Bearing health index construction method based on prognosis standard embedding and fusion process constraint
By embedding prognostic criteria and constraining the fusion process, feature weights are optimized, which solves the problems of insufficient feature selection and disconnection of prognostic criteria in the existing technology, and realizes accurate characterization of the degradation trajectory and life prediction of bearings throughout their entire life cycle.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2026-01-23
- Publication Date
- 2026-05-15
AI Technical Summary
Existing methods for constructing health indicators suffer from insufficient feature selection and a disconnect from prognostic standards during the fusion process, resulting in insufficient characterization capabilities of single features and difficulty in meeting the needs of degradation characterization and life prediction throughout the entire bearing life cycle.
We adopt a method of embedding prognostic criteria and constraining the fusion process. We optimize feature weights through alternating direction multiplier method and projection operator to construct health indicators. Combined with monotonicity and trend constraints, we ensure that feature selection matches prognostic requirements.
It enables precise characterization of the degradation trajectory of bearings throughout their entire life cycle, improves the monotonicity, trend, and robustness of health indicators, and enhances the timeliness of fault diagnosis and the accuracy of life prediction.
Smart Images
Figure CN122046207A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of rotating machinery fault diagnosis and prognostic maintenance, specifically involving a method for constructing bearing health indicators based on the embedding and constraint fusion process of prognostic standards. Background Technology
[0002] As a core supporting component of rotating machinery, the health status of rolling bearings directly determines the reliability and safety of equipment operation. Failure to provide timely warnings of bearing failures can lead to equipment downtime, production interruptions, and even safety accidents, resulting in significant economic losses. In a fault prediction and health maintenance system, health indicators serve as a crucial bridge connecting raw monitoring data with prognostic models; their quality directly impacts the timeliness of fault diagnosis and the accuracy of remaining life prediction. Therefore, constructing health indicators that accurately depict the bearing degradation trajectory and meet prognostic requirements is key to achieving early warning and life prediction of bearing failures.
[0003] Existing methods for constructing health indicators are mainly divided into two categories: physical health indicators and virtual health indicators. Physical health indicators are directly derived from monitoring signals such as vibration and temperature. They are simple to calculate and have clear physical meanings. However, a single physical health indicator can only capture one aspect of bearing degradation. For example, although the root mean square has good monotonicity, it has low sensitivity to early failures; kurtosis is sensitive to impact signals and can monitor early failures, but it lacks a stable degradation trend and is difficult to comprehensively describe the performance degradation process of the bearing throughout its entire life cycle, resulting in weak generalization ability.
[0004] To address the limitations of single features, researchers construct virtual health indicators through multi-feature fusion, with common methods including principal component analysis, local preservation projection, and linear discriminant analysis. However, existing fusion methods have certain drawbacks: some methods follow a process of first screening features and then fusing them, resulting in the neglect of features that were not screened; at the same time, the fusion process is disconnected from prognostic criteria, making it difficult to ensure that the final indicator meets core requirements such as monotonicity and trend, leading to larger errors in subsequent life expectancy prediction.
[0005] To address the aforementioned issues, this invention proposes a method for constructing health indicators based on prognostic criteria embedding and constrained fusion processes. This method integrates the advantages of multiple features while ensuring that the indicators meet prognostic requirements through constrained optimization. The alternating direction multiplier method, as an efficient distributed optimization algorithm, can solve objective functions with regularization terms in high-dimensional feature spaces, providing an ideal technical path for solving feature weight objective functions. The constrained optimization model is solved by combining projection operators. Therefore, this invention proposes a bearing health indicator construction method based on prognostic criteria embedding and constrained fusion processes. It achieves feature selection and prognostic guidance through a dual regularization mechanism, and combines monotonicity and trend constraints to improve the degradation characterization ability and robustness of health indicators. Summary of the Invention
[0006] To construct bearing health indicators that deeply integrate prognostic criteria and feature fusion, this invention adopts the following technical solution: This invention provides a method for constructing bearing health indicators based on prognostic criterion embedding and constrained fusion process, used for degradation assessment and life prediction of rolling bearings throughout their entire life cycle. The method comprises the following steps: Step S1, collecting vibration signals throughout the bearing's entire life cycle and performing data preprocessing, dividing the data into a model training set and a test set; Step S2: constructing degradation labels for the training set, using root mean square 3D model data... The criteria determine early failure points, with the healthy segment as 0 and the faulty segment as 1; Step S3: Extract features from dimensions such as time domain, frequency domain, sparsity features, entropy features, and envelope spectrum features, and standardize dimensional features such as peak values to make them dimensionless; Step S4: Construct a health hybrid criterion (HM) as a quantitative indicator of the prognostic standard to evaluate the degradation characterization ability of each feature; Step S5: Construct an optimization objective function with double regularization based on the prognostic criteria constructed in S4; Step S6: Add the monotonicity and trend constraints of the health indicator itself to the objective function constructed in S5 to obtain the overall optimization model; Step S7: Use the alternating direction multiplier method (ADMM) combined with the projection operator on the training set to solve the objective function under constraints to obtain feature weights; Step S8: Based on the weights obtained in S7, construct health indicators and verify performance on the test set.
