Centrifugal pump cavitation state recognition method based on self-adaptive enhancement algorithm

By installing vibration sensors on the centrifugal pump, collecting and processing vibration signals, building an adaptive neural network model and using Adaboost algorithm for adaptive enhancement training, the problem of traditional methods being difficult to accurately identify the cavitation state of the centrifugal pump is solved, and accurate and real-time cavitation state recognition is achieved, adapting to changes in different working conditions, ensuring the normal operation of the centrifugal pump.

CN119646573APending Publication Date: 2025-03-18ZHEJIANG SCI-TECH UNIV
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Patent Information

Application Number
CN202411702436.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-26
Publication Date
2025-03-18

AI Technical Summary

Technical Problem

Traditional methods are difficult to accurately identify the cavitation state of the centrifugal pump and cannot adapt to different operating conditions, resulting in low recognition accuracy and robustness.

Method used

The centrifugal pump cavitation state recognition method based on the adaptive enhancement algorithm is adopted. By installing multiple vibration sensors, vibration signals are collected, preprocessed and feature extraction are performed, adaptive neural network model is constructed, and adaptive enhancement training is used to achieve real-time recognition and optimization.

Benefits of technology

It realizes accurate identification and real-time monitoring of the cavitation status of the centrifugal pump, adapts to changes in different working conditions, improves the adaptability and continuous optimization capabilities of the identification model, and ensures the normal operation of the centrifugal pump and the safety of the equipment.

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Abstract

The invention discloses a centrifugal pump cavitation state recognition method based on an adaptive enhancement algorithm. The method comprises the steps that a vibration sensor is installed to acquire vibration signals of the centrifugal pump in the working state, the vibration signals are processed to obtain a vibration feature set, the vibration feature set serves as a data set, and then a centrifugal pump cavitation state recognition model is constructed to recognize the cavitation state of the centrifugal pump. Then, training the centrifugal pump cavitation state recognition model to obtain a trained centrifugal pump cavitation state recognition model, collecting a to-be-detected vibration signal of the centrifugal pump in real time, and inputting the to-be-detected vibration signal into the trained centrifugal pump cavitation state recognition model to obtain a centrifugal pump cavitation state recognition value; and processing according to the centrifugal pump cavitation state recognition value to obtain a real-time centrifugal pump cavitation state recognition result. According to the method, accurate and real-time recognition of the cavitation state of the centrifugal pump is achieved, the self-adaptive enhancement capacity and the continuous optimization capacity of the recognition model are improved, and the method has important significance in guaranteeing normal operation of the centrifugal pump and reducing equipment damage and production accident risks.
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Description

Technical Field

[0001] The invention belongs to the technical field of centrifugal pump state detection, and in particular relates to a centrifugal pump cavitation state identification method based on an adaptive enhancement algorithm. Background Art

[0002] Centrifugal pumps are a type of fluid conveying equipment commonly used in current industrial production. Cavitation may occur during the operation of centrifugal pumps. Cavitation refers to a process in which part of the liquid turns into a vapor state due to a decrease in pressure. When the local pressure is lower than the saturated vapor pressure of the liquid at that temperature during the flow of the liquid, the liquid vaporizes to form cavitation bubbles and expands rapidly. When the cavitation bubbles at low pressure move to high pressure with the flow of the liquid, the cavitation bubbles shrink and collapse. The process of cavitation formation, expansion, contraction and collapse is called cavitation. The occurrence of cavitation in a centrifugal pump not only reduces the pump head and efficiency, but also damages the flow-through components, greatly reducing the service life and reliability of the equipment. At the same time, the vibration noise associated with cavitation will also affect the acoustic stealth of national defense equipment.

[0003] Although reasonable design of flow components and increasing inlet pressure can play a certain role in suppressing cavitation, it is difficult to completely eliminate cavitation. Therefore, it is of great significance to monitor and identify the cavitation state of centrifugal pumps in real time.

