Sensorless Performance Parameter Prediction Method for Centrifugal Pumps Based on Data-Mechanism Coupling

Abstract

The present invention discloses a method for predicting performance parameters of a sensorless centrifugal pump by data-mechanism coupling, belonging to the technical field of predicting the flow rate, dynamic head resistance loss coefficient and head of a centrifugal pump. It includes the following processes: 1) data acquisition; 2) data processing; 3) instant learning data processing; 4) posterior probability data processing; 5) establishment of a performance parameter prediction model for the centrifugal pump; 6) prediction of performance parameters of the centrifugal pump. The present invention simultaneously utilizes a data modeling model that combines the similarity measure of the Euclidean weighted distance of instant learning, posterior probability, Gaussian process regression and the mechanism formula of the centrifugal pump. The model has good generalization performance and prediction accuracy, and is not affected by the change of the performance parameter curve of the centrifugal pump. At the same time, because it is in a sensorless mode, the expenditure on sensor costs can be reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of sensorless prediction of centrifugal pump performance parameters, and specifically designs a method for predicting the performance parameters of a centrifugal pump based on a Gaussian process regression (GPR) model combined with a centrifugal pump mechanism model using the Euclidean weighted distance and the maximum a posteriori probability (MEPP) in Just-in-Time Learning (JITL) under the condition of no sensors. Background Art

[0002] The performance parameters of a centrifugal pump reflect the working characteristics of the centrifugal pump during operation, and reflect the overall working performance of the centrifugal pump during operation. In addition, due to the variable working environment of the centrifugal pump, the centrifugal pump operates under harsh conditions in many cases that are not the designed working conditions, and the performance parameter curve of the centrifugal pump will suddenly increase or decrease, which increases the difficulty of predicting the performance parameters of the centrifugal pump. The performance parameters of the centrifugal pump include the dynamic head resistance loss coefficient (K value), flow rate (Q value), and head (H value), and the operating conditions of the centrifugal pump under different working conditions are represented by the external characteristic curve. When the centrifugal pump is working, its working state will change due to the influence of the external working environment. Especially under non-designed working conditions, the centrifugal pump in the small flow rate section has a large pressure pulse, which has a great impact on the flow field of the centrifugal pump. At the same time, due to leakage, secondary flow, vortex, pressure pulse, etc. occurring when the centrifugal pump is working, it is very difficult to accurately predict the performance parameters of the centrifugal pump.

[0003] So far, the mainstream method for predicting the performance parameters of a centrifugal pump is mainly to use computational fluid dynamics (CFD) for prediction. However, due to the relatively large relative error of the results predicted by computational fluid dynamics, and when using computational fluid dynamics, the selection of the turbulence model, the division of the grid, and the setting of the boundary conditions all depend on the experience of the designer, and for models with complex structures, the high-fidelity simulation cost is high, the simulation process is very complex, and the computational performance requirements for the computing platform are relatively high. At the same time, the numerical simulation results obtained by using computational fluid dynamics do not have universality. When changing to a different model, it is necessary to re-model, and the generalization performance is poor. Therefore, using computational fluid dynamics to predict the performance parameters of a centrifugal pump is relatively time-consuming and laborious.

[0004] Currently, the commonly used methods for predicting the performance of a centrifugal pump require performance detection sensors, as well as supporting data acquisition, transmission, and analysis systems. Installing additional sensors requires wires, which makes the installation more troublesome and increases the cost. At the same time, the reliability of the sensors is relatively low, they are vulnerable to interference, and are prone to failure. Summary of the Invention

[0005] To solve the above problems existing in the prior art of centrifugal pump performance parameter prediction, the purpose of the present invention is to provide a new model that combines a Gaussian process regression model based on the posterior probability of instant Euclidean weighted learning and a mechanism model to predict the performance parameters of a centrifugal pump in a sensorless mode. The present invention can be simply described as using the rotational frequency of the centrifugal pump impeller and the opening degree of the inlet valve to predict the flow rate, the dynamic head resistance loss coefficient, and the head.