[0007] This invention provides a method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion processes. It may also include the following feature: in step S1, vibration signals throughout the bearing's life cycle are collected using an accelerometer, followed by signal preprocessing.
[0008] This invention provides a method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion processes. It may also have the following feature: in step S2, based on root mean square (RMS) and... The criteria determine the bearing degradation initiation point (FPT). A certain number of smoothed RMS sequences are selected as data for the normal phase, and their mean is calculated. with standard deviation Set the dynamic threshold to When the current RMS value exceeds the dynamic threshold, the first threshold-exceeding point is determined as FPT.
[0009] This invention provides a method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion processes. It also features the following characteristic: in step S3, the following parameters are selected: mean, peak value, kurtosis, skewness, peak factor, impulse factor, shape factor, margin factor, coefficient of variation, sparsity index, Gini coefficient, zero-crossing rate, permutation entropy, spectral peak value, peak frequency, specially designed frequency bandwidth energy, spectral centroid, mean square frequency, envelope spectral peak value, spectral flatness, spectral entropy, spectral kurtosis, harmonic ratio, and signal-to-noise ratio. The extracted dimensional features are then Z-score standardized to eliminate dimensional differences.
[0010] This invention provides a method for constructing bearing health indicators based on the embedding of prognostic criteria and the constraint fusion process. It may also have the following feature: in step S4, HM is obtained by weighting four sub-indices: separability, monotonicity, trend, and robustness.
[0011] This invention provides a method for constructing bearing health indicators based on prognostic criterion embedding and constrained fusion processes. It also features that, in step S5, the objective function consists of three parts: a data fitting term for basic fault determination, a feature sparsity term, and a prognostic criterion constraint term, used for subsequent feature weight calculation.
[0012] This invention provides a method for constructing bearing health indicators based on pre-criteria embedding and constraint fusion processes. It also features that, in step S6, the constraints consist of two parts: first, the monotonicity constraint of the fault segment within the health indicator itself; and second, the trend constraint of the fault segment within the health indicator itself.
[0013] This invention provides a method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion processes. It may also have the following feature: in step S7, the objective function is iteratively solved using the ADMM method and projection operator to obtain the feature weight matrix.
[0014] This invention provides a method for constructing bearing health indicators based on prognostic standard embedding and constrained fusion processes. It may also include the following feature: in step S8, the standardized feature matrix is multiplied by the feature weight matrix in the test set, and smoothed using a moving average method to obtain the health indicators. Further performance verification is then performed.
[0015] Invention Function and Effect This invention discloses a method for constructing bearing health indicators based on the embedding and constrained fusion process of prognostic criteria, used for accurate assessment of bearing health status and life prediction. The method includes the following steps: acquiring vibration signals throughout the bearing's life cycle and performing preprocessing and data segmentation; extracting features from the preprocessed signals in multiple dimensions, including time domain, frequency domain, envelope spectrum, and nonlinearity, and standardizing these features to construct a feature matrix; designing a hybrid health criterion indicator that integrates separability, monotonicity, trend, and robustness to evaluate the prognostic performance of each feature; constructing a composite objective function including data fitting terms, sparse regularization terms, and HM-guided regularization terms; constructing a mathematical model including monotonicity and trend constraints for the health indicators; solving for feature weights using the alternating direction multiplier method and projection operators to achieve prognostic knowledge guidance and monotonicity and trend constraints; and constructing a health indicator with clear physical meaning based on the fusion of multiple features using weight vectors, followed by smoothing. This method effectively characterizes the complete degradation trajectory of a bearing from normal state to failure, solving the problems of insufficient traditional single-feature representation capabilities and the disconnect between the fusion process and prognostic requirements. Furthermore, this invention embeds the health hybrid criterion into the optimization objective and introduces a dual regularization mechanism and prognostic criterion constraints to achieve the screening and fusion of feature sets. This results in significant improvements in monotonicity, trend, robustness, and separability, as verified on a self-built test bench and public datasets, providing a more reliable input basis for bearing remaining life prediction. Attached Figure Description
[0016] Figure 1 This is a flowchart of the bearing health index construction method based on the pre-criteria embedding and constraint fusion process according to an embodiment of the present invention; Figure 2 This is a flowchart of the solution method according to an embodiment of the present invention; Figure 3 This is a diagram showing the health indicator construction results of an embodiment of the present invention; Detailed Implementation
[0017] The specific embodiments of the present invention will be described below with reference to the accompanying drawings and examples.
