A VF-SLP framework using least squares hybrid scaling for RBDO

Using computationally cheap low-fidelity (LF) model and more accurate but expensive high-fidelity (HF) model, variable fidelity (VF) model has been widely used in engineering design to replace the actual computationally expensive experiments or computer simulations. To further extend the application of VF to reliability-based design optimization (RBDO), a new framework based on sequential linear programming (SLP) is proposed in this paper. Combining the advantages of additive scaling method and multiplicative scaling method, a hybrid scaling method based on least squares (LSHS) is developed. In LSHS method, the VF model is introduced to replace the implicit performance function in RBDO by using the HF function values and gradient values at all evaluated points around the current design. With the failure probability and its gradient calculated by Monte Carlo Simulation (MCS) at current design, SLP is adopted to calculate the next design. A novel method which considers the target reliability index and the influence domain at the current design is also developed to determine the step size in every sub-optimization problem. Two numerical examples and the shape optimization problem of a curved beam are analyzed in order to demonstrate the performance of the proposed methodology. The comparison results show that the proposed method is very accurate and efficient.