Bearing fault diagnosis method based on feature mode decomposition and heterogeneous model fusion

Abstract

The invention discloses a bearing fault diagnosis method based on feature mode decomposition and heterogeneous model fusion, and belongs to the technical field of mechanical fault diagnosis. An original vibration signal of the rolling bearing is collected; independent of any bearing geometric parameter or fault characteristic frequency information, a finite impulse response (FIR) filter is iteratively optimized to maximize a correlation kurtosis (CK) value, and a plurality of intrinsic mode functions (IMF) are adaptively decomposed; selecting first M IMFs with the highest CK value, extracting time domain, frequency domain and nonlinear complexity features of the IMFs, generating high-order derivative features by adopting depth feature synthesis DFS, and constructing an enhanced fusion feature vector; and finally, inputting a stacked integrated classifier consisting of six types of heterogeneous basic learners and an XGBoost element learner, and outputting a fault diagnosis result. According to the method, high-precision and high-robustness diagnosis can still be realized under the working conditions of speed change, strong noise and weak faults.

Description

Technical Field

[0001] This invention relates to the field of mechanical fault diagnosis technology, and in particular to a bearing fault diagnosis method based on characteristic mode decomposition and heterogeneous model fusion. Background Technology

[0002] In the field of intelligent fault diagnosis of rolling bearings, existing technologies mainly rely on envelope analysis, empirical mode decomposition, or deep learning models to process vibration signals. However, these methods generally suffer from three major bottlenecks: First, they are highly dependent on prior information about fault characteristic frequencies or rotational speeds, and their performance deteriorates sharply under variable speed conditions or unknown equipment parameters. Second, traditional mode decomposition methods, such as EMD, are susceptible to noise interference, resulting in mode aliasing and making it difficult to effectively separate weak fault impact components. Third, single models, such as SVM or CNN, have limited generalization capabilities and insufficient robustness under complex conditions such as strong noise and complex faults. Therefore, there is an urgent need for a diagnostic method that requires no prior knowledge, can adaptively extract fault-sensitive features, and possesses high discriminative power.

[0003] Existing technologies, such as the Chinese invention patent with publication number CN118395336B, employ intelligent optimization algorithms to improve VMD decomposition of vibration signals and combine it with CNN-LSTM networks for fault prediction. While this improves diagnostic accuracy to some extent, it still requires pre-setting the number of modes or relying on frequency domain separation criteria, essentially failing to escape the implicit dependence on prior signal characteristics. More importantly, this method cannot directly and adaptively extract sensitive components that highly match the physical mechanism of the fault from the original vibration signal without any fault characteristic frequency or rotational speed information. Furthermore, its end-to-end deep model lacks interpretable multi-domain feature support, making it difficult to effectively distinguish between weak or complex faults.

[0004] Therefore, there is an urgent need for a decomposition mechanism that is driven by the intrinsic characteristics of the fault, requires no prior parameters, and can adaptively focus on fault-sensitive information, combined with a multi-heterogeneous model fusion strategy with high discriminative power and interpretability, so as to achieve bearing fault diagnosis with high robustness and high accuracy. Summary of the Invention

[0005] In view of this, this invention proposes a bearing fault diagnosis method based on Eigenmode Decomposition and heterogeneous model fusion. This solution addresses the industry challenge of drastically reduced diagnostic performance under conditions of no prior knowledge, variable speed, and strong interference by employing a technical approach that combines CK-driven Eigenmode Decomposition (FMD), multi-domain fusion feature engineering, deep feature synthesis (DFS) enhancement, and multi-heterogeneous model fusion.

[0006] This invention provides a bearing fault diagnosis method based on characteristic mode decomposition and heterogeneous model fusion, comprising the following steps: S1 collects the raw vibration signals during the operation of the rolling bearing; S2 does not rely on any bearing geometric parameters or fault characteristic frequency information. It uses the correlation kurtosis CK as the optimization objective function and iteratively updates the coefficients of the finite impulse response (FIR) filter to adaptively extract multiple intrinsic mode functions (IMFs) from the original vibration signal. The CK is used to simultaneously characterize the periodic impact and transient impulse caused by the fault. S3 selects the top M IMFs with the highest CK values ​​as the dominant modes, where M≥1; S4 extracts time-domain features, frequency-domain features, and nonlinear complexity features for each dominant mode to construct a multi-domain feature vector; the multi-domain feature vector is input into the deep feature synthesis (DFS) module to generate derived features, and the derived features are concatenated with the original multi-domain features to form an enhanced fusion feature vector; S5 inputs the multi-domain fusion feature vector into the heterogeneous stacked ensemble classifier and outputs the bearing fault diagnosis result; wherein, the heterogeneous stacked ensemble classifier includes multiple heterogeneous basic learners in the first layer and a meta-learner in the second layer, the multiple heterogeneous basic learners output fault category probabilities in parallel, and the meta-learner outputs the final diagnosis result after nonlinear fusion based on the probabilities.

[0007] Furthermore, the formula for calculating CK is as follows: , in Peak factor; The filtered signal The original vibration signal, and satisfies h(t) is an FIR filter. Original vibration signal The output after convolution with the FIR filter h(t); The fault period is the number of sampling points corresponding to the fault characteristic frequency for adaptive estimation. ,in Ts is the fault frequency of the inner / outer ring, etc., and Ts is the sampling period. It is a fourth-order moment; It is the second moment, and its mean square value.

[0008] Furthermore, the time-domain features include statistical moments, energy indices, impulsivity indices, and envelope correlation features; the statistical moments include mean, variance, skewness, and kurtosis; the energy indices include root mean square and sum of absolute values; the impulsivity indices include peak factor, waveform factor, and shape factor; and the envelope correlation features include envelope mean, impact interval, and difference in amplitude between two impacts. The frequency domain features are obtained by performing a Fast Fourier Transform (FFT) on the dominant mode, including the dominant frequency, harmonic ratio, spectral statistics, and the energy of the four sub-bands; the spectral statistics include the mean and standard deviation. The nonlinear complexity features include Shannon entropy, discrete entropy, fractal dimension, and Hearst exponent.

[0009] Furthermore, the deep feature synthesis (DFS) module generates derived features with fault-detection capabilities in the following manner: For any two primitive features from different domains and And satisfy Calculate its normalized combination: , in This indicates operations involving multiplication, ratio, or difference. To prevent division by zero constant; Features in the time domain; Frequency domain characteristics; It is characterized by non-linear complexity. Alternatively, local statistics can be calculated within a sliding window w for a single-class feature sequence; The concatenation of the derived features with the original multi-domain features significantly improves the classifier's ability to distinguish between weak and complex faults.

