CN110751173A - Critical heat flux density prediction method based on deep learning support vector machine - Google Patents

Critical heat flux density prediction method based on deep learning support vector machine Download PDF

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CN110751173A
CN110751173A CN201910854049.6A CN201910854049A CN110751173A CN 110751173 A CN110751173 A CN 110751173A CN 201910854049 A CN201910854049 A CN 201910854049A CN 110751173 A CN110751173 A CN 110751173A
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蒋波涛
徐新
黄新波
蒋卫涛
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Abstract

The invention discloses a critical heat flux density prediction method based on a deep learning support vector machine, which is implemented according to the following steps: step 1: the collected critical heat flux density raw data is divided into two parts: 70% of the original data was used as training set, with X { (X)1,y1),(x2,y2),…(xi,yi)…(xn,yn) Denotes, for x in the obtained training data setiCarrying out normalization processing by adopting linear transformation to obtain data points x 'after normalization processing'i(ii) a In addition, 30% of original data is used as a test set for testing the prediction accuracy of the prediction model obtained by training; step 2: normalizing data points x 'obtained in step 1'iI-1, 2, …, n, exploiting the potential for adding informationSelecting experimental data by subtractive clustering; and step 3: and (3) carrying out cross validation on the experimental data obtained in the step (2) by a leave-one-out method to optimize parameters of the support vector machine, and training by adopting a restricted Boltzmann machine in deep learning to obtain an optimal prediction model and optimal parameters. The prediction method can more accurately predict the critical heat flux density.

Description

Critical heat flux density prediction method based on deep learning support vector machine
Technical Field
The invention belongs to the technical field of reactor core safety analysis methods, and particularly relates to a critical heat flux density prediction method based on a deep learning support vector machine.
Background
The nuclear reactor is one of the key parts of a nuclear power plant and is high-strength heat exchange equipment. However, since the heat flux density in the core is limited by the critical heat flux density, the power level of the reactor is also limited by the critical heat flux density. Therefore, in a nuclear reactor system, the critical heat flux density is an important parameter in the thermal hydraulic design of the reactor core, and has a very important influence on the safe operation of the nuclear reactor.
The critical heat flux density is also called maximum heat flux density, and means that under the condition of heating at a fixed temperature, when the degree of superheat of the wall surface rises to a certain value, steam on the heating surface begins to polymerize into a gas film, the heat transfer condition rapidly deteriorates, and the heat flux density reaches the maximum value. If the superheat continues to increase, the heat flux density begins to decrease and the boiling curve has a turning point. There are two basic types of critical heat flux density, namely off-nucleate boiling and dry-out. The deviation from nucleate boiling and drying is due to the different mechanisms causing the disappearance of the liquid phase on the walls under different conditions, leading to different heat transfer crisis. Because the critical heat flow phenomenon is usually caused by that the heat transfer efficiency is greatly reduced due to the disappearance of a wall liquid phase caused by the strong evaporation of the wall surface of the heat exchange equipment, the temperature of the wall is sharply increased in a short time so as to exceed the allowable temperature of equipment materials and cause burning, not only property loss but also possibly serious accidents are caused, and therefore, the accurate prediction of the critical heat flow density has important practical significance for improving the heat exchange capacity of the heat exchange equipment to the maximum extent and ensuring the safe operation of the heat exchange equipment. Currently, the conventional critical heat flux density prediction methods are roughly divided into three types: (1) a look-up table method; (2) empirical relational method; (3) and (4) an analytical method. The traditional three critical heat flow density prediction methods develop the critical heat flow density prediction method to a certain extent, but all the methods can be used only within a specific parameter range. Since the critical heat flux density is affected by various uncertainties, there has not been established a theory to accurately predict the critical heat flux density until now. In order to overcome the defect, advanced information data processing technology is required to predict the critical heat flux density
Therefore, the critical heat flux density prediction method based on the deep learning support vector machine is provided, the predicted critical heat flux density is more accurate, and a powerful basis is provided for nuclear reactor thermal hydraulic design and safety analysis.
