Prediction method of external characteristics of centrifugal pump based on Gaussian process regression

Abstract

The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression belongs to the technical field of prediction of the external characteristics of a centrifugal pump. It includes the following steps: 1) data acquisition; 2) data processing: analyzing the recorded data, and obtaining the input data of the model after normalization; 3) establishing a prediction model for the external characteristics of a centrifugal pump; 4) evaluating the monitoring model results. The present invention predicts the external characteristics of a centrifugal pump by combining the operation data processing of the centrifugal pump with the Gaussian process regression model. It can analyze the existing operation data of the centrifugal pump and predict the external characteristics of the centrifugal pump without conducting an external characteristic experiment of the centrifugal pump; at the same time, the variance uncertainty provided by the Gaussian process regression model helps the accuracy of the model prediction, and is suitable for situations where the operating conditions change greatly; the present invention eliminates the data in the starting interval of the centrifugal pump, so that its prediction is more accurate, and at the same time, the risk of the model being disturbed is relatively small.

Description

Technical Field

[0001] The invention belongs to the technical field of centrifugal pump external characteristic prediction methods, and in particular relates to a centrifugal pump external characteristic prediction method based on Gaussian process regression. Background Art

[0002] The external characteristics of a centrifugal pump reflect the working characteristics of the centrifugal pump when it is working, and reflect the overall working performance of the centrifugal pump when it is running. The external characteristics of a centrifugal pump include its head, efficiency, and power. The external characteristic curve represents the operating conditions of the centrifugal pump under different working conditions. When a centrifugal pump is working, its working state will change due to the influence of the external working environment. At the same time, due to leakage, backflow, secondary flow, etc. when the centrifugal pump is working, it is difficult to accurately predict the external characteristics of the centrifugal pump.

[0003] In addition, the working environment of centrifugal pumps is changeable. Centrifugal pumps are often in harsh working conditions. At the same time, the efficiency-flow curve of the external characteristic curve of the centrifugal pump is prone to hump areas, which also increases the difficulty of predicting the external characteristics of the centrifugal pump. At present, most methods for predicting centrifugal pumps use computational fluid dynamics (CFD) to predict the external characteristic curve of the centrifugal pump. However, due to the above problems, the prediction error is relatively large. At the same time, when using computational fluid dynamics, the selection of turbulence models, grid division, and setting of boundary conditions all require design experience. It is difficult to have a unique standard, and the simulation process is complex and requires high calculation requirements. Using computational fluid dynamics to predict the external characteristics of centrifugal pumps is relatively time-consuming and laborious.

[0004] When using the relevant mechanisms of centrifugal pumps to predict their external characteristics, such as the similarity law of pumps, the external characteristics at different speeds are predicted. However, when the speed changes greatly, the accuracy of the prediction will be greatly reduced. At the same time, the prediction accuracy at the same speed will also be reduced due to the cavitation generated during the operation of the pump. Summary of the invention

[0005] In view of the above-mentioned problems existing in the prior art, the purpose of the present invention is to provide a method which combines the operation data processing of a centrifugal pump with a Gaussian process regression model to analyze the operation data of the existing centrifugal pump and predict the external characteristics of the centrifugal pump without conducting an external characteristics experiment of the centrifugal pump. The prediction is more accurate and the risk of the model being disturbed is lower.

[0006] The present invention provides the following technical solution: a method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression, characterized in that it comprises the following steps:

[0007] 1) Data collection: Before the start of the centrifugal pump external characteristic experiment, open the inlet valve to the maximum, set the motor frequency to the preset frequency, adjust the outlet valve to stabilize the outlet pressure indication at the preset value, and this valve opening is the initial valve opening. At the preset frequency, adjust the outlet valve opening until the outlet valve opening is adjusted to the maximum, and record the outlet valve opening, inlet pressure, outlet pressure, and pump outlet flow in turn, and obtain the corresponding centrifugal pump external characteristics;

[0008] 2) Data processing: Analyze the recorded experimental data of the external characteristics of the centrifugal pump and the external characteristics obtained based on the experimental data, and obtain the input data of the model after normalization;

[0009] 3) Establishment of a prediction model for the external characteristics of a centrifugal pump: In the experimental data after data processing in step 2), the inlet pressure, outlet pressure, outlet flow rate, and outlet valve opening of each group of normalized centrifugal pumps are used as input features, and the head, efficiency, and power of the centrifugal pumps after normalization are used as output features. The input features and output features are imported into the training model. When establishing a Gaussian process regression model, the radial basis kernel function is selected as the covariance function. The estimation of the hyperparameters in the Gaussian process regression uses the maximum likelihood estimation to make the model prediction more accurate. Then, the experimental data of the external characteristics of the centrifugal pump are trained and simulated through the established Gaussian process regression model to build a prediction model. Finally, the corresponding relationship between the inlet and outlet pressures, outlet flow rate, outlet valve opening, and head, efficiency, and power of the centrifugal pump is obtained.

