Polynomial-Chaos-Based Decentralized Dynamic Parameter Estimation Using Langevin MCMC

This paper develops a polynomial-chaos-expansion (PCE)-based approach for decentralized dynamic parameter estimation. Under Bayesian inference framework, the non-Gaussian posterior distributions of the parameters can be obtained through Markov Chain Monte Carlo (MCMC). However, the latter method suffers from a prohibitive computing time for large-scale systems. To overcome this problem, we develop a decentralized generator model with the PCE-based surrogate, which allows us to efficiently estimate some generator parameter values. Furthermore, the gradient of the surrogate model can be easily obtained from the PCE coefficients. This allows us to use the gradient-based Langevin MCMC in lieu of the traditional Metropolis-Hasting algorithm so that the sample size can be greatly reduced. Simulations carried out on the New England system reveal that the proposed method can achieve a speedup factor of three orders of magnitude as compared to the traditional method without losing the accuracy.