A Linked Stochastic Kriging for Multi-Layer Systems with Noisy Response

Systems consisting of multiple coupled sub-models, called multi-layer systems, are common in engineering design and optimization, calling for the effective and efficient surrogate model for such systems. Nowadays the existing methods involves the structural method instead of the All-in-ones (AIO) method that treats the system as a black box. Among them, the Linked Gauss Process (LGP) has attracted attention because its strong theoretical basis and the robust performance of its fundamental model Kriging. However, the existing LGP can not handle the situation with noisy response within the multi-layer systems, since the ordinary Kriging is designed for the deterministic simulation. To solve this, this paper proposes a novel linked emulator for the multi-layer stochastic simulation, called Linked Stochastic Kriging (LinkedSK). This method replaces the ordinary Kriging with stochastic Kriging within the linked emulator, aiming to build an appropriate model for multi-layer systems with the noisy response. Numerical experiments exhibit the significant and robust performance of the proposed LinkedSK compared to other existing methods.