[0018] <Example> This embodiment provides a method for constructing bearing health indicators based on the embedding of prognostic criteria and the constraint fusion process, which is used for constructing health indicators of rolling bearings.
[0019] Figure 1 This is a flowchart of a bearing health index construction method based on the pre-criteria embedding and constraint fusion process according to an embodiment of the present invention.
[0020] The following combination Figure 1 The bearing health index construction method based on the pre-criteria embedding and constrained fusion process in this embodiment is described.
[0021] Step S1: Collect the vibration signal of the bearing throughout its entire lifespan, preprocess the signal using wavelet denoising, divide it into segments of fixed length, and calculate the characteristics of each segment; Step S2, based on the root mean square value and 3 The criteria are to adaptively determine the first prediction time and construct labels for the training set, where healthy data is 0 and faulty data is 1. Step S3: Extract multiple features from the dimensions of time domain, frequency domain, envelope spectrum, entropy features, sparse features, including kurtosis, peak factor, spectral entropy, envelope spectrum kurtosis, and permutation entropy, and perform dimensionless processing on the dimensional features to form a feature matrix. Step S4: Construct the Health Hybrid Criterion (HM) as a quantitative indicator of prognostic criteria to evaluate the degradation characterization ability of each feature; Step S5: Construct an optimization objective function with double regularization, using the prognostic criteria constructed in S4 as constraints.
[0022] Step S6: Add the monotonicity and trend constraints of the health indicators themselves to the objective function constructed in S5 to obtain the overall optimized model. In this embodiment, a mathematical model is established for the prognostic criteria guidance of each feature, the objective function of feature sparsification and fitting error term, and the prognostic criteria constraints of the health indicators themselves, and the solution is obtained using the alternating direction multiplier method and projection operator.
[0023] In this embodiment, the objective function includes a data fitting term, a feature sparsity term, and a prognostic scoring term, with constraints being monotonicity and trend constraints.
[0024] Specifically, as follows: (1) (2) (3) (4) in: For the sample size, For sample index, For the first The feature vectors of samples, total One characteristic, For the characteristic matrix, For category tags, These are the normalized values for the time points during the failure phase, ranging from [0,1]. For the feature fusion weights of the demand solution, Let L1 sparsity and weighted L2 smoothing regularization coefficients be used. This is a sample index set for the fault phase. This is the point where the fault begins. It is a monotonicity tolerance parameter. Maximum allowable deviation for the trend band The first term of the objective function is the fitting error term, used to ensure the closeness of the constructed health indicator sequence to the degradation labels (healthy segment = 0, faulty segment = 1), so that the health indicators have basic stage separability. The second term of the objective function is L1 norm regularization, used for feature sparsity control. The third term of the objective function is weighted L2 norm regularization, used to select features that conform to prognosticity. Let be a diagonal matrix, defined as Since a higher HM value indicates a better characterization feature, The smaller the value, the higher the L2 regularization term. Will to Features with low values are penalized more severely, suppressing their weights. This embeds prior knowledge based on degraded physical properties into the weight optimization process, guiding the model to prioritize high-quality features and enhancing the interpretability of health indicators.
[0025] The solution is obtained by combining the idea of constraint set projection with the alternating direction multiplier method. Figure 2 This is a flowchart of the solution method according to an embodiment of the present invention. Specific solution steps: Step T1: Variable decomposition and problem restructuring; variable decomposition introduces auxiliary variables. At the same time, health indicator constraints are separated into: , , = The problem can be transformed into the following formula. (5) (6) (7) (8) in, It is a set of monotonic and trend constraints.