Disclosure of Invention
The invention aims to provide a critical heat flux density prediction method based on a deep learning support vector machine, the predicted critical heat flux density is more accurate, and a powerful basis is provided for nuclear reactor thermal hydraulic design and safety analysis.
The technical scheme adopted by the invention is that the critical heat flux density prediction method based on the deep learning support vector machine is implemented according to the following steps:
step 1: the collected critical heat flux density raw data is divided into two parts: 70% of the original data was used as training set, with X { (X)1,y1),(x2,y2),…(xi,yi)…(xn,yn) Denotes, for x in the obtained training data setiCarrying out normalization processing by adopting linear transformation to obtain data points x 'after normalization processing'i(ii) a In addition, 30% of original data is used as a test set for testing the prediction accuracy of the prediction model obtained by training;
wherein x isiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points, yiDenotes xiThe corresponding critical heat flux density; n represents the number of samples;
step 2: normalizing data points x 'obtained in step 1'iI-1, 2, …, n, using subtractive clustering with added information potential to select experimental data;
and step 3: and (3) carrying out cross validation on the experimental data obtained in the step (2) by a leave-one-out method to optimize parameters of the support vector machine, and training by adopting a restricted Boltzmann machine in deep learning to obtain an optimal prediction model and optimal parameters.
The present invention is also characterized in that,
in step 1, xiNormalization processing by linear transformation to generate x'iThe calculation formula of the linear transformation is shown as formula (1):
Figure BDA0002197774210000031
wherein, b>x′i>a, a and b are positive integers. x is the number ofiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points; x is the number ofminFor the smallest data point in the training set, xmaxThe largest data point in the training set; n represents the number of samples.
The step 2 is implemented according to the following steps:
step 2.1: calculate normalized data points x'iDensity index D ofiThe calculation formula is shown in formula (2):
wherein D isiRepresents data point x'iI ═ 1,2, …, n; r isaRepresents data point x'iThe neighborhood of (a), is a positive number; x is the number ofkDenotes divisor data point x'iOther data than the above;
and all resulting density indices are labeled D ═ D1,D2,…,Di,…Dn}；
Step 2.2: in all density indexes D ═ D1,D2,…,Di,…DnSequentially selecting k density indexes with the highest density indexesIs denoted as xckThe density index is DckWherein k is<n, using the selected k data points with the highest density index as k clustering centers, and performing the treatment on the n-k data points x except the k clustering centerskDensity index D ofkAnd (3) correcting the density index, wherein the formula of the density index correction is shown as the formula (3):
Figure BDA0002197774210000041
wherein: d'kIs a data point xkCorrected density index, rbA neighborhood with a significantly reduced density index function is a constant;
reselecting k data points with the highest density index from the corrected n-k data points and the k clustering centers as new k clustering centers, which are also called cluster centers;
and 2.3, adding information potential to measure the information amount on the basis of acquiring k clustering centers in the step 2.2, calculating the potential of each data point in n points, and calculating by using a formula (4):
Figure BDA0002197774210000042
wherein: r isβRepresenting the neighborhood radius, cjIs the center of the jth cluster, Pj+1(k) Potential of non-cluster-centered other data points, P, representing the j +1 th clusterj(k) Indicating the potential of other data points not in the center of the cluster other than the jth cluster,denotes the jth cluster center cjThe potential of (d);
after the potential of each data point in the n points is corrected by the formula (4), the data point with the highest potential is selected as the j +1 cluster center, and the termination conditions of the formulas (2), (3) and (4) are that when the inequality is not equal to
Figure BDA0002197774210000044
When true, otherwise repeat the calculation, ifAnd finally, the calculation is terminated in the Nth step, so that N cluster centers are obtained, and the N clusters are obtained and are experimental data.
