CN116894406A - 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
- Publication number
- CN116894406A CN116894406A CN202310905675.XA CN202310905675A CN116894406A CN 116894406 A CN116894406 A CN 116894406A CN 202310905675 A CN202310905675 A CN 202310905675A CN 116894406 A CN116894406 A CN 116894406A
- Authority
- CN
- China
- Prior art keywords
- matrix
- temperature field
- power
- modal
- data snapshot
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 25
- 239000011159 matrix material Substances 0.000 claims abstract description 73
- 239000013598 vector Substances 0.000 claims abstract description 25
- 238000004364 calculation method Methods 0.000 claims abstract description 11
- 238000013528 artificial neural network Methods 0.000 claims abstract description 5
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 4
- 239000003795 chemical substances by application Substances 0.000 claims abstract description 4
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 4
- 238000010248 power generation Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
- G06N3/08—Learning methods
- G06N3/084—Backpropagation, e.g. using gradient descent
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/08—Fluids
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- General Engineering & Computer Science (AREA)
- Evolutionary Computation (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Computing Systems (AREA)
- Software Systems (AREA)
- Data Mining & Analysis (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Geometry (AREA)
- Algebra (AREA)
- Artificial Intelligence (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Computational Linguistics (AREA)
- Life Sciences & Earth Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Molecular Biology (AREA)
- Health & Medical Sciences (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Medical Informatics (AREA)
- Fluid Mechanics (AREA)
- Databases & Information Systems (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
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.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310905675.XA CN116894406B (en) | 2023-07-21 | 2023-07-21 | Model order reduction-based space thermal ion reactor temperature field rapid prediction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310905675.XA CN116894406B (en) | 2023-07-21 | 2023-07-21 | Model order reduction-based space thermal ion reactor temperature field rapid prediction method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116894406A true CN116894406A (en) | 2023-10-17 |
| CN116894406B CN116894406B (en) | 2024-01-30 |
Family
ID=88314737
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310905675.XA Active CN116894406B (en) | 2023-07-21 | 2023-07-21 | Model order reduction-based space thermal ion reactor temperature field rapid prediction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116894406B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117171934A (en) * | 2023-11-03 | 2023-12-05 | 成都大学 | POD-ANNS-based overhead transmission line galloping response prediction method |
| CN118467979A (en) * | 2024-07-09 | 2024-08-09 | 西安航天动力研究所 | Engine thermal assembly heat transfer prediction method, device and equipment |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20220100916A1 (en) * | 2019-11-25 | 2022-03-31 | Akselos S.A. | Methods and systems for component-based reduced order modeling for industrial-scale structural digital twins |
| CN115270660A (en) * | 2022-08-04 | 2022-11-01 | 上海交通大学 | Multi-scale multi-physical field coupling analysis method for transient behavior of space thermionic reactor |
| CN115793432A (en) * | 2022-11-11 | 2023-03-14 | 西安交通大学 | Space thermionic nuclear power supply control method based on model predictive control |
| CN116070424A (en) * | 2022-12-30 | 2023-05-05 | 南华大学 | Thermal layering reduced-order analysis method for lead-bismuth fast reactor lead pool |
-
2023
- 2023-07-21 CN CN202310905675.XA patent/CN116894406B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20220100916A1 (en) * | 2019-11-25 | 2022-03-31 | Akselos S.A. | Methods and systems for component-based reduced order modeling for industrial-scale structural digital twins |
| CN115270660A (en) * | 2022-08-04 | 2022-11-01 | 上海交通大学 | Multi-scale multi-physical field coupling analysis method for transient behavior of space thermionic reactor |
| CN115793432A (en) * | 2022-11-11 | 2023-03-14 | 西安交通大学 | Space thermionic nuclear power supply control method based on model predictive control |
| CN116070424A (en) * | 2022-12-30 | 2023-05-05 | 南华大学 | Thermal layering reduced-order analysis method for lead-bismuth fast reactor lead pool |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117171934A (en) * | 2023-11-03 | 2023-12-05 | 成都大学 | POD-ANNS-based overhead transmission line galloping response prediction method |
| CN117171934B (en) * | 2023-11-03 | 2024-01-26 | 成都大学 | POD-ANNS-based overhead transmission line galloping response prediction method |
| CN118467979A (en) * | 2024-07-09 | 2024-08-09 | 西安航天动力研究所 | Engine thermal assembly heat transfer prediction method, device and equipment |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116894406B (en) | 2024-01-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN116894406B (en) | Model order reduction-based space thermal ion reactor temperature field rapid prediction method | |
| Atwell et al. | Reduced order controllers for Burgers' equation with a nonlinear observer | |
| CN113746087B (en) | Power grid transient stability sample controllable generation and evaluation method and system based on CTGAN | |
| Shen et al. | Nonlinear modeling and adaptive fuzzy control of MCFC stack | |
| Pagels et al. | Nonanalytic Behavior of the Σ Term in π− N Scattering | |
| Bae et al. | Accelerated multifidelity emulator modeling for probabilistic rotor response study | |
| CN114137829B (en) | Proton exchange membrane fuel cell subspace identification method based on ALMBO optimization algorithm | |
| Zhang et al. | Taking the guess work out of the initial guess: A solution interval method for least-squares parameter estimation in nonlinear models | |
| Kircher et al. | Global reaction neural networks with embedded stoichiometry and thermodynamics for learning kinetics from reactor data | |
| Shao et al. | A simulation data-driven design approach for rapid product optimization | |
| Xining et al. | Location layout design of aircraft parts assembly based on MSVR | |
| Sedlaczek et al. | Topology optimization of large motion rigid body mechanisms with nonlinear kinematics | |
| Akbari et al. | Numerical Assessment of a Nonintrusive Surrogate Model Based on Recurrent Neural Networks and Proper Orthogonal Decomposition: Rayleigh–Bénard Convection | |
| Mekjian | Cluster distributions in physics and genetic diversity | |
| CN115048846B (en) | Model order reduction and stability judgment method and system for tube bundle fluid bullet system | |
| CN116861736A (en) | Multi-scale material intelligent computing platform combining artificial intelligence | |
| Cheng et al. | Gramian-based model reduction of directed networks | |
| Ren et al. | Particle swarm optimization based predictive control of proton exchange membrane fuel cell (pemfc) | |
| CN108345729B (en) | Symmetrical cable-strut structure shape finding method based on group theory | |
| CN108229054B (en) | Symmetrical tensioning integral structure shape finding method based on group theory | |
| Camarda et al. | A parallel chemical reactor simulation using Cactus | |
| Yoshimura et al. | Hierarchical parallel processes of genetic algorithms for design optimization of large-scale products | |
| Dar et al. | Generalization of Numerical Approaches for Fractional-order Differential Equations: A Review | |
| Theodoropoulos et al. | A reduced input/output dynamic optimisation method for macroscopic and microscopic systems | |
| Farcas et al. | Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |