction branch.
[0009] The global physical trend component and the local residual component are linearly superimposed to obtain the remaining lifetime prediction value and uncertainty index.
[0010] A hybrid loss function is constructed, and the prediction model is trained end-to-end using the gradient descent algorithm. After saving the optimal parameters, the trained prediction model is obtained. The remaining life of the target rolling bearing is then predicted based on the trained prediction model.
[0011] Furthermore, the parameter estimation branch includes physical parameter estimators;
[0012] The specific method for extracting time-varying physical parameters from normalized time series sample data through parameter estimation branch is as follows:
[0013] Normalized time series sample data are input into the parameter estimation branch to extract features; based on the extracted features, time-varying physical parameters are extracted using a physical parameter estimator, including material constants and geometric parameters.
[0014] Furthermore, the specific method for calculating the global physical trend component based on time-varying physical parameters through the physical mechanism branch is as follows:
[0015] Time-varying physical parameters are input into the physical mechanism branch, and the global physical trend component is calculated based on the discretized crack propagation law.
[0016] Furthermore, the residual correction branch includes the KAN network;
[0017] The specific method for calculating local residual components based on normalized time series sample data using residual correction branches is as follows:
[0018] The normalized time series sample data is input into the residual correction branch, and the activation function of the inter-layer mapping of the KAN network is set as a linear combination of the basis function and the learnable spline function.
[0019] After passing through the KAN network, the local residual components of the residual correction branch output are obtained.
[0020] Furthermore, the uncertainty index includes the mean and variance of the remaining lifetime predictions, and the variance of the remaining lifetime predictions is used as the uncertainty confidence interval.
[0021] Based on Bayesian inference strategy, normalized time series sample data are analyzed. The next random forward propagation is calculated. The mean and variance of the remaining lifetime predictions obtained from the random forward propagation are used as uncertainty indicators to quantify the uncertainty of the remaining lifetime predictions.
[0022] Furthermore, the hybrid function is constructed based on mean square error, physical constraints, and monotonicity constraints.
[0023] Secondly, this application proposes an electronic device, including: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the bearing life prediction method based on adaptive physical information and KAN network.
[0024] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the aforementioned bearing life prediction method based on adaptive physical information and a KAN network.
[0025] Fourthly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the aforementioned bearing life prediction method based on adaptive physical information and KAN network.
[0026] The beneficial effects of adopting the above technical solution are as follows: The bearing life prediction method based on adaptive physical information and KAN network provided by this invention constructs a prediction model, including a parameter estimation branch, a physical mechanism branch, and a residual correction branch. The parameter estimation branch of this invention solves the model defects through an adaptive physical parameter evolution mechanism. The parameter estimator enables the material constants and geometric parameters in the crack propagation law to evolve dynamically over time, accurately reflecting the degradation process of the material's fatigue resistance and solving the problem of inaccurate prediction in the accelerated failure stage of the static physical model. The physical mechanism branch acts as an anchor point under complex working conditions. Under complex working conditions such as high speed and low load, when the feature extraction capability of the pure data-driven model decreases, the physical branch of this invention can constrain the prediction trajectory to not deviate from the physical law, ensuring the model's strong robustness. The introduction of KAN network in the residual correction branch effectively overcomes spectral bias. KAN network utilizes learnable B-spline activation functions on the edges, which can efficiently approximate the high-frequency nonlinear residuals that are difficult for traditional multilayer perceptrons to capture, effectively solving the oversmoothing problem and significantly improving prediction accuracy. Attached Figure Description
[0027] Figure 1 Flowchart of the bearing life prediction method based on adaptive physical information and KAN network provided in Embodiment 1 of the present invention;
[0028] Figure 2 The time-frequency characteristic diagram of the rolling bearing vibration signal provided in Embodiment 1 of the present invention;
[0029] Figure 3 The adaptive physical parameters evolution curves over time provided in Embodiment 1 of the present invention include (a) the material constant evolution curve over time and (b) the geometric parameters evolution curve over time.
[0030] Figure 4 The schematic diagram of the global-local decoupling mechanism provided in Embodiment 1 of the present invention is shown in which (a) is the end-to-end prediction result output by the prediction model, (b) is the curve of the global physical trend component change, and (c) is the curve of the local residual component change.
