CN113553673B - Centrifugal pump efficiency prediction method based on data-driven modeling - Google Patents
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Abstract
A method for predicting the efficiency of a centrifugal pump based on data-driven modeling comprises the following steps of 1) dividing the efficiency of the centrifugal pump into two different intervals by analyzing the related process knowledge of the centrifugal pump; 2) The process of the efficiency curve of the centrifugal pump at different rotating speeds is identified by using the prediction variance output by the Gaussian process regression GPR model, and two intervals can be automatically divided; 3) Approximate working conditions are measured by using the prediction variance of GPR and the posterior probability index measurement of Bayesian theorem, data under different rotating speeds are measured, and various groups of data with approximate pair height are selected to form a training set training global model. The method improves the prediction performance of the centrifugal pump process efficiency prediction.
Description
Technical Field
The invention relates to the technical field of centrifugal pump efficiency prediction models, in particular to a centrifugal pump efficiency prediction method based on data-driven modeling.
Background
The pump is a widely used mechanical type. The pump consumes nearly 22% of the global energy provided by the motor, and has huge energy-saving potential. Centrifugal pumps are the largest class of pump machines and are widely applied to the fields of water diversion engineering, agricultural irrigation and urban water supply, so that energy conservation and stable operation are always the key points of research.
Because the cost reduction when the frequency conversion technique, adjust the rotational speed of centrifugal pump and then satisfy the operating mode demand through the variable frequency drive ware, finally realize energy-conservation, consequently the frequency conversion technique is by extensive application in the centrifugal pump field. However, the position and size of the maximum efficiency point (BEP) of the centrifugal pump may vary depending on the rotational speed. Meanwhile, when the centrifugal pump is connected with a water supply system, the actual working point of the centrifugal pump is determined by the performance curve of the centrifugal pump and the system pipeline curve together, so that the overall efficiency of the centrifugal pump is also influenced by the system pipeline. If the operating efficiency of the centrifugal pump under different rotating speeds can be accurately predicted, the energy-saving effect of the frequency conversion technology can be more effectively exerted, and meanwhile, the phenomenon that the centrifugal pump operates under severe working conditions for a long time to reduce the service life is avoided.
At present, the similar law of the centrifugal pump is mainly used for predicting the running state of the centrifugal pump at different rotating speeds, but the law assumes that the efficiency of the pump is unchanged at different rotating speeds, and in practical cases, the volumetric efficiency (eta) of the centrifugal pump is changed when the rotating speed of the centrifugal pump is changed v ) Hydraulic efficiency (. Eta.) h ) Mechanical efficiency (η) w ) Also subject to variation, in particular eta w With decreasing speed η w Increases and results in a change in the size and location of the BEP of the centrifugal pump. Some researchers also associate the new efficiency with the original efficiency to obtain some empirical formulas, and other researchers believe that the efficiency is a function of the Reynolds number and the pipe wall roughness, so that the empirical formulas are arranged to predict the efficiency at different rotating speeds.
The friction loss of a pipeline system is not considered by an empirical formula based on a centrifugal pump mechanism, so that the empirical error exists, the difference of the rotating speed of the centrifugal pump exceeds the application range of the empirical formula, and the prediction performance of the centrifugal pump is greatly reduced. When the centrifugal pump is connected with a system with a static head, the prediction precision can be greatly reduced due to the influence of the static head of the system. The efficiency estimation of the centrifugal pump only considers the efficiency change of the centrifugal pump, and ignores the efficiency change of the variable-frequency driver after the rotating speed is changed and the efficiency change of the motor for driving the centrifugal pump to rotate.
The above empirical formula based on the centrifugal pump mechanism and the similar law of the pump are basically dependent on the rotational speed of the centrifugal pump, but in some engineering applications the rotational speed is not readily available. The rotating speed of the centrifugal pump is mainly adjusted by adjusting the frequency of the variable-frequency driver, and the frequency of the variable-frequency driver cannot be directly converted into the rotating speed of the centrifugal pump, because the rotating speed of the centrifugal pump is not equal to the rotating speed of the motor when the centrifugal pump is connected with the motor, and the slip rate exists when the frequency of the variable-frequency driver is adjusted.