[0004] Traditional methods mainly rely on parameters such as pressure and temperature to determine the state of the pump, but these methods have limitations and cannot accurately determine the cavitation state. The cavitation phenomenon of centrifugal pumps may behave differently under different operating conditions. Traditional identification models often show low accuracy and robustness in practical applications because they cannot dynamically adjust their parameters. Summary of the invention

[0005] The object of the present invention is to provide a centrifugal pump cavitation state identification method based on an adaptive enhancement algorithm to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A centrifugal pump cavitation state identification method based on an adaptive enhancement algorithm comprises the following steps:

[0008] S1. Install multiple vibration sensors on the centrifugal pump, collect vibration signals of the centrifugal pump under working conditions through the vibration sensors, process the vibration signals to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets.

[0009] S2. Construct a centrifugal pump cavitation state recognition model, and use the data set obtained in step S1 to train the centrifugal pump cavitation state recognition model to obtain a trained centrifugal pump cavitation state recognition model.

[0010] S3. Real-time collection of the vibration signal to be measured of the centrifugal pump and input into the trained centrifugal pump cavitation state recognition model to obtain a centrifugal pump cavitation state recognition value, and processing the centrifugal pump cavitation state recognition value to obtain a real-time centrifugal pump cavitation state recognition result.

[0011] The step S1 is specifically as follows:

[0012] S11. Install multiple vibration sensors on the centrifugal pump to collect vibration signals of the centrifugal pump when it is in working state.

[0013] S12. Preprocess the vibration signal collected in step S11 to obtain a preprocessed vibration signal.

[0014] S13. Use a convolutional neural network to extract features from the preprocessed vibration signal to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets.

[0015] In the step S11, the locations where the vibration sensor is installed include: the impeller, the pump shaft, the bearing seat, the pump inlet, the pump outlet, the volute tongue area, and the connection between the pump body and the pump cover.

[0016] The acquired vibration signals include: vibration amplitude, vibration frequency, vibration phase and vibration acceleration.

[0017] The step S12 is specifically as follows:

[0018] 1) The vibration signal collected in step S11 is decomposed into multiple intrinsic mode functions using an empirical mode decomposition method, and the eigenmode functions dominated by noise are removed to obtain a denoised vibration signal.

[0019] The empirical mode decomposition method is set according to the following formula:

[0020]

[0021] Where x(t) is the vibration signal at time step t, and IMF i (t) is the i-th intrinsic mode function at time step t, and r(t) is the residual term at time step t.

[0022] 2) Performing linear amplification processing on the obtained denoised vibration signal to obtain a linearly amplified vibration signal.

[0023] The linear amplification process is set according to the following formula:

[0024] y(t)=k*x'(t)

[0025] Among them, y(t) is the vibration signal after amplification at time step t, k is the amplification factor, and x'(t) is the vibration signal after denoising at time step t.

[0026] 3) Using a second-order bandpass filter to filter the linearly amplified vibration signal to obtain a filtered vibration signal;

[0027] 4) performing standardization processing on the obtained filtered vibration signal to obtain a standardized vibration signal; the standardization processing is set according to the following formula:

[0028]

[0029] Where z(t) is the standardized signal, y'(t) is the filtered vibration signal, μ and σ are the mean and standard deviation of the vibration signal, respectively.

[0030] 5) Adopting an adaptive filter of a minimum mean square error algorithm to perform adaptive filtering processing on the standardized vibration signal, so as to obtain a vibration signal after adaptive filtering, that is, to obtain a preprocessed vibration signal.

[0031] The vibration characteristics in step S13 include: time domain characteristics, frequency domain characteristics, time-frequency characteristics and nonlinear characteristics.

[0032] The step S2 is specifically as follows:

[0033] S21. Adopt adaptive neural network to construct centrifugal pump cavitation state recognition model.

[0034] S22, inputting the data set obtained in step S1 into a centrifugal pump cavitation state recognition model for model training to obtain an initial centrifugal pump cavitation state recognition model.

[0035] S23, using an adaptive enhancement algorithm to perform adaptive enhancement training on the initial centrifugal pump cavitation state recognition model obtained in step 22 to obtain a trained centrifugal pump cavitation state recognition model.

