Branch and Bound Algorithm for Optimal Sensor Network Design

doi:10.3182/20131218-3-IN-2045.00143

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Branch and Bound Algorithm for Optimal Sensor Network Design

Journal Article•DOI•

Branch and Bound Algorithm for Optimal Sensor Network Design

Govind Menon¹, M. Nabil¹, Sridharakumar Narasimhan¹•Institutions (1)

Indian Institute of Technology Madras¹

01 Dec 2013-IFAC Proceedings Volumes (Elsevier)-Vol. 46, Iss: 32, pp 690-695

TL;DR: In this article, a branch and bound algorithm is proposed for solving the sensor network design problem, which uses certain heuristics to obtain a solution faster, such as low rank factorization to reduce the size of the relaxed problem.

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About: This article is published in IFAC Proceedings Volumes.The article was published on 2013-12-01. It has received 3 citations till now. The article focuses on the topics: Branch and cut & Branch and bound.

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Proceedings Article•DOI•

Optimal actuator placement for linear systems with limited number of actuators

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Prasad Vilas Chanekar¹, Nikhil Chopra¹, Shapour Azarm¹•Institutions (1)

University of Maryland, College Park¹

24 May 2017

TL;DR: The optimal actuator placement problem is presented as a 0/1-mixed integer semidefinite programming problem, and is solved using the branch-and-bound procedure, and the solution procedure does not require an initial controllable actuator combination.

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Abstract: A completely controllable linear dynamical system can be steered from any given initial state to any specified final state with an application of input control energy. The input control energy is provided through a combination of actuators. It is desirable to have a limited number of actuators, which also presents the possibility of multiple actuator combinations that render the system completely controllable. Hence, the optimal actuator placement problem very important in system design. Previous studies have been mainly focused on solving the optimal actuator placement problem using greedy heuristic methods which can provide a sub-optimal solution. In this work, the optimal actuator placement problem is presented as a 0/1-mixed integer semidefinite programming problem, and is solved using the branch-and-bound procedure. The problem formulation can be applied to both stable and unstable systems, and the solution procedure does not require an initial controllable actuator combination (starting point). Although no theoretical guarantees regarding optimality of the computed solution is provided in this work, numerical simulations performed on two examples yield the global optimal solution for the optimal actuator placement problem.

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29 citations

Cites background from "Branch and Bound Algorithm for Opti..."

...The problem can be solved using branch-and-bound procedure [28]....
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Book Chapter•DOI•

Optimal sensor placement strategies for large scale systems

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Bala Shyamala Balaji¹, Sridharakumar Narasimhan¹•Institutions (1)

Indian Institute of Technology Madras¹

01 Jan 2017

TL;DR: A focus is on minimizing the estimation error which is quantified by a scalar norm of the covariance matrix of the estimates of process variables in terms of the linear model, sensor locations and the respective instrument variances.

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Abstract: Sensors play an important role in process industries for measurement, monitoring, control and diagnosis. There is a limitation on the number of measurement locations due to restrictions on cost, installation, maintenance, power and safety requirements. Hence sensor placement can be posed as an optimal design problem where the objective is to optimize a utility function subject to constraints. Our focus is on minimizing the estimation error which is quantified by a scalar norm of the covariance matrix of the estimates of process variables. Given a linear steady state or dynamic model of the process, it is possible to express the covariance matrix in terms of the linear model, sensor locations and the respective instrument variances. In this work, we propose two approximate methods to arrive at near optimal solutions to large scale problems. In the first method, we decompose the problem into two sub-problems and use a heuristic approach. In the second approach, we use Extended Cutting Plane (ECP) algorithms to arrive at near optimal solutions. We demonstrate the ideas on large scale systems and compare the results.

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1 citations

Optimal selection of sensors and controller parameters for economic optimization of process plants

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M. Nabil

01 Jan 2014

References

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Proceedings Article•DOI•

YALMIP : a toolbox for modeling and optimization in MATLAB

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Johan Löfberg

02 Sep 2004

TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.

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Abstract: The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems

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7,676 citations

"Branch and Bound Algorithm for Opti..." refers methods in this paper

...Globally optimal solutions to the above problem have been found for test cases, using the branch and bound solver available in the YALMIP software package (J. Löfberg (2004))....
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Book•

Optimization of Chemical Processes

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Thomas F. Edgar, David M. Himmelblau, Leon S. Lasdon

01 Oct 1987

TL;DR: The Nature and Organization of Optimization Problems are discussed in this article, where the authors develop models for optimisation problems and develop methods for optimization problems in the context of large scale plant design and operation.

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Abstract: I Problem Formulation 1 The Nature and Organization of Optimization Problems 2 Developing Models for Optimization 3 Formulation of the Objective Function II Optimization Theory and Methods 4 Basic Concepts of Optimization 5 Optimization for Unconstrained Functions: One- Dimensional Search 6 Unconstrained Multivariable Optimization 7 Linear Programming and Applications 8 Nonlinear Programming with Constraints 9 Mixed-Integer Programming 10 Global Optimization for Problems Containing Continuous and Discrete Variables IIIApplications of Optimization 11 Heat Transfer and Energy Conservation 12 Separation Processes 13 Fluid Flow Systems 14 Chemical Reactor Design and Operation 15 Optimization in Large-Scale Plant Design and Operations 16 Integrated Planning, Scheduling, and Control in the Process Industries Appendixes

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967 citations

Book•

Data reconciliation & gross error detection: an intelligent use of process data

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Shankar Narasimhan¹, Cornelius Jordache•Institutions (1)

Indian Institute of Technology Madras¹

01 Dec 1999

TL;DR: This work focuses on Steady State Data Reconciliation for Bilinear Systems, which combines linear algebra, graph theory, and measurement Errors and Error Reduction techniques with a focus on Gross Error Detection.

