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Title: A scalable design of experiments framework for optimal sensor placement

Abstract

Here, we present a scalable design of an experiments framework for sensor placement in systems described by partial differential equations (PDEs). In particular, we aim to compute optimal sensor locations by minimizing the uncertainty of parameters estimated from Bayesian inverse problems and where the system. The resulting problem is a computationally intractable mixed-integer nonlinear program constrained by PDEs. We approach this problem with two heuristics used in compressed sensing and optimal control literature: a sparsity-inducing approach and a sum-up rounding approach. We also investigate 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). Using an application in natural gas pipelines, we conclude that the sum-up rounding approach approach gives the best results and produces shrinking gaps with increasing mesh resolution. 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 a uniform distribution of sensors along the pipeline while for the flow variance design the distribution is unstructured.

Authors:
 [1];  [2];  [3]
  1. Univ. of Chicago, Chicago, IL (United States)
  2. Univ. of Wisconsin-Madison, Madison, WI (United States)
  3. Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Lemont, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1460969
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Process Control
Additional Journal Information:
Journal Volume: 67; Journal Issue: C; Journal ID: ISSN 0959-1524
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Sensor data; Sensor placement; Estimation; Scalable

Citation Formats

Yu, Jing, Zavala, Victor M., and Anitescu, Mihai. A scalable design of experiments framework for optimal sensor placement. United States: N. p., 2017. Web. doi:10.1016/j.jprocont.2017.03.011.
Yu, Jing, Zavala, Victor M., & Anitescu, Mihai. A scalable design of experiments framework for optimal sensor placement. United States. doi:10.1016/j.jprocont.2017.03.011.
Yu, Jing, Zavala, Victor M., and Anitescu, Mihai. Tue . "A scalable design of experiments framework for optimal sensor placement". United States. doi:10.1016/j.jprocont.2017.03.011. https://www.osti.gov/servlets/purl/1460969.
@article{osti_1460969,
title = {A scalable design of experiments framework for optimal sensor placement},
author = {Yu, Jing and Zavala, Victor M. and Anitescu, Mihai},
abstractNote = {Here, we present a scalable design of an experiments framework for sensor placement in systems described by partial differential equations (PDEs). In particular, we aim to compute optimal sensor locations by minimizing the uncertainty of parameters estimated from Bayesian inverse problems and where the system. The resulting problem is a computationally intractable mixed-integer nonlinear program constrained by PDEs. We approach this problem with two heuristics used in compressed sensing and optimal control literature: a sparsity-inducing approach and a sum-up rounding approach. We also investigate 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). Using an application in natural gas pipelines, we conclude that the sum-up rounding approach approach gives the best results and produces shrinking gaps with increasing mesh resolution. 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 a uniform distribution of sensors along the pipeline while for the flow variance design the distribution is unstructured.},
doi = {10.1016/j.jprocont.2017.03.011},
journal = {Journal of Process Control},
number = C,
volume = 67,
place = {United States},
year = {2017},
month = {4}
}

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