[0031] Figure 5 A schematic diagram of three-dimensional visualization of latent feature manifolds provided in Embodiment 1 of the present invention;
[0032] Figure 6 The multi-performance index evaluation radar chart provided in Embodiment 1 of the present invention includes (a) a performance index evaluation radar chart of different models under working condition 1, (b) a performance index evaluation radar chart of different models under working condition 2, and (c) a performance index evaluation radar chart of different models under working condition 3.
[0033] Figure 7The remaining lifetime prediction trajectory comparison chart based on different models provided in Embodiment 1 of the present invention;
[0034] Figure 8 The robustness assessment heatmap for remaining life prediction under different operating conditions provided in Embodiment 1 of the present invention;
[0035] Figure 9 The remaining lifetime prediction results under different failure modes provided in Embodiment 1 of the present invention are shown in the following diagrams: (a) is a diagram of the remaining lifetime prediction results under failure mode 1, (b) is a diagram of the remaining lifetime prediction results under failure mode 2, and (c) is a diagram of the remaining lifetime prediction results under failure mode 3.
[0036] Figure 10 The schematic diagram of the Bayesian uncertainty quantification result provided in Embodiment 1 of the present invention is shown in which (a) is a schematic diagram of probability degradation trend prediction and (b) is a schematic diagram of the comparison between deterministic and probabilistic prediction. Detailed Implementation
[0037] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.
[0038] Example 1:
[0039] A bearing life prediction method based on adaptive physical information and KAN network, such as Figure 1 As shown, it includes the following steps:
[0040] S1 acquires the full-life-cycle vibration signal of the rolling bearing, uses the sliding window method to extract time series sample data, and performs normalization processing on the time series sample data;
[0041] S2 decomposes the problem of predicting the remaining life of rolling bearings into the problem of obtaining deterministic global physical trend components and stochastic local residual components. It adopts a global-local decoupling strategy to construct the prediction model API-KAN. The prediction model API-KAN includes a parameter estimation branch, a physical mechanism branch, and a residual correction branch. The parameter estimation branch is used to extract time-varying physical parameters from normalized time-series sample data. The physical mechanism branch is used to calculate the global physical trend components based on the time-varying physical parameters, capturing the deterministic damage accumulation trend and solving the problem of poor interpretability of pure data-driven models. The residual correction branch is used to calculate local residual components based on normalized time-series sample data, using a unique spline activation function to capture high-frequency random residuals that cannot be described by physical models, thereby solving the model defects and spectral bias problems existing in traditional methods.
[0042] S3 extracts features from normalized time-series sample data through the parameter estimation branch, adaptively identifies time-varying physical parameters from the extracted features through the physical mechanism branch, and calculates global physical trend components based on the discretized crack propagation law.
[0043] S4 inputs normalized time series sample data into the residual correction branch and outputs local residual components; the residual correction branch includes a KAN network, which uses a learnable B-spline activation function to fit high-frequency details;
[0044] S5 linearly superimposes the global physical trend component and the local residual component to obtain the final remaining lifetime prediction; it adopts the Monte Carlo Dropout (MC Dropout) strategy as a specific implementation of Bayesian inference to quantify the uncertainty of the prediction;
[0045] S6 constructs a hybrid loss function that includes physical constraints and monotonicity constraints, uses the gradient descent algorithm to train the API-KAN prediction model end-to-end, saves the optimal parameters to obtain the trained prediction model, and uses the trained prediction model to predict the remaining life of the target rolling bearing.
[0046] The parameter estimation branch of S3 includes a physical parameter estimator; this embodiment describes the crack propagation rate based on the traditional Paris law, discretizes it, and introduces a time variable to address the model defects of static physical models. The specific process of S3 is as follows:
[0047] Normalized time series sample data The parameter estimation branch of the input prediction model API-KAN extracts features. Using a physical parameter estimator The time-varying physical parameters, including material constants and geometric parameters, are output as follows:
[0048] ;
[0049] in, For material constants, For geometric parameters, The function is a physical constraint used to ensure that time-varying physical parameters are non-negative. These are the network weights for the physical parameter estimator.
[0050] The identified time-varying physical parameters are input into the physical mechanism branch, and the global physical trend component is calculated based on the discretized crack propagation law. As shown in the formula below:
[0051] ;
[0052] In the formula, This represents the critical failure crack size of the bearing. for The equivalent crack size at any given moment. This is a geometric factor. This step allows the physical model to be dynamically adjusted over time, accurately reflecting the degradation process of the material's fatigue resistance.