[0010] Furthermore, the multiple heterogeneous basic learners include random forest, support vector machine, K-nearest neighbors, Naive Bayes, decision tree and LightGBM, whose inductive biases are mutually orthogonal, covering multiple decision paradigms such as rule, margin, probability and neighborhood.

[0011] Furthermore, the meta-learner is an XGBoost regressor, and the input features are formed by concatenating the probability vectors output by each heterogeneous basic learner. The class probability vectors output by each basic learner are weighted and fused, and the logistic loss function is used during training to perform soft label fusion for multiple types of faults.

[0012] Furthermore, the process of iteratively updating the coefficients of the finite impulse response (FIR) filter is as follows: in each round of iterative optimization, the correlation kurtosis CK of the current filter output signal is calculated, and the filter parameters are adjusted using at least one of the gradient descent method, particle swarm optimization (PSO) algorithm, or genetic algorithm, so that the CK value gradually increases until convergence.

[0013] Furthermore, the objective function for the iterative optimization of the FIR filter is: , in Let be the coefficient vector of the k-th FIR filter, used to extract specific modes from the original signal or residual signal. Let K be the adaptively estimated fault period corresponding to the k-th mode, where K is the total number of extracted modes, and satisfying the following conditions: The goal is to maximize the sum of the correlation kurtosis (CK) of all K modes.

[0014] Furthermore, the present invention also provides a bearing fault diagnosis system based on eigenmode decomposition and heterogeneous model fusion, comprising: The system includes a vibration signal acquisition module, an FMD adaptive decomposition module, a multi-domain feature engineering module, a heterogeneous stacked integrated classification module, and a result output module. The FMD adaptive decomposition module is configured to perform CK-driven FIR filter optimization, and the heterogeneous stacked integrated classification module is configured to run a two-level stacked architecture of six heterogeneous basic learners and XGBoost meta-learners.

[0015] The present invention has the following advantages over the prior art: First, in the signal decomposition stage, this invention eliminates any dependence on bearing geometric parameters, rotational speed, or fault characteristic frequencies, using the correlation kurtosis (CK) as the optimization target to drive the adaptive iteration of the finite impulse response (FIR) filter. Since CK can simultaneously characterize the periodic impact and transient impulsivity caused by the fault, this method can directly and accurately extract the most discriminative fault-sensitive components from the original vibration signal, effectively overcoming the problems of mode aliasing, noise interference, and parameter presets caused by the lack of physical guidance in traditional EMD or VMD methods. It can even stably separate weak fault features under variable speed and high-noise operating conditions.

[0016] Secondly, at the feature construction level, this invention integrates three types of multi-dimensional features: time domain, frequency domain, and nonlinear complexity. Furthermore, it introduces deep feature synthesis (DFS) technology, which generates derived features with clear physical meaning by performing high-order combination operations (such as product, ratio, and moving statistics) on features from different domains. This enhanced fusion feature vector not only comprehensively characterizes the energy, spectral structure, and dynamic complexity of faults, but also significantly improves the ability to distinguish between early weak faults and complex faults, enhancing the discriminative power and robustness of the model input.

[0017] Finally, in the classification decision-making stage, this invention designs a heterogeneous stacked integrated architecture. The first layer integrates six mutually orthogonal basic learners with inductive biases in parallel, covering multiple decision paradigms such as rule-based, margin-based, probability-based, and neighborhood-based models. The second layer uses an XGBoost meta-learner to nonlinearly weight and fuse the probabilities output by each basic model. This strategy effectively reduces the bias and variance of individual models, improving the overall generalization ability and anti-interference performance of the system while ensuring high accuracy, and providing a certain degree of interpretability support for fault diagnosis results.

[0018] In summary, this invention achieves intelligent bearing fault diagnosis that requires no prior knowledge, is highly accurate and robust, and has engineering application value. It effectively solves the core bottleneck of insufficient diagnostic performance of existing technologies under unknown working conditions, strong noise, and weak fault scenarios. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 The FMD-HMF framework of this invention is used on the CWRU dataset; Figure 3 The FMD-HMF framework of this invention is used in the PU dataset; Figure 4 The FMD-HMF framework of this invention is used on the uOttawa dataset; Figure 5 The FMD-HMF framework of this invention is used in the JNU dataset. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] Traditional spectral analysis methods (such as Fast Fourier Transform, FFT) are based on the assumption of signal stationarity, making it difficult to effectively capture the transient pulse components generated by bearing faults. While time-frequency analysis techniques such as wavelet transform and Empirical Mode Decomposition (EMD) possess adaptive decomposition capabilities, they are prone to mode aliasing and end-effect artifacts. Variational Mode Decomposition (VMD) provides a more rigorous mathematical framework, but its performance is highly sensitive to manually set parameters (especially the number of modes and penalty factor), limiting its robustness in unknown industrial scenarios. Although several hybrid methods have recently shown potential, they often fail to simultaneously optimize the inherent impulsive and periodic characteristics of bearing fault features.

[0023] A promising alternative is Feature Mode Decomposition (FMD). Unlike EMD or VMD, FMD designs adaptive finite impulse response (FIR) filters by maximizing the correlation kurtosis (CK), an explicit quantification of the periodic and impulsive co-occurrence of fault-related components. This allows FMD to effectively isolate fault-sensitive modes without prior knowledge of the defect's characteristic frequencies, a significant advantage in real-world industrial environments where operating speeds and fault types are often unpredictable and variable. However, existing FMD-based research primarily relies on shallow classifiers or finite feature sets, thus failing to fully exploit its diagnostic potential.

[0024] In the field of machine learning, although deep learning models such as CNN-LSTM and attention-based networks have achieved high diagnostic accuracy on benchmark datasets, they often suffer from poor interpretability, over-reliance on large labeled datasets, and weak cross-domain generalization ability. In contrast, ensemble methods (such as random forests or lightweight GBM) offer a better balance between performance, efficiency, and robustness—especially when the input features are well-designed. However, no research has yet systematically combined multi-domain features extracted via FMD with heterogeneous ensemble strategies to maximize diagnostic reliability under diverse industrial operating conditions.

