CN108549757B - Model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method - Google Patents

Model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method Download PDF

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CN108549757B
CN108549757B CN201810288855.7A CN201810288855A CN108549757B CN 108549757 B CN108549757 B CN 108549757B CN 201810288855 A CN201810288855 A CN 201810288855A CN 108549757 B CN108549757 B CN 108549757B
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刘毅
邓鸿英
张生昌
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Zhejiang University of Technology ZJUT
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Abstract

The invention discloses a model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method, which comprises the following steps: (1) determining input and output variables of a prediction model, and collecting modeling samples; (2) establishing a partial GPR model of the discharge flow rate of the reciprocating type mixed delivery pump; (3) establishing a weighted GPR model of the discharge flow rate of the reciprocating type mixed delivery pump; (4) establishing an instant GPR model of the discharge flow rate of the reciprocating type mixing delivery pump; (5) automatically selecting a suitable prediction model for each new input sample point based on the prediction probability information; (6) and (5) repeating the steps (2) to (5), finding the most appropriate prediction model for each input sample point under a new working condition from the local GPR, the weighted GPR and the instant GPR models, and then obtaining the discharge flow rate curve of the reciprocating type mixed delivery pump under the new working condition.

Description

Model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method
Technical Field
The invention relates to an important parameter modeling and predicting method for a reciprocating type mixed transportation pump in a design stage, in particular to a model self-selection reciprocating type mixed transportation pump discharge flow rate predicting method suitable for complex frequency-dependent oil-gas mixed transportation working conditions.
Background
The reciprocating type mixing and conveying pump has the functions of a pump and a compressor, and can effectively increase the yield of oil and natural gas in the oil exploitation process. When the reciprocating pump delivers incompressible medium, the piston and the inlet and outlet valves are moved cyclically so that the pump chamber discharge flow rate equals the rate of change of its volume, the pump chamber discharge flow rate curve for one stroke exhibiting a sinusoidal variation. When the reciprocating pump delivers compressible and incompressible mixed media such as oil gas and the like, the open and close hysteresis phenomena of the inlet and outlet valves can be induced by the heterogeneous flow frequency-variable impact load generated in the pump. Due to the compressible and incompressible nature of the gas, the lag in opening of the outlet valve will cause the pump chamber flow rate to rise rapidly to a peak, with the fluctuations then returning to a sinusoidal variation, exhibiting abrupt segments on the discharge flow rate curve; a short and small backflow occurs after the closing delay of the outlet valve, and a backflow section is presented on the discharge flow rate curve. It can be seen that under the condition of oil-gas mixture transportation, the pump cavity discharge flow rate curve of one stroke of the reciprocating pump presents four stages of a zero flow section, a sudden change section, a sine section and a backflow section. The sudden change phenomenon in the flow discharge process of the reciprocating pump is one of the main reasons for intensifying flow pulsation, inducing noise and vibration and reducing pump efficiency. Therefore, the research on the interaction between the discharge flow rate characteristic of the reciprocating pump and the oil-gas mixed transportation working condition has important significance for guiding the design of the mixed transportation pump engineering and ensuring the stable operation of the mixed transportation pump.
The scholars at home and abroad mainly study the flow characteristics of screw-type, vane-type and gear-type mixed delivery pumps on the basis of a mechanism model and a Computational Fluid Dynamics (CFD) simulation technology. As a newly used mixed transportation pump type, research on the flow characteristics of a reciprocating oil-gas mixed transportation pump is rarely carried out. The instantaneous flow of the pump under several mixed transportation working conditions is obtained by means of a CFD modeling tool only in Zhang Shengchang and the like without considering any volume loss, and the flow pulsation characteristics of the pump are researched. In general, most of the above studies on various multiphase pumps do not consider leakage and energy loss of the pumps, and the reduction of the in-pump flow pattern into homogeneous flow is not enough to describe the flow characteristics of the multiphase pumps which are frequency-variant and complicated. Meanwhile, mechanism models describing various mixed delivery pumps are complex, and parameters such as valve clearance instantaneous pressure, temperature, flow coefficient and the like in the models are difficult to obtain from experiments, so that the engineering application of the models is limited. In addition, the division of dynamic meshes, selection of multiphase flow and turbulence models, user-defined functions and other CFD modeling processes are highly dependent on the experience of the research and designer. Therefore, it is necessary to establish a reciprocating type multiphase pump discharge flow rate model with strong universality and high accuracy to adapt to complex frequency-dependent oil-gas multiphase working conditions.
