CN113268822A - Centrifugal pump performance prediction method based on small sample nuclear machine learning - Google Patents

Centrifugal pump performance prediction method based on small sample nuclear machine learning Download PDF

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CN113268822A
CN113268822A CN202110385957.2A CN202110385957A CN113268822A CN 113268822 A CN113268822 A CN 113268822A CN 202110385957 A CN202110385957 A CN 202110385957A CN 113268822 A CN113268822 A CN 113268822A
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赵旭涛
张德胜
孙龙月
杨港
薛加磊
沈熙
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Abstract

A centrifugal pump performance prediction method based on small sample nuclear machine learning belongs to the technical field of centrifugal pump performance prediction and mainly comprises the following steps: (1) performing feature selection and standardization processing on the collected sample data; (2) constructing a small sample kernel machine learning Gaussian process regression prediction model; (3) selecting a suitable nonlinear kernel function; (4) training unknown hyper-parameters of the model based on the training data; (5) the validity of the model is verified based on the test data. The method takes the impeller structure and design parameters as basic data, learns the nonlinear relation between the impeller parameters and the lift and the efficiency of the centrifugal pump through a kernel machine learning Gaussian process regression model, and further realizes the prediction of the performance of the centrifugal pump. The invention fully and secondarily utilizes the design data of the existing centrifugal pump, has low requirements on the number of training samples by the prediction model, has low model construction difficulty, high model precision and good stability, and is more suitable for rapidly predicting the performance of the centrifugal pump in engineering design and optimization.

Description

Centrifugal pump performance prediction method based on small sample nuclear machine learning
Technical Field
The invention belongs to the field of centrifugal pump performance prediction, and particularly relates to a centrifugal pump performance prediction method based on small sample nuclear machine learning.
Background
Centrifugal pumps are widely used in many industrial fields as a general purpose machine. The impeller is one of the most important hydraulic components in the centrifugal pump, converts the mechanical energy of the motor into the energy of liquid, and further realizes the conveying of the liquid, and the reasonable design of the impeller is very important to the performance of the whole pump. The impeller has many structural parameters such as outlet width, blade number, impeller external diameter etc. and the change of some of them parameter will lead to the impeller in the rotation process, and its inside appears many complicated flow phenomena, such as secondary flow, wake efflux, vortex etc. some of them flow structure can consume the energy of inside liquid, and then influence centrifugal pump's performance, such as lift and efficiency. Due to the complexity of the internal flow of the impeller, the complex nonlinear relationship among the structural parameters of the impeller, the internal flow and the external characteristics of the impeller, the influence degree of the change of a certain parameter of the impeller on the performance of the impeller cannot be quantitatively measured, so that the design or the optimized design of the centrifugal pump becomes difficult, and the preliminary prediction of the performance of the centrifugal pump becomes very important.
The conventional centrifugal pump performance prediction methods mainly include a flow field analysis method based on numerical simulation, an empirical statistical method and a machine learning method based on data driving. The performance of the pump is generally estimated in the modern design of the pump based on a numerical simulation method, but for a physical model with a complex structure, the calculation cost is difficult to bear, and the process is complicated. The empirical statistical method is to calculate various losses in the pump through a semi-empirical semi-theoretical formula, and find the relationship between various losses and pump structure parameters after certain simplification and assumption of convection action, so as to establish a hydraulic loss prediction model. This approach is not universal and generalizable due to differences between the various pump types.
Gaussian Process Regression (GPR) is a data-based kernel machine learning method that is not only suitable for non-linear prediction under small samples, but also has many other advantages, such as it provides not only prediction values but also variances to assess prediction uncertainty in the prediction Process; the hyper-parameters are less sensitive to the prediction result; as a core machine learning method, the method has a plurality of core functions, can adapt to data with different characteristics, and can develop corresponding core functions according to the characteristics of the data. The GPR structure has high efficiency, few required training samples and strong nonlinear relation learning capacity, so that the design efficiency of the centrifugal pump can be greatly improved and the performance prediction time can be shortened when the GPR structure is applied to the performance prediction of the centrifugal pump.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting centrifugal pump performance based on small sample nuclear machine learning, which can predict the hydraulic performance of a centrifugal pump efficiently and accurately according to impeller parameters with a small amount of sample support.