[0025] To address these issues, this invention proposes the FMD-HMF framework, a novel bearing fault diagnosis framework that organically integrates adaptive signal decomposition, multi-domain feature engineering, and heterogeneous model fusion. The main contributions of this invention are summarized below: (1) A new diagnostic framework, FMD-HMF, is proposed (e.g. Figure 1 As shown in the figure, this framework uses Feature Pattern Decomposition (FMD) as its core decomposition engine. By synergistically enhancing the characteristics of impulse and periodic faults and combining multi-domain feature extraction with heterogeneous ensemble learning, this framework achieves high-precision and robust fault identification under complex operating conditions—without prior knowledge of the fault feature frequencies.

[0026] (2) A 43-dimensional multi-domain feature set was constructed, which integrates time-domain statistical indicators, FFT-based spectral descriptions, and nonlinear complexity measures extracted from the Intrinsic Mode Function (IMF). This representation comprehensively captures the dynamic characteristics of bearing faults and enriches the characterization of fault states.

[0027] (3) A heterogeneous model fusion strategy was designed to integrate six different basic learners—random forest (RF), decision tree (DT), support vector machine (SVM), light GBM, K-nearest neighbor (KNN), and Naive Bayes (NB)—into a stack-based ensemble predictor. This architecture significantly enhances generalization ability and decision stability.

[0028] (4) The method proposed in this invention has been systematically validated on four public datasets, including constant / variable speed, manually set / naturally occurring faults, and multi-load conditions. The framework achieved 100.00% accuracy on the CWRU, PU, ​​and uOttawa datasets, and 98.33% accuracy on the most challenging JNU dataset of this invention, which is significantly better than the existing state-of-the-art methods.

[0029] In one embodiment of the present invention, such as Figure 1 As shown, the overall architecture for rolling bearing fault diagnosis proposed in this invention based on Feature Mode Decomposition and Heterogeneous Model Fusion (FMD-HMF) is clearly divided into three closely connected core stages, which together constitute an intelligent diagnostic system with no prior knowledge, adaptability, and high robustness.

[0030] Phase 1: Feature Mode Decomposition (FMD) to adaptively extract fault-sensitive components.

[0031] This stage uses the original vibration signal as input, without relying on any bearing geometry parameters or fault characteristic frequency information. It iteratively optimizes a finite impulse response (FIR) filter to maximize the correlation kurtosis (CK) of the filtered output signal. CK, as a composite index integrating periodicity and transient impulsivity, can precisely guide the filter to focus on periodic impact events caused by local defects in the bearing. Through this process, the original signal is adaptively decomposed into multiple intrinsic mode functions (IMFs), with the top M IMFs with the highest CK values ​​selected as the dominant modes, serving as input for subsequent feature engineering. The core of this stage lies in explicitly embedding the physical mechanism of the fault into the decomposition objective function, thereby achieving effective enhancement and noise suppression of weak fault components.

[0032] In one specific implementation, this stage corresponds to steps S1, S2, and S3 of the present invention.

[0033] Specifically, step S1: Collect the raw vibration signals during the operation of the rolling bearing; It should be noted that before performing step S2, the original vibration signal acquired in step S1 is preprocessed to zero mean, that is, the mean of the signal is subtracted to eliminate DC offset.

[0034] Step S2: Without relying on any bearing geometric parameters or fault characteristic frequency information, using the correlation kurtosis CK as the optimization objective function, the coefficients of the finite impulse response (FIR) filter are iteratively updated to adaptively extract multiple intrinsic mode functions (IMFs) from the original vibration signal, wherein CK is used to simultaneously characterize the periodic impact and transient impulse caused by the fault. The formula for calculating CK is: , in The peak factor measures the concentration of periodic shocks in a signal and is used to assess the significance of fault-related modes. The filtered signal The original vibration signal, and satisfies h(t) is an FIR filter, i.e. Original vibration signal The output after convolution with the FIR filter h(t); The fault period is the number of sampling points corresponding to the fault characteristic frequency for adaptive estimation. ,in Ts is the fault frequency of the inner / outer ring, etc., and Ts is the sampling period. It is a fourth-order moment, reflecting the intensity of the signal impulse, and is sensitive to non-Gaussian pulses; Let be the second moment, mean square value, representing the signal energy level, used for normalization. When the filtered signal y(t) exhibits strong periodic impulses and... When aligning, CK( When the value reaches its maximum, it indicates that the filter has successfully extracted the target fault mode.

[0035] It is worth noting that this section proposes an adaptive mode decomposition mechanism with correlation kurtosis (CK) as the optimization objective function. The core of this mechanism is that CK is used not only as an evaluation index but also as a physical guiding criterion for driving the signal decomposition process. Specifically, by iteratively updating the coefficients of the finite impulse response (FIR) filter, the CK value of the filtered output signal is maximized, thereby directly extracting the intrinsic mode function (IMF) that best reflects the essential characteristics of local bearing faults from the original vibration signal.

[0036] The IMF waveform exhibits a distinct periodic impact sequence with stable intervals between adjacent impacts, corresponding to the period traversed by the roller at the bearing defect. Its spectrum shows energy concentration in the resonant frequency band, consistent with the vibration propagation mechanism of local faults.

[0037] Each IMF corresponds to a local maximum CK value, and the delay τ corresponding to the CK peak value is the adaptively estimated fault cycle. This τ is consistent with the theoretical fault frequency within the allowable error range (e.g., relative error <5%).

[0038] After FMD decomposition, the signal-to-noise ratio (SNR) of the first M IMFs is significantly higher than that of the original signal, while the CK value of the remaining IMFs is close to zero, indicating that the energy is dispersed and they are determined to mainly contain noise components.

[0039] The CK here is not the traditional kurtosis, but rather introduces a time delay. The correlation peaks, whose numerators can simultaneously capture the energy concentration and periodic repetitive structure of transient pulses, precisely correspond to the periodic impact physical phenomenon caused by bearing failure. The fault cycle, as an adaptive estimate, does not need to be given in advance and can be searched synchronously during the optimization process, truly realizing the extraction of fault-sensitive components without prior knowledge and driven by data.

[0040] In contrast, conventional signal decomposition methods such as EMD and VMD either rely on mathematical orthogonality or require preset parameters such as the number of modes and center frequency, lacking explicit modeling of fault mechanisms.

