Approximate Bayesian Computation Inverse Method With Variational Autoencoder Applied To Sheet Metal Forming And Development Of Software

In modern product manufacturing,metal sheet forming technology has become an essential manufacturing method and it is widely used in various fields.Generally,the sheet metal forming process is accompanied by multiple complex physical phenomena,such as elastoplastic deformation,friction loss,large deformation,and contact collision.Because of the complexity of sheet metal forming,the unreasonable design of forming parameters often leads to the defects such as cracking and wrinkling of the formed sheet metal,and even directly leads to the scrap of parts.With the improvement of computer performance,the development of finite element theory and the application of reverse theory,the selection of the best forming parameters through these technical means has become an important research direction in this field.To improve the quality of sheet metal forming and avoid forming defects,an approximate Bayesian computation inverse method based on variational autoencoder is proposed to reverse the forming parameters in this paper.The main contents of this paper are as follows:Although the traditional hybrid numerical method is an effective method to obtain the forming parameters,it ignores the uncertainty in the reverse process.For the existence of uncertainty,the reverse method of forming parameters based on approximate Bayesian calculation is determined.The key to the efficiency and accuracy of the approximate Bayesian computation is the selection of summary statistics.If the dimension of summary statistics is too high,although it contains a large amount of data information,it will produce a large calculation cost.On the contrary,if the dimension of summary statistics is too low,it will make the reverse calculation complete quickly,but it contains too little data information and it is difficult to get accurate calculation results.Therefore,based on the advantages of variational autoencoder in feature extraction and sample reconstruction,the hidden variables in variational autoencoder are used as the summary statistics in approximate Bayesian computation.It can effectively balance the information loss and calculation efficiency in the reverse process.For the defects of traditional forming quality evaluation criteria,a new imagebased evaluation criterion is proposed in this paper.The hidden variables encoded by the variational autoencoder are used to replace the forming limit diagram,which can more fully and comprehensively reflect the forming quality.Meanwhile,separating the working area and non-working area on the forming limit diagram,and only the working area is reserved to prevent the non-working area from interfering with the reverse result.In addition,in order to complete the inverse calculation of the parameters,a target image with all elements in the safe area of the finite element model is reconstructed based on the existing forming limit diagram(excluding the non working area).The hidden variable corresponding to the target image is taken as the observation vector in approximate Bayesian calculation,which makes the reverse result more reliable.Finally,the effectiveness and feasibility of the proposed method are verified by three specific engineering examples.Besides,based on the MATLAB/GUI platform,the “Image Based Approximate Bayesian Computing Reverse System” software is developed,which encapsulates the proposed method and provides a convenient and fast operating platform for the reverse calculation of sheet metal forming parameters.