Hydraulic machinery state monitoring method based on anomaly detection and fault diagnosis

Abstract

The invention discloses a hydraulic machinery state monitoring method based on anomaly detection and fault diagnosis. The method comprises the following steps: S1, collecting and preprocessing an original vibration signal; s2, multi-domain feature extraction based on TFFVMD is carried out; s3, carrying out anomaly detection based on SVDD; s4, fault diagnosis based on SVM classification; and S5, equipment online maintenance and model iterative optimization are carried out. According to the method, through the steps of data acquisition, multi-domain feature extraction, anomaly detection, fault diagnosis and model updating, a monitoring closed loop covering the full period of equipment operation is formed, hydraulic machinery state features are fully extracted from multiple dimensions such as time domain and frequency domain, detection and accurate recognition of uncertain fault types are achieved, the fault misdiagnosis rate is reduced, and the fault diagnosis efficiency is improved. And a solution is provided for intelligent operation and maintenance of hydraulic machinery.

Description

Technical Field

[0001] This invention relates to the field of power engineering technology, and in particular to a method for monitoring the condition of hydraulic machinery based on anomaly detection and fault diagnosis. Background Technology

[0002] Hydraulic machinery is a key piece of equipment for converting water energy or lifting and transporting water, playing a vital role in water resource development and utilization, energy production, and people's livelihood. The maintenance of hydraulic machinery involves two main tasks: condition monitoring and control. Control relies on the results of condition monitoring; therefore, reliable condition monitoring results are a crucial prerequisite for making reasonable control decisions. Vibration signals are an important source of information for equipment health monitoring, so existing research often utilizes vibration signals to detect or diagnose various faults in hydraulic machinery. Vibration characteristics typically include time-domain, frequency-domain, and time-frequency-domain features. The limitation of these feature extraction methods is that features from a single or two domains can only reflect limited sample information, and time-frequency-domain methods used to filter signal noise may filter out some crucial information. On the other hand, deep learning is playing an increasingly important role in the anomaly detection and fault diagnosis of hydraulic machinery. However, the excellent performance of deep learning models often depends on massive amounts of data. For hydraulic machinery lacking sufficient fault data in the early stages of operation, deep learning models may perform poorly. Furthermore, due to a lack of training data, most current condition monitoring models struggle to simultaneously meet the needs of "early warning" and "fault location," cannot handle uncertain faults, and have low diagnostic accuracy.

[0003] Variational Mode Decomposition (VMD) is an adaptive signal processing method that can decompose complex multi-component signals into several intrinsic mode functions (IMFs) with specific frequency characteristics. It is often used for signal denoising and feature extraction.

[0004] Support Vector Data Description (SVDD) is a machine learning algorithm used for anomaly detection. It identifies anomalous data that deviates from the distribution of the training data by constructing a closed hypersphere to enclose the training data.

[0005] Support Vector Machine (SVM) is a mathematical model based on statistical learning theory and structural risk minimization. It can solve binary and multi-class classification problems and is widely used in tasks such as classification, regression, and anomaly detection. Its core idea is to find the optimal hyperplane to separate data into different categories, and it performs well in scenarios with small samples and high-dimensional data.

[0006] Given that existing methods suffer from insufficient feature extraction and inability to handle uncertain faults in hydraulic machinery condition monitoring, we propose a hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis. By using the multi-domain feature extraction method TFF_VMD and combining it with SVDD and SVM methods, a condition monitoring framework including anomaly detection and fault diagnosis is constructed. This method can form a monitoring closed loop covering the entire operation cycle of hydraulic machinery, solve the problem of early warning and diagnosis under the scarcity of fault data in the early stage of equipment operation, reduce the false diagnosis rate of faults, and initially realize intelligent operation and maintenance of hydraulic machinery.

[0008] To achieve the above objectives, this application provides a hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis, comprising the following steps:

[0009] S1. Acquisition and preprocessing of raw vibration signals; S2. Multi-domain feature extraction based on TFF_VMD; S3. Anomaly detection based on SVDD; S4. Fault diagnosis based on SVM classification; S5. Online equipment maintenance and model iteration optimization; The multi-domain feature extraction based on TFF_VMD includes VMD decomposition, TFF multi-domain feature extraction, and feature normalization. VMD decomposition is used to decompose the original vibration signal into multiple IMFs. TFF multi-domain feature extraction is used to extract time-domain statistical features, frequency-domain features, and power spectrum features from the original vibration signal and IMFs, respectively. Feature normalization is used to normalize the multi-domain features of each original vibration signal as input samples for anomaly detection and fault diagnosis.

[0010] In S1, hydraulic machinery condition monitoring data are collected, including operating condition data and vibration data from different monitoring points. These data are then processed into samples of uniform length and centered to form a sample set. For a one-dimensional time series t is a time variable. For the observation corresponding to time t, its centering formula is: ; In the formula, for The mean.

[0011] In S2, time-domain statistical features include maximum, minimum, median, mean, mean amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor.