[0036] The adaptive neural network in step S21 adopts a long short-term memory network or a gated recurrent unit network.

[0037] The adaptive boosting algorithm in step S23 adopts the Adaboost algorithm.

[0038] The step S3 is specifically as follows:

[0039] S31. Use a vibration sensor to collect the vibration signal to be measured of the centrifugal pump in real time.

[0040] S32, inputting the vibration signal to be measured collected in the first time step into the centrifugal pump cavitation state recognition model trained in step S2 to obtain the centrifugal pump cavitation state recognition value of the first time step.

[0041] S33, judging the centrifugal pump cavitation state recognition value and the centrifugal pump cavitation state recognition threshold to obtain the centrifugal pump cavitation state recognition result, and optimizing the centrifugal pump cavitation state recognition threshold according to the centrifugal pump cavitation state recognition value to obtain an optimized centrifugal pump cavitation state recognition model.

[0042] S34, inputting the vibration signal to be measured collected at the next time step into the optimized centrifugal pump cavitation state identification model, and obtaining the centrifugal pump cavitation state identification value at the next time step.

[0043] S35. Repeat steps S33 and S34 to obtain the centrifugal pump cavitation state identification results at different time steps.

[0044] In step S33, the centrifugal pump cavitation state identification threshold is optimized according to the following formula:

[0045]

[0046] Among them, η t+1 is the centrifugal pump cavitation state recognition threshold after the update of time step t, η0 is the benchmark centrifugal pump cavitation state recognition threshold, α is the adjustment coefficient, θ t is the cavitation state identification value of the centrifugal pump at time step t, θ i is the cavitation state identification value of the centrifugal pump at time step i.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The present invention realizes accurate identification of the cavitation state of a centrifugal pump through a centrifugal pump cavitation state identification method based on an adaptive enhancement algorithm, and adapts to changes in different working conditions.

[0049] 2. The centrifugal pump cavitation state recognition model of the present invention adopts an adaptive enhancement algorithm, which has the characteristics of adaptive enhancement and realizes the beneficial effect of continuously optimizing the centrifugal pump cavitation state recognition model according to the collected vibration signal to be measured in real time, and can continuously improve the recognition performance in practical applications.

[0050] 3. The present invention can effectively ensure the normal operation of the centrifugal pump and reduce the risk of equipment damage and production accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] A centrifugal pump cavitation state identification method based on an adaptive enhancement algorithm of the present invention comprises the following steps:

[0054] S1. Install multiple vibration sensors on the centrifugal pump, collect vibration signals of the centrifugal pump under working conditions through the vibration sensors, process the vibration signals to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets.

[0055] Step S1 is specifically as follows:

[0056] S11, installing multiple vibration sensors on the centrifugal pump to collect vibration signals of the centrifugal pump in a working state;

[0057] In step S11, the locations where the vibration sensor is installed include: the impeller, the pump shaft, the bearing seat, the pump inlet, the pump outlet, the volute tongue area, and the connection between the pump body and the pump cover.

[0058] The acquired vibration signals include: vibration amplitude, vibration frequency, vibration phase and vibration acceleration.

[0059] S12. Preprocess the vibration signal collected in step S11 to obtain a preprocessed vibration signal.

[0060] Step S12 is specifically as follows:

[0061] 1) The vibration signal collected in step S11 is decomposed into multiple intrinsic mode functions using an empirical mode decomposition method, and the eigenmode functions dominated by noise are removed to obtain a denoised vibration signal.

[0062] The empirical mode decomposition method is set according to the following formula:

[0063]

[0064] Where x(t) is the vibration signal at time step t, and IMF i (t) is the i-th intrinsic mode function at time step t, and r(t) is the residual term at time step t.

[0065] 2) Performing linear amplification processing on the obtained denoised vibration signal to obtain a linearly amplified vibration signal.

[0066] The linear amplification process is set according to the following formula:

[0067] y(t)=k*x'(t)

[0068] Among them, y(t) is the vibration signal after amplification at time step t, k is the amplification factor, and x'(t) is the vibration signal after denoising at time step t.