[0026] Step T2: To solve this type of optimization problem, a shrinking dual variable is introduced. Penalty parameter structure Define the augmented Lagrange function: (9) Step T3: Use ADMM iteration to perform the following steps respectively. Sub-problem update, Sub-problem update, The subproblem (constraint set projection) is solved using Dykstra's alternating projection method: Temporary health indicators are as follows. (10) Index set during fault phase Perform convex set projection on top: (11) Finally, the dual variable is updated.
[0027] Step T4: Convergence determination involves calculating the original residual and dual residual, where the value is less than the error. The iteration may stop once the maximum number of iterations is reached. The final sparse weight vector is obtained. Used to build health metrics for the test set.
[0028] Step S7: The feature weights are obtained above.
[0029] Step S8: Based on the weights obtained in S7, construct health metrics and verify performance on the test set. Calculate monotonicity, trend, separability, and robustness.
[0030] In this embodiment, the health indicators of three bearings under two operating conditions are constructed and compared with other methods.
[0031] The results obtained by the bearing health index construction method based on prognostic standard embedding and constrained fusion process in this embodiment are compared with the results constructed by other methods in terms of monotonicity, trend, separability, and robustness, as shown in Table 1: Table 1 Comparison of prognostic criteria for health indicators constructed by different methods Bearing4 PCA LDA LPP RMS LLE ISOMAP ADMM_PRO Monotonicity 0.1172 0.1435 0.0986 0.239 0.0449 0.0219 0.3817 robustness 0.9934 0.9948 0.9867 0.9942 0.9691 0.9811 0.9949 Trend 0.3408 0.8162 0.3947 0.8773 0.9032 0.814 0.9639 Separability 13.5431 17.4268 4.7245 4.5562 0.0718 / 3.7942 Bearing 2_7 Monotonicity 0.04 0.0551 0.0045 0.0788 0.003 0.0126 0.0435 robustness 0.9943 0.9924 0.9833 0.9931 0.9802 0.9859 0.9882 Trend 0.7496 0.801 0.8047 0.9475 0.5629 0.6053 0.932 Separability 10.6732 7.6954 / 5.6669 0.2805 / 1.4236 Bearing 13 Monotonicity 0.039 0.0148 0.024 0.1363 0.0089 0.0423 0.1505 robustness 0.9985 0.9975 0.9857 0.9989 0.9936 0.9926 0.9987 Trend 0.1888 0.4865 0.2435 0.9295 0.3038 0.9159 0.9706 Separability 48.6531 12.3086 / 5.9985 / / 3.7262 ADMM_PRO represents the Alternating Direction Method of Multipliers combined with the Projection operator (ADMM_PRO); PCA represents Principal Component Analysis (PCA); Root Mean Square (RMS) represents the Root Mean Square (RMS); LPP represents Locality Preserving Projections (LPP); ISOMAP represents Isometric Mapping (ISOMAP); LLE represents Locally Linear Embedding (LLE); and LDA represents Linear Discriminant Analysis (LDA).
[0032] The results in Table 1 show that ADMM_PRO performs well on Mon, Ten, and Rob indicators in most cases, but is somewhat lacking on Sep. This is because the requirement for the indicator to satisfy trend may result in some loss of separability. However, as can be seen from the table, the proposed method can use 3 The criteria detected degradation points, which were roughly the same as those proposed by RMS. In Bearing 2_7, degradation points were detected earlier, and an upward trend was observed after the degradation point. The metrics calculated by the method proposed in Bearing 4 were the best among several methods in terms of monotonicity, trend, and robustness, especially in monotonicity, which was 59.7% higher than RMS. Bearing 2_7 showed good robustness and trend, but due to the instability of the features, its monotonicity was poor and it might be affected by noise and other interference, although it could identify degradation points relatively early. In Bearing 2_7, monotonicity and trend were the best among several methods, exceeding the RMS method by 10.4% and 4.4%, respectively. Figure 3 This is a diagram showing the health indicator construction results of an embodiment of the present invention.
[0033] The workflow for constructing health indicators consists of steps S1 to S8.
