|Title||A Scalable Design of Experiments Framework for Sensor Placement |
|Publication Type||Journal Article |
|Year of Publication||2016 |
|Authors||Yu, J, Zavala, VM, Anitescu, M |
|Journal||Journal of Process Control |
|Date Published||04/2017 |
|Other Numbers||ANL/MCS-P6001-0416 |
|Abstract||We present a scalable design of an experiments framework for sensor placement in the context of state estimation of natural gas networks. We aim to compute optimal sensor locations where observational data are collected, by minimizing the uncertainty in parameters estimated from Bayesian inverse problems, which are governed by partial differential equations. The resulting problem is a mixed-integer nonlinear program. We approach it with two recent heuristics that have the potential to be scalable for such problems: a sparsity-inducing approach and a sum-up rounding approach. We investigate two metrics to guide the design of experiments (the total flow variance and the A-optimal design criterion) and analyze the effect of different noise structures (white and colored). We conclude that the sum-up rounding approach produces shrinking gaps with increased meshes. We also observe that convergence for the white noise measurement error case is slower than for the colored noise case. For A-optimal design, the solution is close to the uniform distribution, but for the total flow variance the pattern is noticeably different.