In recent years, data-driven empirical models have been used to predict variables with large measurement lags in nonlinear industrial processes without substantial knowledge of complex internal phenomena and without much experience on the part of designers. These advantages can solve the above mechanism and CFD modeling problem simultaneously, and provide a new method for modeling and predicting the discharge flow rate of the multiphase pump.
Under different mixing and transportation working conditions, the discharge flow rate curve presents different process characteristics; under the same mixed transportation working condition, the zero flow section, the abrupt change section, the sine section and the backflow section of the discharge flow rate curve also present different local characteristics, and the discharge flow rate of the abrupt change section presents the characteristics of rapid nonlinear change and the like. In addition, the few multi-phase flow meter products on the market have the limitations of high manufacturing cost, measurement lag and the like, and the prediction performance is very difficult to improve by acquiring a large amount of reliable modeling data from experiments. By considering the factors, the characteristics of the whole complex process can be more completely described by using the prediction uncertainty information provided by a Gaussian Process Regression (GPR) model and adopting an adaptive hybrid modeling method. However, literature search revealed that the GPR model was not used to predict the discharge flow rate of reciprocating compound pumps.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method suitable for the complex frequency-dependent oil-gas mixed transportation working condition.
Aiming at the defects and shortcomings existing in the mechanism and the CFD modeling process, the invention provides a self-adaptive modeling and predicting method utilizing GPR prediction uncertainty, which can automatically select a proper prediction model for each test point based on limited samples and improve the prediction accuracy and reliability of the discharge flow rate.
The model self-selection reciprocating type multiphase pump discharge flow rate prediction method comprises the following steps:
(1) determining input variables and output variables of a prediction model, collecting a modeling sample set S, and classifying the sample set S to obtain M sample subsets, namely S ═ (S)1，…，sm)TM is 1, …, M; the mth subset of samples is denoted as
Figure GDA0001708337650000031
Wherein N ismRepresents the m-th sampleSample number of the subset;
(2) partial GPR model for establishing discharge flow rate of reciprocating type mixed delivery pump
Performing learning training on each sample subset independently, and establishing a partial GPR prediction model of the discharge flow rate;
according to GPR definition, m local model GPRmThe output of (d) is expressed as:
Figure GDA0001708337650000032
in the formula, CmRepresents a covariance matrix whose i row and j column elements are represented as:
Figure GDA0001708337650000033
in the formula, xm，idDenotes xm，iThe d-th element of (1); j, then δm，ij1, otherwise δ m，ij0; d is the training sample point xm，iThe input dimension of (a); thetam＝[am，0，am，1，vm，0，wm，1，…，wm，d，bm]TIs the model coefficient;
using formula (1) and formula (2), M partial GPR models complete off-line modeling, defined as GPRm，m＝1，…，M；
Testing sample set for new input
Figure GDA0001708337650000041
Where T represents the number of newly input test sample sets, NtNumber of samples, x, representing the t-th new input test sample sett，iDenotes xtThe ith sample point; GPRmFor xt，iPredicted output of (2)
Figure GDA0001708337650000042
Sum variance
Figure GDA0001708337650000043
Respectively, as follows:
Figure GDA0001708337650000044
Figure GDA0001708337650000045
in the formula (I), the compound is shown in the specification,
Figure GDA0001708337650000046
representing the covariance between the new input test sample and the training sample; k is a radical ofm，ti＝C(xt，i，xt，i) Is the covariance of the newly input test sample;
for a new input test sample point, calculating and obtaining M online prediction information based on the local GPR model from the formula (3) and the formula (4);
