# Real-time, large scale optimization of water network systems using a subdomain approach.

## Abstract

Certain classes of dynamic network problems can be modeled by a set of hyperbolic partial differential equations describing behavior along network edges and a set of differential and algebraic equations describing behavior at network nodes. In this paper, we demonstrate real-time performance for optimization problems in drinking water networks. While optimization problems subject to partial differential, differential, and algebraic equations can be solved with a variety of techniques, efficient solutions are difficult for large network problems with many degrees of freedom and variable bounds. Sequential optimization strategies can be inefficient for this problem due to the high cost of computing derivatives with respect to many degrees of freedom. Simultaneous techniques can be more efficient, but are difficult because of the need to solve a large nonlinear program; a program that may be too large for current solver. This study describes a dynamic optimization formulation for estimating contaminant sources in drinking water networks, given concentration measurements at various network nodes. We achieve real-time performance by combining an efficient large-scale nonlinear programming algorithm with two problem reduction techniques. D Alembert's principle can be applied to the partial differential equations governing behavior along the network edges (distribution pipes). This allows us to approximatemore »

- Authors:

- (Carnegie Mellon University, Pittsburgh, PA)

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 988560

- Report Number(s):
- SAND2005-1655C

TRN: US201018%%559

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: Proposed for presentation at the EWRI Congress 2005 held May 16-18, 2005 in Anvhrage, AL.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; CONTAMINATION; DEGREES OF FREEDOM; DISTRIBUTION; DRINKING WATER; EFFICIENCY; NONLINEAR PROGRAMMING; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; TIME DELAY; WATER; WINDOWS

### Citation Formats

```
van Bloemen Waanders, Bart Gustaaf, Biegler, Lorenz T., and Laird, Carl Damon.
```*Real-time, large scale optimization of water network systems using a subdomain approach.*. United States: N. p., 2005.
Web.

```
van Bloemen Waanders, Bart Gustaaf, Biegler, Lorenz T., & Laird, Carl Damon.
```*Real-time, large scale optimization of water network systems using a subdomain approach.*. United States.

```
van Bloemen Waanders, Bart Gustaaf, Biegler, Lorenz T., and Laird, Carl Damon. Tue .
"Real-time, large scale optimization of water network systems using a subdomain approach.". United States.
```

```
@article{osti_988560,
```

title = {Real-time, large scale optimization of water network systems using a subdomain approach.},

author = {van Bloemen Waanders, Bart Gustaaf and Biegler, Lorenz T. and Laird, Carl Damon},

abstractNote = {Certain classes of dynamic network problems can be modeled by a set of hyperbolic partial differential equations describing behavior along network edges and a set of differential and algebraic equations describing behavior at network nodes. In this paper, we demonstrate real-time performance for optimization problems in drinking water networks. While optimization problems subject to partial differential, differential, and algebraic equations can be solved with a variety of techniques, efficient solutions are difficult for large network problems with many degrees of freedom and variable bounds. Sequential optimization strategies can be inefficient for this problem due to the high cost of computing derivatives with respect to many degrees of freedom. Simultaneous techniques can be more efficient, but are difficult because of the need to solve a large nonlinear program; a program that may be too large for current solver. This study describes a dynamic optimization formulation for estimating contaminant sources in drinking water networks, given concentration measurements at various network nodes. We achieve real-time performance by combining an efficient large-scale nonlinear programming algorithm with two problem reduction techniques. D Alembert's principle can be applied to the partial differential equations governing behavior along the network edges (distribution pipes). This allows us to approximate the time-delay relationships between network nodes, removing the need to discretize along the length of the pipes. The efficiency of this approach alone, however, is still dependent on the size of the network and does not scale indefinitely to larger network models. We further reduce the problem size with a subdomain approach and solve smaller inversion problems using a geographic window around the area of contamination. We illustrate the effectiveness of this overall approach and these reduction techniques on an actual metropolitan water network model.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2005},

month = {3}

}