[0012] The calculation formulas for time-domain statistical feature extraction are as follows: Maximum value: ; Minimum value: ; Median: ; average value: ; Average amplitude: ; Root mean square: ; Standard deviation: ; Range: ; Skewness: ; kurtosis: ; Waveform factor: ; Peak factor: ,in ; Pulse factor: ; Margin factor: ; In the formula, x This represents the FFT amplitude spectrum of a one-dimensional time series. N For sequence x Length, It is a sequence x The i Values.

[0013] The method for frequency domain feature extraction is as follows: Fast Fourier Transform is performed on the original signal and IMF to obtain the amplitude spectrum in the frequency domain. The maximum value, minimum value, median, average value, average amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor are extracted from the amplitude spectrum to capture fault-related characteristic frequencies.

[0014] The power spectrum characteristics include the power spectrum centroid, power spectrum broadening, and average power spectrum.

[0015] The calculation formulas for power spectrum feature extraction are as follows: Power spectrum centroid: ; Power spectral broadening: ; Average power spectrum: ; In the formula, K The length of the power spectrum obtained by the Fast Fourier Transform. It is the first of the Fast Fourier Transform. i One frequency, It is the first power spectrum i Values.

[0016] The feature standardization uses the min-max normalization method to map all features to... The range, maximum and minimum normalization formula is: ; In the formula, x Indicates original features, This represents the features after normalization. The range of values ​​is .

[0017] In S3, anomaly detection based on SVDD includes the following steps: S3-1. Construct an SVDD model based on normal samples; S3-2. Calculate the radius of the hypersphere by solving a convex quadratic programming optimization problem. and center ; S3-3, Set the rules for anomaly detection.

[0018] A support vector data description model is trained using normal-state data to construct a closed hyperspherical boundary surrounding the normal samples. , m For the feature dimension, the expression for SVDD is: ; ; ; In the formula, It is the radius of the hypersphere. It is the center of the hypersphere. It is a slack variable. This represents the penalty factor, used to control the balance between model size and the number of external data samples. express Projection features; When normal samples cannot be effectively enclosed by a linear hypersphere in the original feature space, SVDD maps the data to a high-dimensional feature space using a kernel function, thereby fitting the nonlinear distribution of the original space with a linear hypersphere in the high-dimensional space. The radial basis function kernel is chosen, and its expression is: ; In the formula, This represents the kernel function, given two input samples. , , Let represent the squared Euclidean distance between two samples. Represents the hyperparameters of the kernel function; After introducing the kernel function, the optimization problem is transformed into a dual form. At this point, the hypersphere center *a* and radius *R* are calculated using support vectors. Based on the Lagrange multiplier method, the dual programming problem expression in the above equation is obtained: ; ; ; In the formula, These are Lagrange multipliers, where the formulas for calculating the center *a* and radius *R* of the hypersphere are: ; ; In the formula, Let the support vectors have coefficients that satisfy... , ; radius The final expression is: ; In the formula, For the set of support vectors SV The number of samples included. This represents a sample in the support vector set SV. Represents all training samples. Represents the Lagrange multipliers; The anomaly detection rules based on SVDD are as follows: The TFF_VMD multi-domain features of the original vibration signal are used as samples to input into the trained SVDD model. At least 10 samples are detected each time, and the distances of each sample to the center of the hypersphere are compared. and hypersphere radius The size, if more than 60% of the samples meet the requirements L > R If the condition is met, it indicates a device malfunction and triggers an alarm; otherwise, it indicates the device is operating normally. The decision boundary of the SVDD model is defined as follows: ; In the formula, This represents the distance from the sample to be tested to the center 'a' of the hypersphere. This represents the kernel function mapping.

[0019] In S4, fault diagnosis based on SVM classification includes the following steps: S4-1, SVM model establishment; The decision function of a nonlinear SVM classifier is expressed as: ; In the formula, and It is an adjustable parameter of the decision function. The input is The output of the time classifier express Mapping features in the new feature space; The SVM optimization problem is transformed by constructing a hinge loss function: ; ; ; In the formula, , representing the penalty factor, and Inversely proportional, As slack variables, The normal vector of the classification hyperplane, For the bias term of the classification hyperplane, This represents the total number of training samples. For the first i Original samples The result after feature mapping; The RBF radial basis function was chosen as the kernel function for SVM, and Introducing the Lagrange multiplier method, we obtain the dual problem of the above equation as follows: ; ; ; In the formula, and It is a Lagrange multiplier. and They represent the first i The first sample and the first j The label of each sample It is the total number of samples. It is a regularization parameter; SVM classification hyperplane intercept The decision functions are expressed as follows: ; ; In the formula, The normal vector of the classifying hyperplane is represented by T, and its transpose is also represented by T. Indicates the first i Original samples The result after feature mapping Here is the kernel function used to calculate the th kernel. j Sample and the i-th sample Inner product in high-dimensional feature space, This is the result after feature mapping of the new sample z. The sample to be classified; Key parameters of the SVM model include the penalty factor. C Given the kernel function parameters, the training set is input into the SVM model with the determined kernel function and optimal parameters. The optimal classification hyperplane is constructed by solving a convex quadratic programming problem, with the mathematical objective being:

[0020] in, Let be the normal vector of the hyperplane. b For bias terms, For kernel function mapping, As slack variables, For sample labels; S4-2, SVM fault diagnosis; When the SVDD model detects an anomaly, it inputs the TFF multi-domain features corresponding to the anomaly sample into the trained SVM model. The model determines the category of the sample based on the distance from the hyperplane, thereby determining the specific fault type and outputting the diagnostic result.

