A method and system for predicting the vibration characteristics of a pipe

By constructing a three-dimensional model of the pipeline and combining various neural network models to process vibration data, the problem of real-time prediction of abnormal vibration in natural gas station pipeline networks and explanation of the root causes of faults was solved, achieving high-precision prediction of pipeline network vibration characteristics and determination of fault causes.

CN120832739BActive Publication Date: 2026-01-23中国石油集团工程材料研究院有限公司 +1
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Patent Information

Application Number
CN202511318050.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-09-16
Publication Date
2026-01-23
Estimated Expiration
2045-09-16

AI Technical Summary

Technical Problem

Existing technologies struggle to predict abnormal vibrations in natural gas station pipelines in real time and accurately. Traditional methods rely on manual inspections and fixed-threshold alarm systems, which cannot adapt to complex and ever-changing operating conditions. Furthermore, data-driven methods ignore the overall system correlation of the pipeline network and cannot explain the root causes of failures.

Method used

By combining the three-dimensional model of the pipeline and the intrinsic orthogonal decomposition method, various neural network models (MLP, CNN, LSTM) are used to process vibration data. The vibration characteristics of the pipeline are predicted by reduced-order basis vectors and coefficients, and the cause of the failure is determined by inverse fact deduction.

Benefits of technology

It enables accurate prediction of pipeline vibration and early detection of anomalies, can quickly identify local anomalies, provide clear explanations of the causes of failures, and guide maintenance work.

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Abstract

The application discloses a pipeline vibration characteristic prediction method and system, and belongs to the technical field of natural gas station pipeline vibration prediction, wherein the method comprises pipeline three-dimensional model construction, pipeline vibration data obtained by fluid and structure dynamics method calculation, reduced order basis vector obtained based on intrinsic orthogonal decomposition method, reduced order coefficient obtained by using a neural network model, and vibration prediction realized by coupling the reduced order basis vector and the reduced order coefficient. The application can quickly predict the pipeline vibration change condition by combining the reduced order coefficient and the neural network model. The method can perceive the change of the overall dynamic characteristics of the pipeline network caused by the slight change of the key parameters, has very high detection sensitivity for early and local abnormalities which are difficult to be found by the traditional method, and realizes the accurate prediction of the pipeline vibration.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of natural gas station pipeline vibration prediction, and particularly relates to a pipeline vibration characteristic prediction method and system. BACKGROUND

[0002] The natural gas station is a key hub in the energy pipeline network, and its safe and stable operation is crucial. Due to the complexity of the internal pipeline system of the station, a large number of equipment and components such as compressors, buffer tanks, valves, elbows, tees, etc. are contained, and when high-pressure natural gas flows at high speed in the system, complex fluid-structure coupling effects are induced. Mechanical vibration of the compressor and fluid pulsation can cause mechanical vibration of the pipeline and its supporting structure. If the vibration exceeds the normal range, it can not only cause loose connection of the equipment, but also can cause fatigue damage of the pipeline, crack and even rupture, causing natural gas leakage and posing a major safety hazard.

[0003] Currently, there are still many limitations in the technical means for vibration monitoring of industrial pipeline networks. The traditional safety operation and maintenance mode largely depends on periodic manual inspection and alarm systems based on fixed thresholds. However, the frequency of manual inspection is limited, and it is difficult to capture transient or intermittent abnormal vibration, and the judgment result depends on the personal experience of the inspection personnel. The alarm system based on fixed thresholds can achieve continuous monitoring, but its core defect is that it cannot adapt to the complex and variable operating conditions of the pipeline network. For example, during the peak period of gas transmission, the power of the compressor increases, and the flow rate in the pipeline increases. At this time, the vibration amplitude will naturally be higher than during stable operation. Simple threshold alarms cannot distinguish between normal vibration caused by changes in operating conditions and abnormal vibration caused by equipment failure, so they are prone to produce a large number of false alarms or missed alarms, reducing the reliability and practical value of the system.