[0041] It should be noted that the process of iteratively updating the coefficients of the finite impulse response (FIR) filter is as follows: in each round of iterative optimization, the correlation kurtosis CK of the current filter output signal is calculated, and the filter parameters are adjusted using at least one of the gradient descent method, particle swarm optimization (PSO) algorithm, or genetic algorithm, so that the value of CK gradually increases until convergence.

[0042] The objective function for the iterative optimization of the FIR filter is: , in Let be the coefficient vector of the k-th FIR filter, used to extract specific modes from the original signal or residual signal. Let K be the adaptively estimated fault period corresponding to the k-th mode, where K is the total number of extracted modes, and satisfying the following conditions: The goal is to maximize the sum of the correlation kurtosis (CK) of all K modes.

[0043] Understandably, the iterative optimization process of an FIR filter is as follows: This is achieved by maximizing the sum of the correlation kurtosis (CK) values ​​for all modes, aiming to enhance the detectability of fault features. Specifically, the objective function is defined as the sum of the CK values ​​for each mode, i.e. ,in This represents the number of modes obtained from the decomposition. This is used to solve for the optimal filter coefficients. The gradient descent method is used to differentiate the objective function with respect to the FIR coefficients, and the filter parameters are updated stepwise using the chain rule. The update rule is as follows: ,in The learning rate controls the step size for each iteration. Alternatively, Particle Swarm Optimization (PSO) or Genetic Algorithms can be chosen as alternative optimization strategies. In these methods, the relevance kurtosis (CK) is used as the fitness function to evaluate the quality of each candidate solution. It is recommended to set the initial population size to 20 to 50 individuals. The search should stop and the optimal filter coefficients output when the fitness does not improve significantly after several generations or when the preset maximum number of iterations is reached. This optimization process ensures that fault-related modes with high discriminative power can be effectively extracted even under complex operating conditions, thereby improving overall diagnostic performance.

[0044] In addition, the gradient of the FIR filter can be automatically calculated using frameworks such as PyTorch / TensorFlow.

[0045] A. Adaptive Signal Decomposition Based on FMD Given an original vibration signal The FMD algorithm of length L decomposes the impulse response (EMD) into K intrinsic mode functions (IMFs) by designing a set of adaptive finite impulse response (FIR) filters. Unlike EMD or VMD, the FMD algorithm explicitly optimizes the impulsive and periodic characteristics through the correlation kurtosis (CK) metric, which is defined as: , in , The filtered signal The original vibration signal, and satisfies h(t) is an FIR filter. For the adaptively estimated fault period, L is the signal length, and * denotes convolution operation. When the filtered signal... When exhibiting strong performance, CK reaches its maximum value.

[0046] Repetitive pulses and periods Alignment. The FMD optimization problem can be described as:

[0047] in Let be the coefficient vector of the k-th FIR filter, used to extract specific modes from the original signal or residual signal. Let K be the adaptively estimated fault period corresponding to the k-th mode, where K is the total number of extracted modes, and satisfying the following conditions: The goal is to maximize the sum of the correlation kurtosis (CK) of all K modes.

[0048] In each iteration, the filter is updated step by step using the gradient descent method. To maximize its corresponding The value is used to obtain the corresponding intrinsic mode function (IMF), i.e. ,in This is the current residual signal. This process continues until K modes are extracted, or the residual energy is lower than a preset threshold, at which point the process terminates.

[0049] Step S3: Select the top M IMFs with the highest CK values ​​as the dominant modes, where M≥1; It is important to note that not all IMFs contain fault information. To select the most representative components, the CK value is calculated for each IMF, and the top M modes with the highest CK scores are retained. To determine the optimal M value, this invention conducted extensive experiments and found that M=2 achieves the best diagnostic performance on multiple datasets. However, this does not mean that M=2 is the optimal choice in all cases. In practice, the selection of M should be adjusted based on the specific application scenario and requirements. Generally, M should meet the following principles: Minimum sufficiency principle: M should ensure that the selected IMF can adequately characterize the bearing failure characteristics, while avoiding the introduction of too much noise components.

[0050] Adaptive strategy: Consider dynamically adjusting the M value according to the signal characteristics, for example, automatically selecting the top M dominant modes based on the CK value distribution.

[0051] Phase 2: Multi-domain feature engineering to construct a high-discrimination feature space.

[0052] In one specific implementation, this stage corresponds to step S4 of the present invention. Specifically, step S4 involves: extracting time-domain features, frequency-domain features, and nonlinear complexity features for each dominant mode to construct a multi-domain feature vector; inputting the multi-domain feature vector into the deep feature synthesis (DFS) module to generate derived features; and concatenating the derived features with the original multi-domain features to form an enhanced fusion feature vector. For each leading IMF, this phase extracts a comprehensive feature set covering three areas: The temporal characteristics (23 dimensions) include statistical moments (mean, variance, skewness, kurtosis), energy indices (root mean square, sum of absolute values), impact indices (peak factor, waveform factor, shape factor, etc.) and envelope correlation characteristics (envelope mean, impact interval, double impact amplitude, etc.), as detailed in Table 1. These characteristics reflect the transient impact characteristics caused by local defects.

[0053] Table 1: Temporal characteristics.

[0054]

[0055] Frequency domain features (12 dimensions): By performing a Fast Fourier Transform (FFT) on the IMF, the dominant frequency (FFT peak frequency), harmonic ratio, spectral statistics (FFT mean, standard deviation, spectral entropy, spectral skewness, etc.), and the energy of the four sub-bands are extracted to reflect the resonance characteristics and spectral structure caused by the fault; detailed features are shown in Table 2. Table 2: Frequency domain characteristics.

[0056]

[0057] Nonlinear complexity characteristics include Shannon entropy, discrete entropy, fractal dimension, and Hearst exponent, as shown in Table 3. These characteristics quantify the irregularity, self-similarity, and long-range correlation of the signal, and are particularly sensitive to early weak faults. They reflect the irregularity and long-range dependence of the signal and help to distinguish subtle fault evolution.

[0058] Table 3: Nonlinearity and complexity characteristics.

[0059]

[0060] The feature vector of the i-th sample is constructed by concatenating all selected IMF features, ultimately forming The representation is given by the expression, where D = 43 × M. Based on this, to further explore the potential higher-order interactions between features, this study introduces Deep Feature Synthesis (DFS) technology. This technology takes the original 43-dimensional engineered feature vector as input and automatically generates derived features with intuitive physical meaning by recursively applying mathematical operations and physical rules.