[0069] 3) A second-order bandpass filter is used to filter the linearly amplified vibration signal to obtain a filtered vibration signal. The parameters of the filter are determined according to the frequency characteristics of the vibration signal after the linear method.

[0070] 4) The obtained filtered vibration signal is standardized to eliminate the influence of different characteristic quantities on subsequent analysis and obtain a standardized vibration signal.

[0071] The normalization process is set according to the following formula:

[0072]

[0073] Where z(t) is the standardized signal, y'(t) is the filtered vibration signal, μ and σ are the mean and standard deviation of the vibration signal, respectively.

[0074] 5) The adaptive filter of the minimum mean square error algorithm is used to perform adaptive filtering on the standardized vibration signal to obtain the vibration signal after adaptive filtering, that is, the preprocessed vibration signal. The adaptive filter can adjust the filtering parameters in real time, thereby enhancing the flexibility of signal processing.

[0075] S13. Use a convolutional neural network to extract features from the preprocessed vibration signal to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets.

[0076] The vibration characteristics in step S13 include: time domain characteristics, frequency domain characteristics, time-frequency characteristics and nonlinear characteristics.

[0077] Time domain features are features extracted directly from the time domain, such as mean, variance, and peak.

[0078] The frequency domain feature is to convert the signal into the frequency domain through Fourier transform and extract the spectrum and power spectrum features.

[0079] The time-frequency feature combines the information of time and frequency, using short-time Fourier transform and wavelet transform.

[0080] The nonlinear features are extracted approximate entropy and sample entropy to capture the nonlinear dynamic behavior in the signal.

[0081] S2. Construct a centrifugal pump cavitation state recognition model, and use the data set obtained in step S1 to train the centrifugal pump cavitation state recognition model to obtain a trained centrifugal pump cavitation state recognition model.

[0082] Step S2 is specifically as follows:

[0083] S21. Adopt adaptive neural network to construct centrifugal pump cavitation state recognition model.

[0084] The adaptive neural network in step S21 adopts a long short-term memory network or a gated recurrent unit network.

[0085] S22, inputting the data set obtained in step S1 into a centrifugal pump cavitation state recognition model for model training to obtain an initial centrifugal pump cavitation state recognition model.

[0086] S23, using an adaptive enhancement algorithm to perform adaptive enhancement training on the initial centrifugal pump cavitation state recognition model obtained in step 22 to obtain a trained centrifugal pump cavitation state recognition model.

[0087] The adaptive boosting algorithm in step S23 adopts the Adaboost algorithm.

[0088] S3, using the multiple vibration sensors installed in step S1 to collect the vibration signals to be measured during the operation of the centrifugal pump in real time and input them into the trained centrifugal pump cavitation state recognition model to obtain the centrifugal pump cavitation state recognition value, and obtain the real-time centrifugal pump cavitation state recognition result according to the centrifugal pump cavitation state recognition value.

[0089] Step S3 is specifically as follows:

[0090] S31. Use a vibration sensor to collect the vibration signal to be measured of the centrifugal pump in real time.

[0091] S32, inputting the vibration signal to be measured collected in the first time step into the centrifugal pump cavitation state recognition model trained in step S2 to obtain the centrifugal pump cavitation state recognition value of the first time step; the time step refers to the time period.

[0092] S33, judging the centrifugal pump cavitation state recognition value and the centrifugal pump cavitation state recognition threshold to obtain the centrifugal pump cavitation state recognition result, and optimizing the centrifugal pump cavitation state recognition threshold according to the centrifugal pump cavitation state recognition value to obtain an optimized centrifugal pump cavitation state recognition model.

[0093] In step S33, the centrifugal pump cavitation state identification threshold is optimized according to the following formula:

[0094]

[0095] Among them, η t+1is the centrifugal pump cavitation state recognition threshold after the update of time step t, η0 is the benchmark centrifugal pump cavitation state recognition threshold, α is the adjustment coefficient, θ t is the cavitation state identification value of the centrifugal pump at time step t, θ i is the cavitation state identification value of the centrifugal pump at time step i.