[0006] The present invention provides the following technical solutions: A method for predicting the performance parameters of a centrifugal pump under sensorless conditions by data-mechanism coupling, characterized by including the following specific steps:

[0007] 1) Data acquisition: Before the centrifugal pump performance test starts, open the inlet and outlet valves of the pump to the maximum, set the motor frequency to the preset frequency, adjust the inlet valve to make the readings of the inlet and outlet pressure gauges stable. This valve opening degree is the initial valve opening degree. At the preset frequency, adjust the opening degree of the inlet valve until the inlet valve opening degree is adjusted to the maximum. Record the inlet valve opening degree, inlet pressure, outlet pressure, and pump outlet flow rate in sequence.

[0008] 2) Data processing: Use the recorded centrifugal pump performance test data, as well as the performance parameters obtained based on the experimental data: the flow rate Q value, the head H value, and the dynamic head resistance loss coefficient K value, as the training data for the prediction model. Among them, the frequency N and the valve opening degree V are used as data features, and the flow rate Q value, the head (H value), and the dynamic head resistance loss coefficient K value are used as data labels respectively.

[0009] 3) Instant learning data processing: Select 8 similar samples through similarity measurement among all historical data sample features for a set of data features to be measured (the data features to be measured include the frequency N and the valve opening degree V) according to the Euclidean weighted distance similarity criterion.

[0010] 4) Posterior probability data processing: Randomly select 4 similar samples from the 8 similar samples to form a new sample set. Use the posterior probability MEPP to select the sample set with the maximum probability among all the new sample sets as the training data feature set for the data feature to be measured, and form new training data label sets respectively with the historical data labels (flow rate Q value, head H value, and dynamic head resistance loss coefficient K value) corresponding to the training data feature set.

[0011] 5) Establishment of the prediction model for the performance parameters of the centrifugal pump: Using the training data feature set, Gaussian process regression (GPR) prediction models are established respectively with the training data label set of the flow rate Q value and the training data label set of the dynamic head resistance loss coefficient K value. The established models correspond to the flow rate Q value JITL-MEPP-GPR (abbreviation: Q-JITL-MEPP-GPR) prediction model and the dynamic head resistance loss coefficient K value JITL-MEPP-GPR (abbreviation: K-JITL-MEPP-GPR) prediction model respectively;

[0012] 6) Prediction of the performance parameters of the centrifugal pump: Substitute the feature of the data to be measured into the above Q-JITL-MEPP-GPR prediction model and K-JITL-MEPP-GPR prediction model, predict the flow rate and the dynamic head resistance loss coefficient respectively, and finally, using the mechanism formula of the centrifugal pump, the head of the centrifugal pump can be calculated.

[0013] Furthermore, in step 2), the formulas for calculating the dynamic head resistance loss coefficient K value and the head Q value according to the parameters obtained from the experiment are as follows:

[0014]

[0015] Among them: H represents the total head of the pump, m;

[0016] H st represents the static head of the pump, m;

[0017] P out represents the outlet pressure of the pump, Pa;

[0018] P in represents the inlet pressure of the pump, Pa;

[0019] ρ represents the density of mass transfer, kg / m 3 (ρ 水 = 1000 kg / m 3 ).

[0020]

[0021] Among them: H represents the total head of the pump, m;

[0022] H st represents the static head of the pump, m;

[0023] Q represents the flow rate of the pump, m 3 / h.

[0024] Furthermore, in step 3), the Euclidean weighted distance formula is adopted as the criterion for similarity measurement, and its formula expression is:

[0025]

[0026] Among them: {N m , V m} represents the historical data sample characteristics;

[0027] {N n , V n} represents the characteristics of the data to be measured;

[0028] 0.01×N m represents the weight.

[0029] Furthermore, in step 4), the specific process of the posterior probability is as follows: all new sample sets and the corresponding flow rate sets are respectively input into different GPR models, and according to the prediction variances of different GPR models, a standard is formulated in combination with Bayes' theorem to measure the approximation of the characteristics of the data to be measured.

