Artificial neural network-based multi-fidelity modeling technique for various types of input variables

Abstract

Multi-fidelity surrogate (MFS) modeling technology, which efficiently constructs surrogate models using low-fidelity (LF) and high-fidelity (HF) data, has been studied to enhance the predictive capability of engineering performances. However, existing multi-fidelity (MF) NNs have been developed assuming identical sets of input variables for LF and HF data, a condition that is often not met in practical engineering systems. Furthermore, there are still several limitations in examining the exact behavior of an engineering products for HF data. Product’s information about variables or performances is often insufficient in the real industry. Also, it is difficult to completely replace products with simulation models. Thus, statistical model calibration is studied to construct the calibrated surrogate model of a product’s performance by modeling the relationship between the experiments and simulations. Machine learning techniques such as Gaussian process (GP) and neural network (NN) model are widely used to predict the performances of products. In the field of statistical model calibration, GP-based method has been discussed a lot. However, it has several disadvantages such as instability of inverse matrix calculation for training and limitation of the number of training data. Therefore, this study proposes enhanced NN-based MF surrogate modeling methods to solve these two problems. Firstly, this study proposes a new structure of composite NN designed for MF data with different input variables. The proposed network structure includes an input mapping network that connects the LF and HF data’s input variables. Even when the physical relationship between these variables is unknown, the input mapping network can be concurrently trained during the process of training the whole network model. Customized loss functions and activation variables are suggested in this study to facilitate forward and backward propagation for the proposed NN structures when training MF data with different inputs. Secondly, this study proposes a new model calibration method based on the NN model. By using the NN model, it is advantageous for problem with big data as well as prediction for highly non-linear or discrete model. In this study, new NN structure using a Bayesian neural network is proposed to consider the uncertainty of experimental data. Finally, the proposed methodology is applied to numerical examples to compare with existing method. The effectiveness of the proposed method, in terms of prediction accuracy, is demonstrated through mathematical examples and practical engineering problems related to tire and vehicle performances. The results confirm that the proposed method offers better accuracy than existing surrogate models in most problems. Moreover, the proposed method proves advantageous for surrogate modeling of nonlinear or discrete functions, a characteristic feature of NN-based methods.