The invention provides the following technical scheme: a centrifugal pump performance prediction method based on small sample nuclear machine learning comprises the following steps.
(1) The collected sample data is subjected to a normalization process.
(2) And constructing a small sample kernel machine learning Gaussian process regression prediction model.
(3) A suitable non-linear kernel function is selected.
(4) Unknown hyper-parameters of the model are trained based on the training data.
(5) The validity of the model is verified based on the test data.
In the foregoing scheme, in step (1), in order to reduce training time of the prediction model and ensure prediction accuracy thereof, the collected sample data is normalized to make the sample data satisfy a standard normal distribution with a mean value of 0 and a variance of 1, and a specific formula is as follows:
Figure BDA0003014005970000021
wherein,
Figure BDA0003014005970000022
for normalized data, xiFor raw data, μ is the mean of data of the same dimension, and σ is the variance of data of the same dimension.
In the above scheme, in the step (2), according to a mathematical principle of gaussian process regression, a priori distribution between a known training sample and an unknown test sample is constructed in MATLAB, and a formula thereof is as follows:
Figure BDA0003014005970000023
wherein y represents a set of training sample output variables; f. of*An output representing an unknown test sample; k (X, X) denotes the kernel functional relationship between the training sample input variables, K (X, X)*) And K (x)*X) each represent a kernel function relationship between a training sample input variable and a test sample input variable, K (X)*,x*) Representing the kernel function relationship between the test sample input variables,
Figure BDA0003014005970000031
representing noise and I representing an identity matrix.
In the above scheme, the posterior distribution of the output variables of the unknown test sample can be expressed as
Figure BDA0003014005970000032
Wherein
Figure BDA0003014005970000033
The mean of the posterior distribution whose value represents the unknown output variable of the test sample, cov (f)*) For the variance of the posterior distribution, the uncertainty of the output variable can be characterized, which can be expressed as the following two equations, respectively:
Figure BDA0003014005970000034
Figure BDA0003014005970000035
in the above scheme, in the step (3), by comparing the performances of three common Square Exponential (SE) nonlinear kernel functions, Rational Quadratic (RQ) nonlinear kernel functions and Matern5/2 nonlinear kernel functions, the SE kernel function is finally adopted to construct the nonlinear relationship between the impeller parameters and the centrifugal pump performance, and the formula is as follows:
Figure BDA0003014005970000036
wherein
Figure BDA0003014005970000037
Called signal variance, controlling the output magnitude of the kernel function;
Figure BDA0003014005970000038
l is called the characteristic length and controls the influence degree of the characteristic attribute of each dimension of the input variable on the output result.
In the above scheme, in the step (4), an initial value of an unknown hyper-parameter is randomly given, and an optimal value of the hyper-parameter can be obtained through training. An objective function for an unknown hyperparameter in a training Gaussian process regression can be expressed as
Figure BDA0003014005970000039
Wherein
Figure BDA00030140059700000310
The unknown parameters in the model are included, and the minimum value of the objective function NLML relative to each unknown hyper-parameter partial derivative is solved through a gradient descent method, so that the optimal hyper-parameter value can be obtained.
In the above scheme, in the step (5), after the optimal value of the hyper-parameter is obtained through training, the impeller parameter value of the standardized test sample is input into the model, the mean value and the variance of the corresponding performance value of the centrifugal pump can be obtained through the trained model, and the mean value and the variance are subjected to denormalization, wherein the denormalized mean value can represent the prediction result of the performance of the centrifugal pump, and the denormalized variance can represent the uncertainty of the prediction result. The accuracy and the effectiveness of the proposed centrifugal pump prediction model can be checked by calculating the relative error between the predicted centrifugal pump performance value and the real experimental value.