[0030] 4.1) Input the characteristics of the data to be measured into the trained GPR model, and the calculation formula for the prediction variance of its prediction output set is as follows:

[0031]

[0032]

[0033] Among them: k t,i = [C(x t,i , x1), C(x i,i , x2), …, C(x t,i , x N )] T is the covariance vector of the newly input data and the training data;

[0034] k t,i = C(x t,i , x t,i ) is the covariance of the newly input data;

[0035] is the prediction variance output by the GPR model;

[0036] 4.2) According to the prediction variances of different GPRs, combine the prediction variances with the Bayesian posterior probability to obtain a standard for measuring the similarity of new sample sets at different rotational speeds, and select the group of sample sets with the highest probability as the training data characteristic set of the characteristics of the data to be measured. The new training data label set is respectively composed of the historical data labels (flow rate Q value, head H value, and dynamic head resistance loss coefficient K value) corresponding to the training data characteristic set, and its formula is as follows:

[0037]

[0038]

[0039]

[0040] Where: N l represents the number of samples in the training sample subset;

[0041] N t represents the number of samples in the test set;

[0042] represents the prediction uncertainty of the GPR model for x t,i ;

[0043] MEPP represents the mean value of the posterior probability. The higher its value, the higher the similarity between the training sample subset and the test set, and vice versa.

[0044] Further, in step 6), the formula for predicting the head (H value) using the mechanism formula of the centrifugal pump is as follows:

[0045] H = H st + KQ 2

[0046] Where: H represents the total head of the pump, m;

[0047] H st represents the static head of the pump, m;

[0048] K represents the dynamic head resistance coefficient;

[0049] Q represents the flow rate of the pump, m 3 / h.

[0050] The present invention has the following beneficial technical effects:

[0051] 1) The present invention relates to a method for predicting the performance parameters of a centrifugal pump under sensorless conditions by using two parameters, namely the rotation frequency and valve opening of the centrifugal pump, and applying a data-mechanism coupling method for predicting the performance parameters of a centrifugal pump under sensorless conditions. While improving the disadvantages of time-consuming and laborious computational fluid dynamics, it greatly improves the prediction accuracy and the generalization performance of the model.

[0052] 2) The premise for constructing the prediction model of the present invention is to predict the performance parameters of the centrifugal pump without using any sensors. Therefore, during the entire process of predicting the performance parameters of the centrifugal pump, the use of sensors for the centrifugal pump is reduced, which can greatly reduce the expenditure on sensor costs.

[0053] 3) The prediction model constructed by the present invention predicts only the performance parameters corresponding to one frequency and valve opening at a time. Therefore, it is not affected by the sudden sharp change of the performance curve of the centrifugal pump, has good generalization performance, and can accurately predict the performance parameters at the sharp change of the curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is the flow chart for modeling the performance parameter prediction model of the centrifugal pump of the present invention;

[0055] Figure 2 It is the model prediction flow chart;

[0056] Figure 3 It is the predicted flow rate Q value graph of four groups of test set samples;

[0057] Figure 4 It is the relative error graph of the predicted flow rate Q value of four groups of test set samples;

[0058] Figure 5 It is the predicted dynamic head resistance loss coefficient K value graph of four groups of test set samples;

[0059] Figure 6 It is the relative error graph of the predicted dynamic head resistance loss coefficient K value of four groups of test set samples;

[0060] Figure 7 It is the comparison graph of the predicted head H value of four groups of test set samples;

[0061] Figure 8 It is the relative error graph of the predicted head H value of four groups of test set samples. Specific implementation mode

[0062] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0063] On the contrary, the present invention covers any alternatives, modifications, equivalent methods and solutions made within the essence and scope of the present invention defined by the claims. Further, in order to enable the public to have a better understanding of the present invention, some specific details are described in detail in the following detailed description of the present invention. Those skilled in the art can fully understand the present invention without the description of these details.

[0064] Embodiment:

[0065] Please refer to Figure 1-2 , a sensorless centrifugal pump performance parameter prediction method based on data-mechanism coupling, the method includes the following steps:

[0066] Step 1): Obtain the performance parameter data set of the centrifugal pump at different speeds, and the process is as follows:

[0067] Before the centrifugal pump performance test, open the pump inlet valve to the maximum, set the motor frequency to the preset frequency, adjust the inlet valve to make the readings of the inlet and outlet pressure gauges stable. This valve opening is the initial valve opening. At the preset frequency, adjust the inlet valve opening until the inlet valve opening is adjusted to the maximum. Record the inlet valve opening V, the inlet pressure P i , the outlet pressure P o , and the pump outlet flow rate Q.

