A scalable design of experiments framework for optimal sensor placement

Yu, Jing; Zavala, Victor M.; Anitescu, Mihai

doi:10.1016/j.jprocont.2017.03.011

A scalable design of experiments framework for optimal sensor placement

Journal Article · Tue Apr 11 00:00:00 EDT 2017 · Journal of Process Control

DOI:https://doi.org/10.1016/j.jprocont.2017.03.011· OSTI ID:1460969

Yu, Jing ^[1]; Zavala, Victor M. ^[2]; Anitescu, Mihai ^[3]

Univ. of Chicago, Chicago, IL (United States)
Univ. of Wisconsin-Madison, Madison, WI (United States)
Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Lemont, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1460969

Alternate ID(s):: OSTI ID: 1550469

Journal Information:: Journal of Process Control, Journal Name: Journal of Process Control Journal Issue: C Vol. 67; ISSN 0959-1524

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (16)

Optimal experiment design for nonlinear dynamic (bio)chemical systems using sequential semidefinite programming Telen, Dries; Logist, Filip; Quirynen, Rien AIChE Journal, Vol. 60, Issue 5 https://doi.org/10.1002/aic.14389	journal	March 2014
On the theory of optimal sensor placement Chmielewski, Donald J.; Palmer, Tasha; Manousiouthakis, Vasilios AIChE Journal, Vol. 48, Issue 5 https://doi.org/10.1002/aic.690480510	journal	May 2002
Using integer programming techniques for the solution of an experimental design problem Harris, Carl M.; Hoffman, Karla L.; Yarrow, Leslie-Ann Annals of Operations Research, Vol. 58, Issue 3 https://doi.org/10.1007/BF02032134	journal	May 1995
The integer approximation error in mixed-integer optimal control Sager, Sebastian; Bock, Hans Georg; Diehl, Moritz Mathematical Programming, Vol. 133, Issue 1-2 https://doi.org/10.1007/s10107-010-0405-3	journal	September 2010
Leak detection methods for pipelines Billmann, L.; Isermann, R. Automatica, Vol. 23, Issue 3 https://doi.org/10.1016/0005-1098(87)90011-2	journal	May 1987
Modelling of high-pressure gas transmission lines van Deen, J. K.; Reintsema, S. R. Applied Mathematical Modelling, Vol. 7, Issue 4 https://doi.org/10.1016/0307-904X(83)90080-X	journal	August 1983
Stochastic optimal control model for natural gas networks Zavala, Victor M. Computers & Chemical Engineering, Vol. 64 https://doi.org/10.1016/j.compchemeng.2014.02.002	journal	May 2014
Instrumentation design based on optimal Kalman filtering Musulin, Estanislao; Benqlilou, Chouaib; Bagajewicz, Miguel J. Journal of Process Control, Vol. 15, Issue 6 https://doi.org/10.1016/j.jprocont.2005.03.002	journal	September 2005
Simulation and State Estimation of Transient Flow in Gas Pipeline Networks Using a Transfer Function Model Reddy, H. Prashanth; Narasimhan, Shankar; Bhallamudi, S. Murty Industrial & Engineering Chemistry Research, Vol. 45, Issue 11 https://doi.org/10.1021/ie050755k	journal	May 2006
Sensor Location for Stable Nonlinear Dynamic Systems: Multiple Sensor Case Singh, Abhay K.; Hahn, Juergen Industrial & Engineering Chemistry Research, Vol. 45, Issue 10 https://doi.org/10.1021/ie0511175	journal	May 2006
Sensor Placement in Municipal Water Networks Berry, Jonathan W.; Fleischer, Lisa; Hart, William E. Journal of Water Resources Planning and Management, Vol. 131, Issue 3 https://doi.org/10.1061/(ASCE)0733-9496(2005)131:3(237)	journal	May 2005
Sensor Placement in Municipal Water Networks with Temporal Integer Programming Models Berry, Jonathan; Hart, William E.; Phillips, Cynthia A. Journal of Water Resources Planning and Management, Vol. 132, Issue 4 https://doi.org/10.1061/(ASCE)0733-9496(2006)132:4(218)	journal	July 2006
Efficient Sensor Placement Optimization for Securing Large Water Distribution Networks Krause, Andreas; Leskovec, Jure; Guestrin, Carlos Journal of Water Resources Planning and Management, Vol. 134, Issue 6 https://doi.org/10.1061/(ASCE)0733-9496(2008)134:6(516)	journal	November 2008
Compressed sensing Donoho, D. L. IEEE Transactions on Information Theory, Vol. 52, Issue 4 https://doi.org/10.1109/TIT.2006.871582	journal	April 2006
Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin's Maximum Principle Sager, Sebastian SIAM Journal on Control and Optimization, Vol. 51, Issue 4 https://doi.org/10.1137/110835098	journal	January 2013
A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification Alexanderian, Alen; Petra, Noemi; Stadler, Georg SIAM Journal on Scientific Computing, Vol. 36, Issue 5 https://doi.org/10.1137/130933381	journal	January 2014

Cited By (3)

Multidimensional sum-up rounding for integer programming in optimal experimental design Yu, Jing; Anitescu, Mihai Mathematical Programming https://doi.org/10.1007/s10107-019-01421-z	journal	September 2019
Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems Attia, Ahmed; Alexanderian, Alen; Saibaba, Arvind K. Inverse Problems, Vol. 34, Issue 9 https://doi.org/10.1088/1361-6420/aad210	journal	July 2018
Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems Attia, Ahmed; Alexanderian, Alen; Saibaba, Arvind K. arXiv https://doi.org/10.48550/arxiv.1802.06517	text	January 2018

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42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Estimation
Scalable
Sensor data
Sensor placement

A scalable design of experiments framework for optimal sensor placement

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