The invention has the beneficial effects that: the centrifugal pump performance prediction method based on small sample nuclear machine learning realizes the flexible learning of the nonlinear relation between the centrifugal pump impeller parameters and the centrifugal pump performance according to different kernel functions in the Gaussian process under the support of a small number of training samples, and further accurately predicts the centrifugal pump performance. The unknown parameters required to be set in the prediction model are less, the influence of the value of the unknown parameters on the prediction result is small, the construction efficiency of the model is greatly improved, and the method is more suitable for performance prediction of the centrifugal pump in engineering practice.
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FIG. 1 is a flow chart of a method of predicting centrifugal pump performance in accordance with the present invention.
FIG. 2 is a graph comparing the predictive power of three different non-linear kernel functions.
Fig. 3 is a graph comparing the predicted lift results of 14 test samples with experimental values.
FIG. 4 is a graph comparing efficiency prediction results with experimental values for 14 test samples.
Fig. 5 is a graph comparing the head predictions obtained from four different methods for 14 test samples.
FIG. 6 is a graph comparing the efficiency predictions obtained from four different methods for 14 sets of test samples.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
(1) The collected sample data is subjected to a normalization process. 68 groups of impeller hydraulic model data with different specific speeds are collected as a whole sample set through modern pump theory and design, wherein model input variables can be impeller parameters such as specific speed, impeller outlet width, blade number and the like, and output variables can be performance parameters such as centrifugal pump head, efficiency and the like. And selecting 14 groups of sample data with the rotation speed from small to large from the whole sample set as test samples, and using the rest samples as training samples. And carrying out standardization treatment on the whole sample set to ensure that the same attribute of all samples meets normal distribution with the mean value of 0 and the variance of 1. Some sample data are shown in table 1.
TABLE 1 centrifugal Pump sample data
Figure BDA0003014005970000051
(2) And (5) constructing a prediction model. And compiling a corresponding program in MATLAB according to a mathematical principle that the small sample nuclear machine learning Gaussian process regresses to obtain posterior distribution through prior distribution, so as to obtain a prediction model of the small sample nuclear machine learning Gaussian process. Three kernel functions with strong nonlinear learning ability in the Gaussian process are selected to learn the nonlinear relation between the centrifugal pump impeller parameter and the centrifugal pump lift and efficiency. The three kernel functions are respectively an SE kernel function, an RQ kernel function and a Matern5/2 kernel function. Comparing and analyzing the centrifugal pump performance prediction results based on the three kernel functions, and selecting the most suitable for learning between the centrifugal pump impeller parameters and the centrifugal pump performanceA kernel function of the relationship. FIG. 2 shows four statistical indicators reflecting the learning ability and prediction accuracy of the kernel function, namely, the Root Mean Square Error (RMSE), the mean relative error (MAPE), the maximum relative error (MARE), and the coefficient of determination (R) between the predicted value and the experimental value2). As can be seen from fig. 2, the SE kernel-based gaussian process regression prediction model has the highest prediction accuracy for the centrifugal pump head and efficiency, so that the SE kernel is determined and selected as the kernel for learning the relationship between the centrifugal pump impeller parameters and the centrifugal pump performance.
(3) And (5) training a prediction model. Firstly, giving an initial value of unknown hyper-parameters, wherein the initial value of the unknown hyper-parameters has better adaptivity due to a Gaussian process regression model, the size of the initial value of the unknown hyper-parameters can not generate more sensitive influence on the performance prediction result of the centrifugal pump, so 20 groups of initial values of the unknown hyper-parameters are randomly given in a space satisfying normal distribution with the mean value of 0 and the variance of 2, then based on training data, the unknown hyper-parameters are optimally trained by a gradient descent algorithm, and the optimized objective function is
Figure BDA0003014005970000061
Wherein
Figure BDA0003014005970000062
The unknown hyper-parameters in the model are included. And after the 20 groups of initial values of the hyper-parameters are optimized, selecting the group of unknown initial values of the hyper-parameters, which enable the target function NLML to reach the minimum, as the initial values of the prediction model for predicting the performance of the centrifugal pump.