[0004] In order to improve the accuracy of prediction, the industry has also tried to use numerical simulation methods of structural dynamics and computational fluid dynamics. These methods can finely describe the vibration behavior of the pipeline from the physical mechanism, but the huge computational cost makes it difficult to meet the real-time requirements, and it is usually used for offline design verification or post-analysis, and cannot provide forward-looking guidance for online operation. With the development of artificial intelligence technology, some data-driven methods have also been applied to the analysis of vibration signals. However, these methods often treat the vibration signals of each measuring point as isolated time series data, ignoring the inherent physical correlation of the pipeline network as a whole system. The root cause of any abnormality in the pipeline network may be far away, and its influence will also propagate along the pipeline. This spatial coupling effect cannot be captured by isolated analysis of single-point data. In addition, such pure data-driven "black box" models can identify deviations in data patterns, but cannot provide explanations that conform to physical logic, i.e. cannot answer the question "what is the root cause of the fault" which is most concerned by operation and maintenance personnel. SUMMARY

[0005] The application aims to provide a pipeline vibration characteristic prediction method and system to solve the problems in the background art.

[0006] To achieve the above-mentioned purpose, the application provides the following technical solution: a pipeline vibration characteristic prediction method, comprising:

[0007] A pipeline three-dimensional model is constructed, and pipeline vibration data under different working condition data is calculated based on the pipeline three-dimensional model, and a vibration data matrix under each working condition data is constructed;

[0008] The vibration data matrix under different working conditions is processed by the intrinsic orthogonal decomposition method to obtain the reduced basis vector under different working conditions;

[0009] Based on at least one trained neural network model, the reduced order coefficient corresponding to the vibration data matrix under different working condition data is obtained;

[0010] Real-time working condition data is obtained, and the predicted vibration data is output based on the reduced basis vector and the reduced order coefficient under the real-time working condition data.

[0011] Further, the neural network model is provided with multiple, and based on multiple trained neural network models, the reduced order coefficient corresponding to the vibration data matrix is obtained, comprising:

[0012] Each trained neural network model outputs a branch reduced order coefficient respectively, and multiple branch reduced order coefficients are obtained;

[0013] The multiple branch reduced order coefficients are stacked and fused to obtain the reduced order coefficient corresponding to the vibration data matrix under different working condition data.

[0014] Further, the neural network model includes MLP, CNN and LSTM.

[0015] Further, the method further comprises preprocessing of real-time working condition data, and the preprocessing includes filtering, standardization and normalization processing of real-time working condition data.

[0016] Further, the pipeline vibration data is obtained based on fluid and structural dynamics calculation method.

[0017] Further, the method further comprises calculating the reconstruction error, and detecting the vibration anomaly when the reconstruction error is greater than the set threshold, and determining the fault reason after detecting the vibration anomaly.

[0018] Further, the vibration anomaly detection includes single-point anomaly detection, continuous anomaly detection and energy conservation verification.

[0019] Further, the determination of the fault reason comprises:

[0020] generate a plurality of fault hypotheses, modify the real-time working condition data based on each fault hypothesis to obtain modified working condition data corresponding to each fault hypothesis;

[0021] output abnormal vibration data based on the reduced-order basis vector and the reduced-order coefficient under the modified working condition data;

[0022] determine the fault cause based on a comparison result of the abnormal vibration data and the real-time vibration data.

[0023] Further, the prediction method further includes incrementally training a neural network model with the abnormal vibration data and the real-time working condition data corresponding thereto as samples.

[0024] Another aspect of the present application discloses a pipeline vibration characteristic prediction system, comprising:

[0025] a construction module configured to construct a pipeline three-dimensional model, calculate pipeline vibration data under different working condition data based on the pipeline three-dimensional model, and construct a vibration data matrix under different working condition data;

[0026] a processing module configured to process the vibration data matrix under different working conditions by an intrinsic orthogonal decomposition method to obtain a reduced-order basis vector under different working conditions;

[0027] a generation module configured to obtain a reduced-order coefficient corresponding to the vibration data matrix under different working condition data based on at least one trained neural network model;

[0028] a prediction module configured to obtain real-time working condition data, and output predicted vibration data based on the reduced-order basis vector and the reduced-order coefficient under the real-time working condition data.