[0061] Statistical aggregation primitives—such as product, ratio, and sliding window statistics—are expressed as follows: , The final input to the subsequent heterogeneous ensemble classifier is constructed by horizontally concatenating the original features with the derived features XD generated by DFS, thus forming an enhanced composite feature vector Z. The expression is as follows:

[0062] Furthermore, the deep feature synthesis (DFS) technique is used to perform high-order combinations of the original features (such as cross-domain product, ratio, and sliding window statistics) to generate derived features with physical meaning, which are then concatenated with the original features to form an enhanced fusion feature vector, significantly improving the discriminative ability of the feature set.

[0063] The deep feature synthesis (DFS) module generates derived features with fault-detection capabilities in the following manner: For any two primitive features from different domains and And satisfy Calculate its normalized combination: , in This indicates operations involving multiplication, ratio, or difference. To prevent division by zero constant; Features in the time domain; Frequency domain characteristics; It is characterized by non-linear complexity. Alternatively, local statistics can be calculated within a sliding window w for a single-class feature sequence to capture the trend and pattern of feature changes over time.

[0064] The derived features are concatenated with the original multi-domain features to form an enhanced fusion feature vector, thereby improving the classifier's ability to distinguish between weak and complex faults.

[0065] Phase 3: Heterogeneous stacking and integrated classification to achieve robust and high-precision diagnosis.

[0066] In one specific implementation, this stage corresponds to step S5 of the present invention.

[0067] Step S5: Input the multi-domain fusion feature vector into the heterogeneous stacked ensemble classifier and output the bearing fault diagnosis result; wherein, the heterogeneous stacked ensemble classifier includes multiple heterogeneous basic learners in the first layer and a meta-learner in the second layer, the multiple heterogeneous basic learners output fault category probabilities in parallel, and the meta-learner outputs the final diagnosis result after nonlinear fusion based on the probabilities.

[0068] This stage employs a two-level stacking integration strategy: The first layer deploys six mutually orthogonal inductive bias base learners in parallel, including Random Forest (RF), Decision Tree (DT), Support Vector Machine (SVM), LightGBM, K Nearest Neighbors (KNN), and Naive Bayes (NB), which learn fault modes from different perspectives such as rules, margins, probabilities, and neighborhoods. The second layer receives fault category probability vectors from each base model via the XGBoost meta-learner, and outputs the final diagnostic result through nonlinear weighted fusion. This heterogeneous fusion mechanism effectively overcomes the limitations of a single model, maintaining high accuracy and robustness even under complex operating conditions such as variable speed, strong noise, and complex faults.

[0069] To maximize the discriminative power of multi-domain feature extraction and ensure robust performance under different operating conditions, this invention designs an integrated architecture based on a two-layer stack, which integrates heterogeneous base learners with complementary inductive biases. In the first layer, six different classifiers are trained in parallel on an enhanced feature set: Random Forest (RF) and Decision Tree (DT) are used for interpretable hierarchical partitioning; Support Vector Machine (SVM) enforces structural risk minimization in high-dimensional space; Light GBM is used for efficient gradient boosting sequential learning; K-Nearest Neighbors (KNN) captures local similarity patterns; and Naive Bayes (NB) provides probabilistic inference under the feature independence assumption.

[0070] Each base model outputs a class prediction probability vector, which are concatenated to form meta-feature representations, thus encoding diverse decision-making perspectives. In the second layer, an XGBoost regressor is used as the meta-learner to perform nonlinear adaptive fusion of these meta-features. Unlike simple averaging or voting mechanisms, this hierarchical design enables the meta-learner to discover higher-order synergistic effects and error compensation relationships among the base models, effectively suppressing biases in individual models while enhancing consensus signals. This model can be expressed as: , This fusion strategy is particularly well-suited for fault diagnosis, where subtle differences between fault types (e.g., inner circle vs. sphere defects) require both global pattern recognition and local discriminative sensitivity. As validated in Section 4, the proposed framework achieves perfect classification accuracy of 100% on the CWRU, PU, ​​and uOttawa datasets, and 98.33% on the more challenging JNU dataset. The confusion matrix shows a near-diagonal clustering distribution—indicating that the fusion not only achieves high accuracy but also maintains strong inter-class separability. The success of this approach underscores the effectiveness of deep decision-level fusion in transforming rich multi-domain features into reliable diagnostic results.

[0071] This invention also provides a bearing fault diagnosis system based on eigenmode decomposition and heterogeneous model fusion, comprising: The system includes a vibration signal acquisition module, an FMD adaptive decomposition module, a multi-domain feature engineering module, a heterogeneous stacked integrated classification module, and a result output module. The FMD adaptive decomposition module is configured to perform CK-driven FIR filter optimization, and the heterogeneous stacked integrated classification module is configured to run a two-level stacked architecture of six heterogeneous basic learners and XGBoost meta-learners.

[0072] This invention evaluated four widely used bearing datasets through experiments, and the results are summarized in Table 4: Table 4: Dataset Summary.

[0073]

[0074] Data preprocessing and evaluation metrics: Each raw signal is segmented using an overlapping sliding window, generating several segments for each record. Each segment is labeled according to its original category. Subsequently, the dataset is stratified by category into a training set (80%) and a test set (20%).

[0075] To address the multi-class and potentially imbalanced nature of fault diagnosis tasks, this invention employs three complementary metrics: accuracy, F1 score, and area under the curve (AUC). Accuracy reflects overall correctness, while the F1 score focuses on performance across individual classes—particularly important for a few fault types. AUC evaluates the model's discriminative ability across all classification thresholds, providing a robust measure of generalization capability.

[0076] Table 5 summarizes the core evaluation metrics for the four datasets—accuracy, area under the curve (AUC), and F1 score. The model achieved a perfect score (1.000) on the CWRU, PU, ​​and uOttawa datasets, achieving not only 100% classification accuracy but also a perfect balance between precision and recall for each category. This demonstrates that the combination of FMD-HMF feature representation and heterogeneous stacking ensemble can construct decision boundaries that completely distinguish all fault categories—even those with subtle spectral differences (e.g., defects of 0.007'' and 0.021'' in CWRU).

