Abstract
Estimating unknown parameters or conditions based on observation in a numerical model is a problem considered in data assimilation. In this study, we investigate a data assimilation approach using an image-processing deep neural network (DNN) as a likelihood function. The DNN is trained by observed images and tests visualized images generated by numerical simulation. This approach does not provide exact comparison of observed and simulated images for constructing the likelihood function. However, it would be effective when exact comparison is difficult due to noise or complex measurement procedures. The effectiveness of this approach is investigated by a vortex flow around a circular cylinder moving freely in the crossflow direction, realizing vortex-induced vibration (VIV). The DNN trained by wake visualization images from the VIV experiment tests pseudo-wake images from the numerical simulation to estimate VIV amplitude and frequency parameters. By evaluating the confidence score of the DNN from the simulated images with different amplitude and frequency values, these input parameters can be estimated based on the experimental VIV images, resulting in data assimilation with a likelihood function based on the DNN. The results showed that the amplitude and frequency of the VIV can be approximated from the experimental images.
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Funding
This work was partially supported by JSPS KAKENHI Grant Number 17K17592.
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The videos of the VIV experiment are available from the journal website (Seyed-Aghazadeh and Modarres-Sadeghi 2015). The annotation of experimental images was conducted using an annotation tool VoTT (Microsoft 2019) and the resulting bounding box coordinates are available on the data repository (Misaka 2019). YOLOv3 for deep learning used here is the same as on Redmon’s website (Redmon and Farhadi 2018), where the output part of the confidence score was slightly modified to calculate the average. The Kriging code is implemented by Fortran based on Jones et al. (1998). The MCMC routine is based on a standard algorithm (Bishop 2011). The Fortran code for the VIV simulation can be made available by request to interested researchers via the corresponding author.
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Misaka, T. Image-based fluid data assimilation with deep neural network. Struct Multidisc Optim 62, 805–814 (2020). https://doi.org/10.1007/s00158-020-02537-z
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DOI: https://doi.org/10.1007/s00158-020-02537-z