[0029] Compared with the prior art, the present application has the following beneficial effects:

[0030] 1. The present application combines the reduced-order basis vector and the neural network model, which can quickly predict the pipeline vibration change. This method can perceive the change of the overall dynamic characteristics of the pipeline network caused by the slight change of the key parameters, has extremely high prediction sensitivity for early and local abnormalities that are difficult to find by traditional methods, and realizes accurate prediction of the pipeline vibration.

[0031] 2. After determining the pipeline anomaly, the present application determines the fault cause by counterfactual reasoning, simulates specific physical faults (such as decreased support stiffness and increased fluid pulsation), and observes the matching degree of the prediction result and the real anomaly, which can infer the root physical cause of the anomaly and provide clear and feasible guidance for subsequent maintenance work. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 for the method flowchart of the present application;

[0033] Figure 2 for the fault cause determination flowchart. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work belong to the scope of protection of the present application.

[0035] A pipeline vibration characteristic prediction method, referring to Figure 1 , comprising:

[0036] S100: constructing a pipeline three-dimensional model, calculating pipeline vibration data under different working condition data based on the pipeline three-dimensional model, and constructing a vibration data matrix under each working condition data;

[0037] S200: processing the vibration data matrix under different working conditions by the intrinsic orthogonal decomposition method to obtain the reduced order basis vector under different working conditions;

[0038] S300: obtaining the reduced order coefficient corresponding to the vibration data matrix under different working condition data based on at least one trained neural network model;

[0039] S400: obtaining real-time working condition data, and outputting predicted vibration data based on the reduced order basis vector and the reduced order coefficient under the real-time working condition data.

[0040] Specifically, in step S100, the pipeline three-dimensional model is constructed to digitize the physical structure of the natural gas station booster area pipeline, and a three-dimensional model representation is constructed. Specifically, by obtaining the specific information (such as buffer tank, elbow, valve, support, flange, compressor, air cooler, oil remover, etc.) of the physical entities in the pipeline system, such as size, material, real-time working condition parameters, high-precision structure data is obtained to clarify the actual physical connection relationship between these physical entities, that is, the pipeline three-dimensional model can be constructed accordingly. At the same time, the standard pipeline design drawings, completion data, and maintenance records can be collected as auxiliary references for structure modeling and parameter completion. Through global pipeline system conversion to digital information, the physical topological association and mutual influence between pipeline, valve, support and other components can be fully considered. Compared with the isolated analysis of the measuring point by the traditional method, the present application can start from the system level to predict the vibration characteristic distribution of the whole pipeline network in real time and accurately, and provide global situational awareness for the operation personnel, greatly improving the prediction accuracy and breadth.

[0041] On the basis of the pipeline three-dimensional model, the finite element method is used to calculate the natural gas flow and heat transfer characteristics in the pipeline. The obtained natural gas pressure load and pipe wall temperature load are introduced into the transient structural dynamics model to complete the multi-physical field coupling analysis and obtain the stress and deformation distribution of the pipeline. Based on this method, a large amount of calculation and analysis is carried out to obtain the influence law of key parameters such as natural gas flow, temperature, pressure, etc. on the vibration characteristics of the pipeline, and a pipeline vibration characteristic database is constructed, i.e. vibration data under different working conditions are obtained.

[0042] After obtaining the pipeline vibration data under different working conditions, a vibration data matrix can be established based on the pipeline vibration data, and the vibration data matrix is processed by the proper orthogonal decomposition method (POD) to obtain the basis vector of the vibration data matrix, thereby reducing the calculation complexity and extracting the key vibration mode characteristics. Specifically, in step S200, for example, the vibration data matrix is , and the eigenvalue decomposition of the covariance matrix of the vibration data matrix satisfies formula (1):

[0043] (1)

[0044] In formula (1), represents the eigenvector, and represents the eigenvalue.

[0045] The first k eigenvectors are selected to form the reduced basis vector Φ of the vibration data matrix, which satisfies the energy ratio:

[0046] (2)

[0047] Through accurate eigenvalue decomposition, the basis vectors with a cumulative energy contribution rate of not less than 95% are selected. These basis vectors effectively represent the main vibration mode of the data and ensure comprehensive characterization of the pipeline vibration. In addition, the data is segmented into different time windows for processing, allowing the energy threshold of the reduced basis to be adjusted according to the specific dynamics of different time periods, thereby ensuring the dimension reduction accuracy under all working conditions.

