CN116341399A - Thermodynamic hydraulic heat exchange coefficient prediction method based on physical constraint neural network - Google Patents

Thermodynamic hydraulic heat exchange coefficient prediction method based on physical constraint neural network Download PDF

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CN116341399A
CN116341399A CN202111526480.1A CN202111526480A CN116341399A CN 116341399 A CN116341399 A CN 116341399A CN 202111526480 A CN202111526480 A CN 202111526480A CN 116341399 A CN116341399 A CN 116341399A
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熊琰
谭超
李飞
谢政权
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China Nuclear Power Operation Technology Corp Ltd
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Abstract

The invention belongs to the field of thermal hydraulic simulation of nuclear power stations, and particularly relates to a thermal hydraulic heat exchange coefficient prediction method based on a physical constraint neural network. The method comprises the following steps: s1, acquiring a training set and a testing set; s2, constructing a physical constraint neural network model, wherein the physical constraint neural network model comprises a neural network model body and a PDE conservation equation based on an automatic differentiation mechanism, and constructing a first type of loss function based on the neural network model body and a second type of loss function based on the PDE conservation equation respectively; s3, training the physical constraint neural network model based on the training set and the testing set; s4, predicting the thermodynamic and hydraulic heat exchange coefficient based on the trained physical constraint neural network model. The advantages are that: PDE equations based on physical laws are effectively coupled so that better training accuracy is achieved in relatively fewer training sets; meanwhile, generalization of the training model is improved, and universality is stronger.

Description

Thermodynamic hydraulic heat exchange coefficient prediction method based on physical constraint neural network
Technical Field
The invention belongs to the field of thermal hydraulic simulation of nuclear power stations, and particularly relates to a thermal hydraulic heat exchange coefficient prediction method based on a physical constraint neural network.
Background
Complex fluids are ubiquitous in nature and industrial processes, and accurately simulating the basic heat transfer behavior of fluids is indispensable in research in many disciplines such as chemical, thermal and aerospace. Often, researchers need to measure a large amount of experimental data (e.g., temperature, speed, pressure, etc.) to build models in order to perform parametric analysis, performance characterization, and model optimization. The traditional machine learning method (depth/convolution/recurrent neural network) can maximally utilize the information contained in the data to construct a high-fidelity heat transfer model so as to accurately describe the association relationship between input and output, and can be further used for state monitoring, product quality control and risk prediction. However, for most of complex heat exchange devices with microscopic and closed characteristics (such as a microscale heat exchanger and a high-temperature radiation heat exchanger), the measurement cost of key information data of an internal physical field is high, even the measurement is difficult, and researchers often need to construct a model or make decisions under the condition of small data with sparse data, so that most of traditional machine learning methods lack robustness and cannot provide convergence guarantee. In addition, it should be noted that the fluid system inside the heat exchange device is generally controlled by a highly nonlinear PDE equation set, the physical constraints are constrained by basic physical laws, and learning the physical field information blindly by a data driving method may obtain results that are difficult to interpret and even violate the physical laws.
Disclosure of Invention
The invention aims to provide a thermodynamic and hydraulic heat exchange coefficient prediction method based on a physical constraint neural network, which can be effectively coupled with a nonlinear partial differential equation set (such as a PDE equation) based on a physical law, can solve the problem of supervised learning under the conditions of less quantity of boundaries and sampling data, and has high prediction precision and stronger universality.
The technical scheme of the invention is as follows: a thermodynamic hydraulic heat exchange coefficient prediction method based on a physical constraint neural network comprises the following steps:
s1, acquiring a training set and a testing set;
s2, constructing a physical constraint neural network model, wherein the physical constraint neural network model comprises a neural network model body and a PDE conservation equation based on an automatic differentiation mechanism, and constructing a first type of loss function based on the neural network model body and a second type of loss function based on the PDE conservation equation respectively;
s3, training the physical constraint neural network model based on the training set and the testing set;
s4, predicting the thermodynamic and hydraulic heat exchange coefficient based on the trained physical constraint neural network model.
