CN109871602A - A kind of critical heat flux density prediction technique returned based on Gaussian process - Google Patents
A kind of critical heat flux density prediction technique returned based on Gaussian process Download PDFInfo
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Abstract
The invention discloses a kind of critical heat flux density prediction techniques returned based on Gaussian process, it is specifically implemented according to the following steps: step 1: collected data set is divided into two parts, wherein 70% data are denoted as: D as training set, remaining 30% data as test set*={ (X*,y*)}；Step 2: training set data and test set data pre-processing data using standard normal variable method, make training set D and test set D*Mean value be 0 and standard deviation is 1；Step 3: using Gaussian process recurrence, between training input variable and training objective output, relationship is inferred, obtains critical heat flux density prediction model；Step 4: using obtained critical heat flux density prediction model, critical heat flux density being predicted by system pressure P, mass velocity G and balance vapor content Xe.This method can accurately and effectively predict critical heat flux density.
Description
Technical field
The invention belongs to reactor core safety analysis fields, and in particular to a kind of critical heat returned based on Gaussian process
Current density prediction technique.
Background technique
In nuclear reactor safety evaluation, critical heat flux density is a kind of important thermal-hydraulic limitation parameter, it refers to
Heating wall temperature is ascended to heaven cause to burn before the maximum heat flow density that can bear.Once heat flow density is more than critical heat flux density
It will lead to wall surface temperature overheat, burnt so as to cause element.Therefore, accurately predict critical heat flux density for reactor
Safety and economy have very important meaning.
Since critical heat flux density is a kind of sufficiently complex phenomenon, although have more than in the past few decades more than 500 kinds it is critical
Heat flow density prediction technique occurs in the literature, but can accurately predict critical heat still without unified theory so far
Current density, this is but also critical heat flux density becomes a kind of research most extensive the phenomenon that being but least appreciated that.Currently, traditional to face
Boundary's heat flow density prediction technique is roughly divided into three kinds: (1) inquiry table method；(2) rule-of-thumb relation method；(3) analytic approach.However, by
There are disadvantage and use condition limitation in every kind of method, therefore since the nineties in last century, artificial neural network is as a kind of
Advanced intellectual technology is widely used in critical heat flux density prediction.The country also has related scholar to carry out grinding in this respect
Study carefully, but research achievement is less and the time is more early.Although artificial neural network can overcome traditional critical heat flux to a certain extent
The shortcomings that density prediction method, but since artificial neural network is a kind of method based on structural risk minimization, deposit
The disadvantages of being difficult to select, be easy to fall into minimum, over-fitting and poor Generalization Ability in structure.
Therefore, the invention proposes a kind of critical heat flux density prediction technique returned based on Gaussian process, this predictions
Method has smaller error amount under identical operating condition, and its prediction result is also closer to experiment value.
Summary of the invention
The object of the present invention is to provide a kind of critical heat flux density prediction technique returned based on Gaussian process, this method energy
It is enough that critical heat flux density is accurately and effectively predicted.
The technical scheme adopted by the invention is that a kind of critical heat flux density prediction technique returned based on Gaussian process,
It is specifically implemented according to the following steps:
Step 1: collected data set is divided into two parts, wherein 70% data are denoted as training set:Wherein xi∈Rd, yi∈ R, xiIt include system pressure P, quality for i-th of input vector in D
Flow velocity G and balance vapor content Xe, yiIndicate that i-th of target output is critical heat flux density in D；Remaining 30% data is as survey
Examination collection, is denoted as: D*={ (X*,y*)}；
Step 2: training set data and test set data pre-processing data using standard normal variable method, make to instruct
Practice collection D and test set D*Mean value be 0 and standard deviation is 1, shown in pretreated calculation formula such as formula (1):
Wherein, n is data total number,Shi Suoyou mean value, s are the variance of data, UnData after indicating standard normal；
Step 3: using Gaussian process recurrence, between training input variable and training objective output, relationship is inferred, obtains
To critical heat flux density prediction model；
Step 4: using obtained critical heat flux density prediction model, being contained by system pressure P, mass velocity G and balance
Vapour amount Xe predicts critical heat flux density.
