A method for predicting and judging the unbalance response of a centrifugal pump impeller
By combining CFD and finite element coupled simulation with nonlinear kernel methods and machine learning, the accurate prediction and judgment of the impeller imbalance state of centrifugal pumps can be achieved, which solves the problem of difficult impeller imbalance identification in the existing technology and improves equipment safety and maintenance efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG SCI-TECH UNIV
- Filing Date
- 2025-11-13
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies struggle to accurately identify the location and mass of centrifugal pump impeller imbalances, leading to increased vibration, bearing wear, and unplanned shutdowns, making early warning and quantitative diagnosis impossible.
The pressure load on the impeller surface is obtained by CFD numerical simulation. Combined with finite element harmonic response analysis, the unbalanced response is predicted and judged by nonlinear kernel method and machine learning. Online diagnosis and early warning are realized by support vector machine algorithm.
Accurately predict the location and quality of imbalances, improve equipment safety and maintenance efficiency, reduce unplanned downtime, and lower maintenance costs.
Smart Images
Figure CN122389682A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of fluid machinery and centrifugal pump technology, specifically relating to a method for predicting and judging the impeller imbalance response of a centrifugal pump. Background Technology
[0002] Centrifugal pumps are core fluid transport equipment widely used in industrial fields. Their impellers, as critical rotating components, are prone to uneven mass distribution during long-term operation due to wear, scaling, corrosion, or manufacturing defects, leading to unbalanced responses. This imbalance generates periodic centrifugal forces, causing increased pump body vibration, bearing wear, seal failure, and even structural fatigue fracture, severely impacting equipment safety and lifespan.
[0003] Statistics show that impeller imbalance is one of the main causes of centrifugal pump failures, accounting for over 30%. In rotating machinery failures, approximately 40% are related to mass imbalance. Unplanned downtime due to impeller imbalance accounts for more than 35% of total centrifugal pump downtime, causing significant economic losses to enterprises. Currently, traditional vibration monitoring methods rely heavily on empirical thresholds or simple spectral analysis, making it difficult to accurately identify the location and magnitude of imbalance, let alone achieve early warning and quantitative diagnosis.
[0004] Therefore, there is an urgent need in this field for a method that can accurately predict and intelligently judge impeller imbalance response based on actual operating data and by combining numerical simulation and machine learning techniques, so as to improve equipment reliability and reduce maintenance costs. Summary of the Invention
[0005] This invention provides a method for predicting and judging the unbalanced response of a centrifugal pump impeller. The method obtains the pressure load on the impeller surface through CFD numerical simulation and performs finite element harmonic response analysis using the load as an excitation. This method can accurately predict the unbalanced location, mass, and confidence level, significantly improving the operational safety and maintenance efficiency of the centrifugal pump, thereby solving the problems mentioned in the background art.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting and judging the impeller imbalance response of a centrifugal pump, comprising the following steps: Step S1: Obtain the pressure load on the impeller surface using numerical simulation; Step S2: Use the obtained load data as excitation to perform harmonic response analysis of the structure through finite element calculation; Step S3: Obtain the numerical response magnitudes of displacement, velocity, and acceleration at the natural frequency value, as well as the harmonic response curves and other unbalanced response characteristics to simulate the forced vibration state of the impeller in actual operation. Step S4: Select unbalanced masses with different positions and masses, and use the unbalanced response calculation method to obtain the corresponding unbalanced response characteristics. The harmonic response obtained in each calculation is denoted as Zi (i=1,2,…,n). Step S5: Take the amplitude distribution at different frequencies in the harmonic response curve as input, use the nonlinear kernel method to map the original input through nonlinear mapping, and then calculate the number of principal components in the mapped space to reduce computational complexity. Step S6: Repeat the above process to learn and classify the unbalanced response features caused by unbalanced position and unbalanced mass under different conditions, and obtain the final prediction model.
[0007] Preferably, in step S1, the specific method of numerical simulation is to perform three-dimensional modeling and fluid dynamics simulation analysis of the impeller using CFD software to obtain the pressure load distribution on the impeller surface during fluid flow under different working conditions.
[0008] Preferably, in step S2, the harmonic response analysis of the structure specifically adopts the following coupling equation: ; in It is the fluid mass matrix. It is the fluid damping matrix. It is the fluid stiffness matrix. It is the coupling quality matrix.
[0009] Preferably, in step S3, the harmonic response curve includes displacement, velocity, and acceleration responses in the X, Y, and Z directions, and the resonant frequency and vibration mode are identified by peak detection.
[0010] Preferably, in step S4, the unbalanced mass parameters include mass size, position angle, and distribution pattern, and the parameter combination is optimized through orthogonal experimental design.
[0011] Preferably, in step S5, the specific steps of the nonlinear kernel method include: First, the covariance matrix of the feature space is calculated using the following formula: , Where Φ(xi) is scaled to zero mean; the solution is obtained The principal components of the input matrix can be extracted by calculating the projection of the eigenvalues and eigenvectors onto the eigenvector Vk in Φ(xi). , The contribution rate ηk of each principal component to the total variance is calculated using the following formula. , where λk is the variance of the k-th principal component; m is the total number of principal components; The input principal component data is categorized into different types: Where C is the penalty factor; ξi is the slack variable, and the hyperplane equation can be expressed as: .