(4) And (5) testing the effectiveness of the prediction model. After the training of the prediction model is completed, the nonlinear relation between the centrifugal pump impeller parameters in the provided training samples and the lift and the efficiency of the centrifugal pump is basically learned, the impeller parameters of 14 groups of test samples determined in the first step are used as input data of the prediction model, the mean value and the variance of the lift and the efficiency corresponding to the 14 groups of impeller parameters can be predicted through the model, the 14 groups of mean values and the variance which are output preliminarily are subjected to denormalization, the mean value after the denormalization can represent the predicted values of the lift and the efficiency, and the variance can represent the uncertainty of the obtained prediction result. The comparison between the predicted head and efficiency and their experimental values is shown in fig. 3 and 4, respectively, where the shaded area represents the 95% confidence interval derived from the variance of the prediction, and the narrower the range, the less uncertainty and the higher reliability of the prediction result.
As can be seen from fig. 3, the predicted lift value is well matched with the experimental value, the 95% confidence interval is sufficiently narrow in the first 10 test samples, and in the last four test samples, due to the increase of the specific speed, the training data in the large specific speed range is relatively less, so that the prediction uncertainty becomes larger. From the efficiency prediction situation of fig. 4, compared with the prediction result of the head, the efficiency prediction accuracy is slightly lower, the predicted value of the efficiency is basically lower than the experimental value, and the change rule of the predicted value and the experimental value is basically consistent. The uncertainty of the efficiency prediction is relatively large, but the experimental value of the efficiency prediction is basically within the 95% confidence interval obtained by the efficiency prediction, which indicates that the confidence interval contains the true value of the efficiency prediction, so that the prediction result is still credible. The absolute relative error between the predicted values of the head and efficiency of the 14 test samples and the experimental values thereof is further calculated. In all test samples, the maximum absolute relative error between the predicted lift value and the experimental value is 6.66%, most absolute relative errors are lower than 4%, the maximum absolute relative error between the predicted efficiency value and the experimental value is 10.54%, most absolute relative errors are lower than 8%, and the prediction precision meets the prediction requirement of the centrifugal pump in actual engineering design.
Table 2 shows a comparison between the centrifugal pump performance prediction method based on small sample kernel machine learning proposed in the present invention and three common prediction models, namely, Back Prediction Neural Network (BPNN), Radial Basis Function Neural Network (Radial Basis Function Neural Network) and Support Vector Regression (SVR). From the combination of the results of the four performance evaluation indexes shown in table 2, the GPR predicts the centrifugal pump lift and efficiency with the highest precision and the best stability in the four models under the same training sample.
TABLE 2 comparison of Performance of four centrifugal Pump prediction models
Figure BDA0003014005970000071
Figure BDA0003014005970000081
Fig. 5 and 6 visually illustrate the comparison between the predicted values of the four models of head and efficiency and their experimental values. From the comparison of the lift, in the test data, the predicted values of the four models are basically consistent with the change rule of the experimental value, so that the nonlinear relation between the input variable and the lift is fully learned, and the defined input variable can well represent the influence characteristics of the lift. From the comparison of efficiency, the change rule of the model predicted value and the experimental value is basically consistent. In a whole view, the lift and the efficiency obtained through GPR prediction are closer to the experimental values, and the prediction precision is higher.
Compared with a common centrifugal pump performance prediction method based on numerical simulation, the method for predicting the performance of the centrifugal pump by using the impeller parameters based on the GPR model can perform secondary utilization on existing data in engineering design application, and the centrifugal pump performance prediction is short in period, low in difficulty and strong in universality. Compared with other common prediction models based on data, the prediction model based on the GPR requires less training data in the performance prediction of the centrifugal pump, so that the difficulty of data collection is reduced; the constructability of the model is strong, and the influence of the parameters of the model on the predictive performance is small, so that the training is easier; the GPR model has good stability, can provide a prediction result, can also provide the uncertainty degree corresponding to the prediction result, and has stronger reliability.
In summary, the above embodiments are not intended to be limiting embodiments of the present invention, and modifications and equivalent variations made by those skilled in the art based on the spirit of the present invention are within the technical scope of the present invention.