The features of the present invention also characterized in that
Step 3 is specifically implemented according to the following steps:
Step 3.1: establish Gaussian process regression equation:
Y=f (x)+ε (2)
Wherein, f (x)~GP (m (x), k (x, x ')), ε are the white Gaussian noise independently of f (x), andm
It (x) is mean function, k (x, x ') is covariance function, σnFor variance；
The input of training set D and output are constituted into a Gaussian process, as shown in formula (3):
Step 3.2: Gaussian process returns hyper parameterDetermination:
By establishing the negative log-likelihood function of training sample and it is enabled to seek local derviation to θ each single item, then pass through conjugate gradient
Local derviation minimizing is obtained, as shown in (4) formula:
Wherein,α=C-1Y, K (X, X)=(k (xi,xj)) be n × n rank symmetric positive definite association side
Poor matrix, InFor n unit matrix, k (xi,xj) it is covariance kernel function.
In step 3.2, k (xi,xj) specifically as shown in formula (5):
Wherein,For kernel function signal variance, l is variance measure.
Step 4 is specifically implemented according to the following steps:
Step 4.1: utilizing test set D*={ (X*,y*) establish target output y and test set target output y*Joint it is high
This distribution, as shown in formula (6):
Wherein, K (X, X*)=K (X*,X)TFor training data X and test data x*Between the rank covariance matrix of n × 1；k
(x*,x*) it is test point x*The covariance of itself；k(xi,xj) it is covariance kernel function,
Step 4.2:y*Posterior probability distribution seek, as shown in formula (7):
Wherein:
Utilize x*To y*It is accurately sought, i.e., critical heat flux density is accurately predicted.
The invention has the advantages that this method establishes critical heat flux density prediction model to facing using Gaussian process recurrence
Boundary's heat flow density carry out Accurate Prediction, this method to carry out critical heat flux density prediction when its predict error can control ±
Within 5%, this method has higher precision of prediction compared to other methods.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the critical heat flux density prediction technique returned based on Gaussian process of the present invention；
Fig. 2 is using a kind of prediction knot that the critical heat flux density prediction technique returned based on Gaussian process is obtained of the present invention
Fruit.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention it is a kind of based on Gaussian process return critical heat flux density prediction technique, as shown in Figure 1, specifically according to
Lower step is implemented:
Step 1: collected data set is divided into two parts, wherein 70% data are denoted as training set:Wherein xi∈Rd, yi∈ R, xiIt include system pressure P, quality for i-th of input vector in D
Flow velocity G and balance vapor content Xe, yiIndicate that i-th of target output is critical heat flux density in D；Remaining 30% data is as survey
Examination collection, is denoted as: D*={ (X*,y*)}；
Step 2: training set data and test set data pre-processing data using standard normal variable method, make to instruct
Practice collection D and test set D*Mean value be 0 and standard deviation is 1, shown in pretreated calculation formula such as formula (1):
Wherein, n is data total number,Shi Suoyou mean value, s are the variance of data, UnData after indicating standard normal；
Step 3: using Gaussian process recurrence, between training input variable and training objective output, relationship is inferred, obtains
To critical heat flux density prediction model；
Step 3 is specifically implemented according to the following steps:
Step 3.1: establish Gaussian process regression equation:
Y=f (x)+ε (2)
Wherein, f (x)~GP (m (x), k (x, x ')), ε are the white Gaussian noise independently of f (x), andm
It (x) is mean function, k (x, x ') is covariance function, σnFor variance；
The input of training set D and output are constituted into a Gaussian process, as shown in formula (3):
Step 3.2: Gaussian process returns hyper parameterDetermination:
By establishing the negative log-likelihood function of training sample and it is enabled to seek local derviation to θ each single item, then pass through conjugate gradient
Local derviation minimizing is obtained, as shown in (4) formula:
Wherein,α=C-1Y, K (X, X)=(k (xi,xj)) be n × n rank symmetric positive definite association side
Poor matrix, InFor n unit matrix, k (xi,xj) it is covariance kernel function, the covariance kernel function that the present invention uses is a square index
Function, as shown in formula (5):
Wherein,For kernel function signal variance, l is variance measure；
Step 4: using obtained critical heat flux density prediction model, being contained by system pressure P, mass velocity G and balance
Vapour amount Xe predicts critical heat flux density.
Step 4 is specifically implemented according to the following steps:
Step 4.1: utilizing test set D*={ (X*,y*) establish target output y and test set target output y*Joint it is high
This distribution, as shown in formula (6):
Wherein, K (X, X*)=K (X*,X)TFor training data X and test data x*Between the rank covariance matrix of n × 1；k
(x*,x*) it is test point x*The covariance of itself；k(xi,xj) it is covariance kernel function,
Step 4.2:y*Posterior probability distribution seek, as shown in formula (7):
Wherein:
Utilize x*To y*It is accurately sought, i.e., critical heat flux density is accurately predicted.
The present invention trains and tests Gaussian process regression model as database using 2006 inquiry tables published,
Obtained best hyper parameter group is combined intoIt obtains as shown in Figure 2 as a result, knot
Fruit shows: in trained and test phase error all within ± 5%.
Claims (4)
1. a kind of critical heat flux density prediction technique returned based on Gaussian process, which is characterized in that specifically according to the following steps
Implement:
Step 1: collected data set is divided into two parts, wherein 70% data are denoted as training set:Wherein xi∈Rd, yi∈ R, xiIt include system pressure P, quality for i-th of input vector in D
Flow velocity G and balance vapor content Xe, yiIndicate that i-th of target output is critical heat flux density in D；Remaining 30% data is as survey
Examination collection, is denoted as: D*={ (X*,y*)}；
Step 2: training set data and test set data pre-processing data using standard normal variable method, make training set
D and test set D*Mean value be 0 and standard deviation is 1, shown in pretreated calculation formula such as formula (1):
Wherein, n is data total number,Shi Suoyou mean value, s are the variance of data, UnData after indicating standard normal；
Step 3: using Gaussian process recurrence, between training input variable and training objective output, relationship is inferred, is faced
Boundary's heat flow density prediction model；
Step 4: using obtained critical heat flux density prediction model, passing through system pressure P, mass velocity G and balance vapor content
Xe predicts critical heat flux density.
2. a kind of critical heat flux density prediction technique returned based on Gaussian process according to claim 1, feature are existed
In step 3 is specifically implemented according to the following steps:
Step 3.1: establish Gaussian process regression equation:
Y=f (x)+ε (2)
Wherein, f (x)~GP (m (x), k (x, x ')), ε are the white Gaussian noise independently of f (x), andm
It (x) is mean function, k (x, x ') is covariance function, σnFor variance；
The input of training set D and output are constituted into a Gaussian process, as shown in formula (3):
Step 3.2: Gaussian process returns hyper parameterDetermination:
By establishing the negative log-likelihood function of training sample and it enabled to seek local derviation to θ each single item, then by conjugate gradient to inclined
Minimizing is led to obtain, as shown in (4) formula:
Wherein,α=C-1Y, K (X, X)=(k (xi,xj)) be n × n rank symmetric positive definite covariance square
Battle array, InFor n unit matrix, k (xi,xj) it is covariance kernel function.
3. a kind of critical heat flux density prediction technique returned based on Gaussian process according to claim 2, feature are existed
In, in step 3.2, k (xi,xj) specifically as shown in formula (5):
Wherein,For kernel function signal variance, l is variance measure.
4. a kind of critical heat flux density prediction technique returned based on Gaussian process according to claim 3, feature are existed
In step 4 is specifically implemented according to the following steps:
Step 4.1: utilizing test set D*={ (X*,y*) establish target output y and test set target output y*Joint Gauss point
Cloth, as shown in formula (6):
Wherein, K (X, X*)=K (X*,X)TFor training data X and test data x*Between the rank covariance matrix of n × 1；k(x*,
x*) it is test point x*The covariance of itself；k(xi,xj) it is covariance kernel function,
Step 4.2:y*Posterior probability distribution seek, as shown in formula (7):
Wherein:
Utilize x*To y*It is accurately sought, i.e., critical heat flux density is accurately predicted.
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| CN113836480A (en) * | 2020-06-23 | 2021-12-24 | 中核武汉核电运行技术股份有限公司 | Heat exchanger efficiency prediction method based on Gaussian process regression |
| CN114330035A (en) * | 2022-03-09 | 2022-04-12 | 中国空气动力研究与发展中心计算空气动力研究所 | High-speed aircraft aerodynamic performance evaluation method |
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| CN113836480B (en) * | 2020-06-23 | 2024-01-12 | 中核武汉核电运行技术股份有限公司 | Heat exchanger efficiency prediction method based on Gaussian process regression |
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Application publication date: 20190611 |