In step S1, acquiring the training set and the test set includes the following steps:
s11 collecting data x from highly trusted simulations or experiments k The method comprises the steps of carrying out a first treatment on the surface of the x represents flow field characteristic variable
S12 preparing a training target set y=f (x) based on PDE solution data;
s13, obtaining data xk from the data; and selecting proper data from the training target set Y=f (x), and respectively performing dimension reduction processing on the selected data to serve as a training set and a testing set of the physical constraint neural network model.
In step S11, for the collected data xk; preprocessing to ensure that data obtained from various sources is consistent with conservation equations in terms of dimension and averaging methods of operation;
in step S11, principal Component Analysis (PCA) is also employed to reduce the dimensionality of the data for large data sets.
In step S13, respectively carrying out normalization processing on the collected data of the training set and the test set; each feature in the dataset is subtracted from its mean and divided by variance, respectively.
The PDE conservation equation includes a mass conservation equation and an energy conservation equation,
the mass conservation equation is:
Figure BDA0003409178410000021
Figure BDA0003409178410000031
the energy conservation equation is
Figure BDA0003409178410000032
Figure BDA0003409178410000033
Wherein the cross-sectional area A, the pressure P and the internal energy u of the liquid f Internal energy of gas u g Volume fraction alpha f Cavitation fraction alpha g Mass fraction X of non-condensable gas (air) n Flow velocity v of gas phase g Flow velocity v of liquid phase f Heat transfer quantity Q of wall surface W Density ρ of gas phase g Density ρ of liquid phase f Rate of phase-to-phase net mass transfer Γ g Mass transfer Γ between fluids ig Mass transfer gamma of wall W 。
The loss function of the PINN network is:
L PINN ＝L NN +L M +L E
wherein the first type of loss function is a network self loss function L NN The second class of loss functions includes loss functions L based on conservation of mass constraints M And is a loss function L based on energy conservation constraint E 。
Figure BDA0003409178410000034
Figure BDA0003409178410000035
Figure BDA0003409178410000036
Wherein Q is W The actual heat transfer from the wall surface of the node,
Figure BDA0003409178410000037
heat transfer is performed for the wall surface of the node predicted by the network; a is the cross-sectional area of the pipe to be predicted, the pressure (P), the internal energy of the liquid and gas (u f ，u g ) Cavitation fraction (alpha) g ) Mass fraction of non-condensable gas (air) (X n ) Liquid and gas velocity (v f ,v g )。
Training the physical constraint neural network model based on the training set and the test set includes:
s31, adjusting model sealing parameters based on machine learning based on a PINN algorithm to obtain a corresponding sealing relation: ML (X) ≡Y;
s32, solving a thermodynamic hydraulic conservation equation by using the closed relation ML (X) ≡Y;
s33, judging whether the calculated value in the step S32 is converged in a tolerance interval from the target value, if the calculated value does not pass the convergence test, turning to the step S31, continuing to adjust and acquire a new closed relation until the calculated value passes the convergence test, and storing and outputting the closed relation, wherein the tolerance interval is selected as a preset value.
The invention has the beneficial effects that: in the process of establishing a network, the invention adds additional physical equation constraint, effectively couples PDE equations based on physical laws, and enables better training accuracy to be obtained in relatively fewer training sets; meanwhile, generalization of the training model is improved, and universality is stronger.
Drawings
FIG. 1 is a schematic flow chart of a thermodynamic coefficient of heat exchange prediction method based on a physical constraint neural network;
FIG. 2 is a schematic diagram of a physical constraint neural network model according to an embodiment of the present invention;
FIG. 3 is a schematic workflow diagram of another embodiment of the prediction method of the present invention;
FIG. 4 is a schematic diagram of the structure of the data sources of the training set and the test set in the embodiment shown in FIG. 1;
FIG. 5 is a graph showing the comparison of PINN and DNN test results for a test set (three control sticks dropped);
FIG. 6 is a comparative schematic diagram of PINN and DNN test relative error structures of a test set (three control sticks dropped).