Recently, as a new approach, through data-driven empirical models developed in the field of fluid mechanics. Compared with a mechanism model, the data-driven model does not need deep knowledge of the mechanism and experience of a lot of designers, and reflects internal rules mainly through data per se. As is well known, the accuracy of the empirical model for data-driven modeling depends on the reliability of modeling data, but in practical situations, the modeling data has certain procedural property, and data in different stages have different characteristics, so that the traditional modeling method is difficult to meet the requirement. In data-driven empirical modeling methods, therefore, effective strategies must be developed to enhance the predictive performance of the model.
In order to reasonably predict the operating efficiency of the centrifugal pump under different rotating speeds, the data driving model suitable for the small sample condition is more suitable. A Gaussian process regression model (GPR) is used as a probability modeling method and can be well suitable for the condition of small samples. For the efficiency curve of the centrifugal pump at different rotating speeds, the efficiency curve can be divided into two stages through process knowledge, namely an efficiency increasing stage and an efficiency decreasing stage. If the two phases of the efficiency curve at the new speed can be predetermined, two partial GPR models for the efficiency-up phase and the efficiency-down phase can be established separately. Therefore, the characteristics of each stage are fully learned by the two local GPR models, and the prediction effect is improved.
Disclosure of Invention
Aiming at the technical defects, the invention provides a centrifugal pump efficiency prediction method based on data-driven modeling by combining the prediction variance of the regression GPR in the Gaussian process with the Bayes theorem, measures data at different rotating speeds, selects various groups of data with similar pair heights to form a training set training global model, and improves the prediction performance of the model.
The technical scheme of the invention is as follows:
a method of predicting centrifugal pump efficiency based on data-driven modeling, the method comprising the steps of:
1) Collecting a data set in the operation process of the centrifugal pump as a sample, determining the characteristics of the centrifugal pump by analyzing the change of efficiency along with flow at different rotating speeds, and determining an input variable and an output variable of a prediction model;
selecting an input variable as the inlet pressure P s Outlet pressure Pd, outlet valve opening V of the water supply system, outlet flow Q, i.e. x i ＝{P si ，P di ，V i ，Q i } T (ii) a The output variable chosen is the actual efficiency, y i ＝η i (ii) a Wherein x i Input variables representing the ith sample, i.e. each sample x i Containing 4 input variables, y i An output variable representing the ith sample;
2) Training a GPR model by combining the prediction variance of the regression GPR in a Gaussian process with Bayesian theorem and a Bayesian method;
for the output variable y i The GPR model is in Gaussian prior distribution, and the mean value is a regression function of zero or a discrete regression function;
(y i ，…，y N ) T ～G(0，C) (1)
where T is a transposed symbol, G is a Gaussian distribution symbol, and C represents the i-th element C = (x) i ，x i ) Nxn covariance matrix of (a); training a GPR model by using a Bayesian method to estimate C; with N being t Test sample set of input samples
t＝1，…，T，X t Is a set, x t，i Is a sub-element of a set, i represents 1 to N t A plurality of; output variable
And its variance
The calculation method of (2) is as follows:
wherein k is t，i ＝[C(x t，i ，x 1 )，C(x t，i ，x 2 )，…，C(x t，i ，x N )] T Is the covariance vector, k, of the new input data and the training data t，i ＝C(x t，i ，x t，i ) Is the covariance of the new input data,
is the prediction variance of the GPR model output, where equation (3) provides the confidence of the prediction;
the variance of the trained GPR model presents different stage characteristics and respectively corresponds to the rising stage and the falling stage of the efficiency curve, so that probability information can be used for stage identification;
3) By predicting variance in GPR model
Posterior probability P (GPR) combined by combining Bayes theorem l |X t ) The average value MEPP of the indexes measures the similarity of all groups of sample sets at different rotating speeds;
respectively training a plurality of GPR models through sample subsets at different rotating speeds, and evaluating a single GPR model and a test sample set
Is expressed by Bayes-based conditional probability, namely P (GPR) l |X t ) An index, defined by the formula:
P(x t，i |GPR l ) Is shown in sample set X t Meet GPR in the first place l This model, again, satisfies at x t，i The probability of this subset of samples;
P(GPR l ) Represents a sample set X t Satisfy GPR l The probability of this model;