[0010] Among them, the formula for establishing a prediction model based on the Gaussian process regression model is:

[0011] y~N(μ(X),K(X,X))

[0012] Where y represents the external characteristic data of the centrifugal pump output in the training data;

[0013] X represents the measured data of the centrifugal pump external characteristic test in the training data;

[0014] μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic test in the training data;

[0015] K represents the covariance matrix of each set of measurement data for the centrifugal pump external characteristic experiment;

[0016] N represents normal distribution;

[0017] Among them, the prediction formula of the external characteristics of the centrifugal pump based on the prediction model is as follows:

[0018]

[0019] Where y represents the external characteristic data of the centrifugal pump output in the training data;

[0020] X represents the measured data of the centrifugal pump external characteristic experiment in the training data;

[0021] X * Represents the measured data of the centrifugal pump external characteristic experiment in the test data;

[0022] f * represents the external characteristic data of the centrifugal pump predicted by the Gaussian process regression model;

[0023] μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the training data;

[0024] μ(X * ) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the test data;

[0025] K represents the covariance matrix of each group of measurement data in the centrifugal pump external characteristic experiment;

[0026] σ n It represents the variance value of each group of measurement data in the centrifugal pump external characteristic experiment;

[0027] T represents the transpose of the matrix;

[0028] N represents normal distribution;

[0029] 4) Evaluate the monitoring model results: According to the prediction model established in step 3), by inputting four sets of input data to be tested, compare the fitting of the centrifugal pump external characteristics prediction results based on the prediction model with the results obtained based on the actual centrifugal pump external characteristics experiment, so as to determine the accuracy of the prediction model established in step 3).

[0030] The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression is characterized in that in step 1), the adjustment of the valve opening increases accordingly according to the increase in the outlet flow rate.

[0031] The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression is characterized in that in step 2), the experimental data of the external characteristics of the centrifugal pump and the external characteristics obtained based on the experimental data are normalized, and the normalization formula is:

[0032]

[0033] in: Indicates the result after normalization of a parameter;

[0034] x represents the value of a parameter before normalization;

[0035] x min Indicates the minimum value of a parameter; x max Indicates the maximum value of a parameter;

[0036] After normalization, all the experimental data values ​​of the centrifugal pump external characteristic data and the external characteristic data obtained are floating point numbers between [0, 1).

[0037] The centrifugal pump external characteristic prediction method based on Gaussian process regression is characterized in that in step 3), the radial basis kernel function is expressed as follows:

[0038]

[0039] in and l represent kernel parameters (hyperparameters);

[0040] represents the bandwidth of the covariance function;

[0041] l represents the characteristic length scale of the covariance function;

[0042] X i Represents the i-th sample input in the training sample;

[0043] X j Represents the jth sample input in the training sample;

[0044] x i，d Represents X i the d-th element of ;

[0045] x j，d Represents X j the d-th element of ;

[0046] Among them, the covariance function of all possible combinations of training sample inputs is expressed as follows:

[0047]

[0048] The covariance function of the test sample input and all possible combinations of the test sample input is expressed as follows:

[0049] K * =(k(X * , X1), k(X * , X2),…,k(X * , X n ))

[0050] The covariance function of all possible combinations of test sample inputs is expressed as follows:

[0051] K ** =(k(X * , X * )).