In step 2.2, rb＝(1.2～1.5)raWherein: r isaRepresents x'iThe neighborhood of the data points is a positive number; r isbThe neighborhood for which the density index function is significantly reduced is a constant.
Step 3 is specifically implemented according to the following steps:
step 3.1, the experimental data obtained in step 2 is represented by S ═ S1,s2,…sp…,sNDenotes wherein spDenotes the p-th cluster, and spAs test data, divide by spOther experimental data are used as training data, penalty parameters C and non-negative relaxation factors ξ of the support vector machine are optimized by using leave-one-out cross validation, and a support vector machine model M is subjected to limited Boltzmann machine in deep learningpTraining is carried out, and in the training process, the visible layer state v and the hidden layer state h of the restricted Boltzmann machine follow the formula (5):
Figure BDA0002197774210000051
wherein: p (v, h) represents the distribution of v, Z is the normalized constant of the joint distribution; v represents a visible layer state and h represents a hidden layer state; energy (v, h) represents an energy function, and a formula for specifically calculating the energy function is shown in formula (6):
energy(v,h)＝hWv+b'v+c'h (6)
wherein: b' is the bias of the visible layer; c' is the bias of the hidden layer; w is a weight matrix between layers;
step 3.2, calculating a support vector machine model MpThe predicted error and the average error of (2) are expressed as a support vector machine model M by equations (7) and (8), respectivelypThe calculation formula of the estimated error and the average error is as follows:
Figure BDA0002197774210000052
Figure BDA0002197774210000053
wherein: err (r)iIndicating the estimated error of the ith data,
Figure BDA0002197774210000054
is based on a support vector machine model MpThe corresponding predicted critical heat flux density, err, is the support vector machine model MpAverage error of (2);
penalty parameter C and non-negative relaxation factor ξ for support vector machine through leave-one-out cross validationiAnd optimizing and training a limited Boltzmann machine in deep learning to finally obtain n models, selecting the model with the minimum err value from the n models to be the optimal model, wherein the parameter of the model is the optimal parameter, and finally obtaining the prediction model of the deep learning support vector machine.
The method has the advantages that the subtraction clustering algorithm is adopted in the selection of the training data set to select the data with effective information points as the training set, the uncertainty caused by random or artificial selection is avoided, the training speed can be further accelerated, the deep learning algorithm is combined with the support vector machine, the prediction capability of the model is further improved, the prediction accuracy is improved, and a powerful theoretical basis is provided for the design of the thermal hydraulic power of the nuclear reactor and the safety analysis.
Drawings
FIG. 1 is a flow chart of a critical heat flux density prediction method based on a deep learning support vector machine according to the present invention;
FIG. 2 is a graph of experimental results obtained using the method of the present invention to predict critical heat flux density;
fig. 3 is a graph of experimental results obtained by predicting critical heat flux density using an artificial neural network method.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a critical heat flux density prediction method based on a deep learning support vector machine, which is implemented according to the following steps:
step 1: the collected critical heat flux density raw data is divided into two parts: 70% of the original data was used as training set, with X { (X)1,y1),(x2,y2),…(xi,yi)…(xn,yn) Denotes, for x in the obtained training data setiCarrying out normalization processing by adopting linear transformation to obtain data points x 'after normalization processing'i(ii) a In addition, 30% of original data is used as a test set for testing the prediction accuracy of the prediction model obtained by training;
wherein x isiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points; y isiDenotes xiThe corresponding critical heat flux density; n represents the number of samples;
in step 1, xiNormalization processing by linear transformation to generate x'iThe calculation formula of the linear transformation is shown as formula (1):
Figure BDA0002197774210000071
wherein, b>x′i>a, a and b are positive integers. x is the number ofiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points, i ═ 1,2, …, n; x is the number ofminFor the smallest data point in the training set, xmaxThe largest data point in the training set; n represents the number of samples.