P(x t，i ) Represents a sample set X t Is x t，i The probability of this subset of samples;
integrated posterior probability P (GPR) l |X t ) The average MEPP of (d) may be defined as:
wherein N is l Number of samples, N, representing a subset of training samples t Represents the number of samples of the test set,
express GPR l For x t，i (iv) prediction uncertainty of;
4) Selecting a sample subset as a training sample subset, and segmenting the training sample subset;
selecting MEPP l，t Larger three GPRs l The training sample subset of the model constitutes a training sample set X l (ii) a Prediction test set X t The position of the maximum prediction is obtained, and the test set is divided into a test set X with an efficiency ascending interval and an efficiency descending interval t，m And X t，n ；
Taking segmentation measures by utilizing the position of the maximum efficiency point (BEP), and training set X l Training set X divided into efficiency-up and efficiency-down intervals l，m And X t，m ：
Q t Is the flow of the training set, is a parameter data of the training set, the characteristic parameter of the former input sample refers to the sample composed of the input parameters, namely x i ＝{P si ，P di ，V i ，Q i } T ；Q i Q can be determined by the known BEP point i In a position of
The flow corresponding to the highest efficiency point;
5) Training the model, outputting a predicted new test set, and obtaining the prediction efficiency of the test sample set;
training set X through different phases l，m And X t，m Training two local GPR models, LGPR m And LGPR n Separately predicting test sets X of corresponding stages t，m And X t，n ；
6) Integrating the prediction efficiency of the two stages to obtain a test sample set X t The prediction efficiency of (2).
The beneficial effects of the invention are: providing a new centrifugal efficiency prediction method, combining the stage identification of the prediction variance of a GPR model to an efficiency curve, and providing the sectional treatment of the efficiency curve; predicting different stages of the efficiency curve by creating local GPR models of different stages; therefore, compared with a single model, the segmented model predicts aiming at different stages so as to improve the prediction performance of the model, and meanwhile, the method is not dependent on the running rotating speed of the centrifugal pump, and is beneficial to the prediction of the efficiency of the centrifugal pump.
Drawings
FIG. 1 is a diagram of the composition phases of a segmentation model in accordance with the present invention;
FIG. 2 is a flow chart of the piecewise modeling of the present invention;
FIG. 3 is a graph of the training results and variance of the global GPR model of the present invention.
Detailed Description
The invention is further described with reference to the drawings and examples.
Referring to FIGS. 1-3:
a centrifugal pump efficiency prediction method based on data-driven modeling comprises the following steps:
1) The characteristics of the centrifugal pump are determined by analyzing the change of efficiency with flow at different rotating speeds, so that the input variable and the output variable of the sample are determined.
First, the input variable is the inlet pressure P s Outlet pressure P d Outlet valve opening V, outlet flow Q of the water supply system, namely:
x i ＝{P si ，P di ，V i ，Q i } T
actual efficiency being an output variable, i.e. y i ＝η i . Wherein the input data is from experimental data using a self-priming centrifugal pump as a test pump.
2) The GPR model is trained by the predictive variance of Gaussian Process Regression (GPR) in combination with bayesian theorem bayesian methods.
For the output variable y, the GPR model gaussian prior distribution, the mean value is the regression function of zero:
(y i ，…，y N ) T ～G(0，C)
wherein C represents the i-th element C = (x) i ，x i ) N × N covariance matrix. C can be estimated by training the GPR model using a bayesian approach. By having N t Test sample set of input samples
T =1, …, T, output variable
And its variance
The calculation method of (2) is as follows:
wherein k is t，i ＝[C(x t，i ，x 1 )，C(x t，i ，x 2 )，…，C(x t，i ，x N )] T Is the covariance vector, k, of the new input data and the training data t，i ＝C(x t，i ，x t，i ) Is the covariance of the new input data,
is the predicted variance of the GPR model output.
The variance of the trained GPR model presents different stage characteristics, wherein a turning point is a highest efficiency point (BEP), and the left side and the right side of the point respectively correspond to an ascending stage and a descending stage of an efficiency curve, so probability information can be used for stage identification.
A global GPR model is trained by using samples at a rated rotating speed, the training result is shown in FIG. 3, and according to different characteristics of training variance, a mark 1 can be found * ～3 * The efficiency curve is divided into an efficiency ascending stage and an efficiency descending stage by the 3 points, and meanwhile, a high efficiency interval of the centrifugal pump can be identified.