[0052] The centrifugal pump external characteristic prediction method based on Gaussian process regression is characterized in that in the step 3), the centrifugal pump external characteristic prediction formula based on the prediction model is solved as follows:

[0053]

[0054] f * The best estimate of is the mean of this distribution:

[0055] f * =K * K -1 y

[0056]

[0057] Where C is the covariance matrix,

[0058] The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression is characterized in that: in step 3), the maximum likelihood estimation is used to estimate the hyperparameters of the Gaussian process regression model, based on the selection of the radial basis kernel function as the covariance function, and when the noise term is added, its expression is as follows:

[0059]

[0060] where σ n represents the noise variance;

[0061] δ ij represents the Kronecker symbol, when i and j are equal, δ ij is 1 otherwise δ ij is 0;

[0062] From the above formula, we can see that the model has three hyperparameters, and the hyperparameter set is:

[0063] θ={σ f , l, σ n}

[0064] Maximum likelihood estimation constructs a likelihood function using samples and unknown parameters, and obtains the hyperparameter estimation value of the model by maximizing the likelihood function. When one of the parameters maximizes the probability of the sample appearing, that is, the likelihood function value is the largest, the parameter is used as the output of the hyperparameter estimation.

[0065] According to Bayesian theory, the posterior probability distribution can be written as follows:

[0066]

[0067] P(y|X,θ) is the marginal likelihood function. When the noise follows a Gaussian distribution Its log-likelihood function is expressed as:

[0068]

[0069] Where C is the covariance matrix,

[0070] Take the partial derivative of the above likelihood function:

[0071]

[0072] The optimization method is used to find the zero value when the probability is maximum, and the conjugate gradient method is used to find the model hyperparameters.

[0073] By adopting the above technology, compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] 1) The present invention relates to the processing of centrifugal pump operation data and the application of Gaussian process regression model in predicting the external characteristics of centrifugal pumps. Through the combination of the two, it is possible to analyze the existing centrifugal pump operation data and predict the external characteristics of the centrifugal pump without conducting centrifugal pump external characteristic experiments; at the same time, the variance uncertainty provided by the Gaussian process regression model helps the accuracy of the model prediction, which is suitable for situations where the operating conditions vary greatly.

[0075] 2) The present invention takes into account that the data during the startup process of the centrifugal pump is too small and the data changes dramatically, and the centrifugal pump does not work completely. The data in the startup interval is eliminated to make the prediction more accurate and the risk of the model being disturbed is smaller. At the same time, the inventive method can also provide corresponding guidance and reference for the design of centrifugal pumps. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression of the present invention;

[0077] Figure 2 It is a comparison diagram of the absolute error distribution of the flow-lift external characteristic predicted by GPR and LSSVR of the present invention respectively;

[0078] Figure 3 It is a comparison diagram of the absolute error distribution of the flow-efficiency external characteristics predicted by GPR and LSSVR of the present invention respectively;

[0079] Figure 4 This is a comparison diagram of the absolute error distribution of the flow-power external characteristics predicted by GPR and LSSVR of the present invention respectively. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments of the specification. 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.

[0081] On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims. Further, in order to make the public have a better understanding of the present invention, some specific details are described in detail in the detailed description of the present invention below. Those skilled in the art can fully understand the present invention without the description of these details.

[0082] See also Figure 1-4 , during the operation of the centrifugal pump, the external characteristic prediction method of the centrifugal pump based on Gaussian process regression includes the following steps:

[0083] 1) Data collection: Through the external characteristic experimental method of the centrifugal pump, all the measurement data of the centrifugal pump during operation are obtained, and the measurement data are grouped according to type, roughly four types, a group of inlet pressure data, a group of outlet pressure data, a group of outlet flow data and one type of outlet valve opening data. Record the external characteristic historical data of the corresponding centrifugal pump under the measurement data, and establish a historical external characteristic data sequence library;

[0084] 2) Data processing: normalize the external characteristic data in the historical external characteristic data sequence library and the measurement data of the centrifugal pump during the external characteristic experiment, and finally obtain the corresponding historical data sequence library after data processing;

[0085] The measured data of the centrifugal pump external characteristic experiment, the outlet flow data and the centrifugal pump external characteristic data are normalized, and the normalization formulas are:

[0086]

[0087] in: Indicates the result after normalization of a parameter;

[0088] x represents the value of a parameter before normalization;

[0089] x min Indicates the minimum value of a parameter;

[0090] x max Indicates the maximum value of a parameter;

[0091] After normalization, all centrifugal pump measurement data, outlet flow and external characteristic data are floating point numbers between [0, 1).

[0092] For example, after the outlet pressure is normalized between 1000-3000W, the outlet pressure is a floating point number between [0, 1). The original 1000W becomes a floating point number of 0 after processing.