[0053] The residual correction branch of S4 includes a KAN network to overcome the spectral bias of traditional multilayer perceptrons (MLPs). The input to the residual correction branch is normalized time-series sample data. .
[0054] The core feature of the KAN network is that it sets a learnable nonlinear activation function (B-spline function) on the connection weights (i.e., edges) between neurons, rather than on the neuron nodes as in the traditional multilayer perceptron (MLP). This structure enables the KAN network to efficiently capture high-frequency random residuals.
[0055] Set the activation function for inter-layer mapping in the KAN network. For a linear combination of basis functions and learnable spline functions, the formula is as follows:
[0056] ;
[0057] In the formula, and For trainable scaling factors, Use the basis activation function; The number of grid intervals, For B-spline basis functions, For control coefficients;
[0058] The KAN network updates the control coefficients. This is used to fit the high-frequency nonlinear characteristics in the residuals. After calculation by the KAN network, the final output of the residual correction branch is the predicted local residual component. .
[0059] The specific method for step S5 is as follows:
[0060] First, the global physical trend components and local residual components Linear superposition is performed to obtain the final predicted remaining lifetime value. The calculation formula is:
[0061] ;
[0062] To quantify the uncertainty of prediction, this embodiment employs the Monte Carlo Dropout (MC Dropout) strategy as a specific implementation of Bayesian inference. Dropout is kept enabled during the test inference phase, and the normalized time-series sample data is processed... The next random forward propagation is calculated. The mean of the remaining lifetime predictions obtained from the random forward propagation As shown in the formula below:
[0063] ;
[0064] in, For the first The remaining lifetime prediction value obtained from the first forward propagation;
[0065] Calculate the variance of the remaining life prediction. The uncertainty confidence interval is shown in the following formula:
[0066] ;
[0067] in, These are learnable parameters used to characterize the inherent random noise introduced by the data acquisition environment and sensor accuracy limitations.
[0068] The specific method for S6 to perform end-to-end training of the API-KAN prediction model is as follows:
[0069] Constructing a hybrid loss function The prediction model API-KAN is optimized end-to-end using the following formula:
[0070] ;
[0071] in, The mean square error of the remaining lifetime prediction; , These are the weighting coefficients; For physical constraints, The monotonicity constraint is used to penalize time steps in the physical branch output that violate the principle of irreversible degradation. In this embodiment, the monotonicity constraint... Defined as:
[0072] ;
[0073] This embodiment selects the accelerated life dataset of rolling bearings from Xi'an Jiaotong University (XJTU-SY) as the experimental object to verify the effectiveness of the proposed method. The experimental platform for collecting the accelerated life dataset of rolling bearings from Xi'an Jiaotong University includes an AC motor, a hydraulic loading system, a speed controller, and a data acquisition system. The vibration signal sampling frequency is 25.6 kHz, with sampling every 1 minute and each sampling duration of 1.28 seconds. In this embodiment, 15 rolling bearings (LDK UER204) under 3 different working conditions were selected for full life cycle testing. The experimental cutoff condition was that the vibration amplitude exceeded 20g. The typical time-frequency characteristics of the vibration signal of this dataset are as follows: Figure 2 As shown in Table 1, the experimental parameters for selecting the bearing are listed respectively. The first two bearings under each working condition are used as the training set, and the remaining three bearings are used as the test set to evaluate the generalization ability of the model.
[0074] Table 1. Experimental parameter settings under different working conditions;
[0075]
[0076] The normalized vibration signal samples are extracted using a sliding window method and input into the API-KAN prediction model. First, deep features are extracted through a shared convolutional neural network encoder, and then input into the parameter estimation branch and residual correction branch respectively. In the parameter estimation branch, the physical parameter estimator outputs time-varying physical parameters, including material constants and geometric parameters. The evolution curves of the time-varying physical parameters over time are shown below. Figure 3 As shown, (a) is a graph showing the evolution of material constants over time, and (b) is a graph showing the evolution of geometric parameters over time. The principle of the global-local decoupling mechanism in this embodiment is as follows: Figure 4 As shown, (a) is the end-to-end prediction result, (b) is the global physical trend component variation curve, and (c) is the local residual component variation curve. Figure 4 The evolution curves of the physical parameters revealed that the identified geometric parameter m(t) exhibits a nonlinear increasing trend over time, which is consistent with the physical fact that the crack propagation rate gradually accelerates during the fatigue process of metallic materials, proving that the model successfully captured the physical degradation law. Subsequently, based on these time-varying parameters, the global physical trend that conforms to fracture mechanics constraints was calculated using the discretized crack propagation law.