[0077] On the JNU dataset, performance showed a slight decrease: accuracy = 0.9833, AUC = 0.9984, and F1 score = 0.9805. This decrease was expected and informative: unlike other datasets, JNU data was collected at three different motor speeds (600 / 800 / 1000 rpm) without speed normalization, resulting in stronger industrial noise and weaker fault harmonics in the signal. The high AUC (>0.998) confirms the model's excellent discriminative ability within the decision threshold range, while the slight decrease in the F1 score reflects a slight imbalance in recall for certain fault types—possibly due to overlapping time-frequency characteristics between inner race faults and rolling element faults under variable speed conditions. Nevertheless, the experimental results remain highly competitive, highlighting the robustness of the method in real-world scenarios.

[0078] Table 5: Performance evaluation of FMD-HMF on all four datasets.

[0079]

[0080] As shown in Table 6, FMD-HMF achieves 100.00% accuracy on the CWRU dataset, reaching the performance level of the current state-of-the-art deep learning methods. However, unlike these "black box" models, FMD-HMF extracts interpretable handcrafted features based on physically meaningful mode decomposition, achieving a balance between transparency and high performance.

[0081] Table 6: Performance comparison of FMD-HMF and SOTA methods on the CWRU dataset.

[0082]

[0083] Figure 2 This is the normalized confusion matrix of the FMD-HMF framework on the CWRU dataset (10 categories: 1 health state + 9 different fault conditions of varying location and severity). Perfect classification (100.00% accuracy) is achieved for all categories, including the ability to distinguish fine defect sizes such as 0.007 inches, 0.014 inches, and 0.021 inches.

[0084] Figure 2 This paper presents the normalized confusion matrix of the FMD-HMF framework on the CWRU bearing dataset. This dataset contains 10 categories: one health state and nine different fault conditions with varying locations and severity, covering three typical fault types: inner race, outer race, and rolling element (Ball). It is further subdivided into multiple defect sizes (e.g., 0.007", 0.014", 0.021"), demonstrating extremely high classification granularity and challenge. Figure 2 As can be seen, all samples were correctly classified, indicated by non-zero values ​​on the diagonal (such as 56, 15, 46, etc.) and zero values ​​at other positions, demonstrating that the model achieved 100.00% accuracy, meaning there were no misclassifications or missed classifications in all 10 classes. This perfect classification performance not only demonstrates that the FMD-HMF method can effectively capture subtle vibration differences caused by minute defects, but also verifies its powerful feature representation and generalization capabilities under complex and variable working conditions. Particularly noteworthy is that even when faced with defect sizes differing by only a few milliinches (e.g., 0.007" vs. 0.014"), the model can still achieve accurate differentiation. This is attributed to its adaptive extraction of intrinsic mode functions strongly correlated with the physical mechanism of the fault through Eigenmode Decomposition (FMD), combined with multi-domain feature engineering and heterogeneous stacking integration strategies to construct a highly discriminative and robust decision boundary. Therefore, this result not only proves the superiority of FMD-HMF on standard benchmark datasets but also highlights its enormous potential for handling early and subtle fault identification tasks in real-world industrial scenarios.

[0085] Figure 2The CWRU confusion matrix shows that all off-diagonal elements in all 10 categories are zero. This perfect diagonal concentration indicates that the model can not only distinguish between healthy and faulty states, but also resolve subtle differences—such as fault location (IR vs. OR vs. Ball) and severity (0.007'' vs. 0.014'' vs. 0.021''). This accuracy is crucial for predictive maintenance, as early fault detection (such as a defect as small as 0.007'') directly impacts the assessment of remaining service life.

[0086] Compared to artificially implanted defects, this defect can more realistically simulate the actual wear of the bearing.

[0087] As shown in Table 7, the FMD-HMF model achieved an accuracy of 100.00%, surpassing recent deep learning models such as AMDC-CNN (99.80%) and ResNet with feature mapping (99.70%). This demonstrates that the invention is not only applicable to idealized laboratory data but also performs exceptionally well in real and noisy industrial environments.

[0088] Table 7: Performance comparison of FMD-HMF and SOTA methods on the PU dataset.

[0089]

[0090] Figure 3 This is the normalized confusion matrix of FMD-HMF on the PU dataset (4 categories: Healthy, IR, OR, and Combined). All samples are correctly classified, demonstrating robustness to natural evolution failures in accelerated life tests.

[0091] Figure 3 The confusion matrix shown visually demonstrates the classification performance of the proposed FMD-HMF method on the uOttawa bearing dataset. The graph is presented as a heatmap, with the horizontal axis representing the predicted class label and the vertical axis representing the true class label. The intensity of the color corresponds to the number of classified samples—the darker the color, the more classification results are available at that location. Figure 3As can be seen, all off-diagonal elements are white or close to zero, while the four cells on the main diagonal (corresponding to the Healthy, IR, OR, and Combined categories, respectively) are significantly darker, indicating that the model accurately classified all test samples into their true categories without any misclassification. Specifically, 880 Healthy samples, 880 Inner Ring Fault (IR) samples, 879 Outer Ring Fault (OR) samples, and 880 Combined Fault samples were all correctly identified, achieving 100% classification accuracy. This result not only verifies the excellent discriminative ability of the FMD-HMF framework in handling naturally evolved faults, but also demonstrates that the features extracted through Eigenmode Decomposition and Multi-Domain Heterogeneous Integration possess high inter-class separability and intra-class consistency. Particularly noteworthy is that combined faults typically contain coupled vibration responses of multiple damage modes, making them easily confused with other single faults, yet the model can still accurately distinguish them, fully demonstrating the robustness and engineering practicality of this method under complex conditions.

[0092] Figure 3 It was confirmed that all four categories (Healthy, IR, OR, and IR-OR combination) were perfectly classified. Notably, composite fault categories with complex and overlapping spectral features were correctly identified without being confused with single fault types. This highlights the advantage of FMD in separating coupled fault modes into distinct modal components, which can then be effectively characterized by FFT-based spectral features.

[0093] As shown in Table 8, the performance of the baseline models drops significantly: LSTM achieves only 77.00%, while even advanced hybrid models like Conv LSTM only reach 97.68%. In contrast, FMD-HMF achieves 100.00% accuracy. This outstanding result stems from two key design choices: (1) FMD's adaptability to non-stationary signals, which decomposes transient dynamics into physically coherent IMFs without assuming fixed basis functions (unlike wavelets or EMD); and (2) multi-domain feature engineering, which simultaneously captures temporal local impulses (through time-domain features) and frequency modulation patterns (through FFT of the IMF).

[0094] Table 8: Performance comparison of FMD-HMF and SOTA methods on the UOTTAWA dataset.

