Gappy POD

– Introducing a smart simulation technology that restores the entire flow field using partial data.

It is impossible to fully capture data for all points using a limited number of sensor reading. While CFD analysis can provide the full dataset, performing CFD calculations whenever needed is often impractical due to the significant computational resources and long processing times required.

What is Gappy POD?

Gappy POD is an extended version of the existing Proper Orthogonal Decomposition (POD)-based order reduction technique, which reconstructs the entire physical field (flow field) using data that only partially exists.

Core principles of technology

  • Building a Reduced Order Model (ROM) using the POD technique
    • Obtaining high-resolution datasets using CFD
    • Extraction of basis modes and weight coefficients that represent the main characteristics of the system
    • Create a reduced order model
  • Coefficient estimation and flow field reconstruction
    • Defining an optimization problem between limited data (Gappy Data) and POD mode
    • Calculating weighting coefficients to reconstruct the entire flow field
    • The entire flow field is reconstructed by linearly combining the derived coefficients and basis modes.

Advantages and Uses of Gappy POD

  • Data reduction – capture full physical quantities with fewer sensors and measurement points
  • Reduced computational costs – fast flow field estimation without having to perform high-resolution CFD every time.
  • Real-time applicability – Use sensor data from digital twins, control systems, and monitoring systems to see the status of the entire system.

Implemented with OpenFOAM code

  • Developed OpenFOAM utility – baramPODgappyReconstruction
  • Read sensor data file
  • Generate POD coefficient equations that approximate sensor data with least squares error.
  • In case of parallel analysis, reduce and process the equation generated by local mode/observation value.
  • Solve the equation with the Eigen library to obtain the POD coefficients.
  • Full-domain field reconstruction by linearly combining the entire mode

Application Cases

  • Validation of temperature distribution predictions for two-dimensional rectangular plates
    • The upper surface is assigned temperature boundary conditions of T1, and the remaining three surfaces are assigned temperature boundary conditions of T2.
    • Perform interpretation on 20 samples
    • Learning the analysis results according to the temperature conditions of the boundary surface
    • Perform Gappy POD, giving random temperature conditions at 25 points and comparing with ground truth.
    • RMS error between full CFD results and Gappy POD results: 0.11%
  • Reconstruction of the entire flow field from airfoil surface pressure sensor data.
    • Estimation of spatial data (23,552 cells) from surface data (150 points)
    • 2 seconds required, average error 0.2%
(Left) Reconstructed with Gappy POD, (Right) CFD analysis results
  • Reconstructing the entire flow field from submarine surface pressure sensor data.
    • Estimation of spatial data (459,378 cells) from surface data (500 points)
    • 8 seconds, average error 0.1%
(Left) Reconstructed with Gappy POD, (Right) CFD analysis results