[0034] Functions and effects of the embodiments This embodiment provides a method for constructing bearing health indicators based on the embedding and constraint fusion process of prognostic criteria, used for constructing bearing Ganacon indicators. The method includes the following steps: acquiring the bearing's full-life-cycle vibration signal and performing preprocessing and data segmentation; extracting features from the preprocessed signal in multiple dimensions, including time domain, frequency domain, envelope spectrum, and nonlinearity, and standardizing these features to construct a feature matrix; designing a hybrid health criterion indicator that integrates separability, monotonicity, trend, and robustness to evaluate the prognostic performance of each feature; constructing a composite objective function containing data fitting terms, sparse regularization terms, and HM-guided regularization terms; constructing a mathematical model containing monotonicity and trend constraints for the health indicators; solving for feature weights using the alternating direction multiplier method and projection operator to achieve prognostic knowledge guidance and monotonicity and trend constraints; and constructing a health indicator with clear physical meaning based on the fusion of multiple features using weight vectors, followed by smoothing. The health indicator construction method of this invention exhibits good monotonicity, trend, robustness, and separability, providing a more reliable input basis for predicting the remaining life of bearings.
[0035] Furthermore, the health indicators in this embodiment can enable health assessment and lifespan prediction.
[0036] The bearing health index construction method based on the embedding and constraint fusion process of prognostic criteria provided in this embodiment makes full use of prognostic criteria to ensure that the final index meets the core requirements such as monotonicity and trend, and provides a basis for subsequent health assessment.
[0037] The above embodiments are only used to illustrate specific implementations of the present invention, and the present invention is not limited to the scope of the description of the above embodiments.
Claims
1. A method for constructing bearing health indicators based on prognostic criterion embedding and constrained fusion process, used for bearing health assessment, characterized in that, Includes the following steps: Step S1: Collect vibration signals throughout the bearing's life cycle and perform data preprocessing to divide the model training set and test set; Step S2: Construction of degenerate labels for the training set, using root mean square 3 The criteria determine early failure points, with a healthy segment valued at 0 and a faulty segment at 1. Step S3: Extract features from dimensions such as time domain, frequency domain, sparsity features, entropy features, and envelope spectrum features, and standardize dimensional features such as peak values to make them dimensionless; Step S4: Construct the Health Hybrid Criterion (HM) as a quantitative indicator of prognostic criteria to evaluate the degradation characterization ability of each feature; Step S5: Construct an optimization objective function with double regularization, using the prognostic criteria constructed in S4 as constraints; Step S6: Add the monotonicity and trend constraints of the health indicators themselves to the objective function constructed in S5 to obtain the overall optimization model; Step S7: Use the Alternating Direction Multiplier Method (ADMM) combined with the projection operator on the training set to solve the objective function under constraints and obtain the feature weights; Step S8: Based on the weights obtained in S7, construct health metrics and verify performance on the test set.
2. The bearing health index construction method based on prognostic standard embedding and constrained fusion process according to claim 1, characterized in that, in, In step S1, vibration signals throughout the bearing's life cycle are collected using an accelerometer. Signal preprocessing is then performed.
3. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S2, the bearing degradation initiation point (FPT) is determined based on the root mean square (RMS) and 3σ criterion. A certain number of smoothed RMS sequences are selected as normal stage data, and their mean μ and standard deviation σ are calculated. A dynamic threshold is set as μ+3σ. When the current RMS value exceeds the dynamic threshold, the first threshold-exceeding point is determined to be the FPT.
4. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S3, the following parameters were selected: mean, peak value, kurtosis, skewness, peak factor, impulse factor, shape factor, margin factor, coefficient of variation, sparsity index, Gini coefficient, zero-crossing rate, permutation entropy, spectral peak value, peak frequency, custom frequency bandwidth energy, spectral centroid, mean square frequency, envelope spectral peak value, spectral flatness, spectral entropy, spectral kurtosis, harmonic ratio, and signal-to-noise ratio. The extracted dimensional features were then Z-score standardized to eliminate dimensional differences.
5. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S4, HM is obtained by weighting four sub-indicators: separability, monotonicity, trend, and robustness.
6. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S5, the objective function consists of three parts: a data fitting term for basic fault determination, a feature sparsity term, and a prognostic standard constraint term, which are used for subsequent feature weight calculation.
7. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S6, the constraints consist of two parts: one is the monotonicity constraint of the fault segments of the health indicator itself, and the other is the trend constraint of the fault segments of the health indicator itself.
8. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S7, the objective function is solved iteratively using the ADMM method and projection operator to obtain the feature weight matrix.
9. The method for constructing bearing health indicators based on pre-criteria embedding and constrained fusion process according to claim 1, characterized in that, in, In step S8, the standardized feature matrix and the feature weight matrix are multiplied in the test set, and smoothed using a moving average method to obtain the health index. Further performance verification is then performed.