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
As shown in fig. 1, the invention discloses a thermodynamic hydraulic heat exchange coefficient prediction method based on a physical constraint neural network, which comprises the following steps:
s1, acquiring a training set and a testing set;
s2, constructing a physical constraint neural network model, wherein the physical constraint neural network model comprises a neural network model body and a PDE conservation equation based on an automatic differentiation mechanism, and constructing a first class of loss function based on the neural network model body and a second class of loss function based on the PDE conservation equation respectively;
s3, training the physical constraint neural network module based on the training set and the testing set;
s4, predicting the thermodynamic and hydraulic heat exchange coefficient based on the trained physical constraint neural network model.
In a preferred embodiment, in step S1, the step of obtaining the training set and the test set includes the following steps:
s11, collecting data xk from high-reliability simulation or experiment; x represents a flow field characteristic variable;
s12, preparing a training target set y=f (x) based on PDE method solving data, wherein Y represents a heat exchange coefficient;
s13, obtaining data xk from the data; and selecting proper data from the corresponding training target set y=f (x) as candidate data of a training set and a testing set, and respectively performing dimension reduction processing on the candidate data to serve as the training set and the testing set of the physical constraint neural network model.
In step S1, the data calculated by the thermodynamic and hydraulic program of the two-phase flow PDE are first solved, and then appropriate data are selected from the above data sources as training data and test data of the model.
The flow field characteristic variable x can be the primary loop side coolant temperature, the secondary loop side gas phase temperature, the liquid phase temperature, the cavitation share, the node pressure, the liquid phase internal energy, the gas phase internal energy and the wall surface heat transfer quantity Q W And so on, further, in step S11, for the collected flow field characteristic variable data xk; preprocessing is performed to ensure that the data obtained from the various sources is consistent with the conservation equation PDE in terms of dimensions and averaging methods of operation. Furthermore, in the present embodiment, for a large data set, principal Component Analysis (PCA) is also employed to reduce the dimensionality of the data for data normalization processing so as to make the weights of each data source approximately equal.
In step S12, a training target set y=f (x) may be prepared by solving the data according to the PDE method, and the training target set y=f (x) may be obtained, and then step S13 is performed, where appropriate data are selected from the data calculated by the thermodynamic hydraulic program for solving the two-phase flow PDE, and are used as the test set and the training set, respectively.
In step S13, in order to make the training data and the test data identifiable to the model, the collected training set and test set data are further normalized respectively to achieve dimension reduction. As a preferred option, each feature in the training set and test set may be normalized by subtracting its mean and dividing by the variance.
In this embodiment, as shown in fig. 4, in step S1, one of the steam generators in the simulation program is selected as a data set source, and the steam generator is divided into four nodes in the simulation program, and the first-loop side coolant temperature and the second-loop side gas phase temperature, the liquid phase temperature, the cavitation share, the node pressure, the liquid phase internal energy, the gas phase internal energy, the wall heat transfer amount and the node relative position of the four nodes are extracted respectively. The steam generator is a vertical U-shaped pipe steam generator, and the temperature of coolant at the side of a loop is divided into the temperature of coolant at an ascending section and the temperature of coolant at a descending section; the simulation program is based on RELAP5, in which RELAP5 it is assumed that steam is generated in saturation, so that the heat transfer of the wall to the gas phase occurs during boiling of the near-wall boundary layer
Figure BDA0003409178410000061
The heat transfer of the wall-to-near-wall boundary layer is entirely transferred to the liquid phase, i.e.)>
Figure BDA0003409178410000062
The input of the relative positions of the nodes is to construct mass conservation constraint, and the positions of the nodes from bottom to top are respectively 1, 2, 3 and 4, and the node diagram of the steam generator is shown in fig. 4.