[0093] 3) Establishment of the external characteristic model of the centrifugal pump: In the experimental data after data processing, the inlet pressure, outlet pressure, outlet flow rate, and outlet valve opening of each group of normalized centrifugal pumps are used as input features, and the head, efficiency, and power of the centrifugal pumps after normalization are used as output features. These input features and output features are imported into the training model, and the centrifugal pump external characteristic experimental data are trained and simulated through the Gaussian process regression model to build a prediction model. Finally, the corresponding relationship between the inlet and outlet pressures, outlet flow rate, outlet valve opening and the head, efficiency, and power of the centrifugal pump is obtained.

[0094] The formula for establishing a prediction model based on the Gaussian process regression model is:

[0095] y~N(μ(X),K(X,X))

[0096] Where y represents the external characteristic data of the centrifugal pump output in the training data;

[0097] X represents the measured data of the centrifugal pump external characteristic test in the training data;

[0098] μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic test in the training data;

[0099] K represents the covariance matrix of each set of measurement data for the centrifugal pump external characteristic experiment;

[0100] N represents normal distribution.

[0101] The prediction formula of the external characteristics of the centrifugal pump based on the prediction model is as follows:

[0102]

[0103] Where y represents the external characteristic data of the centrifugal pump output in the training data;

[0104] X represents the measured data of the centrifugal pump external characteristic experiment in the training data;

[0105] X * Represents the measured data of the centrifugal pump external characteristic experiment in the test data;

[0106] f * represents the external characteristic data of the centrifugal pump predicted by the Gaussian process regression model;

[0107] μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the training data;

[0108] μ(X* ) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the test data;

[0109] K represents the covariance matrix of each group of measurement data in the centrifugal pump external characteristic experiment;

[0110] σ n It represents the variance value of each group of measurement data in the centrifugal pump external characteristic experiment;

[0111] T represents the transpose of the matrix;

[0112] N represents normal distribution.

[0113] Taking the self-priming centrifugal pump as an example, the external characteristic experiment was carried out to measure the inlet and outlet pressures and valve openings of the self-priming centrifugal pump with different outlet flow rates of 720r / min, 1260r / min, 1500r / min, and 1680r / min, and the output head, efficiency, and power of the self-priming centrifugal pump were obtained. After data normalization, the input data and output data of 720r / min, 1260r / min, and 1680r / min were used as training data, and the Gaussian process regression model was obtained through the training data.

[0114]

[0115] The above formula is used to predict the external characteristics of a self-priming centrifugal pump at a speed of 1500r / min. * That is, the external characteristic data of the self-priming centrifugal pump predicted by the trained model.

[0116] contrast Figure 2 , Figure 3 and Figure 4 It can be seen that the prediction results of the centrifugal pump external characteristics based on Gaussian process regression (GPR) are higher than those of the minimum support vector regression (LSSVR). The feasibility of the Gaussian process regression model for predicting the external characteristics of the centrifugal pump is verified, and its prediction accuracy is higher. At the same time, it provides a new design idea for the design of the centrifugal pump.