Claims (7)

1. A centrifugal pump performance prediction method based on small sample nuclear machine learning is characterized by comprising the following steps:
(1) performing feature selection and standardization processing on the collected sample data;
(2) constructing a small sample kernel machine learning Gaussian process regression prediction model;
(3) selecting a suitable nonlinear kernel function;
(4) training unknown hyper-parameters of the model based on the training data;
(5) the validity of the model is verified based on the test data.
2. The method according to claim 1, wherein in step (1), in order to reduce the training time of the prediction model and ensure the prediction accuracy thereof, the collected sample data is normalized so that the sample data satisfies a standard normal distribution with a mean value of 0 and a variance of 1, and the specific formula is as follows:
Figure FDA0003014005960000011
wherein,
Figure FDA0003014005960000012
for normalized data, xiFor raw data, μ is the mean of data of the same dimension, and σ is the variance of data of the same dimension.
3. The method for predicting the performance of the centrifugal pump based on the small sample nuclear machine learning as claimed in claim 1, wherein in the step (2), the prior distribution between the known training sample and the unknown test sample is constructed in MATLAB software according to the mathematical principle of gaussian process regression, and the formula is as follows:
Figure FDA0003014005960000013
wherein y represents a set of training sample output variables; f. of*An output representing an unknown test sample; k (X, X) denotes the kernel functional relationship between the training sample input variables, K (X, X)*) And K (x)*X) each represent a kernel function relationship between a training sample input variable and a test sample input variable, K (X)*,x*) Representing the kernel function relationship between the test sample input variables,
Figure FDA0003014005960000014
representing noise and I representing an identity matrix.
4. The method of claim 1, wherein the posterior distribution of the unknown test sample output variables is expressed as
Figure FDA0003014005960000021
Wherein
Figure FDA0003014005960000022
The mean of the posterior distribution whose value represents the unknown output variable of the test sample, cov (f)*) For the variance of the posterior distribution, the uncertainty of the output variable can be characterized, which can be expressed as the following two equations, respectively:
Figure FDA0003014005960000023
Figure FDA0003014005960000024
5. the method for predicting centrifugal pump performance based on small sample nuclear machine learning of claim 1, wherein in the step (3), the SE kernel is finally used to construct the nonlinear relationship between the impeller parameters and the centrifugal pump performance by comparing the performances of three commonly used Square Exponential (SE) nonlinear kernels, Rational Quadratic (RQ) nonlinear kernels and Matern5/2 nonlinear kernels, and the formula is as follows:
Figure FDA0003014005960000025
wherein
Figure FDA0003014005960000026
Called signal variance, controlling the output magnitude of the kernel function;
Figure FDA0003014005960000027
l is called the characteristic length and controls the influence degree of the characteristic attribute of each dimension of the input variable on the output result.
6. The method for predicting the performance of the centrifugal pump based on the small sample nuclear machine learning as claimed in claim 1, wherein in the step (4), the initial value of the unknown hyper-parameter is randomly given, and the optimal value of the hyper-parameter can be obtained through training. An objective function for an unknown hyperparameter in a training Gaussian process regression can be expressed as
Figure FDA0003014005960000028
Wherein
Figure FDA0003014005960000029
The unknown parameters in the model are included, and the minimum value of the objective function NLML relative to each unknown hyper-parameter partial derivative is solved through a gradient descent method, so that the optimal hyper-parameter value can be obtained.
7. The method for predicting the performance of the centrifugal pump based on the small-sample nuclear machine learning as claimed in claim 1, wherein in the step (5), after the optimal value of the hyper-parameter is obtained through training, the impeller parameter value of the standardized test sample is input into the model, the mean value and the variance of the corresponding performance value of the centrifugal pump can be obtained through the trained model, the mean value and the variance are subjected to anti-standardization, the mean value after the anti-standardization can represent the prediction result of the performance of the centrifugal pump, and the variance after the anti-standardization can represent the uncertainty of the prediction result; the accuracy and the effectiveness of the proposed centrifugal pump prediction model can be checked by calculating the relative error between the predicted centrifugal pump performance value and the real experimental value.
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