The data training network in steady state operation is not expandable, so that data of two control rods dropped at 5s and one control rod dropped at 5s, 15s, 35s and 45s respectively in one minute are collected as a training set, and data of one control rod dropped at 5s, 20s and 40s respectively are collected as a test set.
The network output is wall heat transfer quantity Q W Density ρ of gas phase g Density ρ of liquid phase f Flow velocity v of gas phase g Flow velocity v of liquid phase f Wherein the gas and liquid phase densities and flow rates are all to construct mass conservation constraints. And carrying out normalization processing on the acquired data, and respectively subtracting the mean value and dividing the variance of each characteristic in the data set.
After acquiring the data of the training set and the testing set, the method goes to step S2 to construct a physical constraint neural network model. The PINN network architecture of the architecture is shown in FIG. 2. According to the physical constraint neural network model disclosed by the invention, a PDE conservation equation is constructed by utilizing an automatic differential mechanism, an additional loss function (constraint for increasing boundary conditions) based on the PDE is further added, and then a Back Propagation (Back Propagation) and L-BFGS optimizer is utilized for adjusting the weight coefficient of the neural network, so that the physical constraint is constrained in an equation form, and the accuracy and the universality of model prediction are improved.
In this embodiment, as a preferred scheme, all the connection layers of the physical constraint neural network model including 8 hidden layers are connected in sequence by the Sequential model, each hidden layer includes 20 neurons, and the activation function of the hidden layers is a hyperbolic tangent tanh function. The first type of loss function is the difference LNN between the actual node wall heat transfer and the network predicted node wall heat transfer quantity; the second class of loss functions comprises LE for the mass conservation constraint LM and for the energy conservation constraint, respectively, i.e. the corresponding PINN network has the loss functions:
L PINN ＝L NN +L M +L E
specifically, in this embodiment, the difference between the actual node wall heat transfer and the network predicted node wall heat transfer amount is selected as the first type of loss function.
Figure BDA0003409178410000071
L NN ＝Q
Meanwhile, an automatic differentiation mechanism is utilized to construct a PDE conservation equation, so that an additional loss function based on PDE is added. In this embodiment, as a preferred scheme, mass conservation and energy conservation are selected as constraints, as follows.
Conservation of mass:
Figure BDA0003409178410000072
Figure BDA0003409178410000073
cross-sectional area A, pressure P, internal energy u of liquid f Internal energy of gas u g Cavitation fraction alpha g Flow velocity v of gas phase g Flow velocity v of liquid phase f Density ρ of gas phase g Density ρ of liquid phase f 。
The mass source is not included in the flow, and the liquid generating term is a negative value of the vapor generating term in view of the overall continuity, namely:
Γ f ＝-Γ g
the cross-sectional areas of all nodes in the simulation model are equal, and the cross-sectional area A is not changed along with x. The loss function based on mass conservation constraints in combination with the equation is:
Figure BDA0003409178410000074
conservation of energy:
Figure BDA0003409178410000075
Figure BDA0003409178410000076
cross-sectional area A, pressure P, internal energy u of liquid f Internal energy of gas u g Cavitation fraction alpha g Mass fraction X of non-condensable gas (air) n Flow velocity v of gas phase g Flow velocity v of liquid phase f Heat transfer quantity Q of wall surface W Density ρ of gas phase g Density ρ of liquid phase f 。
The cross-sectional areas of all nodes in the simulation model are equal, and the cross-sectional area A of the node is not changed along with x; the magnitude of the loss function influences the gradient descent speed in the process of back propagation of the neural network, and for the 3, 4, 5, 6 and 7 items on the right side of the equality sign, when the loss function based on energy conservation is constructed, the influence on the loss function is ignored because the loss function is not easy to acquire. The energy conservation constraint-based loss function described above in connection with the equation is:
Figure BDA0003409178410000081
step S3, training the physical constraint neural network model based on the training set and the testing set; in this embodiment, the PINN adds the difference value after the physical equation iteration as a constraint to the loss function during each round of training of the network. The neural network is optimized in training iteration, not only the own loss function of the network, but also the difference of each iteration of the physical equation, and finally the training result can meet the equation serving as the constraint.
