Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

An Acoustic Analysis of Valveless Pulsejet Engines

Valveless pulsejets are extremely simple aircraft engines; essentially cleverly designed tubes with no moving parts. These engines utilize pressure waves, instead of machinery, for thrust generation, and have demonstrated thrust-to-weight ratios over 8 and thrust specific fuel consumption levels below 1 lbm/lbf-hr – performance levels that can rival many gas turbines. Despite their simplicity and competitive performance, they have not seen widespread application due to extremely high noise and vibration levels, which have persisted as an unresolved challenge primarily due to a lack of fundamental insight into the operation of these engines. This thesis develops two theories for pulsejet operation (both based on electro-acoustic analogies) that predict measurements better than any previous theory reported in the literature, and then uses them to devise and experimentally validate effective noise reduction strategies. The first theory analyzes valveless pulsejets as acoustic ducts with axially varying area and temperature. An electro-acoustic analogy is used to calculate longitudinal mode frequencies and shapes for prescribed area and temperature distributions inside an engine. Predicted operating frequencies match experimental values to within 6% with the use of appropriate end corrections. Mode shapes are predicted and used to develop strategies for suppressing higher modes that are responsible for much of the perceived noise. These strategies are verified experimentally and via comparison to existing models/data for valveless pulsejets in the literature. The second theory analyzes valveless pulsejets as acoustic systems/circuits in which each engine component is represented by an acoustic impedance. These are assembled to form an equivalent circuit for the engine that is solved to find the frequency response. The theory is used to predict the behavior of two interacting pulsejet engines. It is validated via comparison to experiment and data in the literature. The technique is then used to develop and experimentally verify a method for operating two engines in anti-phase without interfering with thrust production. Finally, Helmholtz resonators are used to suppress higher order modes that inhibit noise suppression via anti-phasing. Experiments show that the acoustic output of two resonator-equipped pulsejets operating in anti-phase is 9 dBA less than the acoustic output of a single pulsejet.

An Analysis of Principal Attrition in a Large Urban School District

Principal attrition is a national problem particularly in large urban school districts. Research confirms that schools that serve high proportions of children living in poverty have the most difficulty attracting and retaining competent school leaders. Principals who are at the helm of high poverty schools have a higher turnover rate than the national average of three to four years and higher rates of teacher attrition. This leadership turnover has a fiscal impact on districts and negatively affects student achievement. Research identifies a myriad of reasons why administrators leave the role of principal: some leave the position for retirement; some exit based on difficulty of the role and lack of support; and some simply leave for other opportunities within and outside of the profession altogether. As expectations for both teacher and learner performance drive the national education agenda, understanding how to keep effective principals in their jobs is critical. This study examined the factors that principals in a large urban district identified as potentially affecting their decisions to stay in the position. The study utilized a multi-dimensional, web-based questionnaire to examine principals’ perceptions regarding contributing factors that impact tenure. Results indicated that: • having a quality teaching staff and establishing a positive work-life balance were important stay factors for principals; • having an effective supervisor and collegial support from other principals, were helpful supports; and • having adequate resources, time for long-term planning, and teacher support and resources were critical working conditions. Taken together, these indicators were the most frequently cited factors that would keep principals in their positions. The results were used to create a framework that may serve as a potential guide for addressing principal retention.

Assessment and Life-Cycle Analysis of Recycled Materials for Sustainable Highway

Recycled materials replacing part of virgin materials in highway applications has shown great benefits to the society and environment. Beneficial use of recycled materials can save landfill places, sparse natural resources, and energy consumed in milling and hauling virgin materials. Low price of recycled materials is favorable to cost-saving in pavement projects. Considering the availability of recycled materials in the State of Maryland (MD), four abundant recycled materials, recycled concrete aggregate (RCA), recycled asphalt pavement (RAP), foundry sand (FS), and dredged materials (DM), were studied. A survey was conducted to collect the information of current usage of the four recycled materials in States’ Department of Transportation (DOTs). Based on literature review, mechanical and environmental properties, recommendations, and suggested test standards were investigated separately for the four recycled materials in different applications. Constrains in using these materials were further studied in order to provide recommendations for the development of related MD specifications. To measure social and environmental benefits from using recycled materials, life-cycle assessment was carried out with life-cycle analysis (LCA) program, PaLATE, and green highway rating system, BEST-in-Highway. The survey results indicated the wide use of RAP and RCA in hot mix asphalt (HMA) and graded aggregate base (GAB) respectively, while FS and DM are less used in field. Environmental concerns are less, but the possibly low quality and some adverse mechanical characteristics may hinder the widely use of these recycled materials. Technical documents and current specifications provided by State DOTs are good references to the usage of these materials in MD. Literature review showed consistent results with the survey. Studies from experimental research or site tests showed satisfactory performance of these materials in highway applications, when the substitution rate, gradation, temperature, moisture, or usage of additives, etc. meet some requirements. The results from LCA revealed significant cost savings in using recycled materials. Energy and water consumption, gas emission, and hazardous waste generation generally showed reductions to some degree. Use of new recycled technologies will contribute to more sustainable highways.

An Ecological Analysis of the Potential for Moss-Based Green Roof Design

Green roofs are a maturing application of best management practices for controlling urban stormwater runoff. The majority of green roofs are planted with drought resistant, higher plant species, such as the genus Sedum. However, other plant varieties, such as mosses, may be equally applicable. Residential roofs and natural terrestrial communities were sampled in both Maryland and Tennessee to determine moss community structure and species water composition. This served as a natural analog for potential green roof moss communities. During sampling, 21 species of moss were identified throughout the 37 total sites. The average percent moss cover and water composition across all roof sites was 40.7% and 38.6%, respectively and across all natural sites, 76.7% and 47.7%, respectively. Additional maximum water holding capacity procedures were completed on sedum and 19 of the 21 sampled moss species to assess their individual potential for stormwater absorption. Sedum species on average held 166% of their biomass in water, while moss species held 732%. The results of this study are used as a basis to propose moss species that will improve green roof performance.