System of systems uncertainty quantification using machine learning techniques with smart grid application

System‐of‐Systems capability is inherently tied to the participation and performance of the constituent systems and the network performance which connects the systems together. It is imperative for the SoS stakeholders to quantify the SoS capability and performance to any uncertain variations in the system participation and network outages so that the system participation is incentivized and network design optimized. However, given the independent operations, management, and objectives of constituent systems, along with an increasing number of systems that collectively become a part of SoS, it becomes difficult to obtain a closed analytical function for SoS performance characterization. In this paper, we investigate and compare two machine learning techniques, Artificial Neural Network and Parametric Bayesian Estimation, to obtain a predictive model of the SoS given the uncertainty in the constituent system participation and the network conditions. We demonstrate our approach on a smart grid SoS application example and describe how the two machine learning techniques enable SoS robustness and resilience analysis by quantifying the uncertainty in the model and SoS operations. The results of smart grid example establish the value of SoS uncertainty quantification (UQ) and show how smart grid operators can utilize UQ models to maintain the desired robustness as operating conditions evolve and how the designers can incorporate low‐cost networks into the SoS while maintaining high performance and resilience.