[0021] In S5, online equipment maintenance and model iterative optimization include the following steps: If the anomaly detection phase determines that the equipment is in a normal state, then the equipment will continue to operate; if the anomaly detection phase determines that the equipment is in an abnormal state and the specific fault type is identified, then corresponding equipment maintenance recommendations will be given. Newly accumulated normal operation samples are added to the training set of the SVDD model to update the hyperspherical boundary used for anomaly detection and improve anomaly detection accuracy. Newly accumulated fault samples are labeled and added to the training set of the SVM classification model to enhance the diagnostic capability of the SVM classification model, expand the fault identification range of the model, and adapt to the condition monitoring needs of the entire equipment life cycle.

[0022] A method for monitoring the condition of hydraulic machinery based on anomaly detection and fault diagnosis includes the following steps: S1. Acquisition and preprocessing of raw vibration signals; S2. Multi-domain feature extraction based on TFF_VMD; S3. Anomaly detection based on SVDD; S4. Fault diagnosis based on SVM classification; S5. Online equipment maintenance and model iteration optimization; The multi-domain feature extraction based on TFF_VMD includes VMD decomposition, TFF multi-domain feature extraction, and feature normalization. VMD decomposition is used to decompose the original vibration signal into multiple IMFs. TFF multi-domain feature extraction is used to extract time-domain statistical features, frequency-domain features, and power spectrum features from the original vibration signal and IMFs, respectively. Feature normalization is used to normalize the multi-domain features of each original vibration signal as input samples for anomaly detection and fault diagnosis.

[0023] In S1, hydraulic machinery condition monitoring data are collected, including operating condition data and vibration data from different monitoring points. These data are then processed into samples of uniform length and centered to form a sample set. For a one-dimensional time series t is a time variable. For the observation corresponding to time t, its centering formula is: ; In the formula, for The mean.

[0024] In S2, time-domain statistical features include maximum, minimum, median, mean, mean amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor.

[0025] The calculation formulas for time-domain statistical feature extraction are as follows: Maximum value: ; Minimum value: ; Median: ; average value: ; Average amplitude: ; Root mean square: ; Standard deviation: ; Range: ; Skewness: ; kurtosis: ; Waveform factor: ; Peak factor: ,in ; Pulse factor: ; Margin factor: ; In the formula, x This represents the FFT amplitude spectrum of a one-dimensional time series. N For sequence x Length, It is a sequence x The i Values.

[0026] The method for frequency domain feature extraction is as follows: Fast Fourier Transform is performed on the original signal and IMF to obtain the amplitude spectrum in the frequency domain. The maximum value, minimum value, median, average value, average amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor are extracted from the amplitude spectrum to capture fault-related characteristic frequencies.

[0027] The power spectrum characteristics include the power spectrum centroid, power spectrum broadening, and average power spectrum.

[0028] The calculation formulas for power spectrum feature extraction are as follows: Power spectrum centroid: ; Power spectral broadening: ; Average power spectrum: ; In the formula, K The length of the power spectrum obtained by the Fast Fourier Transform. It is the first of the Fast Fourier Transform. i One frequency, It is the first power spectrum i Values.

[0029] The feature standardization uses the min-max normalization method to map all features to... The range, maximum and minimum normalization formula is: ; In the formula, x Indicates original features, This represents the features after normalization. The range of values ​​is .

[0030] In S3, anomaly detection based on SVDD includes the following steps: S3-1. Construct an SVDD model based on normal samples; S3-2. Calculate the radius of the hypersphere by solving a convex quadratic programming optimization problem. and center ; S3-3, Set the rules for anomaly detection.

[0031] A support vector data description model is trained using normal-state data to construct a closed hyperspherical boundary surrounding the normal samples. , m For the feature dimension, the expression for SVDD is: ; ; ; In the formula, It is the radius of the hypersphere. It is the center of the hypersphere. It is a slack variable. This represents the penalty factor, used to control the balance between model size and the number of external data samples. express Projection features; When normal samples cannot be effectively enclosed by a linear hypersphere in the original feature space, SVDD maps the data to a high-dimensional feature space using a kernel function, thereby fitting the nonlinear distribution of the original space with a linear hypersphere in the high-dimensional space. The radial basis function kernel is chosen, and its expression is: ; In the formula, This represents the kernel function, given two input samples. , , Let represent the squared Euclidean distance between two samples. Represents the hyperparameters of the kernel function; After introducing the kernel function, the optimization problem is transformed into a dual form. At this point, the hypersphere center *a* and radius *R* are calculated using support vectors. Based on the Lagrange multiplier method, the dual programming problem expression in the above equation is obtained: ; ; ; In the formula, These are Lagrange multipliers, where the formulas for calculating the center *a* and radius *R* of the hypersphere are: ; ; In the formula, Let the support vectors have coefficients that satisfy... , ; radius The final expression is: ; In the formula, For the set of support vectors SV The number of samples included. This represents a sample in the support vector set SV. Represents all training samples. Represents the Lagrange multipliers; The anomaly detection rules based on SVDD are as follows: The TFF_VMD multi-domain features of the original vibration signal are used as samples to input into the trained SVDD model. At least 10 samples are detected each time, and the distances of each sample to the center of the hypersphere are compared. and hypersphere radius The size, if more than 60% of the samples meet the requirements L > R If the condition is met, it indicates a device malfunction and triggers an alarm; otherwise, it indicates the device is operating normally. The decision boundary of the SVDD model is defined as follows: ; In the formula, This represents the distance from the sample to be tested to the center 'a' of the hypersphere. This represents the kernel function mapping.

