Variational Auto-Encoder Based Approximate Bayesian Computation Uncertian Inverse Method for Sheet Metal Forming Problem

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.