[0095]

[0096] Figure 4This is the normalized confusion matrix of FMD-HMF on the uOttawa dataset (5 categories: Healthy, IR, OR, Ball, and Combined) under a time-varying velocity profile. The framework achieves 100.00% accuracy, demonstrating its effectiveness under non-stationary operating conditions.

[0097] Figure 4 This paper presents the normalized confusion matrix of the FMD-HMF framework on the uOttawa bearing dataset, which contains five categories: Healthy, Inner Ring Fault (IR), Outer Ring Fault (OR), Rolling Element Fault (Ball), and Combined Faults. The test environment under time-varying speed profiles is particularly emphasized. Figure 4 As shown in the figure, all samples were accurately classified, represented by five dark squares on the diagonal, each corresponding to 48 samples, while all other off-diagonal positions were 0, indicating that the model achieved 100.00% classification accuracy. This result fully verifies the excellent robustness of the FMD-HMF method under non-stationary operating conditions—because changes in rotational speed cause the fault characteristic frequency to drift, traditional methods based on fixed frequency bands or preset fault cycles often struggle to adapt and are prone to misclassification. However, FMD-HMF, through adaptive mode decomposition technology, can dynamically extract transient impact components strongly correlated with the physical mechanism of the fault, and combined with a multi-domain feature fusion strategy, effectively suppresses the interference caused by speed fluctuations. Furthermore, this framework does not rely on prior fault cycle information, but automatically estimates the fault characteristic frequency by optimizing physically sensitive indicators such as correlation kurtosis (CK), thereby achieving high-precision identification of naturally evolving and complex coupled faults. Therefore, this figure not only intuitively reflects the model's perfect performance in complex real-world scenarios, but also highlights its strong adaptability and engineering value in handling variable-speed operating conditions in practical industrial applications.

[0098] Figure 4 A fully diagonal confusion matrix covering all five states is presented, demonstrating the model's ability to generalize to different velocity trajectories. This property is crucial for applications such as wind turbines, electric vehicles, or aerospace systems, where the rotational speeds are inherently dynamic.

[0099] The JNU dataset represents the most practical and challenging testing platform, characterized by variable speed, industrial background noise, and limited signal preprocessing. As shown in Table 9, FMD-HMF achieved an accuracy of 98.33%, surpassing state-of-the-art hybrid models such as HGWA-CNN-BiLSTM (97.33%) and CNN-Freq (97.33%).

[0100] This 1% absolute gain is statistically significant in fault diagnosis, demonstrating the superiority of our physical information-based feature design over purely data-driven representation.

[0101] Table 9: Performance comparison of FMD-HMF and SOTA methods on the JNU dataset.

[0102]

[0103] Figure 5 The normalized confusion matrix of FMD-HMF on the JNU dataset (4 categories: Healthy, IR, OR, Ball) shows its performance under multi-velocity and high industrial noise conditions. Only one misclassification occurs between IR and ball fault types, achieving an overall accuracy of 98.33%.

[0104] Figure 5 The normalized confusion matrix of the FMD-HMF framework on the JNU bearing dataset is presented. This dataset contains four main categories: Normal, Inner Ring Fault (IR), Outer Ring Fault (OR), and Rolling Element Fault (Ball). It was tested under complex operating conditions with multi-speed and high industrial noise, simulating common non-ideal operating conditions in real industrial environments. As shown in the figure, the vast majority of samples were correctly classified, represented by dark squares on the diagonal, with values ​​of 10, 30, 29, and 10, indicating high accuracy in identifying each fault category. However, there was one misclassification between category 1 (IR) and category 4 (Ball), where a sample that should have been an inner ring fault was incorrectly predicted as a rolling element fault. This resulted in an overall classification accuracy of 98.33%. Despite this minor error, the results still fully demonstrate the excellent robustness and generalization ability of the FMD-HMF method under strong noise interference and variable speed conditions—especially in the face of challenges such as background noise, vibration coupling, and load fluctuations commonly found in industrial environments, where traditional methods often struggle to maintain stable performance. FMD-HMF effectively extracts fault-related features with high signal-to-noise ratios by introducing a physically-based mode decomposition mechanism, and significantly improves the model's sensitivity to weak impact signals and its anti-interference ability by combining multi-domain feature fusion and adaptive optimization strategies. Therefore, this confusion matrix not only intuitively reflects the model's excellent performance in extremely complex environments but also verifies its practical value and reliability in actual industrial equipment condition monitoring and intelligent diagnostic systems.

[0105] Figure 5A deeper analysis revealed that while most predictions fell on the diagonal, a small number of misjudgments still occurred—primarily in distinguishing between inner race and rolling element faults. From a physical perspective, this phenomenon is reasonable, as the two fault types produce similar repetitive impact frequencies under specific speed conditions, leading to overlapping spectral sidebands. However, the error rate remained consistently below 2% and did not confuse with normal conditions, indicating that the overall prediction system possesses extremely high reliability.

[0106] Table 6-9 and Figures 2-5 Together, they demonstrate that FMD-HMF exhibits state-of-the-art performance across a wide range of diagnostic challenges, from controlled laboratory experiments (CWRU) to natural degradation (PU), non-stationary dynamics (uOttawa), and industrial realities (JNU). The success of this method lies in the synergy between interpretable signal decomposition (FMD) and multi-domain feature engineering.

[0107] Furthermore, the near-perfect consistency across different datasets demonstrates that FMD-HMF does not overfit any single data distribution, but rather learns transferable fault characteristics. This cross-domain generalization capability is a key step in realizing deployable, plug-and-play diagnostic systems suitable for real-world industrial environments.

[0108] To ensure the reproducibility of the experimental results, the present invention adopted the following measures during the experiment: Training / test split ratio: Each raw signal is segmented using an overlapping sliding window, and then the dataset is stratified by category into a training set (80%) and a test set (20%).

[0109] Cross-validation method: Instead of traditional cross-validation, a fixed random seed is used to ensure the reproducibility of each experiment.

[0110] Evaluation metrics: Accuracy, F1 score, and area under the curve (AUC) are used as the main evaluation criteria to comprehensively reflect the classification performance of the model.