[0068] Step 2): Data processing, the process is as follows:

[0069] From the recorded inlet valve opening V, the inlet pressure P in , the outlet pressure P out , and the pump outlet flow rate Q, obtain the dynamic head resistance loss coefficient (K value) and the head (H value) through the following formula.

[0070]

[0071] Where: H represents the total head of the pump, m;

[0072] H st represents the static head of the pump, m;

[0073] P out represents the outlet pressure of the pump, Pa;

[0074] P in represents the inlet pressure of the pump, Pa;

[0075] ρ represents the density of the mass transfer, kg / m 3 (ρ 水 = 1000 kg / m 3 ).

[0076]

[0077] Where: H represents the total head of the pump, m;

[0078] H st represents the static head of the pump, m;

[0079] Q represents the flow rate of the pump, m 3 / h.

[0080] And use this as the training data for the prediction model, where the frequency N and the valve opening V are used as data features, and the flow rate (Q value), the head (H value), and the dynamic head resistance loss coefficient (K value) are used as data labels, denoted as {{N m , V m}, {Q m}} and {{N m , V m , {K m}}.

[0081] Step 3): Instantaneous learning data processing, the process is as follows:

[0082] First, through the Euclidean weighted distance similarity criterion, the formula is as follows, for a set of data features to be measured (the data features to be measured include frequency N and valve opening V, denoted as {N n ,V n}), similarity measurement is performed, and 8 groups of similar samples are selected through similarity measurement among all historical data sample features, denoted as

[0083] C = {{N1, V1}, {N2, V2}, …, {N8, V8}}.

[0084]

[0085] Among them: {N m ,V m} represents the historical data sample features;

[0086] {N n ,V n} represents the data features to be measured;

[0087] 0.01×N m represents the weight

[0088] Step 4): Posterior probability data processing, the process is as follows:

[0089] Step 4.1): Randomly select 4 groups of similar samples from 8 groups of similar samples C = {{N1, V1}, {N2, V2}, …, {N8, V8}} to form a new sample set, denoted as S k = {{N A ,V A}, {N B ,V B , {N C ,V C , {N D ,V D}}, where k = 1, 2, …, 70 (70 is the total number of randomly combined sample sets); 1 ≤ A, B, C, D ≤ 8, and A ≠ B ≠ C ≠ D. Using the posterior probability formula, calculate the probability of each sample set S k respectively.

[0090] The specific process of the posterior probability is as follows:

[0091] Input the data features to be measured into the trained GPR model, and the calculation formula for the prediction variance of its prediction output set is as follows:

[0092]

[0093]

[0094] where: k t,i = [C(x t,i , x1), C(x t,i , x2), …, C(x t,i , x N )] T is the covariance vector of the new input data and the training data;

[0095] k t,i = C(x t,i , x t,i ) is the covariance of the new input data;

[0096] is the predicted variance output by the GPR model.

[0097] According to the predicted variances of different GPRs, the predicted variances are combined with the Bayesian posterior probability to obtain a criterion for measuring the similarity of new sample sets at different rotational speeds. The sample set with the highest probability is selected as the training data feature set of the characteristics of the data to be measured. The new training data label set is respectively composed of the historical data labels (flow rate (Q value), head (H value), and dynamic head resistance loss coefficient (K value)) corresponding to the training data feature set. The formula is as follows:

[0098]

[0099]

[0100]

[0101] where: N l represents the number of samples in the training sample subset;

[0102] N t represents the number of samples in the test set;

[0103] represents the prediction uncertainty of the GPR model for x t,i ;

[0104] represents the predicted value of the GPR model for x t,i ;

[0105] MEPP represents the average value of the posterior probability. The higher its value, the higher the similarity between the training sample subset and the test set, and vice versa.