Step 2: normalizing data points x 'obtained in step 1'iSelecting experimental data by using subtractive clustering of added information potential;
the step 2 is implemented according to the following steps:
step 2.1: calculating normalized data points x′iDensity index D ofiThe calculation formula is shown in formula (2):
wherein D isiRepresents data point x'iI ═ 1,2, …, n; r isaRepresents the data point xi' neighborhood, positive; x is the number ofkDenotes divisor data point x'iOther data than the above;
and all resulting density indices are labeled D ═ D1,D2,…,Di,…Dn}；
Step 2.2: in all density indexes D ═ D1,D2,…,Di,…DnSequentially selecting k data points with the highest density index and marking as xckThe density index is DckWherein k is<n, using the selected k data points with the highest density index as k clustering centers, and performing the treatment on the n-k data points x except the k clustering centerskDensity index D ofkAnd (3) correcting the density index, wherein the formula of the density index correction is shown as the formula (3):
Figure BDA0002197774210000081
wherein: d'kIs a data point xkCorrected density index, rbA neighborhood with a significantly reduced density index function is a constant;
reselecting k data points with the highest density index from the corrected n-k data points and the k clustering centers as new k clustering centers, which are also called cluster centers;
in step 2.2, rb＝(1.2～1.5)raWherein: r isaRepresents x'iThe neighborhood of the data points is a positive number; r isbA neighborhood with a significantly reduced density index function is a constant;
and 2.3, adding information potential to measure the information amount on the basis of acquiring k clustering centers in the step 2.2, calculating the potential of each data point in n points, and calculating by using a formula (4):
Figure BDA0002197774210000082
wherein: r isβRepresenting the neighborhood radius, cjIs the center of the jth cluster, Pj+1(k) Potential of non-cluster-centered other data points, P, representing the j +1 th clusterj(k) Indicating the potential of other data points not in the center of the cluster other than the jth cluster,
Figure BDA0002197774210000083
denotes the jth cluster center cjThe potential of (d);
after the potential of each data point in the n points is corrected by the formula (4), the data point with the highest potential is selected as the j +1 cluster center, and the termination conditions of the formulas (2), (3) and (4) are that when the inequality is not equal to
Figure BDA0002197774210000084
And if the calculation is finally ended in the Nth step, obtaining N cluster centers, and obtaining N clusters which are experimental data.
And step 3: performing cross validation on the experimental data obtained in the step 2 by a leave-one-out method to optimize parameters of a support vector machine, and training by adopting a restricted Boltzmann machine in deep learning to obtain an optimal prediction model and optimal parameters; step 3 is specifically implemented according to the following steps:
step 3.1, the experimental data obtained in step 2 is represented by S ═ S1,s2,…sp…,sNDenotes wherein spDenotes the p-th cluster, and spAs test data, divide by spOther experimental data are used as training data, penalty parameters C and non-negative relaxation factors ξ of the support vector machine are optimized by using leave-one-out cross validation, and a support vector machine model M is subjected to limited Boltzmann machine in deep learningpTraining is carried out, and in the training process, the visible layer state v and the hidden layer state h of the restricted Boltzmann machine follow the formula(5)：
Figure BDA0002197774210000091
Wherein: p (v, h) represents the distribution of v, Z is the normalized constant of the joint distribution; v represents a visible layer state and h represents a hidden layer state; energy (v, h) represents an energy function, and a formula for specifically calculating the energy function is shown in formula (6):
energy(v,h)＝hWv+b'v+c'h (6)
wherein: b' is the bias of the visible layer; c' is the bias of the hidden layer; w is a weight matrix between layers;
step 3.2, calculating a support vector machine model MpThe predicted error and the average error of (2) are expressed as a support vector machine model M by equations (7) and (8), respectivelypThe calculation formula of the estimated error and the average error is as follows:
Figure BDA0002197774210000092
wherein: err (r)iIndicating the estimated error of the ith data,
Figure BDA0002197774210000094
is based on a support vector machine model MpThe corresponding predicted critical heat flux density, err, is the support vector machine model MpAverage error of (2);
penalty parameter C and non-negative relaxation factor ξ for support vector machine through leave-one-out cross validationiAnd optimizing and training a limited Boltzmann machine in deep learning to finally obtain n models, selecting the model with the minimum err value from the n models to be the optimal model, wherein the parameter of the model is the optimal parameter, and finally obtaining the prediction model of the deep learning support vector machine.
And testing the prediction model of the deep learning support vector machine by using the test set, and calculating three parameters, namely an average variance root, a correlation coefficient and an average relative error between the critical heat flux density obtained by the prediction model and the real critical heat flux density of the test set to judge the accuracy of predicting the critical heat flux density. The closer the correlation coefficient is to 1, the smaller the mean variance root and the mean relative error are, and the higher the prediction performance and the higher the accuracy of the deep learning support vector machine prediction model are.
As shown in table 1, the result of predicting the critical heat flux density by the method of the present invention is compared with the result of predicting the critical heat flux density by the neural network, and as can be seen from table 1, the mean variance root and the mean relative error obtained by the method of the present invention are both smaller than those obtained by the neural network prediction method, and the correlation coefficient obtained by the method of the present invention is closer to 1, so that the critical heat flux density predicted by the method provided herein can be demonstrated to be more accurate.
TABLE 1
Fig. 1-2 are graphs showing the comparison between the experimental results obtained by the present invention and the experimental results obtained by the neural network, fig. 1 is the results obtained by the method of the present invention, and it can be seen that the error of the results obtained by the training and testing set is about 3%, and fig. 2 is the results obtained by the artificial neural network, and it can be seen that the error of the results obtained by the training and testing set is about 5%, so that it can be demonstrated that the critical heat flux density predicted by the method of the present invention is more accurate.

Claims (5)

1. The critical heat flux density prediction method based on the deep learning support vector machine is characterized by comprising the following steps:
step 1: the collected critical heat flux density raw data is divided into two parts: 70% of the original data was used as training set, with X { (X)1,y1),(x2,y2),…(xi,yi)…(xn,yn) Means that, for the obtained training data setX ofiCarrying out normalization processing by adopting linear transformation to obtain data points x 'after normalization processing'i(ii) a In addition, 30% of original data is used as a test set for testing the prediction accuracy of the prediction model obtained by training;
wherein x isiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points; y isiDenotes xiThe corresponding critical heat flux density; n represents the number of samples;
step 2: normalizing data points x 'obtained in step 1'iI-1, 2, …, n, using subtractive clustering with added information potential to select experimental data;
and step 3: and (3) carrying out cross validation on the experimental data obtained in the step (2) by a leave-one-out method to optimize parameters of the support vector machine, and training by adopting a restricted Boltzmann machine in deep learning to obtain an optimal prediction model and optimal parameters.
2. The method for predicting the critical heat flux density based on the deep learning support vector machine of claim 1, wherein in step 1, x isiNormalization processing by linear transformation to generate x'iThe calculation formula of the linear transformation is shown as formula (1):
wherein, b>x′i>a, a and b are positive integers; x is the number ofiIs determined by the system pressure P, the mass flow rate G and the equilibrium vapor content XeThe ith vector data point of composition, i ═ 1,2, …, n; x'iIs xiNormalizing the processed data points; x is the number ofminFor the smallest data point in the training set, xmaxThe largest data point in the training set; n represents the number of samples.