[0096] S34, inputting the vibration signal to be measured collected at the next time step into the optimized centrifugal pump cavitation state identification model, and obtaining the centrifugal pump cavitation state identification value at the next time step.

[0097] S35. Repeat steps S33 and S34 to obtain the centrifugal pump cavitation state identification results at different time steps.

[0098] The following is the model building process of the present invention:

[0099] Data collection: Use vibration sensors to comprehensively collect vibration data of centrifugal pumps during operation, including key characteristic parameters such as vibration amplitude, frequency, phase, and acceleration. Ensure that the sensor accuracy and sampling rate meet the analysis requirements, while ensuring the stability of the data collection environment to obtain accurate and reliable data.

[0100] Data preprocessing: Preprocess the collected vibration signals, including filtering to remove noise, amplification to enhance the signal, and standardization of the data to eliminate the impact of dimensional differences between features. Select appropriate filtering methods and standardization strategies to ensure that the preprocessed data can truly reflect the operating status of the centrifugal pump.

[0101] Feature extraction: Extract the key features for identifying the cavitation state of the centrifugal pump from the preprocessed data. Signal processing and feature selection algorithms can be used to extract the most representative features, laying a solid foundation for model training.

[0102] Dataset division: Divide the dataset into training set and test set at a ratio of 80% and 20%. Ensure that the data division is random and uniform to ensure the generalization ability of model training and the accuracy of test evaluation.

[0103] Model definition: Define the appropriate neural network classification model architecture based on actual problem requirements.

[0104] Model training: Use the training set data to train the neural network classification model, define the loss function and optimizer, and adjust the model parameters through multiple iterations to minimize the loss function value. Reasonably select the loss function and optimization algorithm, and monitor the loss and accuracy changes during the training process to ensure that the model converges to the optimal state.

[0105] Adaptive enhancement: Adaboost algorithm is used to adaptively enhance the model.

[0106] Model evaluation: Use the test set data to comprehensively evaluate the model performance, calculate the prediction accuracy, and evaluate the actual effect of the model in the identification of the cavitation state of the centrifugal pump. Select appropriate evaluation indicators and methods, such as accuracy, recall rate, F1 score, etc., to comprehensively and objectively reflect the performance level of the model.

[0107] Result analysis and model practicality judgment: Conduct in-depth analysis of the model's recognition results, output key performance indicators such as accuracy, and judge the practicality of the model based on actual application needs.

[0108] The present invention realizes accurate and real-time identification of the cavitation state of a centrifugal pump and improves the adaptive enhancement capability and continuous optimization capability of the identification model, which is of great significance for ensuring the normal operation of the centrifugal pump and reducing the risk of equipment damage and production accidents.

Claims

1. A centrifugal pump cavitation state identification method based on adaptive enhancement algorithm, characterized in that: The following steps are involved: S1. Install multiple vibration sensors on the centrifugal pump, collect vibration signals of the centrifugal pump in a working state through the vibration sensors, process the vibration signals to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets; S2, constructing a centrifugal pump cavitation state recognition model, using the data set obtained in step S1 to train the centrifugal pump cavitation state recognition model, and obtaining a trained centrifugal pump cavitation state recognition model; S3. Real-time collection of the vibration signal to be measured of the centrifugal pump and input into the trained centrifugal pump cavitation state recognition model to obtain a centrifugal pump cavitation state recognition value, and processing the centrifugal pump cavitation state recognition value to obtain a real-time centrifugal pump cavitation state recognition result.

2. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 1 is characterized in that: The step S1 is specifically as follows: S11, installing multiple vibration sensors on the centrifugal pump to collect vibration signals of the centrifugal pump in a working state; S12, preprocessing the vibration signal collected in step S11 to obtain a preprocessed vibration signal; S13. Use a convolutional neural network to extract features from the preprocessed vibration signal to obtain multiple vibration feature sets, and use the multiple vibration feature sets as data sets.

3. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 2 is characterized in that: In the step S11, the locations where the vibration sensor is installed include: the impeller, the pump shaft, the bearing seat, the pump inlet, the pump outlet, the volute tongue area, and the connection between the pump body and the pump cover; The acquired vibration signals include: vibration amplitude, vibration frequency, vibration phase and vibration acceleration.

4. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 2 is characterized in that: The step S12 is specifically as follows: 1) Decomposing the vibration signal collected in step S11 into multiple intrinsic mode functions by using an empirical mode decomposition method, and removing the noise-dominated intrinsic mode functions to obtain a denoised vibration signal; The empirical mode decomposition method is set according to the following formula: Where x(t) is the vibration signal at time step t, and IMF i (t) is the i-th eigenmode function at time step t, r(t) is the residual term at time step t; 2) performing linear amplification processing on the obtained denoised vibration signal to obtain a linearly amplified vibration signal; The linear amplification process is set according to the following formula: y(t)=k*x'(t) Where y(t) is the vibration signal after amplification at time step t, k is the amplification factor, and x'(t) is the vibration signal after denoising at time step t; 3) Using a second-order bandpass filter to filter the linearly amplified vibration signal to obtain a filtered vibration signal; 4) performing standardization processing on the obtained filtered vibration signal to obtain a standardized vibration signal; The standardization process is set according to the following formula: Where z(t) is the standardized signal, y'(t) is the filtered vibration signal, μ and σ are the mean and standard deviation of the vibration signal respectively; 5) Adopting an adaptive filter of a minimum mean square error algorithm to perform adaptive filtering processing on the standardized vibration signal, so as to obtain a vibration signal after adaptive filtering, that is, to obtain a preprocessed vibration signal.

5. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 2 is characterized in that: The vibration characteristics in step S13 include: time domain characteristics, frequency domain characteristics, time-frequency characteristics and nonlinear characteristics.

6. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 1 is characterized in that: The step S2 is specifically as follows: S21. Adopting adaptive neural network to construct centrifugal pump cavitation state recognition model; S22, inputting the data set obtained in step S1 into the centrifugal pump cavitation state recognition model for model training to obtain an initial centrifugal pump cavitation state recognition model; S23, using an adaptive enhancement algorithm to perform adaptive enhancement training on the initial centrifugal pump cavitation state recognition model obtained in step 22 to obtain a trained centrifugal pump cavitation state recognition model.

7. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 6 is characterized in that: The adaptive neural network in step S21 adopts a long short-term memory network or a gated recurrent unit network.

8. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 6 is characterized in that: The adaptive boosting algorithm in step S23 adopts the Adaboost algorithm.

9. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 6, characterized in that: The step S3 is specifically as follows: S31, using a vibration sensor to collect a vibration signal to be measured from a centrifugal pump in real time; S32, inputting the vibration signal to be measured collected at the first time step into the centrifugal pump cavitation state recognition model trained in step S2 to obtain the centrifugal pump cavitation state recognition value of the first time step; S33, judging the centrifugal pump cavitation state recognition value and the centrifugal pump cavitation state recognition threshold to obtain a centrifugal pump cavitation state recognition result, and optimizing the centrifugal pump cavitation state recognition threshold according to the centrifugal pump cavitation state recognition value to obtain an optimized centrifugal pump cavitation state recognition model; S34, inputting the vibration signal to be measured collected at the next time step into the optimized centrifugal pump cavitation state identification model, and obtaining the centrifugal pump cavitation state identification value at the next time step; S35. Repeat steps S33 and S34 to obtain the centrifugal pump cavitation state identification results at different time steps.

10. The centrifugal pump cavitation state identification method based on the adaptive enhancement algorithm according to claim 9, characterized in that: In step S33, the centrifugal pump cavitation state identification threshold is optimized according to the following formula: Among them, η t+1 is the centrifugal pump cavitation state recognition threshold after the update of time step t, η0 is the benchmark centrifugal pump cavitation state recognition threshold, α is the adjustment coefficient, θ t is the cavitation state identification value of the centrifugal pump at time step t, θ i is the cavitation state identification value of the centrifugal pump at time step i.