CN116894406B - Model order reduction-based space thermal ion reactor temperature field rapid prediction method - Google Patents
Model order reduction-based space thermal ion reactor temperature field rapid prediction method Download PDFInfo
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Abstract
A method for rapidly predicting a temperature field of a space thermal ion stack based on model order reduction comprises the steps of 1, designating an operation power interval of the space thermal ion stack, and randomly generating a power sample space; 2. solving a temperature field of each power in the power sample space to obtain a data snapshot matrix of the whole power sample space; 3. carrying out eigenvalue orthogonal decomposition on the data snapshot matrix to obtain an orthogonal basis matrix and a modal coefficient matrix, decomposing the temperature field of the whole space thermal ion stack into a form of adding the average value of the sample temperature field and the products of a plurality of orthogonal basis vectors and modal coefficients; 4. based on the generalized energy percentage, a certain number of orthogonal basis vectors are selected as a main mode to establish a reduced order model; 5. training a neural network by utilizing each power value and a corresponding modal coefficient in a sample space based on a back propagation algorithm to obtain a proxy model; 6. and inputting power values into the trained agent model to obtain modal coefficients, and combining the modal coefficients with the reduced order model to obtain the temperature values of all grid nodes. The method of the invention has the advantages of rapid calculation and accurate result.
Description
Technical Field
The invention relates to the technical field of space thermal ion stack operation analysis, in particular to a model order reduction-based space thermal ion stack temperature field rapid prediction method.
Background
The space thermal ion stack adopts the in-pile thermal ion power generation technology, the thermal ion power generation efficiency is closely related to the temperature, and the accurate and rapid prediction of the temperature field distribution of the space thermal ion stack has important significance for the on-orbit operation control of the space thermal ion stack. At present, a Computational Fluid Dynamics (CFD) method is adopted to calculate a temperature field of a full-size three-dimensional space thermal ion stack, so that a large amount of calculation resources are required to be consumed, and the calculation time is long. If various working conditions are calculated, the calculation time is multiplied, and the quick prediction of the temperature field is not facilitated. The essence of model reduction is to express high-dimensional data information with low-dimensional data information. The method has the advantages that under the condition that the space dimension and the physical attribute of the problem are reserved, the calculation cost is reduced, and the enough precision requirement can be ensured.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a model order reduction-based rapid prediction method for a temperature field of a space thermal ion stack, which solves the problems of long calculation time, large calculation amount and repeated calculation under similar working conditions in the process of solving the temperature field of the space thermal ion stack by a CFD simulation method.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for rapidly predicting a temperature field of a space thermal ion stack based on model reduction comprises the following steps:
step 1: an operating power interval of the spatial thermionic stack is specified, and a power sample space is randomly generated within the operating power interval.
Step 2: and solving the temperature field of each power in the power sample space by using CFD software, so as to obtain a data snapshot matrix of the whole power sample space.
The specific form of the data snapshot matrix is as follows:
wherein M is the number of grid nodes;
n—number of numerical analog data samples;
a-data snapshot matrix;
X i -the ith column vector of the data snapshot matrix, i=1, 2,3 … N;
x—grid node temperature, K.
Step 3: and carrying out intrinsic orthogonal decomposition on the data snapshot matrix to obtain an orthogonal base matrix and a modal coefficient matrix, decomposing the temperature field of the whole space thermal ion stack into a mode of adding the average value of the sample temperature field and the products of a plurality of characteristic modes and modal coefficients.
Firstly, converting a data snapshot matrix into a square matrix:
[B] N×N ＝[A T ] N×M [A] M×N (2)
b is a square matrix of a data snapshot matrix;
[A T ]-transpose of the data snapshot matrix.
And decomposing the eigenvalue of the square matrix B:
wherein phi is a characteristic vector matrix;
c, a characteristic value matrix;
ψ i -ith eigenvector, i=1, 2,3 … N;
λ i -ith eigenvalue, i=1, 2,3 … N.
The eigenvalues in the eigenvalue matrix C are arranged according to the size thereof in a descending order, and the orthogonal base matrix is obtained in the form of:
wherein, beta-is an orthogonal base matrix;
θ i -i < th > order orthogonal basis vector, i=1, 2,3 … N.
