Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting
Short-term wind forecasting is critical for the dispatch, controllability and stability of a power grid. As a challenging but indispensable work, short-term wind forecasting has attracted considerable attention from researchers. In this paper, Principal Component Analysis (PCA) is applied to Computa...
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2023-02-01
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author | Shi Liu Guangchao Zhang |
author_facet | Shi Liu Guangchao Zhang |
author_sort | Shi Liu |
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description | Short-term wind forecasting is critical for the dispatch, controllability and stability of a power grid. As a challenging but indispensable work, short-term wind forecasting has attracted considerable attention from researchers. In this paper, Principal Component Analysis (PCA) is applied to Computational Fluid Dynamics (CFD) calculation results for feature extraction and then combined with sparse sensing to achieve the rapid reconstruction of a three-dimensional wind speed field and pressure field. Before reconstruction, the relationship between the reconstruction error and the noise level, and a number of the basis vectors is systematically studied. In the simulation, the wind shear effect is introduced into the inlet boundary condition, and the reconstruction errors of the uniform inlet are 0.21% and 6.46%, respectively, while the maximum reconstruction errors including the wind shear effect are 1.21% and 6.41%, respectively, which verifies the feasibility of applying a PCA-based reconstruction algorithm to a 3D wind field reconstruction. In addition, to solve the time-consuming problem of most optimization algorithms based on a brute-force combinatorial search, an innovative optimization algorithm based on the QR pivoting is investigated to determine the sparse sensor placements. Simulation results show that when the number of sensors is equal to the number of basis vectors, the error of random placement is even 20 times of the optimal placement, which illustrates that QR pivoting is a powerful optimization algorithm. Finally, a wind tunnel experiment of velocity field reconstruction is performed, to verify the practicability of the optimized method based on QR pivoting, and the results indicate that a reasonably high accuracy 3D wind field can be obtained with only 10 sensors (the error of most points is less than 5% and the minimum error is only 0.74%). In general, the proposed algorithm incorporating PCA, sparse sensing and QR pivoting can quickly reconstruct the 3D velocity and pressure fields with reduced measurement costs, which is of great significance for the development of short-term wind forecasting methods. |
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spelling | doaj.art-c129311d63574fff9ab5398edd6d3fdc2023-11-17T07:16:56ZengMDPI AGApplied Sciences2076-34172023-02-01135292710.3390/app13052927Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR PivotingShi Liu0Guangchao Zhang1School of Energy Power & Mechanical Engineering, North China Electric Power University, Beijing 102206, ChinaSchool of Energy Power & Mechanical Engineering, North China Electric Power University, Beijing 102206, ChinaShort-term wind forecasting is critical for the dispatch, controllability and stability of a power grid. As a challenging but indispensable work, short-term wind forecasting has attracted considerable attention from researchers. In this paper, Principal Component Analysis (PCA) is applied to Computational Fluid Dynamics (CFD) calculation results for feature extraction and then combined with sparse sensing to achieve the rapid reconstruction of a three-dimensional wind speed field and pressure field. Before reconstruction, the relationship between the reconstruction error and the noise level, and a number of the basis vectors is systematically studied. In the simulation, the wind shear effect is introduced into the inlet boundary condition, and the reconstruction errors of the uniform inlet are 0.21% and 6.46%, respectively, while the maximum reconstruction errors including the wind shear effect are 1.21% and 6.41%, respectively, which verifies the feasibility of applying a PCA-based reconstruction algorithm to a 3D wind field reconstruction. In addition, to solve the time-consuming problem of most optimization algorithms based on a brute-force combinatorial search, an innovative optimization algorithm based on the QR pivoting is investigated to determine the sparse sensor placements. Simulation results show that when the number of sensors is equal to the number of basis vectors, the error of random placement is even 20 times of the optimal placement, which illustrates that QR pivoting is a powerful optimization algorithm. Finally, a wind tunnel experiment of velocity field reconstruction is performed, to verify the practicability of the optimized method based on QR pivoting, and the results indicate that a reasonably high accuracy 3D wind field can be obtained with only 10 sensors (the error of most points is less than 5% and the minimum error is only 0.74%). In general, the proposed algorithm incorporating PCA, sparse sensing and QR pivoting can quickly reconstruct the 3D velocity and pressure fields with reduced measurement costs, which is of great significance for the development of short-term wind forecasting methods.https://www.mdpi.com/2076-3417/13/5/2927principal component analysiscomputational fluid dynamicssparse sensingQR pivotingshort-term wind forecasting |
spellingShingle | Shi Liu Guangchao Zhang Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting Applied Sciences principal component analysis computational fluid dynamics sparse sensing QR pivoting short-term wind forecasting |
title | Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting |
title_full | Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting |
title_fullStr | Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting |
title_full_unstemmed | Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting |
title_short | Numerical Simulation and Experimental Verification of Wind Field Reconstruction Based on PCA and QR Pivoting |
title_sort | numerical simulation and experimental verification of wind field reconstruction based on pca and qr pivoting |
topic | principal component analysis computational fluid dynamics sparse sensing QR pivoting short-term wind forecasting |
url | https://www.mdpi.com/2076-3417/13/5/2927 |
work_keys_str_mv | AT shiliu numericalsimulationandexperimentalverificationofwindfieldreconstructionbasedonpcaandqrpivoting AT guangchaozhang numericalsimulationandexperimentalverificationofwindfieldreconstructionbasedonpcaandqrpivoting |