Specifically, the method comprises the following steps:
s31, adjusting model sealing parameters based on machine learning based on a PINN algorithm to obtain a corresponding sealing relation: ML (X) ≡Y;
s32, solving a thermodynamic hydraulic conservation equation by using the closed relation ML (X) ≡Y;
s33, judging whether the calculated value in the step S32 is converged within a tolerance interval from the target value, if the calculated value does not pass the convergence test, turning to the step S31, continuing to adjust and acquire a new closed relation until the calculated value passes the convergence test, and storing and outputting the closed relation. Wherein, the tolerance interval is selected as a preset value.
In step S31, as a preferred solution, 3 loss functions may be trained and iterated based on the gradient descent algorithm, and when it is determined that all three loss functions are in a descent state, a corresponding closed relation at this time may be obtained: ML (X) ≡Y;
in step S32, substituting the closed relation ML (X) ≡y obtained in step S31 into the mass conservation equation and the energy conservation equation to solve, obtaining the temperature/pressure/cavitation share of each hydraulic node of the loop, taking over the flow and other variables, and then turning to step S33, judging whether the calculated values diverge, i.e. whether the calculated values converge to a tolerance interval from the target value, if the calculated values diverge, indicating that the convergence test is not passed, turning to step S31 to obtain the next closed relation until the requirements are met.
S4, predicting the thermodynamic and hydraulic heat exchange coefficient based on the trained physical constraint neural network model.
The following method for predicting by using DNN network is compared with the prediction method shown in the invention, and the working effect of the invention is further verified. Fig. 5 is a comparison between the predictions of the PINN network, the predictions of the DNN network, and the true values on the test set when three control sticks were dropped. From the graph, it can be seen that the fitting effect of the PINN on the validation set is significantly better than DNN, which does not respond well to parameter fluctuations generated when the control rod is dropped. FIG. 6 is a graph of the relative error of the predicted versus true values for the PINN, DNN network on the validator, from which it can be seen that the relative error of the DNN model is in most cases greater than the relative error of the PINN model; the peak value of the relative error of DNN models at the 1, 2 and 3 nodes is obviously larger than that of a PINN model; the peak of the relative error at the 4-node PINN model is slightly larger than the DNN model.
While the invention has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (10)

1. A thermodynamic hydraulic heat exchange coefficient prediction method based on a physical constraint neural network is characterized by comprising the following steps:
s1, acquiring a training set and a testing set;
s2, constructing a physical constraint neural network model, wherein the physical constraint neural network model comprises a neural network model body and a PDE conservation equation based on an automatic differentiation mechanism, and constructing a first type of loss function based on the neural network model body and a second type of loss function based on the PDE conservation equation respectively;
s3, training the physical constraint neural network model based on the training set and the testing set;
s4, predicting the thermodynamic and hydraulic heat exchange coefficient based on the trained physical constraint neural network model.
2. The method for predicting the thermodynamic and hydraulic heat exchange coefficient based on the physical constraint neural network according to claim 1, wherein in step S1, obtaining the training set and the test set includes the steps of:
s11 collecting data x from highly trusted simulations or experiments k The method comprises the steps of carrying out a first treatment on the surface of the x represents flow field characteristic variable
S12 preparing a training target set y=f (x) based on PDE solution data;
s13 from the data x k The method comprises the steps of carrying out a first treatment on the surface of the The training target set YAnd selecting proper data and performing dimension reduction processing on the selected data respectively to serve as a training set and a testing set of the physical constraint neural network model.