[0077] Next, step S4 is performed to compensate for high-frequency residuals. A Kolmogorov-Arnold network (KAN) branch is constructed. Because the KAN network employs the learnable spline activation function described in the invention, it can efficiently capture high-frequency random fluctuations ignored by the physical branches. Compared to traditional multilayer perceptrons, this structure exhibits stronger fitting ability when processing non-stationary residual signals, effectively overcoming the oversmoothing phenomenon of the prediction results.
[0078] Finally, steps S5 and S6 were performed for model training and uncertainty assessment. The experiments were implemented using the MATLAB DeepLearning Toolbox, and the prediction model structure parameters are shown in Table 2. The physics branch used a 3-layer CNN for feature extraction, while the KAN branch had a grid size of 5 and a spline order of 3. During training, the Adam optimizer was used to update the network weights by minimizing a mixed loss function that includes physical constraints. In the testing phase, a Monte Carlo Dropout strategy was applied to calculate the prediction mean and confidence interval, thus providing a reliable lifetime estimate. Furthermore, the 3D visualization results of the latent feature manifold extracted by the prediction model are shown below. Figure 5 As shown, the topological continuity of the features is verified.
[0079] Table 2. Prediction model API-KAN network structure and parameters;
[0080]
[0081] The trained API-KAN model was applied to a test set. To evaluate its predictive performance, it was compared with a pure physics model (Paris Law), a Transformer model, and a pure KAN model. The prediction results of different methods (expressed as coefficients of determination) are presented. The root mean square error (RMSE) is used as an indicator, as shown in Table 3. Figure 6 As shown, the radar charts for evaluating multiple performance indicators under different operating conditions are as follows: (a) is the radar chart for evaluating the performance indicators of different models under operating condition 1; (b) is the radar chart for evaluating the performance indicators of different models under operating condition 2; and (c) is the radar chart for evaluating the performance indicators of different models under operating condition 3. A comparison chart of the remaining lifetime prediction trajectories obtained based on different models is shown below. Figure 7 As shown in the figure, the robustness assessment heatmap for remaining life prediction under different operating conditions is as follows: Figure 8 As shown.
[0082] Table 3. Comparison of prediction performance results of different methods;
[0083]
[0084] As can be seen from Table 3, the API-KAN method proposed in this embodiment works under all operating conditions. All exceeded 0.98, and the RMSE was significantly lower than the comparison method. Especially under the complex conditions of operating condition 3 (high speed, low load), the traditional data-driven model (Transformer) showed superior performance. The accuracy dropped to 0.8850, while the present invention still maintains a high accuracy of 0.9890. For example... Figure 7The comparison of lifetime prediction curves shown demonstrates that the method in this embodiment not only accurately tracks the early degradation trend but also closely matches the actual lifetime curve in the later accelerated failure stage, without significant hysteresis or oversmoothing, thus verifying the superiority of the method. The specific prediction results of this embodiment under different failure modes are as follows: Figure 9 As shown, the Bayesian uncertainty quantification results are as follows: Figure 10 As shown, the robustness and reliability of the model under complex operating conditions are further demonstrated. This embodiment improves decision reliability through Bayesian uncertainty quantification, and the integrated Monte Carlo Dropout strategy can output a 95% confidence interval for the prediction results, transforming a single point estimate into a probability distribution, providing a visualized risk assessment basis for condition-based maintenance of industrial equipment.
[0085] In summary, the experiments demonstrate that the model proposed in this embodiment outperforms existing pure physical models and mainstream deep learning models in terms of the coefficient of determination and root mean square error in predicting the remaining life of rolling bearings. This indicates that the model combines high accuracy, strong robustness, and physical interpretability, and can effectively solve the prediction problem of such complex nonlinear degradation processes.
