  In this study, an image-assisted Approximate Bayesian Computation (ABC)
parameter inverse method is proposed to identify the design parameters. In the
proposed method, the images are mapped to a low-dimensional latent space by
Variational Auto-Encoder (VAE), and the information loss is minimized by
network training. Therefore, an effective trade-off between information loss
and computational cost can be achieved by using the latent variables of VAE as
summary statistics of ABC, which overcomes the difficulty of selecting summary
statistics in the ABC. Besides, for some practical engineering problems,
processing the images as objective function can effective show the response
result. Meanwhile, the relationship between design parameters and the latent
variables is constructed by Least Squares Support Vector Regression (LSSVR)
surrogate model. With the well-constructed LSSVR model, the simulation
coefficient vectors under given parameters will be determined effectively.
Then, the parameters to be identified are determined by comparing the simulated
and observed coefficient vectors in ABC. Finally, a sheet forming problem is
investgated by the suggested method. The material parameters of the blank and
the process parameters of the forming process are identified. Results show that
the method is feasibility and effective for the identification of sheet forming
parameters.