[0048] In the above step S300, the neural network model is trained based on the working condition data and vibration data calculated by the pipeline three-dimensional model. In order to improve the generalization ability of the neural network model, the L2 regularization technique is used in the data training process to suppress the overfitting of the network. This technique limits the over-amplification of parameters by introducing the square sum of weights in the loss function. In addition, Bayesian optimization is used to search for the optimal Dropout probability p and learning rate η, and the formula is as follows:

[0049] (3)

[0050] ​In equation (3), For loss function, loss function Expected average performance on the validation set.

[0051] Based on the above optimization process, some neuron outputs can be randomly deactivated during training, further breaking the adaptability between neurons and improving the robustness of the model in various environments.

[0052] Meanwhile, in step S300, to improve the accuracy of prediction, this application provides multiple neural network models, and obtains reduction coefficients corresponding to vibration data matrices under different working conditions based on multiple trained neural network models. That is, each neural network model takes the working condition data as input, and the reduction coefficients ( As the output, during the prediction process, multiple branch reduction coefficients corresponding to the same working condition data are obtained through multiple neural network models. Finally, the reduction coefficients from multiple branches are integrated to obtain the reduction coefficients corresponding to the data for this working condition. In some embodiments, this application establishes three neural network models, specifically including MLP (Multilayer Perceptron), CNN (Convolutional Neural Network), and LSTM (Long Short-Term Memory). MLP is suitable for global nonlinear fitting of parameters, CNN captures local spatial correlations between parameters (such as vibration coupling between adjacent measuring points), and LSTM is used to model the temporal dependence of vibration signals (such as pressure wave propagation). Furthermore, after the neural network models are constructed, K-fold cross-validation (K=5) can be used to evaluate the performance of each model, and stacking fusion can be used to output reduced-order coefficients. The formula is as follows:

[0053] (4)

[0054] in w j The weights represent the reduction coefficients of each neural network model, and the weights... w j The mean square error of the validation set is determined through inverse optimization.

[0055] In some embodiments, the specific structure of the above model is as follows:

[0056] MLP: 3 hidden layers (128-64-32 nodes), ReLU activated;

[0057] CNN: 3 layers of 1D convolution (16-32-64 channels), global pooling;

[0058] LSTM: bi-directional structure, 64 hidden units.

[0059] In the actual working condition process, in step S400, the real-time working condition data can be cleaned, that is, the real-time working condition data is preprocessed to ensure the accuracy of the input data. Exemplarily, the preprocessing process includes screening and eliminating abnormal values, eliminating noise and missing data that may exist in the data, and at the same time, in order to enable the data to be effectively processed in the model, the input parameters are standardized and normalized to ensure that the dimensional differences are eliminated and all variables are in a unified scale. In other examples, an adaptive historical data trend analysis tool can be introduced to automatically identify and mark extreme working conditions, thereby enhancing the response capability of the model to abnormal conditions.

[0060] After obtaining the real-time working condition data, the reduced basis vectors and the reduced coefficients of the vibration data matrix corresponding to the real-time working condition data are obtained through the above steps, the reduced vectors and the reduced coefficients are linearly combined, and the pipeline predicted vibration data is output, so that the high-dimensional physical field (such as pipeline vibration) state can be restored, and the real-time prediction of the pipeline vibration characteristics is ensured.

[0061] In some embodiments, with reference to Figure 2 The above method further includes calculating a reconstruction error, and detecting a vibration anomaly when the reconstruction error is greater than a set threshold value, and determining a fault cause after detecting the vibration anomaly.

[0062] Specifically, the threshold setting of the reconstruction error and the detection of the vibration anomaly are realized based on the reduced coefficients and the spatiotemporal gradient to construct a feature vector. Specifically, the vibration feature vector and the distribution parameter are represented as follows:

[0063] Vibration feature vector: reduced coefficient and spatiotemporal gradient c are spliced into joint features .

[0064] Distribution parameter: mean vector , covariance .