[0032] In S4, fault diagnosis based on SVM classification includes the following steps: S4-1, SVM model establishment; The decision function of a nonlinear SVM classifier is expressed as: ; In the formula, and It is an adjustable parameter of the decision function. The input is The output of the time classifier express Mapping features in the new feature space; The SVM optimization problem is transformed by constructing a hinge loss function: ; ; ; In the formula, , representing the penalty factor, and Inversely proportional, As slack variables, The normal vector of the classification hyperplane, For the bias term of the classification hyperplane, This represents the total number of training samples. For the first i Original samples The result after feature mapping; The RBF radial basis function was chosen as the kernel function for SVM, and Introducing the Lagrange multiplier method, we obtain the dual problem of the above equation as follows: ; ; ; In the formula, and It is a Lagrange multiplier. and They represent the first i The first sample and the first j The label of each sample It is the total number of samples. It is a regularization parameter; SVM classification hyperplane intercept The decision functions are expressed as follows: ; ; In the formula, The normal vector of the classifying hyperplane is represented by T, and its transpose is also represented by T. Indicates the first i Original samples The result after feature mapping Here is the kernel function used to calculate the th kernel. j Sample and the i-th sample Inner product in high-dimensional feature space, This is the result after feature mapping of the new sample z. The sample to be classified; Key parameters of the SVM model include the penalty factor. CGiven the kernel function parameters, the training set is input into the SVM model with the determined kernel function and optimal parameters. The optimal classification hyperplane is constructed by solving a convex quadratic programming problem, with the mathematical objective being:

[0033] in, Let be the normal vector of the hyperplane. b For bias terms, For kernel function mapping, As slack variables, For sample labels; S4-2, SVM fault diagnosis; When the SVDD model detects an anomaly, it inputs the TFF multi-domain features corresponding to the anomaly sample into the trained SVM model. The model determines the category of the sample based on the distance from the hyperplane, thereby determining the specific fault type and outputting the diagnostic result.

[0034] In S5, online equipment maintenance and model iterative optimization include the following steps: If the anomaly detection phase determines that the equipment is in a normal state, then the equipment will continue to operate; if the anomaly detection phase determines that the equipment is in an abnormal state and the specific fault type is identified, then corresponding equipment maintenance recommendations will be given. Newly accumulated normal operation samples are added to the training set of the SVDD model to update the hyperspherical boundary used for anomaly detection and improve anomaly detection accuracy. Newly accumulated fault samples are labeled and added to the training set of the SVM classification model to enhance the diagnostic capability of the SVM classification model, expand the fault identification range of the model, and adapt to the condition monitoring needs of the entire equipment life cycle.

[0035] Compared with the prior art, the above-conceptual technical solution conceived in this application has the following beneficial effects: 1. This invention forms a monitoring closed loop covering the entire operation cycle of equipment through data acquisition, multi-domain feature extraction, anomaly detection, fault diagnosis, and model updating. It fully extracts the state characteristics of hydraulic machinery from multiple dimensions such as time domain and frequency domain, and realizes the detection and accurate identification of uncertain fault types, reducing the false diagnosis rate of faults and providing a solution for intelligent operation and maintenance of hydraulic machinery.

[0036] 2. This invention addresses the problem of insufficient feature extraction in existing methods for hydraulic machinery condition monitoring. It designs a novel feature extraction method, TFF_VMD multi-domain feature extraction, which can fully extract the equipment condition features contained in hydraulic machinery vibration signals, reflecting the equipment's health status. Furthermore, to address the shortcomings of existing methods in handling uncertain faults, a comprehensive condition monitoring framework based on SVDD and SVM is proposed. The monitoring task is divided into two parts: anomaly detection based on SVDD and fault diagnosis based on SVM. Combined with data update and model iteration strategies, a monitoring closed loop covering the entire equipment operation cycle is formed, enabling intelligent fault early warning and diagnosis, extending equipment lifespan, and reducing maintenance costs. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0038] Figure 1 The method design steps of this invention are described below.

[0039] Figure 2 This is a flowchart of the TFF_VMD multi-domain feature extraction process of the present invention.

[0040] Figure 3 This is a flowchart of the anomaly detection algorithm of the present invention.

[0041] Figure 4 This is a schematic diagram of the condition monitoring framework of the present invention. Detailed Implementation

[0042] To more clearly illustrate the purpose, technical solution, and beneficial effects of this application, a further detailed description of this application is provided below in conjunction with illustrations and specific embodiments. It should be specifically noted that the specific embodiments described below are only for illustrating the technical content of this application and do not constitute a limitation on the scope of protection of this application.