[0106] Step 4.2): Using the average posterior probability of all the sample sets obtained in Step 4.1), select the sample subset with the largest average posterior probability as the features of the training sample data of the prediction model, and respectively form a new training sample set with the corresponding flow rate (Q value) and dynamic head resistance loss coefficient (K value), denoted as:

[0107]

[0108]

[0109] Step 5): Establishment of the centrifugal pump performance parameter prediction model, the process is as follows:

[0110] Using the training sample set and to train and establish the Gaussian process regression (GPR) prediction model. The established models are respectively the flow rate (Q value) JITL-MEPP-GPR (abbreviation: Q-JITL-MEPP-GPR) prediction model and the dynamic head resistance loss coefficient (K value) JITL-MEPP-GPR (abbreviation: K-JITL-MEPP-GPR) prediction model;

[0111] Step 6): Prediction of the centrifugal pump performance parameters, the process is as follows:

[0112] Substitute the data features to be measured {N n , V n} into the Q-JITL-MEPP-GPR prediction model and the K-JITL-MEPP-GPR prediction model to respectively predict the flow rate (Q value) and the dynamic head resistance loss coefficient (K value). Finally, using the mechanism formula of the centrifugal pump, the head of the centrifugal pump can be calculated. The mechanism formula of the centrifugal pump is as follows:

[0113] H = H st + KQ 2

[0114] Among them: H represents the total head of the pump, m;

[0115] H st represents the static head of the pump, m;

[0116] K represents the dynamic head resistance coefficient;

[0117] Q represents the flow rate of the pump, m 3 / h.

[0118] The above process can calculate the label value corresponding to a frequency and valve opening. Repeating this process can calculate the label values under other frequencies or other valve openings.

[0119] Select four groups of rotational speed test set samples for prediction. The four groups of test rotational speeds include rotational speed values in the high, medium, and low ranges. Substitute the four groups of rotational speed test sets into the prediction model constructed in the present invention. The predicted results of flow rate (Q value), dynamic head resistance loss coefficient (K value), and head (H value) are as follows Figure 3 , 5 , as shown in Figure 7, where Q, K, and H respectively represent the true values of the experiment, Q P , K P , H P represent the prediction results.

[0120] Finally, according to the label value of a complete test rotational speed predicted, the relative error (RE) and root mean square error (RMSE) of the prediction results can be calculated. The formulas are as follows:

[0121]

[0122]

[0123] where: y P represents the model prediction result;

[0124] y represents the experimental result of the centrifugal pump;

[0125] N represents the total number of prediction samples.

[0126] Then, the relative error results of the flow rate (Q value), dynamic head resistance loss coefficient (K value), and head (H value) predicted by the four groups of test rotational speeds are as shown in Figure 4 , 6 , as shown in Figure 8. The root mean square error results of the flow rate (Q value), dynamic head resistance loss coefficient (K value), and head (H value) predicted by the four groups of test rotational speeds are shown in Table 1.

[0127] Table 1

[0128]

[0129] Through Figure 3-8 and Table 1, it can be seen that the prediction model of the centrifugal pump performance parameters of the present invention has good accuracy.

[0130] Through the rotational speeds in the medium, high, and low ranges included in the four groups of test rotational speeds, the accuracy of the prediction results is good, indicating that the model described in the present invention has good generalization performance.

[0131] The above are only the preferred embodiments of the present invention and do not limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention are all included in the protection scope of the present invention.