[0065] Correspondingly, the above set threshold value (i.e., the subsequent anomaly threshold value) (99% confidence interval), when the reconstruction error significantly increases and exceeds the preset anomaly threshold value, it indicates that the current pipeline operating state deviates from the known normal distribution, thereby determining that an abnormal vibration is detected. After detecting the abnormal vibration, further detection of the vibration anomaly is performed, that is, a rapid response primary detection is performed, including single-point anomaly and continuous anomaly:

[0066] Single-point anomaly: (5)

[0067] In formula (5), v t is the vibration feature vector at the current time, μ is the mean vector of the vibration feature under normal working conditions, and is the covariance matrix of the vibration feature under normal working conditions, M ( v t is the Mahalanobis distance, indicating the deviation of the current data from the normal distribution, D th represents a preset abnormal threshold, and if it is exceeded, it is determined to be abnormal.

[0068] Continuous anomaly: sliding window mean out-of-limit triggering (6)

[0069] In formula (6), represents the cumulative sum of the Mahalanobis distance in the sliding window (the last 5 time points).

[0070] After the primary detection, the next level of verification is needed to prevent false positives, and the energy conservation test is performed.

[0071] Energy conservation test: wherein, E pred is the predicted energy value (such as vibration energy or structural response energy), is the measured energy value (such as vibration energy or strain energy collected by the sensor), and if the energy conservation test cannot be met, it is determined to be a sensor failure. After determining abnormal vibration, the determination of the fault cause is needed, specifically, the determination of the fault cause includes:

[0072] Generating a plurality of fault hypotheses, modifying the real-time working condition data based on each fault hypothesis to obtain modified working condition data corresponding to each fault hypothesis;

[0073] Outputting abnormal vibration data based on the reduced order basis vector and the reduced order coefficient under the modified working condition data;

[0074] Determining the fault cause based on the comparison result of the abnormal vibration data and the real-time vibration data.

[0075] Specifically, one or more possible fault hypotheses (such as "loose support") are generated. Define the fault space wherein θ is the physical parameter (such as stiffness k , damping c ), and the generation rule is:

[0076] (7)

[0077] In formula (7), represents a fault hypothesis space, containing all possible fault modes, h i ( θ ) is the first i fault hypothesis, θ is a physical parameter (such as stiffness k, damping c, mass m, etc.), δ indicates the parameter disturbance ratio (such as 0.2 indicating a 20% deviation).

[0078] The fault is input into the above model, and the vibration state of the pipeline under the assumption condition is calculated. Finally, the fault prediction result is compared with the actually observed abnormal vibration data, and the reconstruction error and the physical rationality are comprehensively determined to determine the fault cause, wherein the reconstruction error and the physical rationality are determined as follows:

[0079] (8)

[0080] In formula (8), h * is the optimal fault hypothesis, h i is the first i candidate fault hypothesis, v obs is the observation data, v pred is the predicted data under the fault hypothesis h i , λ is a regularization coefficient.

[0081] The fault hypothesis corresponding to the prediction result most consistent with the true situation is determined as the fault cause of this abnormality.

[0082] In some embodiments, the prediction method further comprises incrementally training the neural network model with abnormal vibration data and corresponding real-time working condition data as samples. Specifically, based on the confirmed new working condition and its data as new effective samples, important weight parameters are retained through EWC (Elastic Weight Consolidation) update:

[0083] (9)

[0084] In formula (9), the updated loss function value is used to optimize or evaluate the model performance, L new is a basic loss term (such as the initial error or objective function value of the current model), is a weight coefficient (or importance factor) that controls the strength of the penalty for deviation of the i-th parameter, is a current parameter value (e.g., model weight, physical parameter, etc.), is a target parameter value (e.g., ideal parameter, reference value, or constraint).

[0085] Based on the above steps, the prediction model is incrementally trained, and through this process, the system realizes the ability of self-evolution and continuous learning.

[0086] Another aspect of the present application discloses a pipeline vibration characteristic prediction system, comprising:

[0087] A construction module configured to construct a pipeline three-dimensional model, calculate pipeline vibration data under different working condition data based on the pipeline three-dimensional model, and construct a vibration data matrix under different working condition data;

[0088] A processing module configured to process the vibration data matrix under different working conditions by an intrinsic orthogonal decomposition method to obtain reduced-order basis vectors under different working conditions;

[0089] A generation module configured to obtain reduced-order coefficients corresponding to the vibration data matrix under different working condition data based on at least one trained neural network model;

[0090] A prediction module configured to obtain real-time working condition data, and output predicted vibration data based on the reduced-order basis vectors and the reduced-order coefficients under the real-time working condition data.