[0086] Example 2:
[0087] This embodiment proposes an electronic device, including: one or more processors, and a memory for storing instructions. When the instructions are executed by the one or more processors, the one or more processors execute the bearing life prediction method based on adaptive physical information and KAN network.
[0088] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the bearing life prediction method based on adaptive physical information and KAN network as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.
[0089] The processor is used to execute all or part of the steps in the bearing life prediction method based on adaptive physical information and KAN network as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.
[0090] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the bearing life prediction method based on adaptive physical information and KAN network described in the above embodiments.
[0091] Example 3:
[0092] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.
[0093] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the bearing life prediction method based on adaptive physical information and KAN network described in the various embodiments of this application.
[0094] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) app stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the bearing life prediction method based on adaptive physical information and KAN networks described above.
[0095] Example 4:
[0096] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned bearing life prediction method based on adaptive physical information and KAN network.
[0097] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.
[0098] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.
[0099] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.
Claims
1. A bearing life prediction method based on adaptive physical information and KAN network, characterized in that, Includes the following steps: The full life cycle vibration signal of the rolling bearing was obtained, and the time series samples were extracted using the sliding window method. The sample data was then normalized to obtain normalized time series sample data. Construct a prediction model, including a parameter estimation branch, a physical mechanism branch, and a residual correction branch; The parameter estimation branch extracts time-varying physical parameters from normalized time-series sample data, the physical mechanism branch calculates global physical trend components based on time-varying physical parameters, and the residual correction branch calculates local residual components based on normalized time-series sample data. The global physical trend component and the local residual component are linearly superimposed to obtain the remaining lifetime prediction value and uncertainty index. A hybrid loss function is constructed, and the prediction model is trained end-to-end using the gradient descent algorithm. After saving the optimal parameters, the trained prediction model is obtained. The remaining life of the target rolling bearing is then predicted based on the trained prediction model.
2. The bearing life prediction method based on adaptive physical information and KAN network according to claim 1, characterized in that, The parameter estimation branch includes the physical parameter estimator; The specific method for extracting time-varying physical parameters from normalized time series sample data through parameter estimation branch is as follows: Normalized time series sample data are input into the parameter estimation branch to extract features; based on the extracted features, time-varying physical parameters are extracted using a physical parameter estimator, including material constants and geometric parameters.
3. The bearing life prediction method based on adaptive physical information and KAN network according to claim 2, characterized in that, The specific method for calculating the global physical trend component based on time-varying physical parameters through physical mechanism branches is as follows: Time-varying physical parameters are input into the physical mechanism branch, and the global physical trend component is calculated based on the discretized crack propagation law.
4. The bearing life prediction method based on adaptive physical information and KAN network according to claim 1, characterized in that, The residual correction branch includes the KAN network; The specific method for calculating local residual components based on normalized time series sample data using residual correction branches is as follows: The normalized time series sample data is input into the residual correction branch, and the activation function of the inter-layer mapping of the KAN network is set as a linear combination of the basis function and the learnable spline function. After passing through the KAN network, the local residual components of the residual correction branch output are obtained.
5. The bearing life prediction method based on adaptive physical information and KAN network according to claim 1, characterized in that, The uncertainty index includes the mean and variance of the remaining life prediction values, and the variance of the remaining life prediction values is used as the uncertainty confidence interval. Based on Bayesian inference strategy, normalized time series sample data are analyzed. The next random forward propagation is calculated. The mean and variance of the remaining lifetime predictions obtained from the random forward propagation are used as uncertainty indicators to quantify the uncertainty of the remaining lifetime predictions.
6. The bearing life prediction method based on adaptive physical information and KAN network according to claim 1, characterized in that, The hybrid function is constructed based on mean square error, physical constraints, and monotonicity constraints.
7. An electronic device, characterized in that, The method includes one or more processors and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the bearing life prediction method based on adaptive physical information and KAN network as described in any one of claims 1 to 6.
8. A computer-readable storage medium, characterized in that, The device stores executable instructions that, when executed, cause the processor to perform the bearing life prediction method based on adaptive physical information and KAN network as described in any one of claims 1 to 6.
9. A computer program product, characterized in that, Includes a computer program or instructions that, when executed by a processor, implement the bearing life prediction method based on adaptive physical information and KAN network as described in any one of claims 1 to 6.