Transpose a of the data snapshot matrix from the orthogonal base matrix β T The characteristic coefficient matrix D can be obtained, and its specific form is:
[D] N×N ＝[A T ] N×M [β] M×N ＝[a 1 a 2 … a N ] (5)
wherein D is a characteristic coefficient matrix;
a i -the modal coefficient of the i-th order orthogonal basis vector, i=1, 2,3 … N.
Each column vector in the data snapshot matrix can be expressed in terms of orthogonal basis vectors and eigenvalues as follows:
after the above process is completed, the temperatures at all grid nodes in the calculation region of the space thermionic stack are decomposed into the form of the average value of the sample temperature field and the product of several orthogonal basis vectors and modal coefficients added:
in the method, in the process of the invention,-temperature predicted value, K;
X 0 -is the average value of the sample temperature field, K;
r-the number of selected characteristic modes.
Step 4: based on the generalized energy percentage, a certain number of orthogonal basis vectors are selected as a main mode to establish a reduced order model.
The generalized energy percentage is in the form of:
wherein E is r -generalized energy percentage;
λ j -a j-th eigenvalue;
epsilon-energy ratio.
Step 5: based on a back propagation algorithm, training a neural network by using each power value and a corresponding modal coefficient in a sample space, thereby obtaining a proxy model.
Step 6: and inputting power values into the trained agent model to obtain modal coefficients, and combining the modal coefficients with the reduced order model to obtain the temperature values of all grid nodes.
Compared with the prior art, the invention has the following outstanding characteristics:
the method for quickly predicting the temperature field of the space thermal ion stack under different power operation conditions based on the model order reduction is provided, an order reduction model is built through a certain amount of CFD software calculation result data, and a high-precision proxy model is obtained through neural network training, so that the temperature field of the space thermal ion stack under different powers is quickly obtained.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
the invention discloses a model order reduction-based rapid prediction method for a temperature field of a space thermal ion stack, which is shown in fig. 1, and specifically comprises the following steps:
step 1: an operating power interval of the spatial thermionic stack is specified, and a power sample space is randomly generated within the operating power interval. This embodiment specifies a power operating range of 50% -100%.
Step 2: and solving the temperature field of each power in the power sample space by using CFD software, so as to obtain a data snapshot matrix of the whole power sample space. This example uses ANSYS Fluent for temperature field solving for 100% power of the space thermionic stack.
The specific form of the data snapshot matrix is as follows:
wherein M is the number of grid nodes;
n—number of numerical analog data samples;
a-data snapshot matrix;
X N -an nth column vector of the data snapshot matrix;
x—grid node temperature, K.
Step 3: and carrying out intrinsic orthogonal decomposition on the data snapshot matrix to obtain an orthogonal base matrix and a modal coefficient matrix, decomposing the temperature field of the whole space thermal ion stack into a mode of adding the average value of the sample temperature field and the products of a plurality of characteristic modes and modal coefficients.
Firstly, converting a data snapshot matrix into a square matrix:
[B] N×N ＝[A T ] N×M [A] M×N (2)
b is a square matrix of a data snapshot matrix;
[A T ]-transpose of the data snapshot matrix.
And decomposing the eigenvalue of the square matrix B:
wherein phi is a characteristic vector matrix;
c, a characteristic value matrix;
ψ N -an nth feature vector;
λ N -nth eigenvalue.
The eigenvalues in the eigenvalue matrix C are arranged according to the size thereof in a descending order, and the orthogonal base matrix is obtained in the form of:
wherein, beta-is an orthogonal base matrix;
θ i -i < th > order orthogonal basis vector, i=1, 2,3 … N.
Transpose a of the data snapshot matrix from the orthogonal base matrix β T The characteristic coefficient matrix D can be obtained, and its specific form is:
[D] N×N ＝[A T ] N×M [β] M×N ＝[a 1 a 2 … a N ] (5)
wherein D is a characteristic coefficient matrix;
a i -the modal coefficient of the i-th order orthogonal basis vector, i=1, 2,3 … N.