(3) establishing a weighted GPR model of the discharge flow rate of the reciprocating type mixed delivery pump;
based on Bayesian inference, conditional probability P (GPR) is proposedm|xt，i) To GPRmEach sample point x of the model and new input sett，iThe relationship between the two is evaluated; p (GPR)m|xt，i) The calculation is as follows:
Figure GDA0001708337650000047
in the formula, P (GPR)m) And P (x)t，i|GPRm) Prior probability and conditional probability, respectively; when there is no process prior knowledge, P (GPR)m|xt，i) Expressed as:
Figure GDA0001708337650000051
for new input test sample point x based on probability analysis methodt，iIn terms of P (GPR)m|xt，i) The larger the GPRmThe more appropriate the model is to predict it;
merging the M partial GPR model pairs xt，iProbability information of prediction, weighting prediction values of GPR model
Figure GDA0001708337650000052
And its variance
Figure GDA0001708337650000053
The expression is as follows:
Figure GDA0001708337650000054
Figure GDA0001708337650000055
(4) establishing an instant GPR model of the discharge flow rate of the reciprocating type mixing delivery pump;
(4.1) from sample set s ═ { xn，ynN1, …, N (N is the total number of samples in the sample set), is a new input test sample point xt，iSelecting a suitable similar modeling sample; definition of
ηt，ni＝exp(-||xn-xt，i||)，n＝1，…，N (9)
Describing a modeled sample point xnAnd new input test sample point xt，iThe similarity relationship of (1); etat，niThe larger the value is, the more similar the relationship between the two is; thus, by setting the appropriate threshold λ, by formula
ηt，ni＞λ (10)
Testing sample points x for new inputst，iSelecting a proper similar modeling sample set;
(4.2) establishing an instant GPR model by using the formula (1) and the formula (2) based on the similar modeling sample set selected by the formula (10); calculating to obtain the sample point x of the instantaneous GPR model from the formula (3) and the formula (4)t，iPredicted value of (2)
Figure GDA0001708337650000061
And its variance
Figure GDA0001708337650000062
(5) Automatically selecting a suitable prediction model for each new input test sample point based on the prediction probability information;
(5.1) for each new input test sample point xt，iSelecting a suitable local GPR prediction model;
based on the probability information provided by equation (6), there is a model of Maximum Conditional Probability (MCP), i.e.
MCPt，i＝maxP(GPRm|xt，i)，m＝1，…，M (11)
Testing sample points x for new inputst，iThe most suitable partial GPR prediction model, the corresponding predicted value and the variance thereof are respectively recorded as
Figure GDA0001708337650000063
And
Figure GDA0001708337650000064
(5.2) test sample points x for each new input from the local, weighted and immediate GPR modelt，iSelecting a proper prediction model;
the predicted variance can be used to describe the input test sample point xt，iAnd uncertainty of its prediction model; if an inappropriate model is used for the new input test sample xt，iIf prediction is performed, the corresponding variance value is large; based on this, can be selected from
Figure GDA0001708337650000065
And
Figure GDA0001708337650000066
in which the model with the smallest variance (MV) is selected, i.e.
Figure GDA0001708337650000067
I.e. new input test sample point xt，iThe most appropriate predictive model;
(6) and (5) repeating the steps (2) to (5), finding the most appropriate prediction model for each input test sample point under the new working condition from the local GPR model, the weighted GPR model and the instant GPR model, and further obtaining the discharge flow rate curve of the reciprocating type multiphase pump under the new working condition.
The model self-selection reciprocating type multiphase pump discharge flow rate prediction method is characterized in that in the step (5), each input test sample point x is described by using the maximum conditional probability and the prediction variancet,iAnd the uncertainty of its prediction model, so that an appropriate model can be selected for prediction.