Claims

1. A method for predicting the performance parameters of a sensorless centrifugal pump by data-mechanism coupling, characterized in that, It includes the following steps: 1) Data acquisition: Before the centrifugal pump performance test starts, open the inlet and outlet valves of the pump to the maximum, set the motor frequency to the preset frequency, adjust the inlet valve to make the readings of the inlet and outlet pressure gauges stable and unchanged. This valve opening is the initial valve opening. At the preset frequency, adjust the valve opening of the inlet valve until the inlet valve opening is adjusted to the maximum, and record the inlet valve opening, inlet pressure, outlet pressure, and pump outlet flow parameters in sequence; 2) Data processing: For the centrifugal pump performance test data recorded, as well as the performance parameters obtained based on the experimental data: flow rate Q value, head H value, and dynamic head resistance loss coefficient K value, these are used as the training data for the prediction model. Among them, frequency N and valve opening V are used as data features for the flow rate Q value, and the head H value and dynamic head resistance loss coefficient K value are used as data labels respectively; 3) Instantaneous learning data processing: Through the Euclidean weighted distance similarity criterion, for a set of data features to be measured, several groups of similar samples are selected through similarity measurement among all historical data sample features; among them, the data features to be measured include frequency N and valve opening V; 4) Posterior probability data processing: Randomly select multiple groups of similar samples from several groups of similar samples to form a new sample set. Use the posterior probability MEPP to select the group of samples with the highest probability in all new sample sets as the training data feature set for the data features to be measured, and the new training data label sets composed of the historical data labels corresponding to the training data feature set respectively; among them, the historical data labels include flow rate Q value, head H value, and dynamic head resistance loss coefficient K value; 5) Establishment of the centrifugal pump performance parameter prediction model: Use the training data feature set to establish Gaussian process regression GPR prediction models with the flow rate Q value training data label set and the dynamic head resistance loss coefficient K value training data label set respectively. The established models correspond to the flow rate Q value instantaneous learning posterior probability Gaussian process regression prediction model Q-JITL-MEPP-GPR and the dynamic head resistance loss coefficient K value instantaneous learning posterior probability Gaussian process regression prediction model K-JITL-MEPP-GPR respectively; 6) Prediction of centrifugal pump performance parameters: Substitute the data features to be measured into the above Q-JITL-MEPP-GPR prediction model and K-JITL-MEPP-GPR prediction models to predict the flow rate and dynamic head resistance loss coefficient respectively. Finally, use the mechanism formula of the centrifugal pump to calculate the head of the centrifugal pump.

2. The sensorless centrifugal pump performance parameter prediction method based on data-mechanism coupling according to claim 1, characterized in that In step 2), the formulas for calculating the dynamic head resistance loss coefficient K value and the head Q value according to the parameters obtained from the experiment are as follows: Where: H represents the total head of the pump, m; H st represents the static head of the pump, m; P out represents the pump outlet pressure, Pa; P in represents the pump inlet pressure, Pa; ρ represents the density of mass transfer, kg / m 3 (ρ 水 = 1000 kg / m 3 ); Where: H represents the total head of the pump, m; H st represents the static head of the pump, m; Q represents the flow rate of the pump, m 3 / h.

3. The data-mechanism coupling-based sensorless centrifugal pump performance parameter prediction method according to claim 1, wherein In the said step 3), the Euclidean weighted distance formula is adopted as the criterion for similarity measurement, and its formula expression is: Where: {N m , V m} represents the characteristics of historical data samples; {N n , V n} represents the characteristics of the data to be measured; 0.01×N m Indicates the weight.

4. The data-mechanism coupling-based sensorless centrifugal pump performance parameter prediction method according to claim 1, characterized in that In the said step 4), the specific process of the posterior probability is: Input all the new sample sets and the corresponding flow rate sets into different GPR models respectively, and formulate a standard according to the prediction variance of different GPR models combined with Bayes' theorem to measure the approximation of the data features to be measured; 4.1) Input the characteristics of the data to be measured into the trained GPR model. The calculation formula for the prediction variance of its prediction output set is as follows: where: k t，i = [C(x t，i , x1), C(x t，i , x2), …, C(x t，i , x N )] T is the covariance vector of the new input data and the training data; k t，i = C(x t，i , x t，i ) is the covariance of the new input data; is the predicted variance output by the GPR model; 4.2) According to the prediction variances of different GPRs, combine the prediction variance with the Bayesian posterior probability to obtain a criterion for measuring the similarity of new sample sets at different rotational speeds. Select the sample set with the highest probability as the training data feature set of the data characteristics to be measured, and a new training data label set composed of the historical data labels corresponding to the training data feature set respectively. The formula is as follows: Where: N l represents the number of samples in the training sample subset; N t represents the number of samples in the test set; Indicates the prediction uncertainty of the GPR model for x t，i ; denote the predicted value of the GPR model for x t，i ; is a process expression; MEPP represents the average value of the posterior probability. The higher its value, the higher the similarity between the training sample subset and the test set, and vice versa.

5. The data-mechanism coupling-based sensorless centrifugal pump performance parameter prediction method according to claim 1, wherein In step 6) described above, the formula for predicting the head H value using the mechanism formula of the centrifugal pump is as follows: H = H st + KQ 2 Where: H represents the total head of the pump, m; H st Represents the static head of the pump, m; K represents the dynamic head resistance coefficient; Q represents the flow rate of the pump, m 3 / h.

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