3) By predicting variance in GPR model
Posterior probability P (GPR) combined by combining Bayes theorem l |X t ) The mean of the indices (MEPP) measures the similarity of the sets of samples at different rotational speeds.
Firstly, respectively training a plurality of GPR models through sample subsets at different rotating speeds, and evaluating the single GPR modelGPR model and test sample set
Can express P (GPR) through Bayes-based conditional probability l |X t ) An index, defined by the formula:
the average value (MEPP) of the integrated a posteriori probabilities P (GPR _ l | X _ t) may be defined as:
wherein N is l Number of samples representing a subset of training samples, N t Represents the number of samples of the test set,
express GPR l For x t，i The prediction uncertainty of (a).
(4) And selecting the sample subset as a training sample subset, and segmenting the training sample subset.
Selecting MEPP l，t Larger three GPRs l The training sample subset of the model constitutes a training sample set X l . Prediction test set X t The position of the maximum prediction is obtained, and the test set is divided into a test set X with an efficiency ascending interval and an efficiency descending interval t，m And X t，n 。
Taking segmentation measures by utilizing the position of the BEP point, and combining the training set X l Training set X divided into efficiency ascending intervals and efficiency descending intervals l，m And X t，m ：
5) And training the model, outputting a predicted new test set, and obtaining the prediction efficiency of the test sample set.
Training set X through different stages l，m And X t，m Training two local GPR models, LGPR m And LGPR n Separately predicting test sets X of corresponding stages t，m And X t，n 。
In order to compare the prediction performances of different models, the invention adopts two general indexes, namely Root Mean Square Error (RMSE) and limit error (ME), which are defined as follows:
wherein
Denotes y t，i Predicted value of (1), N t The number of samples in the t-th test set is indicated.
Example (b):
1) Selecting proper model input and output variables, and establishing a data subset:
based on an empirical formula of the existing centrifugal pump mechanism and characteristic parameters of the centrifugal pump under actual conditions, selecting variables convenient to measure in experiments as input variables of the model: inlet pressure P s Outlet pressure P d The opening degree V of an outlet valve of a water supply system and the outlet flow Q. The output variables are: the actual efficiency y.
The data of the present invention are derived from experimental data based on a self-priming centrifugal pump as a test pump. Obtaining 10 groups of different rotating speeds in an experimental systemMouth pressure P s Outlet pressure P d The opening degree V of an outlet valve of a water supply system and the outlet flow Q. And simultaneously, obtaining shaft power N according to the torque sensor, and calculating the efficiency of different flow points:
where ρ is the density of the transport liquid.
Collecting data of centrifugal pump at different rotating speeds
2) Passing the formula (y) according to the sample subset at different rotating speeds i ，…，y N ) T G (0,C) training multiple GPRs l Model training of multiple GPRs by sample data subsets l And (4) modeling.
3) For a new speed test sample set X t By multiple GPRs l Calculating according to formula by using model to obtain MEPP l，t Selecting MEPP l，t Larger three GPRs l The training sample subset of the model constitutes a training sample set X l
4) Selecting MEPP in step 3 l，t Maximum GPR l Model predictive test set X t The position of the maximum prediction is obtained, and the test set is divided into a test set X with an efficiency ascending interval and an efficiency descending interval t，m And X t，n And simultaneously segmenting and classifying the selected three training sample subsets by utilizing the known positions of the BEP points of the training set to obtain a training set X of an efficiency rising interval and an efficiency falling interval l，m And X l，n
5) Utilizing the new training set X in step 4 l，m And X l，n Training two local GPP models and correspondingly predicting a new test set X t，m And X t，n To output of (c).
6) Finally, the prediction efficiency of the two stages is integrated to obtain a test sample set X t The prediction efficiency of (2).
