Congestion and oversaturated roads pose significant problems and create delays in every major city in the world. Before this problem can be addressed, we must know how much traffic is flowing over the links in the network. We transform a road network into a directed graph with a network flow function, and ask the question, “What subset of vertices (intersections) should be monitored such that knowledge of the flow passing through these vertices is sufficient to calculate the flow everywhere in the graph?” To minimize the cost of placing sensors, we seek the smallest number of monitored vertices. This is known as the Sensor Location Problem (SLP). We explore conditions under which a set of monitored vertices produces a unique solution to the problem and disprove a previous result published on the problem. Finally, we explore a matrix formulation of the problem and present cases when the flow can or cannot be calculated on the graph.

Optimal sensor placement is an important problem with many applications; placing thermostats in rooms, installing pressure sensors in chemical columns or attaching vibration detection devices to structures are just a few of the examples. Frequently, this placement problem is encountered while noise is present. The H_2-optimal control is a strategy designed for systems that have exogenous disturbing inputs. Therefore, one approach for the optimal sensor location problem is to combine it with the H_2-optimal control. In this work the H_2-optimal control is explained and combined with the sensor placement problem to create the H_2-optimal sensor location problem. The problem is examined for the one-dimensional beam equation and the two-dimensional diffusion equation in an L-shaped region. The optimal sensor location is calculated numerically for both models and multiple scenarios are considered where the location of the disturbance and the actuator are varied. The effect of different model parameters such as the weight of the state and the disturbance are investigated. The results show that the optimal sensor location tends to be close to the disturbance location.

The distance to uncontrollability of a controllable linear system is a measure of the degree of perturbation a system can undergo and remain controllable. The definition of the distance to uncontrollability leads to a non-convex optimization problem in two variables. In 2000 Gu proposed the first polynomial time algorithm to compute this distance. This algorithm relies heavily on efficient eigenvalue solvers. In this work we examine two alternative algorithms that result in linear matrix inequalities. For the first algorithm, proposed by Ebihara et. al., a semidefinite programming problem is derived via the Kalman-Yakubovich-Popov (KYP) lemma. The dual formulation is also considered and leads to rank conditions for exactness verification of the approximation. For the second algorithm, by Dumitrescu, Şicleru and Ştefan, a semidefinite programming problem is derived using a sum-of-squares relaxation of an associated matrix-polynomial and the associated Gram matrix parameterization. In both cases the optimization problems are solved using primal-dual-interior point methods that retain positive semidefiniteness at each iteration. Numerical results are presented to compare the three algorithms for a number of benchmark examples. In addition, we also consider a system that results from a finite element discretization of the one-dimensional advection-diffusion equation. Here our objective is to test these algorithms for larger problems that originate in PDE-control. / Master of Science

The current computer models used for simulating water quality in potable water distribution systems assume perfect mixing at pipe junctions and non-dispersive solute transport in pipe flows. To improve the prediction accuracy, the present study examines and expands these modeling assumptions using transport phenomena analyses. Whereas the level of solute mixing at a cross-type junction is evaluated numerically via Computational Fluid Dynamics (CFD), the axial transport in laminar flows is investigated with both CFD simulations and corresponding experimental runs in a single pipe. The findings show that solute mixing at junctions is rather incomplete owing to the limited spatio-temporal interaction that occurs between incoming flows with different qualities. Incomplete mixing shifts the expected propagation patterns of a chemical or microbial constituent from widely-spread to narrowly-concentrated over the service area. On the other hand, solute dispersion is found to prevail over advective transport in laminar pipe flows. Thus, this work develops axial dispersion rates through parameter optimization techniques. By accounting for axial dispersive effects, the patterns of solute delivery shifted from high concentrations over short time periods to lower doses at prolonged exposure times. In addition, the present study integrates the incomplete mixing model into the optimal placement of water quality monitoring stations aimed at detecting contaminant intrusions.

Master of Science / Department of Mechanical and Nuclear Engineering / Mohammad H. Hosni / Each year millions of people travel by commercial aircrafts. The Bureau of Transportation Statistics indicates that about 600 million passengers fly each year in the United States and, of those, roughly 350,000 are international travelers. This number of travelers leaves commercial airliners potentially vulnerable to biological contamination and makes the transmission of diseases a serious threat. The spread of SARS (Severe Acute Respiratory Syndrome) and H1N1 (swine flu) are examples of documented cases. Consequently, considerable research has been and continues to be conducted to study and understand particulate transport mechanisms and dispersion behavior inside aircraft cabins to develop means for detecting, controlling, and removing contaminants from aircraft cabins and to find methods for preventing the aircraft from being used for intentional contaminant deployment. In order to develop means to monitor and control air quality, infectious disease transmission, and particulate transport inside aircraft cabins, an experimental study was conducted to determine the best sensor placement locations for detection and to identify the number of sensors needed to accurately track air quality incidents within a cabin. An 11-row mockup, intended to be representative of a typical wide-body aircraft, was used for the research. The mockup interior is based on the actual dimensions of the Boeing 767 aircraft cabin. Inside the mockup cabin, actual aircraft equipment including seats and air diffusers were used. Each row has seven passenger seats. Particulates were released from different locations in the second row of the mockup cabin. The transported particles were then collected at six different locations in the lateral direction. The best location to place a sensor was defined as the location having the strongest signal (maximum number of particles collected) or the fastest detection time. After determining the best location in the lateral direction, particles were collected at the same location, but in different rows to estimate the differences between the signal strength and the delay time in detecting the signal from row to row. For the later investigation, the particulates were released in Row 2 and in Row 6 as well. For the six locations examined, it was found that the best location for the placement of a sensor in the 11-row mockup in the lateral direction is on the centerline near the cabin floor. Longitudinally, it was found that a sensor may be used for detecting particulates in the same row as the release and a row in front and in back of the release location. For the mockup cabin, a total of 4 sensors was recommended to monitor particulate releases in the 11 row mockup cabin, each of these sensors separated by two rows.