3. The method for predicting the critical heat flux density based on the deep learning support vector machine according to claim 1, wherein the step 2 is implemented by the following steps:
step 2.1: calculate normalized data points x'iDensity index D ofiThe calculation formula is shown in formula (2):
Figure FDA0002197774200000021
wherein D isiRepresents data point x'iI ═ 1,2, …, n; r isaRepresents data point x'iThe neighborhood of (a), is a positive number; x is the number ofkDenotes divisor data point x'iOther data than the above;
and all resulting density indices are labeled D ═ D1,D2,…,Di,…Dn}；
Step 2.2: in all density indexes D ═ D1,D2,…,Di,…DnSequentially selecting k data points with the highest density index and marking as xckThe density index is DckWherein k is<n, using the selected k data points with the highest density index as k clustering centers, and performing the treatment on the n-k data points x except the k clustering centerskDensity index D ofkAnd (3) correcting the density index, wherein the formula of the density index correction is shown as the formula (3):
Figure FDA0002197774200000022
wherein: d'kIs a data point xkCorrected density index, rbA neighborhood with a significantly reduced density index function is a constant;
reselecting k data points with the highest density index from the corrected n-k data points and the k clustering centers as new k clustering centers, which are also called cluster centers;
and 2.3, adding information potential to measure the information amount on the basis of acquiring k clustering centers in the step 2.2, calculating the potential of each data point in n points, and calculating by using a formula (4):
wherein: r isβRepresenting the neighborhood radius, cjIs the center of the jth cluster, Pj+1(k) Potential of non-cluster-centered other data points, P, representing the j +1 th clusterj(k) Indicating the potential of other data points not in the center of the cluster other than the jth cluster,denotes the jth cluster center cjThe potential of (d);
after the potential of each data point in the n points is corrected by the formula (4), the data point with the highest potential is selected as the j +1 cluster center, and the termination conditions of the formulas (2), (3) and (4) are that when the inequality is not equal to
Figure FDA0002197774200000033
And if the calculation is finally ended in the Nth step, obtaining N cluster centers, and obtaining N clusters which are experimental data.
4. The method for predicting the critical heat flux density based on the deep learning support vector machine of claim 3, wherein in step 2.2, r isb＝(1.2～1.5)raWherein: r isaRepresents x'iThe neighborhood of the data points is a positive number; r isbThe neighborhood for which the density index function is significantly reduced is a constant.
5. The method for predicting the critical heat flux density based on the deep learning support vector machine according to claim 1, wherein the step 3 is implemented by the following steps:
step 3.1, the experimental data obtained in step 2 is represented by S ═ S1,s2,…sp…,sNDenotes wherein spDenotes the p-th cluster, and spAs test data, divide by spOther experimental data are used as training data, penalty parameters C and non-negative relaxation factors ξ of the support vector machine are optimized by using leave-one-out cross validation, and a support vector machine model M is subjected to limited Boltzmann machine in deep learningpTraining is carried out, and in the training process, the visible layer state v and the hidden layer state h of the restricted Boltzmann machine follow the formula (5):
Figure FDA0002197774200000034
wherein: p (v, h) represents the distribution of v, Z is the normalized constant of the joint distribution; v represents a visible layer state and h represents a hidden layer state; energy (v, h) represents an energy function, and a formula for specifically calculating the energy function is shown in formula (6):
energy(v,h)＝hWv+b'v+c'h (6)
wherein: b' is the bias of the visible layer; c' is the bias of the hidden layer; w is a weight matrix between layers;
step 3.2, calculating a support vector machine model MpThe predicted error and the average error of (2) are expressed as a support vector machine model M by equations (7) and (8), respectivelypThe calculation formula of the estimated error and the average error is as follows:
Figure FDA0002197774200000041
wherein: err (r)iIndicating the estimated error of the ith data,is based on a support vector machine model MpThe corresponding predicted critical heat flux density, err, is the support vector machine model MpAverage error of (2);
punishment parameter of support vector machine through leave-one-out cross validationC and non-negative relaxation factor ξiAnd optimizing and training a limited Boltzmann machine in deep learning to finally obtain n models, selecting the model with the minimum err value from the n models to be the optimal model, wherein the parameter of the model is the optimal parameter, and finally obtaining the prediction model of the deep learning support vector machine.
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