[0043] Regarding the explanation of terminology: In this application, "and / or" is used to describe the relationship between related objects, covering three possible situations: taking "A and / or B" as an example, it can indicate the situation where only A exists, A and B exist simultaneously, or only B exists; the symbol " / " indicates the "or" relationship between related objects, such as "A / B" which refers to A or B.

[0044] Regarding the description of the embodiments: The terms "exemplary" and "for example" appearing in this application are only used to illustrate the technical solutions through specific examples. It should be particularly emphasized that any implementation method or design scheme marked as "exemplary" or "for example" should not be construed as having an advantage over other solutions. Such expressions are only used to present the technical concepts more intuitively.

[0045] Example 1: See Figure 1 This embodiment provides a hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis, including the following steps: S1. Acquisition and preprocessing of raw vibration signals; S2. Multi-domain feature extraction based on TFF_VMD; S3. Anomaly detection based on SVDD; S4. Fault diagnosis based on SVM classification; S5. Online equipment maintenance and model iteration optimization; The multi-domain feature extraction based on TFF_VMD includes VMD decomposition, TFF multi-domain feature extraction, and feature normalization. VMD decomposition is used to decompose the original vibration signal into multiple IMFs. TFF multi-domain feature extraction is used to extract time-domain statistical features, frequency-domain features, and power spectrum features from the original vibration signal and IMFs, respectively. Feature normalization is used to normalize the multi-domain features of each original vibration signal as input samples for anomaly detection and fault diagnosis.

[0046] This invention addresses the problem of insufficient feature extraction in existing methods for hydraulic machinery condition monitoring. It designs a novel feature extraction method, TFF_VMD multi-domain feature extraction, which fully extracts the equipment condition characteristics contained in hydraulic machinery vibration signals, reflecting the equipment's health status. Furthermore, to address the shortcomings of existing methods in handling uncertain faults, a comprehensive condition monitoring framework based on SVDD and SVM is proposed. The monitoring task is divided into two parts: anomaly detection based on SVDD and fault diagnosis based on SVM. By combining data update and model iteration strategies, a monitoring closed loop covering the entire equipment operation cycle is formed, enabling intelligent fault early warning and diagnosis, extending equipment lifespan, and reducing maintenance costs.

[0047] (1) Acquisition and preprocessing of raw vibration signals.

[0048] Data from hydraulic machinery condition monitoring is collected, including operating condition data and vibration data from different monitoring points. This data is then processed into samples of uniform length, centered, and used to form a sample set. For one-dimensional time series... t is a time variable. For the observation corresponding to time t, its centering formula is: (1) In the formula, for The mean.

[0049] (2) See Figure 2 Multi-domain feature extraction based on TFF_VMD.

[0050] 1) VMD decomposition: The original vibration signal was decomposed into 5 IMFs (Intrinsic Mode Functions) using the VMD method.

[0051] 2) TFF multi-domain feature extraction: The TFF consists of time-domain statistical features (T), fast Fourier transform (FFT) amplitude spectrum statistical features (F), and power spectrum features (F).

[0052] ① Temporal feature extraction: The original vibration signal and 14 time-domain statistical characteristics of 5 IMFs were calculated to reflect the signal amplitude, energy and impact characteristics.

[0053] ② Frequency domain feature extraction: The original signal and five IMFs were subjected to Fast Fourier Transform (FFT) to obtain the amplitude spectrum in the frequency domain. Fourteen time-domain statistical features of the amplitude spectrum were extracted to capture fault-related characteristic frequencies.

[0054] The 14 statistical characteristics are: maximum value, minimum value, median, mean, mean amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor.

[0055] The calculation formulas for statistical feature extraction are as follows: Maximum value: ; indicates the maximum value in the signal.

[0056] Minimum value: ; represents the minimum value in the signal.

[0057] Median: It describes the central trend of a set of data, reflecting the medium level of the data.

[0058] average value: ; indicates the offset of the signal.

[0059] Average amplitude: It reflects the overall energy level or intensity characteristics of the signal.

[0060] Root mean square: ; indicates the energy level of a signal over a period of time.

[0061] Standard deviation: ; indicates the degree of signal fluctuation.

[0062] Range: ; reflects the range of signal variation.

[0063] Skewness: ; measures the degree of skewness of the signal probability density function.

[0064] kurtosis: ; indicates the sharpness of the signal distribution over a period of time.

[0065] Waveform factor: It reflects the sharpness of the signal waveform.

[0066] Peak factor: ,in ; indicates the size of the spike in the signal.

[0067] Pulse factor: Used to detect whether a signal contains an impact component.

[0068] Margin factor: Used to assess the degree of equipment failure.

[0069] In the formula, x This represents the FFT amplitude spectrum of a one-dimensional time series. N For sequence x Length, It is a sequence x The i Values.

[0070] The method for frequency domain feature extraction is as follows: Fast Fourier Transform is performed on the original signal and IMF to obtain the amplitude spectrum in the frequency domain. The maximum value, minimum value, median, average value, average amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor are extracted from the amplitude spectrum to capture fault-related characteristic frequencies.

[0071] ③ Power spectrum feature extraction.

[0072] The power spectrum characteristics include three features: power spectrum centroid, power spectrum broadening, and average power spectrum.