By adopting the technology, compared with the prior art, the invention has the following beneficial effects: the model self-selection reciprocating type mixed transportation pump discharge flow rate prediction method provided by the invention is based on a limited modeling sample, realizes modeling and prediction of the discharge flow rate of the reciprocating type mixed transportation pump under the mixed transportation working condition, and is easy to implement in engineering and high in accuracy compared with the complexity of a mechanism model modeling process, the dependence of a CFD modeling process on the experience level of a designer and the like.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2a to 2d are comparison of experimental results of a new input sample set with self-selected model prediction results according to the present invention, wherein fig. 2a is a graph of local GPR prediction results of the new input sample set, fig. 2b is a graph of weighted GPR prediction results of the new input sample set, fig. 2c is a graph of immediate GPR prediction results of the new input sample set, and fig. 2d is a graph of self-selected prediction results of the new input sample set model.
Detailed Description
The technical scheme of the invention is further explained by combining the drawings and the embodiment of the specification.
Examples
As shown in fig. 1, a model self-selection method for predicting a flow rate of a reciprocating type mixing pump includes the following steps:
(1) determining input variables and output variables of a prediction model, and collecting modeling samples;
in the embodiment, the inlet pressure P is selected by comprehensively considering the influence factors of the flow rate of the reciprocating type mixing and conveying pump and the design parameters of a prototype of the three-cylinder double-acting reciprocating type mixing and conveying pump for experimentss(0.2-0.4 MPa) and outlet pressure Pd(1.0-3.0 MPa), air content beta (0.1-0.8) and crank angle theta (180 degrees-the end of the discharge process) are input variables; considering that the flow rate of the conventional reciprocating pump can be calculated by a theoretical formula from the flow rate of one pump cavity, different numbers of pump cylinders are usually adopted in practical engineering application, and the flow rate Q of one pump cavity of a prototype is selected as an output variable without loss of generality;
acquiring experimental data under different working conditions from an experimental system; samples at different crank angles for one stroke, i.e. with the same inlet pressure, outlet pressure, gas fraction, pump speed, clearance volume, are grouped into a sample subset. The 15 sample subsets obtained are expressed as S ═ (S)1，…，s15)T9 of them are used as training sample set(s)1，…，s9) The remaining 6 are used as test sample sets(s)10，…，s15) The corresponding working conditions are respectively Ps0.3, 0.35, 0.25, 0.2, 0.4MPa, outlet pressure Pd3.0, 2.5, 3.0, 1.0MPa), gas content β (0.5, 0.3, 0.4, 0.1, 0.7, 0.8), crank angle θ (180 ° end of discharge process); in order to illustrate the advantages of the method, 6 test samples are concentrated, the first 3 working conditions are similar to the training working conditions, and the last three working conditions are different;
(2) partial GPR model for establishing discharge flow rate of reciprocating type mixed delivery pump
Establishing 9 local GPR models off line based on the formulas (1) and (2);
based on the formulas (3) and (4), 9 pieces of local GPR model online prediction information can be obtained respectively, and the test sample set S is subjected to10The predicted value and variance of one sample point of (a);
(3) weighted GPR model for establishing discharge flow rate of reciprocating type mixed delivery pump
Based on equations (5) to (8), a weighted GPR model is established, and S is obtained10The predicted value and variance of one sample point of (a);
(4) and establishing an instant GPR model of the discharge flow rate of the reciprocating type multiphase pump.
Based on the formulae (9) and (10), is S10Selecting a suitable similar modeling sample set from one sample point; establishing an instant GPR model based on the formula (1) and the formula (2); calculating a predicted value and a variance of the instant GPR model to the sample point by using a formula (3) and a formula (4);
(5) automatically selecting a suitable prediction model for each new input sample point based on the prediction probability information;
based on formula (11), is S10Selecting the most suitable local GPR model corresponding to the maximum conditional probability; from the local, weighted and immediate GPR model, S, based on equation (12)10Selecting the most suitable model, i.e. the model corresponding to the minimum prediction variance;
(6) repeating steps (2) to (5) for a test sample set S from the local GPR, weighted GPR and immediate GPR models10Finding the most suitable prediction model for each sample point, and then obtaining S10An exhaust flow rate curve;
(7) repeating steps (2) to (6) can obtain the discharge flow rate curves of the remaining 5 test sample sets.