Claims (1)
1. A method for predicting centrifugal pump efficiency based on data-driven modeling, the method comprising the steps of:
1) Collecting a data set in the operation process of the centrifugal pump as a sample, determining the characteristics of the centrifugal pump by analyzing the change of efficiency along with flow at different rotating speeds, and determining an input variable and an output variable of a prediction model;
selecting an input variable as the inlet pressure P s Outlet pressure P d Opening V of an outlet valve of a water supply system, outlet flow Q, i.e. x i ＝{P si ，P di ，V i ，Q i } T (ii) a The selected output variable is the actual efficiency, y i ＝η i (ii) a Wherein x is i Input variables representing the ith sample, i.e. each sample x i Comprising 4 input variables, y i An output variable representing the ith sample;
2) Training a GPR model by combining the prediction variance of the regression GPR in a Gaussian process with Bayesian theorem and a Bayesian method;
for the output variable y, a GPR model is in Gaussian prior distribution, and the mean value is a regression function of zero or a discrete regression function;
(y i ，…，y N ) T ～G(0，C) (1)
where T is a transposed symbol, G is a Gaussian distribution symbol, and C represents the i-th element C = (x) i ，x i ) Nxn covariance matrix of (a); training a GPR model by using a Bayesian method to estimate C; by having N t Test sample set of input samples
X t Is a set, x t，i Is a sub-element of a set, i represents 1 to N t (ii) a Output variable
And its variance
The calculation method of (2) is as follows:
wherein k is t，i ＝[C(x t，i ，x 1 )，C(x t，i ，x 2 )，…，C(x t，i ，x N )] T Is the covariance vector, k, of the new input data and training data t，i ＝C(x t，i ，x t，i ) Is the covariance of the new input data,
is the predicted variance of the GPR model output, where equation (3) provides the confidence of the prediction;
the variance of the trained GPR model presents different stage characteristics which respectively correspond to an ascending stage and a descending stage of an efficiency curve, so probability information is used for stage identification;
3) By predicting variance in GPR model
Posterior probability P (GPR) combined by combining Bayes theorem l |X t ) The average value MEPP of the indexes measures the similarity of all groups of sample sets at different rotating speeds;
training a plurality of GPR models respectively through sample subsets at different rotating speeds, and expressing P (GPR) through Bayes-based conditional probability l |X t ) Indicators, evaluation of individual GPR models and test sample sets
Is defined by the formula:
P(x t，i |GPR l ) Is shown in sample set X t Meet GPR first l This model, again, satisfies at x t，i The probability of this subset of samples;
P(GPR l ) Represents a sample set X t Satisfy GPR l The probability of this model;
P(X t，i ) Represents a sample set X t Is x t，i The probability of this subset of samples;
integrated posterior probability P (GPR) l |X t ) The average MEPP of (a) is defined as:
wherein N is l Number of samples representing a subset of training samples, N t Represents the number of samples of the test set,
express GPR l For x t，i (iv) prediction uncertainty of;
4) Selecting a sample subset as a training sample subset, and segmenting the training sample subset;
selecting MEPP l，t Larger three GPRs l The training sample subset of the model constitutes a training sample set X l (ii) a Predictive test set X t The position of the maximum prediction is obtained, and the test set is divided into an efficiency rising interval and an efficiency falling areaTest set X of cells t，m And X t，n ；
Taking segmentation measures by utilizing the position of the maximum efficiency point (BEP), and training set X i Training set X divided into efficiency-up and efficiency-down intervals l，m And X t，m ：
Q t Is the flow of the training set, is a parameter data of the training set, the characteristic parameter of the former input sample refers to the sample composed of the input parameters, namely x i ＝{P si ，P di ，V i ，Q i } T ；Q i Determining Q by known BEP points i In a position of
The flow corresponding to the highest efficiency point;
5) Training the model, outputting a predicted new test set, and obtaining the prediction efficiency of the test sample set;
training set X through different phases l，m And X t，m Training two local GPR models, LGPR m And LGPR n Separately predicting test sets X of corresponding stages t，m And X t，n ；
6) Integrating the prediction efficiency of the two stages to obtain a test sample set X t The prediction efficiency of (2).
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| CN107918709A (en) * | 2017-11-17 | 2018-04-17 | 浙江工业大学 | Prediction method for transient opening height of one-way valve for multiphase mixed transportation pump |
| CN108510120A (en) * | 2018-04-03 | 2018-09-07 | 浙江工业大学 | A kind of hybrid modeling and prediction technique of reciprocating mixing pump discharge flow rate |
| CN108549757A (en) * | 2018-04-03 | 2018-09-18 | 浙江工业大学 | A kind of reciprocating mixing pump discharge flow rate prediction technique that model selects certainly |
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