[0012] Preferably, in step S5, the nonlinear kernel method employs kernel principal component analysis, and the kernel function is a radial basis function or a polynomial kernel function.
[0013] Preferably, in step S6, the classification and recognition adopts the support vector machine algorithm, and the model parameters are optimized through grid search and cross-validation.
[0014] Preferably, the method further includes step S7: inputting the real-time monitored impeller vibration data into the prediction model to achieve online diagnosis and early warning of the unbalanced state.
[0015] Preferably, the prediction model output includes the location of the imbalance, the mass size, and the confidence level, and the diagnostic results are presented in a visual format.
[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. By using CFD and finite element coupled simulation, the vibration response of the impeller under actual working conditions is accurately simulated.
[0017] 2. By combining nonlinear kernel methods with machine learning, intelligent identification and classification of imbalanced states can be achieved.
[0018] 3. Supports online monitoring and diagnosis, enabling early warning of imbalance faults and reducing unplanned downtime.
[0019] 4. The output results are visualized, making it easier for engineers to make quick judgments and decisions. Attached Figure Description
[0020] Figure 1 This is a schematic diagram of the rotor imbalance response calculation model of the present invention; Figure 2 a represents the harmonic response curve of the impeller center position predicted by CFD calculation in this embodiment of the invention. Figure 1 ; Figure 2 b is the harmonic response curve of the impeller center position predicted by CFD calculation in this embodiment of the invention. Figure 2 ; Figure 2 c represents the harmonic response curve of the impeller center position predicted by CFD calculation in this embodiment of the invention. Figure 3 ; Figure 3 This refers to the contribution calculation result in the unbalanced response calculation method in this embodiment of the invention; Figure 4 This is a comparison of the normalized confusion matrices of different input signals in an embodiment of the present invention. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0022] like Figure 1 As shown, the embodiment of the optimized design method of the present invention mainly obtains the unbalanced response prediction model of the centrifugal pump and the real-time monitoring data of the centrifugal pump impeller through the impeller model. The pressure load on the impeller surface is obtained through numerical simulation, and the obtained load data is used as excitation for finite element calculation to perform harmonic response analysis of the structure. The unbalanced response characteristics, such as the numerical response magnitudes of displacement, velocity, and acceleration at the natural frequency and the harmonic response curves, are obtained to simulate the forced vibration state of the impeller in actual operation. The settlement results are as follows... Figure 2 As shown, various unbalanced masses with different locations and masses are selected, and unbalanced response calculation methods are used to obtain the corresponding unbalanced response characteristics. The harmonic response obtained in each calculation is denoted as Zi (i=1,2,…,n). The amplitude distribution at different frequencies in the harmonic response curve is used as input, and a nonlinear kernel method is used to map the original input through nonlinear mapping. Then, the number of principal components is calculated in the mapped space to reduce computational complexity. The above process is repeated to learn and classify the unbalanced response characteristics caused by unbalanced location and unbalanced mass under different conditions, and the final prediction model is obtained.
[0023] The specific method of numerical simulation is to use CFD software to perform three-dimensional modeling and fluid dynamics simulation analysis of the impeller to obtain the pressure load distribution on the impeller surface during fluid flow under different working conditions.
[0024] The following coupling equations are used to perform harmonic response analysis of the structure: ; in It is the fluid mass matrix. It is the fluid damping matrix. It is the fluid stiffness matrix. It is the coupling quality matrix.
[0025] The harmonic response curve includes displacement, velocity, and acceleration responses in the X, Y, and Z directions, and the resonant frequency and vibration mode are identified through peak detection.
[0026] The unbalanced mass parameters include mass size, position angle, and distribution pattern, and the combination of parameters is optimized through orthogonal experimental design.
[0027] The specific steps of the nonlinear kernel method include: First, the covariance matrix of the feature space is calculated using the following formula: , Where Φ(xi) is scaled to zero mean; the solution is obtained The principal components of the input matrix can be extracted by calculating the projection of the eigenvalues and eigenvectors onto the eigenvector Vk in Φ(xi). , The contribution rate ηk of each principal component to the total variance is calculated using the following formula. , where λk is the variance of the k-th principal component; m is the total number of principal components; The input principal component data is categorized into different types: Where C is the penalty factor; ξi is the slack variable, and the hyperplane equation can be expressed as: .
[0028] The nonlinear kernel method employs kernel principal component analysis, with the kernel function being either a radial basis function or a polynomial kernel function. Classification and identification utilize a support vector machine algorithm, and model parameters are optimized through grid search and cross-validation. Real-time monitored impeller vibration data is input into the prediction model to achieve online diagnosis and early warning of imbalance conditions. The prediction model output includes the imbalance location, mass magnitude, and confidence level, and the diagnostic results are displayed visually.