The prediction results of the 6 test sample sets obtained by the method are compared with the experimental results, and the common index of mean square error (RMSE) is selected as an evaluation standard. For the tth test sample set, the RMSE evaluation criteria are defined as follows:
Figure GDA0001708337650000091
the RMSE index is a non-negative number, and the smaller the value, the better the prediction effect. The comparison results are shown in table 1.
Table 1 prediction performance of the method of the invention for a set of test samples
Figure GDA0001708337650000092
Figure GDA0001708337650000101
As can be seen from the results in Table 1, based on limited modeling samples, the method (i.e., the prediction method based on model self-selection) of the invention can well capture the characteristic information of the first 3 test samples (which are similar to the training condition); main characteristic information of the last 3 test samples (different from the training working condition) can be well captured; compared with a single local GPR, a weighted GPR and an instant GPR prediction model which are directly used, the method can better capture the characteristic information of each test sample set and obtain better prediction performance.
From test sample set S10The detailed prediction results (as shown in fig. 2a to 2d) show that the prediction effect of the local GPR prediction model in the ascending section of the mutation section is better, the prediction effect of the weighted GPR prediction model in the vicinity of the peak value of the mutation section is better, the prediction effect of the immediate GPR prediction model in the zero flow section and the sinusoidal section is better, and the model self-selection method better integrates the advantages of the three prediction models and has the best prediction effect. Therefore, the method automatically selects a proper prediction model for each test sample point by utilizing the probability information provided by the GPR, can better extract the characteristic information in the sample, and improves the overall prediction precision.
Finally, it takes only a few minutes to complete the online prediction of the 6 test sample sets based on the modeling data for the 15 conditions provided by the experiment. Under the same computing resource condition, the traditional CFD modeling link usually takes more than half a month, and the established CFD model is not necessarily accurate and is not necessarily suitable for a test set under a new working condition.
Therefore, the model self-selection prediction method can provide more accurate model and prediction for the discharge flow rate of the reciprocating type mixing and conveying pump. In addition, the simple and reliable implementation method can reduce the design complexity, reduce the design cost, save the modeling time and provide an effective auxiliary means for the design of the current reciprocating type mixing and transporting pump.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (2)

1. A model self-selecting reciprocating type multiphase pump discharge flow rate prediction method comprises the following steps:
(1) determining input variables and output variables of a prediction model, collecting a modeling sample set S, classifying the sample set S to obtain M sample subsets, namely S ═ (S ═1,…,Sm)TM is 1, …, M; the mth subset of samples is denoted as
Figure FDA0003229282130000011
Wherein N ismRepresenting the number of samples of the mth sample subset;
(2) partial GPR model for establishing discharge flow rate of reciprocating type mixed delivery pump
Performing learning training on each sample subset independently, and establishing a partial GPR prediction model of the discharge flow rate;
according to GPR definition, m local model GPRmThe output of (d) is expressed as:
Figure FDA0003229282130000012
in the formula, CmRepresents a covariance matrix whose i row and j column elements are represented as:
Figure FDA0003229282130000013
in the formula, xm,idDenotes xm,iThe d-th element of (1); i is equal to j, and j is equal to,then deltam,ij1, otherwise δm,ij0; d is the training sample point xm,iThe input dimension of (a); thetam＝[am,0,am,1,vm,0,wm,1,…,wm,d,bm]TIs the model coefficient;
using formula (1) and formula (2), M partial GPR models complete off-line modeling, defined as GPRm,m＝1,…,M；
Testing sample set for new input
Figure FDA0003229282130000014
Where T represents the number of newly input test sample sets, NtNumber of samples, x, representing the t-th new input test sample sett,iRepresents XtThe ith sample point; GPRmFor xt,iPredicted output of (2)
Figure FDA0003229282130000015
Sum variance
