Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Wastewater treatment by novel hybrid biological – ion exchange processes

This study presents two novel methods for treating important environmental contaminants from two different wastewater streams. One process utilizes the kinetic advantages and reliability of ion exchanging clinoptilolite in combination with biological treatment to remove ammonium from municipal sewage. A second process, HAMBgR (Hybrid Adsorption Membrane Biological Reactor), combines both ion exchange resin and bacteria into a single reactor to treat perchlorate contaminated waters. Combining physicochemical adsorptive treatment with biological treatment can provide synergistic benefits to the overall removal processes. Ion exchange removal solves some of the common operational reliability limitations of biological treatment, like slow response to environmental changes and leaching. Biological activity can in turn help reduce the economic and environmental challenges of ion exchange processes, like regenerant cost and brine disposal. The second section of this study presents continuous flow column experiments, used to demonstrate the ability of clinoptilolite to remove wastewater ammonium, as well as the effectiveness of salt regeneration using highly concentrated sea salt solutions. The working capacity of clinoptilolite more than doubled over the first few loading cycles, while regeneration recovered more than 98% of ammonium. Using the regenerant brine for subsequent halotolerant algae growth allowed for its repeated use, which could lead to cost savings and production of valuable algal biomass. The algae were able to uptake all ammonium in solution, and the brine was able to be used again with no loss in regeneration efficiency. This process has significant advantages over conventional biological nitrification; shorter retention times, wider range of operational conditions, and higher quality effluent free of nitrate. Also, since the clinoptilolite is continually regenerated and the regenerant is rejuvenated by algae, overall input costs are expected to be low. The third section of this study introduces the HAMBgR process for the elimination of perchlorate and presents batch isotherm experiments and pilot reactor tests. Results showed that a variety of ion-exchange resins can be effectively and repeatedly regenerated biologically, and maintain an acceptable working capacity. The presence of an adsorbent in the HAMBgR process improved bioreactor performance during operational fluctuations by providing a physicochemical backup to the biological process. Pilot reactor tests showed that the HAMBgR process reduced effluent perchlorate spikes by up to 97% in comparison to a conventional membrane bio-reactor (MBR) that was subject to sudden changes in influent conditions. Also, the HAMBgR process stimulated biological activity and lead to higher biomass concentrations during increased contaminant loading conditions. Conventional MBR systems can be converted into HAMBgR’s at a low cost, easily justifiable by the realized benefits. The concepts employed in the HAMBgR process can be adapted to treat other target contaminants, not just perchlorate.

Soft computing based parameter identification in pavements and geomechanical systems

Accurate estimation of road pavement geometry and layer material properties through the use of proper nondestructive testing and sensor technologies is essential for evaluating pavement’s structural condition and determining options for maintenance and rehabilitation. For these purposes, pavement deflection basins produced by the nondestructive Falling Weight Deflectometer (FWD) test data are commonly used. The nondestructive FWD test drops weights on the pavement to simulate traffic loads and measures the created pavement deflection basins. Backcalculation of pavement geometry and layer properties using FWD deflections is a difficult inverse problem, and the solution with conventional mathematical methods is often challenging due to the ill-posed nature of the problem. In this dissertation, a hybrid algorithm was developed to seek robust and fast solutions to this inverse problem. The algorithm is based on soft computing techniques, mainly Artificial Neural Networks (ANNs) and Genetic Algorithms (GAs) as well as the use of numerical analysis techniques to properly simulate the geomechanical system. A widely used pavement layered analysis program ILLI-PAVE was employed in the analyses of flexible pavements of various pavement types; including full-depth asphalt and conventional flexible pavements, were built on either lime stabilized soils or untreated subgrade. Nonlinear properties of the subgrade soil and the base course aggregate as transportation geomaterials were also considered. A computer program, Soft Computing Based System Identifier or SOFTSYS, was developed. In SOFTSYS, ANNs were used as surrogate models to provide faster solutions of the nonlinear finite element program ILLI-PAVE. The deflections obtained from FWD tests in the field were matched with the predictions obtained from the numerical simulations to develop SOFTSYS models. The solution to the inverse problem for multi-layered pavements is computationally hard to achieve and is often not feasible due to field variability and quality of the collected data. The primary difficulty in the analysis arises from the substantial increase in the degree of non-uniqueness of the mapping from the pavement layer parameters to the FWD deflections. The insensitivity of some layer properties lowered SOFTSYS model performances. Still, SOFTSYS models were shown to work effectively with the synthetic data obtained from ILLI-PAVE finite element solutions. In general, SOFTSYS solutions very closely matched the ILLI-PAVE mechanistic pavement analysis results. For SOFTSYS validation, field collected FWD data were successfully used to predict pavement layer thicknesses and layer moduli of in-service flexible pavements. Some of the very promising SOFTSYS results indicated average absolute errors on the order of 2%, 7%, and 4% for the Hot Mix Asphalt (HMA) thickness estimation of full-depth asphalt pavements, full-depth pavements on lime stabilized soils and conventional flexible pavements, respectively. The field validations of SOFTSYS data also produced meaningful results. The thickness data obtained from Ground Penetrating Radar testing matched reasonably well with predictions from SOFTSYS models. The differences observed in the HMA and lime stabilized soil layer thicknesses observed were attributed to deflection data variability from FWD tests. The backcalculated asphalt concrete layer thickness results matched better in the case of full-depth asphalt flexible pavements built on lime stabilized soils compared to conventional flexible pavements. Overall, SOFTSYS was capable of producing reliable thickness estimates despite the variability of field constructed asphalt layer thicknesses.