[0073] The calculation formulas for power spectrum feature extraction are as follows: Power spectrum centroid: It reflects the energy concentration trend of the signal in the frequency domain.

[0074] Power spectral broadening: It reflects the distribution characteristics of the signal in the frequency domain.

[0075] Average power spectrum: It reflects the long-term stability characteristics of the signal in the frequency domain.

[0076] In the formula, KThe length of the power spectrum obtained by FFT (Fast Fourier Transform) is... For the FFT (Fast Fourier Transform) of the th i One frequency, It is the first power spectrum i Values.

[0077] 3) Feature standardization: To eliminate differences in data units between different features and make features of different dimensions comparable, thereby improving the stability and generalization ability of model training, a min-max normalization method is used to map all features to... The range. The maximum and minimum normalization formula is shown in equation (2): (2) In the formula, x Indicates original features, This represents the features after normalization. The range of values ​​is .

[0078] (3) Anomaly detection based on SVDD.

[0079] See Figure 3 Anomaly detection based on SVDD includes the following steps: S3-1. Construct an SVDD model based on normal samples; S3-2. Calculate the radius of the hypersphere by solving a convex quadratic programming optimization problem. and center ; S3-3, Set the rules for anomaly detection.

[0080] Specifically, in S3-1, SVDD, as a classic single-class classification algorithm, transforms the outlier detection problem into comparing the distance from the test sample to the center of the hypersphere with the radius of the hypersphere by constructing a minimum hypersphere that encloses the training samples. If the SVDD model is trained using only normal state data, it can distinguish between abnormal and normal samples, i.e., anomaly detection.

[0081] The mathematical modeling of SVDD can be transformed into a convex quadratic programming problem, with the goal of minimizing the volume of the hypersphere (i.e. minimizing the radius R) while allowing a small number of samples (anomalies or noise) to fall outside the sphere (handled through slack variables).

[0082] Assume the training samples are ( m (where is the feature dimension), the optimization problem corresponding to SVDD modeling can be expressed as: ; ; (3) In the formula, It is the radius of the hypersphere. It is the center of the hypersphere. It is a slack variable. This represents the penalty factor, used to control the balance between model size and the number of external data samples. express The projection features.

[0083] In S3-2, when normal samples cannot be effectively enclosed by a linear hypersphere in the original feature space, SVDD maps the data to a high-dimensional feature space using a kernel function, thereby fitting the nonlinear distribution of the original space with a linear hypersphere in the high-dimensional space. In this method, the radial basis function (RBF) is chosen as the kernel function, and its expression is shown in equation (4): (4) In the formula, This represents the kernel function, given two input samples. , , Let represent the squared Euclidean distance between two samples. This represents the hyperparameters of the kernel function.

[0084] After introducing the kernel function, the optimization problem is transformed into a dual form. At this time, the center a and radius R of the hypersphere are calculated through support vectors. Based on the Lagrange multiplier method, the dual programming problem expression (5) of the above equation is obtained: ; ; (5) In the formula, These are Lagrange multipliers, where the formulas for calculating the center *a* and radius *R* of the hypersphere are: (6) (7) In the formula, Let the support vectors have coefficients that satisfy... , .

[0085] radius The final expression is: (8) In the formula, For the set of support vectors SVThe number of samples included. This represents a sample in the support vector set SV. Represents all training samples. It represents the Lagrange multiplier.

[0086] In S3-3, the anomaly detection rules based on SVDD are as follows: The TFF_VMD multi-domain features of the original vibration signal are used as samples to input into the trained SVDD model. At least 10 samples are detected each time, and the distances of each sample to the center of the hypersphere are compared. and hypersphere radius The size, if more than 60% of the samples meet the requirements L > R If the condition is met, it indicates a device malfunction and triggers an alarm; otherwise, it indicates normal device operation. The decision boundary of the SVDD model is defined as follows: (9) In the formula, This represents the distance from the sample to be tested to the center 'a' of the hypersphere. This represents the kernel function mapping.

[0087] See Figure 4 In S4, fault diagnosis based on SVM classification includes the following steps: S4-1, SVM model establishment; SVM training algorithm is based on training samples A linear or nonlinear model is built that can classify new samples into a certain category. The SVM linear classifier accomplishes the classification task by placing a hyperplane between two linearly separable samples, while the SVM nonlinear classifier classifies nonlinearly separable samples by embedding a kernel function. Mapping to a new feature space yields mapped features that can be separated by a hyperplane within that mapped space. In practice, most problems involve solving nonlinearly separable problems. The decision function of a nonlinear SVM classifier can be expressed as: (10) In the formula, and It is an adjustable parameter of the decision function. The input is The output of the time classifier express Mapping features in the new feature space.

[0088] The SVM optimization problem is transformed by constructing a hinge loss function: ; ; (11) In the formula, , representing the penalty factor, and Inversely proportional, As slack variables, The normal vector of the classification hyperplane, For the bias term of the classification hyperplane, This represents the total number of training samples. For the first i Original samples The result after feature mapping.