Figure FDA0003229282130000016
Respectively, as follows:
Figure FDA0003229282130000017
Figure FDA0003229282130000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003229282130000022
representing the covariance between the new input test sample and the training sample; k is a radical ofm,ti＝C(xt,i,xt,i) Is the covariance of the newly input test sample;
for a new input test sample point, calculating and obtaining M online prediction information based on the local GPR model from the formula (3) and the formula (4);
(3) establishing a weighted GPR model of the discharge flow rate of the reciprocating type mixed delivery pump;
based on Bayesian inference, conditional probability P (GPR) is proposedm|xt,i) To GPRmEach sample point x of the model and new input sett,iThe relationship between the two is evaluated; p (GPR)m|xt,i) The calculation is as follows:
Figure FDA0003229282130000023
in the formula, P (GPR)m) And P (x)t,i|GPRm) Prior probability and conditional probability, respectively; when there is no process prior knowledge, P (GPR)m|xt,i) Expressed as:
Figure FDA0003229282130000024
for new input test sample point x based on probability analysis methodt,iIn terms of P (GPR)m|xt,i) Where M is 1, …, the larger M, the more GPRmThe more appropriate the model is to predict it;
merging the M partial GPR model pairs xt,iProbability information of prediction, weighting prediction values of GPR model
Figure FDA0003229282130000025
And its variance
Figure FDA0003229282130000026
The expression is as follows:
Figure FDA0003229282130000027
Figure FDA0003229282130000028
(4) establishing an instant GPR model of the discharge flow rate of the reciprocating type mixing delivery pump;
(4.1) from sample set S ═ { xn,ynN is 1, …, where N is the total number of sample sets and is the new input test sample point xt,iSelecting a suitable similar modeling sample; definition of
ηt,ni＝exp(-||xn-xt,i||),n＝1,…,N (9)
Describing a modeled sample point xnAnd new input test sample point xt,iThe similarity relationship of (1); etat,niThe larger the value is, the more similar the relationship between the two is; thus, by setting the appropriate threshold λ, by formula
ηt,ni＞λ (10)
Testing sample points x for new inputst,iSelecting a proper similar modeling sample set;
(4.2) establishing an instant GPR model by using the formula (1) and the formula (2) based on the similar modeling sample set selected by the formula (10); calculating to obtain the sample point x of the instantaneous GPR model from the formula (3) and the formula (4)t,iPredicted value of (2)
Figure FDA0003229282130000031
And its variance
Figure FDA0003229282130000032
(5) Automatically selecting a suitable prediction model for each new input test sample point based on the prediction probability information;
(5.1) for each new input test sample point xt,iSelecting a suitable local GPR prediction model;
based on the probability information provided by equation (6), there is a model of maximum conditional probability MCP, i.e.
MCPt,i＝maxP(GPRm|xt,i),m＝1,…,M (11)
Testing sample points x for new inputst,iBest fit of the Chinese traditional medicineThe appropriate local GPR prediction model, the corresponding predicted values and their variances are recorded as
Figure FDA0003229282130000033
And
Figure FDA0003229282130000034
(5.2) test sample points x for each new input from the local, weighted and immediate GPR modelt,iSelecting a proper prediction model;
the prediction variance is used to describe the input test sample point xt,iAnd uncertainty of its prediction model; if an inappropriate model is used for the new input test sample xt,iIf prediction is performed, the corresponding variance value is large; based on this, can be selected from
Figure FDA0003229282130000041
And
Figure FDA0003229282130000042
in which the model with the minimum variance MV is selected, i.e.
Figure FDA0003229282130000043
I.e. new input test sample point xt,iThe most appropriate predictive model;
(6) and (5) repeating the steps (2) to (5), finding the most appropriate prediction model for each input test sample point under the new working condition from the local GPR model, the weighted GPR model and the instant GPR model, and further obtaining the discharge flow rate curve of the reciprocating type multiphase pump under the new working condition.
2. The model self-selecting reciprocating multiphase pump discharge flow rate prediction method of claim 1, wherein in step (5), each input test sample point x is described by the proposed maximum conditional probability and prediction variancet,iAnd the uncertainty of its predictive model,so that a suitable model is selected for prediction.
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