Each column vector in the data snapshot matrix can be expressed in terms of orthogonal basis vectors and eigenvalues as follows:
after the above process is completed, the temperatures at all grid nodes in the calculation region of the space thermionic stack are decomposed into the form of the average value of the sample temperature field and the product of several characteristic modes and mode coefficients added:
in the method, in the process of the invention,-temperature predicted value, K;
X 0 -is the average value of the sample temperature field, K;
r-the number of selected characteristic modes.
Step 4: based on the generalized energy percentage, a certain number of characteristic modes are selected as main modes to establish a reduced order model. In this embodiment, r=3 (for example only, other numbers may be used, depending on the actual problem) when the energy ratio is set to 0.99.
The generalized energy percentage is in the form of:
wherein E is r -generalized energy percentage;
λ j -a j-th eigenvalue;
epsilon-energy ratio.
Step 5: based on a back propagation algorithm, training a neural network by using each power value and a corresponding modal coefficient in a sample space, thereby obtaining a proxy model.
Step 6: and inputting power values into the trained agent model to obtain modal coefficients, and combining the modal coefficients with the reduced order model to obtain temperature information of all grid nodes.
Claims (1)
1. A method for rapidly predicting a temperature field of a space thermal ion stack based on model reduction is characterized by comprising the following steps: the method comprises the following steps:
step 1: designating an operation power interval of the space thermionic stack, and randomly generating a power sample space in the operation power interval;
step 2: solving a temperature field of each power in the power sample space by using CFD software, so as to obtain a data snapshot matrix of the whole power sample space;
the specific form of the data snapshot matrix is as follows:
wherein M is the number of grid nodes;
n—number of numerical analog data samples;
a-data snapshot matrix;
X i -the ith column vector of the data snapshot matrix, i=1, 2,3 … N;
x-grid node temperature, K;
step 3: carrying out intrinsic orthogonal decomposition on the data snapshot matrix to obtain an orthogonal base matrix and a modal coefficient matrix, decomposing the temperature field of the whole space thermal ion stack into a mode of adding the average value of the sample temperature field and the products of a plurality of characteristic modes and modal coefficients;
firstly, converting a data snapshot matrix into a square matrix:
[B] N×N ＝[A T ] N×M [A] M×N (2)
b is a square matrix of a data snapshot matrix;
[A T ]-transpose of the data snapshot matrix;
and decomposing the eigenvalue of the square matrix B:
wherein phi is a characteristic vector matrix;
c, a characteristic value matrix;
ψ i -ith eigenvector, i=1, 2,3 … N;
λ i -ith eigenvalue, i=1, 2,3 … N;
the eigenvalues in the eigenvalue matrix C are arranged according to the size thereof in a descending order, and the orthogonal base matrix is obtained in the form of:
wherein, beta-is an orthogonal base matrix;
θ i -i-th order orthogonal basis vector, i=1, 2,3 … N;
transpose a of the data snapshot matrix from the orthogonal base matrix β T The mode coefficient matrix D is obtained, and the specific form is as follows:
[D] N×N ＝[A T ] N×M [β] M×N ＝[a 1 a 2 …a N ] (5)
wherein D is a modal coefficient matrix;
a i -the modal coefficient of the i-th order orthogonal basis vector, i=1, 2,3 … N;
each column vector in the data snapshot matrix is represented in terms of an orthogonal basis vector and a modal coefficient as follows:
after the above process is completed, the temperatures at all grid nodes in the calculation region of the space thermionic stack are decomposed into the form of the average value of the sample temperature field and the product of several orthogonal basis vectors and modal coefficients added:
in the method, in the process of the invention,-temperature predicted value, K;
X 0 -is the average value of the sample temperature field, K;
r-the number of selected characteristic modes;
step 4: based on the generalized energy percentage, a certain number of orthogonal basis vectors are selected as a main mode to establish a reduced order model;
the generalized energy percentage is in the form of:
wherein E is r -generalized energy percentage;
λ j -a j-th eigenvalue;
epsilon-energy ratio;
step 5: training a neural network by utilizing each power value and a corresponding modal coefficient in a sample space based on a back propagation algorithm, thereby obtaining a proxy model;
step 6: and inputting power values into the trained agent model to obtain modal coefficients, and combining the modal coefficients with the reduced order model to obtain the temperature values of all grid nodes.
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