[0111] This invention proposes a novel bearing fault diagnosis framework, FMD-HMF, which integrates FMD, multi-domain feature engineering, and heterogeneous ensemble learning to achieve high-precision, robust, and interpretable fault identification. FMD adaptively extracts fault-sensitive IMFs from raw vibration signals without prior knowledge of defect feature frequencies. Based on this decomposition, a physically meaningful and discriminative representation is constructed by fusing engineered features from multiple domains—including time-domain statistics, frequency-domain descriptors (e.g., via FFT), and nonlinear complexity measures. Finally, a heterogeneous stacking ensemble strategy is employed to combine predictions from different base learners, further enhancing the model's generalization ability and decision stability. Systematic experiments on four widely used public bearing datasets—CWRU, PU, ​​uOttawa, and JNU—demonstrate the superior performance of FMD-HMF. The method achieves 100% accuracy. On the CWRU, PU, ​​and uOttawa datasets, the classification accuracy, AUC, and F1 score are all 0%, indicating that it can accurately distinguish between healthy and faulty states, while precisely identifying the location (inner race, outer race, rolling element) and severity of the fault (e.g., in CWRU). (Defects). Notably, complex composite faults—such as the inner and outer race coupling failure in the PU dataset—were also successfully identified. On the most challenging JNU dataset, which involves various speeds, strong industrial noise, and weak fault harmonics, FMD-HMF still achieved an accuracy of 98.33% and an AUC of 0.9984, significantly outperforming existing state-of-the-art methods. These results highlight the framework's strong adaptability and reliability in real-world industrial scenarios.

[0112] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A bearing fault diagnosis method based on characteristic mode decomposition and heterogeneous model fusion, characterized in that, Includes the following steps: S1 collects the raw vibration signals during the operation of the rolling bearing; S2 does not rely on any bearing geometric parameters or fault characteristic frequency information. It uses the correlation kurtosis CK as the optimization objective function and iteratively updates the coefficients of the finite impulse response (FIR) filter to adaptively extract multiple intrinsic mode functions (IMFs) from the original vibration signal. The CK is used to simultaneously characterize the periodic impact and transient impulse caused by the fault. S3 selects the top M IMFs with the highest CK values ​​as the dominant modes, where M≥1; S4 extracts time-domain features, frequency-domain features, and nonlinear complexity features for each dominant mode to construct a multi-domain feature vector; the multi-domain feature vector is input into the deep feature synthesis (DFS) module to generate derived features, and the derived features are concatenated with the original multi-domain features to form an enhanced fusion feature vector; S5 inputs the multi-domain fusion feature vector into the heterogeneous stacked ensemble classifier and outputs the bearing fault diagnosis result; wherein, the heterogeneous stacked ensemble classifier includes multiple heterogeneous basic learners in the first layer and a meta-learner in the second layer, the multiple heterogeneous basic learners output fault category probabilities in parallel, and the meta-learner outputs the final diagnosis result after nonlinear fusion based on the probabilities.

2. The method according to claim 1, characterized in that, The formula for calculating CK is: ， in Peak factor; The filtered signal The original vibration signal, and satisfies h(t) is an FIR filter. Original vibration signal The output after convolution with the FIR filter h(t); The fault period is the number of sampling points corresponding to the fault characteristic frequency for adaptive estimation. ,in Ts is the fault frequency of the inner / outer ring, etc., and Ts is the sampling period. It is a fourth-order moment; It is the second moment, and its mean square value.

3. The method according to claim 1, characterized in that, The time-domain features include statistical moments, energy indices, impulsivity indices, and envelope correlation features; the statistical moments include mean, variance, skewness, and kurtosis; the energy indices include root mean square and sum of absolute values; the impulsivity indices include peak factor, waveform factor, and shape factor; and the envelope correlation features include envelope mean, impact interval, and difference in double impact amplitude. The frequency domain features are obtained by performing a Fast Fourier Transform (FFT) on the dominant mode, including the dominant frequency, harmonic ratio, spectral statistics, and the energy of the four sub-bands; the spectral statistics include the mean and standard deviation. The nonlinear complexity features include Shannon entropy, discrete entropy, fractal dimension, and Hearst exponent.

4. The method according to claim 1, characterized in that, The deep feature synthesis (DFS) module generates derived features with fault-detection capabilities in the following manner: For any two primitive features from different domains and And satisfy Calculate its normalized combination: ， in This indicates operations involving multiplication, ratio, or difference. To prevent division by zero constant; Features in the time domain; Frequency domain characteristics; It is characterized by non-linear complexity. Alternatively, local statistics can be calculated within a sliding window w for a single-class feature sequence; The concatenation of the derived features with the original multi-domain features significantly improves the classifier's ability to distinguish between weak and complex faults.

5. The method according to claim 1, characterized in that, The multiple heterogeneous basic learners include random forest, support vector machine, k-nearest neighbors, naive Bayes, decision tree and LightGBM, whose inductive biases are mutually orthogonal, covering multiple decision paradigms such as rule, margin, probability and neighborhood.

6. The method according to claim 1, characterized in that, The meta-learner is an XGBoost regressor. The input features are formed by concatenating the probability vectors output by each heterogeneous base learner. The class probability vectors output by each base learner are weighted and fused. In addition, the logistic loss function is used during training to perform soft label fusion for multiple fault classes.

7. The method according to claim 1, characterized in that, The process of iteratively updating the coefficients of the finite impulse response (FIR) filter is as follows: In each round of iterative optimization, the correlation kurtosis CK of the current filter output signal is calculated, and the filter parameters are adjusted using at least one of the gradient descent method, particle swarm optimization (PSO) algorithm, or genetic algorithm, so that the CK value gradually increases until convergence.

8. The method according to claim 7, characterized in that, The objective function for the iterative optimization of the FIR filter is: ， in Let be the coefficient vector of the k-th FIR filter, used to extract specific modes from the original signal or residual signal. Let K be the adaptively estimated fault period corresponding to the k-th mode, where K is the total number of extracted modes, and satisfying the following conditions: The goal is to maximize the sum of the correlation kurtosis (CK) of all K modes.

9. A bearing fault diagnosis system based on characteristic mode decomposition and heterogeneous model fusion, characterized in that, To implement the method according to any one of claims 1-8, comprising: The system includes a vibration signal acquisition module, an FMD adaptive decomposition module, a multi-domain feature engineering module, a heterogeneous stacked integrated classification module, and a result output module. The FMD adaptive decomposition module is configured to perform CK-driven FIR filter optimization, and the heterogeneous stacked integrated classification module is configured to run a two-level stacked architecture of six heterogeneous basic learners and XGBoost meta-learners.

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