3. The thermodynamic and hydraulic heat exchange coefficient prediction method based on the physical constraint neural network, according to claim 2, is characterized in that: in step S11, for the collected data x k The method comprises the steps of carrying out a first treatment on the surface of the Preprocessing to ensure that data obtained from various sources is consistent with conservation equations in terms of dimension and averaging methods of operation;
in step S11, principal Component Analysis (PCA) is also employed to reduce the dimensionality of the data for large data sets.
4. The method for predicting the thermodynamic and hydraulic heat exchange coefficient based on the physical constraint neural network according to claim 2, wherein in step S13, normalization processing is performed on the collected data of the training set and the test set, respectively; each feature in the dataset is subtracted from its mean and divided by variance, respectively.
5. The thermodynamic and hydraulic heat exchange coefficient prediction method based on the physical constraint neural network, according to claim 1, is characterized in that: the PDE conservation equation includes a mass conservation equation and an energy conservation equation,
the mass conservation equation is:
Figure FDA0003409178400000021
Figure FDA0003409178400000022
the energy conservation equation is
Figure FDA0003409178400000023
Figure FDA0003409178400000024
Wherein the cross-sectional area A, the pressure P and the internal energy u of the liquid f Internal energy of gas u g Volume fraction alpha f Cavitation fraction alpha g Mass fraction X of non-condensable gas (air) n Flow velocity v of gas phase g Flow velocity v of liquid phase f Heat transfer quantity Q of wall surface W Density ρ of gas phase g Density ρ of liquid phase f Rate of phase-to-phase net mass transfer Γ g Mass transfer Γ between fluids ig Mass transfer gamma of wall w 。
6. The method for predicting the thermodynamic and hydraulic heat transfer coefficients based on the physical constraint neural network as claimed in claim 5, wherein the loss function of the PINN network is:
L PINN ＝L NN +L M +L E
wherein the first type of loss function is a network self loss function L NN The second class of loss functions includes loss functions L based on conservation of mass constraints M And is a loss function L based on energy conservation constraint E 。
7. The method for predicting the thermodynamic and hydraulic heat exchange coefficient based on the physical constraint neural network according to claim 6, wherein the method is characterized by comprising the following steps of:
Figure FDA0003409178400000025
Figure FDA0003409178400000026
Figure FDA0003409178400000027
wherein Q is W The actual heat transfer from the wall surface of the node,
Figure FDA0003409178400000028
heat transfer is performed for the wall surface of the node predicted by the network; a is the cross-sectional area of the pipe to be predicted, the pressure (P), the internal energy of the liquid and gas (u f ，u g ) Cavitation fraction (alpha) g ) Mass fraction of non-condensable gas (air) (X n ) Liquid and gas velocity (v f ,v g )。
8. The method for predicting a thermodynamic and hydraulic heat transfer coefficient based on a physical constraint neural network of claim 1, wherein training the physical constraint neural network model based on the training set and the test set comprises:
s31, adjusting model sealing parameters based on machine learning based on a PINN algorithm to obtain a corresponding sealing relation: ML (X) ≡Y.
9. The method of claim 8, wherein training the physical constraint neural network model based on the training set and the test set comprises:
s32, solving a thermodynamic hydraulic conservation equation by using the closed relation ML (X) ≡Y.
10. The method of claim 8, wherein training the physical constraint neural network model based on the training set and the test set comprises:
s33, judging whether the calculated value in the step S32 is converged in a tolerance interval from the target value, if the calculated value does not pass the convergence test, turning to the step S31, continuing to adjust and acquire a new closed relation until the calculated value passes the convergence test, and storing and outputting the closed relation, wherein the tolerance interval is selected as a preset value.
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Publication number Priority date Publication date Assignee Title
CN116777010A (en) * 2023-08-25 2023-09-19 之江实验室 Model training method and task execution method and device

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CN116777010A (en) * 2023-08-25 2023-09-19 之江实验室 Model training method and task execution method and device
CN116777010B (en) * 2023-08-25 2023-12-19 之江实验室 Model training method and task execution method and device

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