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Abstract: Introduction. Measurement Errors and Error Reduction Techniques. Steady State Data Reconciliation for Bilinear Systems. Nonlinear Steady State Data Reconciliation. Data Reconciliation in Dynamic Systems. Introduction to Gross Error Detection. Multiple Gross Error Identification Strategies for Steady State Processes. Gross Error Detection in Dynamic Processes. Design of Sensor Networks. Industrial Applications of Data Reconciliation and Gross Error Detection Technologies. Appendix A: Basic concepts of linear algebra. Appendix B: Basic concepts of Graph Theory. Appendix C: Statistical Hypotheses Testing.

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294 citations

"Branch and Bound Algorithm for Opti..." refers background or methods in this paper

...For this purpose, we use the steam metering system of a methanol synthesis plant, as described by Narasimhan and Jordache (2000). This system contains 11 process units and 28 process streams....
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...The third is a steam metering network described in Narasimhan and Jordache (2000), which is an example of a moderately sized system, with 28 variables....
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...For this purpose, we use the steam metering system of a methanol synthesis plant, as described by Narasimhan and Jordache (2000)....
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...The first, a small system, is the flow network of an ammonia process described in Narasimhan and Jordache (2000). The second, a slightly larger system, is a realistic evaporator system described in Kariwala et....
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...The first, a small system, is the flow network of an ammonia process described in Narasimhan and Jordache (2000)....
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Branch and Bound Methods

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Stephen Boyd, Jacob Mattingley

01 Jan 2003

TL;DR: In these notes the typical and simple examples of branch and bound methods are described, and some typical results are shown, for a minimum cardinality problem.

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Abstract: Branch and bound algorithms are methods for global optimization in nonconvex problems [LW66, Moo91]. They are nonheuristic, in the sense that they maintain a provable upper and lower bound on the (globally) optimal objective value; they terminate with a certificate proving that the suboptimal point found is ǫ-suboptimal. Branch and bound algorithms can be (and often are) slow, however. In the worst case they require effort that grows exponentially with problem size, but in some cases we are lucky, and the methods converge with much less effort. In these notes we describe two typical and simple examples of branch and bound methods, and show some typical results, for a minimum cardinality problem.

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287 citations

"Branch and Bound Algorithm for Opti..." refers methods in this paper

...…calculated in different ways, such as simply rounding each of the relaxed Boolean variables zj to 0 or 1, or first rounding each of the relaxed Boolean variables to 0 or 1, and then, with these values of fixed, solving the resulting convex problem in the variables x ( Boyd and Mattingley (2007))....
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...5, or using information about the Lagrange multipliers corresponding to each constraint ( Boyd and Mattingley (2007))....
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...At the outset, the upper bound may be calculated in different ways, such as simply rounding each of the relaxed Boolean variables zj to 0 or 1, or first rounding each of the relaxed Boolean variables to 0 or 1, and then, with these values of fixed, solving the resulting convex problem in the variables x ( Boyd and Mattingley (2007))....
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...…the variable selection for branching is based on some criterion, such as picking that variable whose value is closest to one or zero, picking the one whose value is closest to 0.5, or using information about the Lagrange multipliers corresponding to each constraint ( Boyd and Mattingley (2007))....
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Journal Article•DOI•

Locating sensors in complex chemical plants based on fault diagnostic observability criteria

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Rao Raghuraj¹, Mani Bhushan¹, Raghunathan Rengaswamy¹•Institutions (1)

Indian Institute of Technology Bombay¹

01 Feb 1999-Aiche Journal

TL;DR: A digraph-based approach is proposed for the problem of sensor location for identification of faults and various graph algorithms that use the developed digraph in deciding the location of sensors based on the concepts of observability and resolution are discussed.

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Abstract: Fault diagnosis is an important task for the safe and optimal operation of chemical processes. Hence, this area has attracted considerable attention from researchers in the past few years. A variety of approaches have been proposed for solving this problem. All approaches for fault detection and diagnosis in some sense involve the comparison of the observed hehavior of the process to a reference model. The process behavior is inferred using sensors measuring the important variables in the process. Hence, the efficiency of the diagnostic approach depends critically on the location of sensors monitoring the process variables. The emphasis of most of the work on fault diagnosis has been more on procedures to perform diagnosis given a set of sensors and less on the actual location of sensors for efficient identification of faults. A digraph-based approach is proposed for the problem of sensor location for identification of faults. Various graph algorithms that use the developed digraph in deciding the location of sensors based on the concepts of observability and resolution are discussed. Simple examples are provided to explain the algorithms, and a complex FCCU case study is also discussed to underscore the utility of the algorithm for large flow sheets. The significance and scope of the proposed algorithms are highlighted.

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158 citations