Tom Altman

A graph-theoretic approach to explicit nonlinear pipe network optimization

Abstract An explicit algorithm for nonlinear constrained pipe network optimization is developed. The explicit approach can be effectively used for directly determining a variety of pipe network characteristics to exactly satisfy defined values of quasi-linear boundary equality constraints. The constraint set represents stated supply pressure and volumetric flow requirements at designated critical nodes and pipes throughout the pipeline system for a range of operating conditions. The solution of the problem is based on an analytical reformulation of the quasi-linear steady-state network equilibrium equation set and the corresponding boundary specifications in terms of selected pipe system parameters. Owing to the presence of nonlinearity in these equations, the incremental Newton-Raphson method is utilized as the basic solution procedure. The solution, which is defined in a continuous variable space, is optimal in the sense that the decision parameters are calculated to meet the specified pressure and flow constraints. Every type of pipe conveying system can be optimized with this method. The solution space is secured through a well-arranged interaction between network topology, boundary constraints, and decision parameters. In order to illustrate the developed algorithm an example application is presented.

An event-driven method for modelling contaminant propagation in water networks

Abstract An efficient computer-oriented methodology is presented for use in analyzing water quality variations in drinking-water distribution systems. The proposed method can be effectively used for modelling chemical, biological, and hydraulic changes that result from distribution system activities and to predict the transient distribution of contaminants throughout the pipe system. It is predicated on the material mass balance accounting for transport and kinetic reaction processes. Perfect advective one-dimensional displacement with complete mixing of material at the network nodes is assumed. The method is event-driven and determines the optimal pipe segmentation scheme with the smallest number of segments necessary to carry out the simulation process. The resulting approach allows for dynamic water quality modelling that is less sensitive to the structure of the network and to the length of the simulation than previously proposed methods. In addition, numerical dispersion of concentration profile resolution is eliminated. The applicability of the method is illustrated using an example water distribution network. Enhancement of distribution system water quality management is a principal benefit of the methodology.

Solving the jigsaw puzzle problem in linear time

Abstract We introduce an algorithm that efficiently matches (fits together) parts of boundaries of two-dimensional objects in order to assemble apictorial jigsaw puzzles. A rotation-independent shape encoding allows us to find the best (longest) match between two shapes in time proportional to the sum of the lengths of their representations. In order to find this match, we use Weiners string matching technique combined with compact position trees to find, in linear time, the longest shared pattern between two strings. The shape matching procedure is then used by two greedy algorithms to assemble the apictorial jigsaw puzzles.

Computer modeling of water quality in large multiple-source networks

Abstract A simple and efficient computer-oriented methodology is presented for use in monitoring and modeling of steady-state water quality patterns in large multiple-source networks. The method is formulated analytically as a boundary value problem from mass balance relationships. It produces an explicit solution for the supply source contribution to delivered flows, chemical concentrations, and a range of water age parameters at designated junction nodes throughout the distribution system for a specified set of operating and loading conditions. The method is robust and reliable, and it is guaranteed to converge in an expeditious manner. The wide range of capabilities and utility of the method are illustrated by using an example network.

Convergence of Newton method in nonlinear network analysis

The convergence of Newton method in nonlinear network analysis is discussed. It is shown that formulating the nonlinear edge flow resistances in terms of edge flow rates (Flow method) or corrected loop flow rates (Loop method) gives better convergence than the nodal head or pressure formulation (Node method). This evaluation is based on the estimation of the magnitude of the radius of attraction for the Newton method. Our result applies to both water and low pressure gas networks.

EXPLICIT CALCULATION OF WATER QUALITY PARAMETERS IN PIPE DISTRIBUTION SYSTEMS

Abstract Explicit algorithms have been developed for use in water quality studies and management of distribution networks with sources of dissimilar quality. The proposed algorithms can be effectively used for directly determining a variety of blended water quality parameters for a given set of network loading and operational conditions. The parameters include the spatial distribution of constituent concentrations, the flow influence characteristics of supply sources, and the water age distribution throughout the system. The developed algorithms are formulated analytically from mass balance relationships as contingent linear boundary value problems in conjunction with a topological sorting methodology. The resulting formulations yield coefficient matrices, of order equal to the number of junction nodes, that are triangular and positive definite. The parameter solutions sought are, thus, derived through a direct application of a one step substitution process. The proposed algorithms are both robust and eff...

On the solvability of water distribution networks with unknown pipe characteristics

Necessary and sufficient conditions for the solvability of water distribution networks with unknown pipe characteristics are developed. They are predicated on the interdependence between the unknown pipe characteristics and the network hydraulic performance. These characteristics are determined to exactly satisfy defined values of nonlinear boundary equality constraints. The constraint set consists of the stated supply pressure or energy grade requirements to be maintained at critical locations throughout the distribution network. The determination of such conditions is important for a comprehensive and effective modelling and optimization of water networks.

HIGEDA: a hierarchical gene-set genetics based algorithm for finding subtle motifs in biological sequences

MOTIVATION Identification of motifs in biological sequences is a challenging problem because such motifs are often short, degenerate, and may contain gaps. Most algorithms that have been developed for motif-finding use the expectation-maximization (EM) algorithm iteratively. Although EM algorithms can converge quickly, they depend strongly on initialization parameters and can converge to local sub-optimal solutions. In addition, they cannot generate gapped motifs. The effectiveness of EM algorithms in motif finding can be improved by incorporating methods that choose different sets of initial parameters to enable escape from local optima, and that allow gapped alignments within motif models. RESULTS We have developed HIGEDA, an algorithm that uses the hierarchical gene-set genetic algorithm (HGA) with EM to initiate and search for the best parameters for the motif model. In addition, HIGEDA can identify gapped motifs using a position weight matrix and dynamic programming to generate an optimal gapped alignment of the motif model with sequences from the dataset. We show that HIGEDA outperforms MEME and other motif-finding algorithms on both DNA and protein sequences. AVAILABILITY AND IMPLEMENTATION Source code and test datasets are available for download at http://ouray.cudenver.edu/~tnle/, implemented in C++ and supported on Linux and MS Windows.

An explicit approach for modelling closed pipes in water networks

Abstract An explicit approach has been developed for use in modelling closed pipes in water distribution networks. The explicit approach is able to directly incorporate the zero-flow effect of closed pipes into the overall network modelling process. The resulting method is based on an analytical reformulation of the quasilinear set of flow continuity and energy equations governing the network hydraulics in terms of energy displacement for the individual closed pipes that exactly meet the corresponding zero-flow boundary constraint imposed. The proposed algorithm is shown to be robust and efficient, and is guaranteed to converge in an expeditious manner. The method compares favorably with others by eliminating numerical diffusion and computational instability or repetitive network topology alterations suffered by the previous procedures. An example application is presented. Enhancement of mathematical modelling of water distribution networks is a principal benefit of this methodology.

Stochastic Adaptive Stabilization via Extremum Seeking in Case of Unknown Control Directions

This technical note presents a novel extremum seeking (ES)-based algorithm for global stabilization of unstable first order linear discrete-time (LDT) stochastic systems with unknown control directions. The probing signal is a martingale difference sequence with a vanishing variance. The controller parameter estimate converges almost surely (a.s.) to the optimizing value. The sample mean-square value of the output converges (a.s.) to the minimal variance.