[0089] The RBF radial basis function was chosen as the kernel function for SVM, and Introducing the Lagrange multiplier method, the dual problem of equation (11) is obtained as follows: ; ; (12) In the formula, and It is a Lagrange multiplier. and They represent the first i The first sample and the first j The label of each sample It is the total number of samples. It is the regularization parameter.

[0090] SVM classification hyperplane intercept The decision functions are expressed by equations (13) and (14), respectively: (13) (14) In the formula, The normal vector of the classifying hyperplane is represented by T, and its transpose is also represented by T. Indicates the first i Original samples The result after feature mapping Here is the kernel function used to calculate the th kernel. j Sample and the i-th sample Inner product in high-dimensional feature space, This is the result after feature mapping of the new sample z. The sample is to be classified.

[0091] Key parameters of the SVM model include the penalty factor C and the kernel function parameters. Using a grid search algorithm, with the classification accuracy of k-fold cross-validation as the objective function, the optimal combination of SVM parameters is sought to avoid overfitting or underfitting. The training set is input into the SVM model with the determined kernel function and optimal parameters. The optimal classification hyperplane is constructed by solving a convex quadratic programming problem, with the mathematical objective being:

[0092] in, Let be the normal vector of the hyperplane. b For bias terms, For kernel function mapping, As slack variables, For sample labels.

[0093] S4-2, SVM fault diagnosis; When the SVDD model detects an anomaly, it inputs the TFF multi-domain features corresponding to the anomaly sample into the trained SVM model. The model determines the category of the sample based on the distance from the hyperplane, thereby determining the specific fault type and outputting the diagnostic result.

[0094] In S5, online equipment maintenance and model iterative optimization include the following steps: 1) Online equipment maintenance. If the equipment is determined to be in a normal state during the anomaly detection phase, the equipment will continue to operate. If the equipment is determined to be in an abnormal state during the anomaly detection phase and the specific fault type is identified, corresponding equipment maintenance suggestions will be given.

[0095] 2) Model Iteration and Optimization. Newly accumulated normal operation samples are added to the training set of the SVDD model to update the hyperspherical boundary used for anomaly detection, thereby gradually improving the anomaly detection accuracy. Newly accumulated fault samples are labeled and added to the training set of the SVM classification model to enhance the diagnostic capability of the SVM classification model, expand the fault identification range of the model, and adapt to the status monitoring needs of the entire equipment life cycle.

[0096] While specific embodiments of the present invention have been described above, those skilled in the art should understand that the specific embodiments described are merely illustrative and not intended to limit the scope of the invention. Modifications and variations made by those skilled in the art in accordance with the spirit of the invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for monitoring the condition of hydraulic machinery based on anomaly detection and fault diagnosis, characterized in that, Includes the following steps: S1. Acquisition and preprocessing of raw vibration signals; S2. Multi-domain feature extraction based on TFF_VMD; S3. Anomaly detection based on SVDD; S4. Fault diagnosis based on SVM classification; S5. Online equipment maintenance and model iteration optimization; The multi-domain feature extraction based on TFF_VMD includes VMD decomposition, TFF multi-domain feature extraction, and feature normalization. VMD decomposition is used to decompose the original vibration signal into multiple IMFs. TFF multi-domain feature extraction is used to extract time-domain statistical features, frequency-domain features, and power spectrum features from the original vibration signal and IMFs, respectively. Feature normalization is used to normalize the multi-domain features of each original vibration signal as input samples for anomaly detection and fault diagnosis.

2. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, In S1, hydraulic machinery condition monitoring data are collected, including operating condition data and vibration data from different monitoring points. These data are then processed into samples of uniform length and centered to form a sample set. For a one-dimensional time series t is a time variable. For the observation corresponding to time t, its centering formula is: ； In the formula, for The mean.

3. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, In S2, time-domain statistical features include maximum, minimum, median, mean, mean amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor.

4. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 3, characterized in that, The calculation formulas for time-domain statistical feature extraction are as follows: Maximum value: ; Minimum value: ; Median: ; average value: ; Average amplitude: ; Root mean square: ; Standard deviation: ; Range: ; Skewness: ; kurtosis: ; Waveform factor: ; Peak factor: ,in ; Pulse factor: ; Margin factor: ; In the formula, x This represents the FFT amplitude spectrum of a one-dimensional time series. N For sequence x Length, It is a sequence x The i Values.

5. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 4, characterized in that, The method for frequency domain feature extraction is as follows: Fast Fourier Transform is performed on the original signal and IMF to obtain the amplitude spectrum in the frequency domain. The maximum value, minimum value, median, average value, average amplitude, root mean square, standard deviation, range, skewness, kurtosis, waveform factor, peak factor, impulse factor, and margin factor are extracted from the amplitude spectrum to capture fault-related characteristic frequencies.

6. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, The power spectrum characteristics include the power spectrum centroid, power spectrum broadening, and average power spectrum.

7. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 6, characterized in that, The calculation formulas for power spectrum feature extraction are as follows: Power spectrum centroid: ; Power spectral broadening: ; Average power spectrum: ; In the formula, K is the length of the power spectrum obtained by the fast Fourier transform. It is the i-th frequency of the Fast Fourier Transform. It is the first power spectrum i Values.

8. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, The feature standardization uses the min-max normalization method to map all features to... The range, maximum and minimum normalization formula is: ； In the formula, x represents the original feature. This represents the features after normalization. The range of values ​​is .

9. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, In S3, anomaly detection based on SVDD includes the following steps: S3-1. Construct an SVDD model based on normal samples; S3-2. Calculate the radius of the hypersphere by solving a convex quadratic programming optimization problem. and center ; S3-3, Set the rules for anomaly detection.

10. A method for monitoring the condition of hydraulic machinery based on anomaly detection and fault diagnosis according to claim 9, characterized in that, A support vector data description model is trained using normal-state data to construct a closed hyperspherical boundary surrounding the normal samples. Where m is the feature dimension, the expression for SVDD is: ； ； ； In the formula, It is the radius of the hypersphere. It is the center of the hypersphere. It is a slack variable. This represents the penalty factor, used to control the balance between model size and the number of external data samples. express Projection features; When normal samples cannot be effectively enclosed by a linear hypersphere in the original feature space, SVDD maps the data to a high-dimensional feature space using a kernel function, thereby fitting the nonlinear distribution of the original space with a linear hypersphere in the high-dimensional space. The radial basis function kernel is chosen, and its expression is: ； In the formula, This represents the kernel function, given two input samples. , , Let represent the squared Euclidean distance between two samples. Represents the hyperparameters of the kernel function; After introducing the kernel function, the optimization problem is transformed into a dual form. At this point, the hypersphere center *a* and radius *R* are calculated using support vectors. Based on the Lagrange multiplier method, the dual programming problem expression in the above equation is obtained: ； ； ； In the formula, These are Lagrange multipliers, where the formulas for calculating the center *a* and radius *R* of the hypersphere are: ； ； In the formula, Let the support vectors have coefficients that satisfy... , ； radius The final expression is: ； In the formula, For the set of support vectors SV The number of samples included. This represents a sample in the support vector set SV. Represents all training samples. Represents the Lagrange multipliers; The anomaly detection rules based on SVDD are as follows: The TFF_VMD multi-domain features of the original vibration signal are used as samples to input into the trained SVDD model. At least 10 samples are detected each time, and the distances of each sample to the center of the hypersphere are compared. and hypersphere radius The size, if more than 60% of the samples meet the requirements L > R If the condition is met, it indicates a device malfunction and triggers an alarm; otherwise, it indicates the device is operating normally. The decision boundary of the SVDD model is defined as follows: ； In the formula, This represents the distance from the sample to be tested to the center 'a' of the hypersphere. This represents the kernel function mapping.

11. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, In S4, fault diagnosis based on SVM classification includes the following steps: S4-1, SVM model establishment; The decision function of a nonlinear SVM classifier is expressed as: ； In the formula, and It is an adjustable parameter of the decision function. The input is The output of the time classifier express Mapping features in the new feature space; The SVM optimization problem is transformed by constructing a hinge loss function: ； ； ； In the formula, , representing the penalty factor, and Inversely proportional, As slack variables, The normal vector of the classification hyperplane, For the bias term of the classification hyperplane, This represents the total number of training samples. For the first i Original samples The result after feature mapping; The RBF radial basis function was chosen as the kernel function for SVM, and Introducing the Lagrange multiplier method, we obtain the dual problem of the above equation as follows: ； ； ； In the formula, and It is a Lagrange multiplier. and They represent the first i The first sample and the first j The label of each sample It is the total number of samples. It is a regularization parameter; SVM classification hyperplane intercept The decision functions are expressed as follows: ； ； In the formula, The normal vector of the classifying hyperplane is represented by T, and its transpose is also represented by T. Indicates the first i Original samples The result after feature mapping Here is the kernel function used to calculate the first... j Sample and the i-th sample Inner product in high-dimensional feature space, This is the result after feature mapping of the new sample z. The sample to be classified; Key parameters of the SVM model include the penalty factor. C Given the kernel function parameters, the training set is input into the SVM model with the determined kernel function and optimal parameters. The optimal classification hyperplane is constructed by solving a convex quadratic programming problem, with the mathematical objective being: ; in, Let be the normal vector of the hyperplane. b For bias terms, For kernel function mapping, As slack variables, For sample labels; S4-2, SVM fault diagnosis; When the SVDD model detects an anomaly, it inputs the TFF multi-domain features corresponding to the anomaly sample into the trained SVM model. The model determines the category of the sample based on the distance from the hyperplane, thereby determining the specific fault type and outputting the diagnostic result.

12. The hydraulic machinery condition monitoring method based on anomaly detection and fault diagnosis according to claim 1, characterized in that, In S5, online equipment maintenance and model iterative optimization include the following steps: If the anomaly detection phase determines that the equipment is in a normal state, then the equipment will continue to operate; if the anomaly detection phase determines that the equipment is in an abnormal state and the specific fault type is identified, then corresponding equipment maintenance recommendations will be given. Newly accumulated normal operation samples are added to the training set of the SVDD model to update the hyperspherical boundary used for anomaly detection and improve anomaly detection accuracy. Newly accumulated fault samples are labeled and added to the training set of the SVM classification model to enhance the diagnostic capability of the SVM classification model, expand the fault identification range of the model, and adapt to the condition monitoring needs of the entire equipment life cycle.

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