[0117] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A centrifugal pump external characteristics prediction method based on Gaussian process regression, characterized by: The following steps are involved: 1) Data collection: Before the start of the centrifugal pump external characteristic experiment, open the inlet valve to the maximum, set the motor frequency to the preset frequency, adjust the outlet valve to stabilize the outlet pressure indication at the preset value, and this valve opening is the initial valve opening. At the preset frequency, adjust the outlet valve opening until the outlet valve opening is adjusted to the maximum, and record the outlet valve opening, inlet pressure, outlet pressure, and pump outlet flow in turn, and obtain the corresponding centrifugal pump external characteristics; 2) Data processing: Analyze the recorded experimental data of the external characteristics of the centrifugal pump and the external characteristics obtained based on the experimental data, and obtain the input data of the model after normalization; 3) Establishment of a prediction model for the external characteristics of a centrifugal pump: In the experimental data after data processing in step 2), the inlet pressure, outlet pressure, outlet flow rate, and outlet valve opening of each group of normalized centrifugal pumps are used as input features, and the head, efficiency, and power of the centrifugal pumps after normalization are used as output features. The input features and output features are imported into the training model. When establishing a Gaussian process regression model, the radial basis kernel function is selected as the covariance function. The estimation of the hyperparameters in the Gaussian process regression uses the maximum likelihood estimation to make the model prediction more accurate. Then, the experimental data of the external characteristics of the centrifugal pump are trained and simulated through the established Gaussian process regression model to build a prediction model. Finally, the corresponding relationship between the inlet and outlet pressures, outlet flow rate, outlet valve opening, and head, efficiency, and power of the centrifugal pump is obtained. Among them, the formula for establishing a prediction model based on the Gaussian process regression model is: y~N(μ(X),K(X,X)) Where y represents the external characteristic data of the centrifugal pump output in the training data; X represents the measured data of the centrifugal pump external characteristic test in the training data; μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic test in the training data; K represents the covariance matrix of each set of measurement data for the centrifugal pump external characteristic experiment; N represents normal distribution; The radial basis kernel function is expressed as follows: in and l represent hyperparameters; represents the bandwidth of the covariance function; l represents the characteristic length scale of the covariance function; X i Represents the i-th sample input in the training sample; X j Represents the jth sample input in the training sample; x i , d Represents X i the d-th element of ; x j , d Represents X j the d-th element of ; Among them, the covariance function of all possible combinations of training sample inputs is expressed as follows: The covariance function of the test sample input and all possible combinations of the test sample input is expressed as follows: K * =(k(X * ,X1),k(X * ,X2),...,k(X * ,X n )) The covariance function of all possible combinations of test sample inputs is expressed as follows: K ** =(k(X * ,X * )); Among them, the prediction formula of the external characteristics of the centrifugal pump based on the prediction model is as follows: Where y represents the external characteristic data of the centrifugal pump output in the training data; X represents the measured data of the centrifugal pump external characteristic experiment in the training data; X * Represents the measured data of the centrifugal pump external characteristic experiment in the test data; f * represents the external characteristic data of the centrifugal pump predicted by the Gaussian process regression model; μ(X) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the training data; μ(X * ) represents the mean value of the measured data of the centrifugal pump external characteristic experiment in the test data; K represents the covariance matrix of each group of measurement data in the centrifugal pump external characteristic experiment; σ n It represents the variance value of each group of measurement data in the centrifugal pump external characteristic experiment; T represents the transpose of the matrix; N represents normal distribution; 4) Evaluate the monitoring model results: According to the prediction model established in step 3), by inputting four sets of input data to be tested, compare the fitting of the centrifugal pump external characteristic prediction results based on the prediction model with the results obtained based on the actual centrifugal pump external characteristic experiment, so as to determine the accuracy of the prediction model established in step 3); In step 3), the maximum likelihood estimation is used to estimate the hyperparameters of the Gaussian process regression model. Based on the selection of the radial basis kernel function as the covariance function and the addition of the noise term, the expression is as follows: where σ n represents the noise variance; δ ij represents the Kronecker symbol, when i and j are equal, δ ij is 1 otherwise δ ij is 0; From the above formula, we can see that the model has three hyperparameters, and the hyperparameter set is: θ={σ f ,l,s n } Maximum likelihood estimation constructs a likelihood function using samples and unknown parameters, and obtains the hyperparameter estimation value of the model by maximizing the likelihood function. When one of the parameters maximizes the probability of the sample appearing, that is, the likelihood function value is the largest, the parameter is used as the output of the hyperparameter estimation. According to Bayesian theory, the posterior probability distribution can be written as follows: P(y|X,θ) is the marginal likelihood function. When the noise follows a Gaussian distribution Its log-likelihood function is expressed as: Where C is the covariance matrix, Take the partial derivative of the above likelihood function: The optimization method is used to find the zero value when the probability is maximum, and the conjugate gradient method is used to find the model hyperparameters.

2. The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression according to claim 1 is characterized in that In the step 1), the valve opening is adjusted to increase accordingly according to the increase of the outlet flow rate.

3. The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression according to claim 1 is characterized in that In the step 2), the centrifugal pump external characteristic experimental data and the external characteristics obtained based on the experimental data are normalized, and the normalization formula is: in: Indicates the result after normalization of a parameter; x represents the value of a parameter before normalization; x min Indicates the minimum value of a parameter; x max Indicates the maximum value of a parameter; After normalization, all the experimental data values ​​of the centrifugal pump external characteristic data and the external characteristic data obtained are floating point numbers between [0, 1).

4. The method for predicting the external characteristics of a centrifugal pump based on Gaussian process regression according to claim 1 is characterized in that In the step 3), the prediction formula of the external characteristics of the centrifugal pump based on the prediction model is solved as follows: f * The best estimate of is the mean of this distribution: f * =K * K -1 y Where C is the covariance matrix,

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