[0091] Although embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting pipeline vibration characteristics, characterized in that, include: A three-dimensional model of the pipeline is constructed, and the pipeline vibration data under different working conditions is calculated based on the three-dimensional model of the pipeline. A vibration data matrix for each working condition is then constructed. Vibration data matrices under different working conditions are processed by the intrinsic orthogonal decomposition method to obtain reduced-order basis vectors under different working conditions; The order reduction coefficients corresponding to vibration data matrices under different working conditions are obtained based on at least one trained neural network model. Multiple neural network models are used, and the order reduction coefficients corresponding to vibration data matrices under different working conditions are obtained based on multiple trained neural network models; including: By outputting a branch reduction coefficient for each trained neural network model, multiple branch reduction coefficients are obtained; Multiple branch reduction coefficients are stacked and fused to obtain reduction coefficients corresponding to vibration data matrices under different working conditions. Acquire real-time operating condition data, and output predicted vibration data based on the reduced-order basis vectors and reduced-order coefficients under the real-time operating condition data; The reconstruction error is calculated, and vibration anomalies are detected when the reconstruction error exceeds a set threshold. After detecting vibration anomalies, the cause of the fault is determined. The determination of the cause of the fault includes: Multiple fault hypotheses are generated, and real-time operating data are modified based on each fault hypothesis to obtain modified operating data corresponding to each fault hypothesis. Output abnormal vibration data based on the reduced-order basis vectors and reduced-order coefficients under modified working condition data; The cause of the fault was determined based on the comparison results between abnormal vibration data and real-time vibration data.

2. The method for predicting pipeline vibration characteristics according to claim 1, characterized in that: Neural network models include MLP, CNN, and LSTM.

3. The method for predicting pipeline vibration characteristics according to claim 1, characterized in that: The method also includes preprocessing of real-time operating data, which includes filtering, standardization and normalization of real-time operating data.

4. The method for predicting pipeline vibration characteristics according to claim 1, characterized in that: The pipeline vibration data were obtained by solving the problem using fluid and structural dynamics calculation methods.

5. The method for predicting pipeline vibration characteristics according to claim 1, characterized in that: Vibration anomaly detection includes single-point anomaly detection, continuous anomaly detection, and energy conservation verification.

6. The method for predicting pipeline vibration characteristics according to claim 1, characterized in that: The prediction method also includes incremental training of the neural network model using abnormal vibration data and corresponding real-time operating condition data as samples.

7. A pipeline vibration characteristic prediction system, characterized in that, include: The module is configured to build a 3D model of the pipeline, calculate the pipeline vibration data under different working conditions based on the 3D model, and build a vibration data matrix under different working conditions. The processing module is configured to process the vibration data matrix under different working conditions using the intrinsic orthogonal decomposition method to obtain the reduced-order basis vectors under different working conditions. The generation module is configured to obtain reduction coefficients corresponding to vibration data matrices under different working conditions based on at least one trained neural network model. Multiple neural network models are configured, and the reduction coefficients obtained based on these models for different working conditions include: By outputting a branch reduction coefficient for each trained neural network model, multiple branch reduction coefficients are obtained; Multiple branch reduction coefficients are stacked and fused to obtain reduction coefficients corresponding to vibration data matrices under different working conditions. The prediction module is configured to acquire real-time operating condition data and output predicted vibration data based on the reduced-order basis vectors and reduced-order coefficients under the real-time operating condition data. The fault determination module is configured to calculate the reconstruction error, detect vibration anomalies when the reconstruction error exceeds a set threshold, and determine the cause of the fault after detecting the vibration anomaly. The determination of the cause of the fault includes: Multiple fault hypotheses are generated, and real-time operating data are modified based on each fault hypothesis to obtain modified operating data corresponding to each fault hypothesis. Output abnormal vibration data based on the reduced-order basis vectors and reduced-order coefficients under modified working condition data; The cause of the fault was determined based on the comparison results between abnormal vibration data and real-time vibration data.

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