[0029] To investigate the impact of the direction of the input vibration signal on the performance of the cavitation recognition model, seven different signal combinations were input into the model. The recognition accuracy and running time are shown in Table 1. Table 1. Model recognition accuracy and running time for different vibration signal inputs. like Figure 3As shown, the contribution rates of each principal component after processing the feature vectors in the X, Y, and Z directions using the nonlinear kernel method are displayed. It can be seen that the contribution rate gradually decreases from PC1 to PC6, and is mainly concentrated in PC1. The contribution rate of PC1 in the Y direction reaches 89.7%, indicating that the nonlinear kernel method has the best dimensionality reduction effect for features in this direction, and the original feature information can be preserved in PC1 as much as possible. The cumulative contribution rates of the principal components are shown in Table 2. Table 2 Cumulative Contribution Rate of Each Principal Component It can be seen that the cumulative contribution rate of the first three principal components has reached over 87%, and the cumulative contribution rate of the first four principal components has reached over 94%, indicating that the nonlinear kernel method can effectively preserve the original cavitation feature information while removing redundant features. Considering the impact of the number of feature dimensions on cavitation recognition efficiency, the first three principal components in the X, Y, and Z directions are selected to reconstruct the feature vectors, which are then used as sample data for the study of classification models.
[0030] like Figure 4 As shown, the confusion matrix quantitatively displays the model's classification results among different categories in a visual form. It is used to intuitively show the misclassification information of each category in multi-classification tasks, which helps to conduct in-depth analysis of the classification results. By using multi-directional vibration signals to identify cavitation states, the model's overall recognition accuracy can be improved by combining the recognition accuracy advantage range of the input signal.
[0031] The present invention provides a method for predicting and judging the unbalanced response of a centrifugal pump impeller, which can accurately predict and judge the unbalanced state of the impeller, providing strong support for the design and optimization of centrifugal pump impellers.
[0032] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for predicting and judging the impeller imbalance response of a centrifugal pump, characterized in that, Includes the following steps: Step S1: Obtain the pressure load on the impeller surface using numerical simulation; Step S2: Use the obtained load data as excitation to perform harmonic response analysis of the structure through finite element calculation; Step S3: Obtain the numerical response magnitudes of displacement, velocity, and acceleration at the natural frequency value, as well as the harmonic response curves and other unbalanced response characteristics to simulate the forced vibration state of the impeller in actual operation. Step S4: Select unbalanced masses with different positions and masses, and use the unbalanced response calculation method to obtain the corresponding unbalanced response characteristics. The harmonic response obtained in each calculation is denoted as Zi (i=1,2,…,n). Step S5: Take the amplitude distribution at different frequencies in the harmonic response curve as input, use the nonlinear kernel method to map the original input through nonlinear mapping, and then calculate the number of principal components in the mapped space to reduce computational complexity. Step S6: Repeat the above process to learn and classify the unbalanced response features caused by unbalanced position and unbalanced mass under different conditions, and obtain the final prediction model.
2. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, In step S1, the specific method of numerical simulation is to perform three-dimensional modeling and fluid dynamics simulation analysis of the impeller using CFD software to obtain the pressure load distribution on the impeller surface during fluid flow under different working conditions.
3. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, In step S2, the harmonic response analysis of the structure is performed using the following coupling equations: ； in It is the fluid mass matrix. It is the fluid damping matrix. It is the fluid stiffness matrix. It is the coupling quality matrix.
4. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, In step S3, the harmonic response curve includes displacement, velocity and acceleration responses in the X, Y and Z directions, and the resonant frequency and vibration mode are identified by peak detection.
5. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 4, characterized in that, In step S4, the unbalanced mass parameters include mass size, position angle, and distribution pattern, and the parameter combination is optimized through orthogonal experimental design.
6. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 5, characterized in that, In step S5, the specific steps of the nonlinear kernel method include: First, the covariance matrix of the feature space is calculated using the following formula: ， Where Φ(xi) is scaled to zero mean; the solution is obtained The principal components of the input matrix can be extracted by calculating the projection of the eigenvalues and eigenvectors onto the eigenvector Vk in Φ(xi). ， The contribution rate ηk of each principal component to the total variance is calculated using the following formula. , where λk is the variance of the k-th principal component; m is the total number of principal components; The input principal component data is categorized into different types: Where C is the penalty factor; ξi is the slack variable, and the hyperplane equation can be expressed as: 。 7. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, In step S5, the nonlinear kernel method employs kernel principal component analysis, and the kernel function is either a radial basis function or a polynomial kernel function.
8. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, In step S6, the classification and recognition adopts the support vector machine algorithm, and the model parameters are optimized through grid search and cross-validation.
9. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, It also includes step S7: inputting the real-time monitored impeller vibration data into the prediction model to achieve online diagnosis and early warning of the unbalanced state.
10. The method for predicting and judging the impeller imbalance response of a centrifugal pump according to claim 1, characterized in that, The predictive model outputs the imbalance location, mass magnitude, and confidence level, and presents the diagnostic results in a visual format.