SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Reaction Control in Quiescent Systems of Free-Radical Retrograde-Precipitation Polymerization

Free-radical retrograde-precipitation polymerization, FRRPP in short, is a novel polymerization process discovered by Dr. Gerard Caneba in the late 1980s. The current study is aimed at gaining a better understanding of the reaction mechanism of the FRRPP and its thermodynamically-driven features that are predominant in controlling the chain reaction. A previously developed mathematical model to represent free radical polymerization kinetics was used to simulate a classic bulk polymerization system from the literature. Unlike other existing models, such a sparse-matrix-based representation allows one to explicitly accommodate the chain length dependent kinetic parameters. Extrapolating from the past results, mixing was experimentally shown to be exerting a significant influence on reaction control in FRRPP systems. Mixing alone drives the otherwise severely diffusion-controlled reaction propagation in phase-separated polymer domains. Therefore, in a quiescent system, in the absence of mixing, it is possible to retard the growth of phase-separated domains, thus producing isolated polymer nanoparticles (globules). Such a diffusion-controlled, self-limiting phenomenon of chain growth was also observed using time-resolved small angle x-ray scattering studies of reaction kinetics in quiescent systems of FRRPP. Combining the concept of self-limiting chain growth in quiescent FRRPP systems with spatioselective reaction initiation of lithography, microgel structures were synthesized in a single step, without the use of molds or additives. Hard x-rays from the bending magnet radiation of a synchrotron were used as an initiation source, instead of the more statistally-oriented chemical initiators. Such a spatially-defined reaction was shown to be self-limiting to the irradiated regions following a polymerization-induced self-assembly phenomenon. The pattern transfer aspects of this technique were, therefore, studied in the FRRP polymerization of N-isopropylacrylamide (NIPAm) and methacrylic acid (MAA), a thermoreversible and ionic hydrogel, respectively. Reaction temperature increases the contrast between the exposed and unexposed zones of the formed microgels, while the irradiation dose is directly proportional to the extent of phase separation. The response of Poly (NIPAm) microgels prepared from the technique described in this study was also characterized by small angle neutron scattering.

MODELING OF TRANSFER PATH FOR DETERMINATION OF COMBUSTION AND NOISE METRICS ON DIESEL ENGINES

Determination of combustion metrics for a diesel engine has the potential of providing feedback for closed-loop combustion phasing control to meet current and upcoming emission and fuel consumption regulations. This thesis focused on the estimation of combustion metrics including start of combustion (SOC), crank angle location of 50% cumulative heat release (CA50), peak pressure crank angle location (PPCL), and peak pressure amplitude (PPA), peak apparent heat release rate crank angle location (PACL), mean absolute pressure error (MAPE), and peak apparent heat release rate amplitude (PAA). In-cylinder pressure has been used in the laboratory as the primary mechanism for characterization of combustion rates and more recently in-cylinder pressure has been used in series production vehicles for feedback control. However, the intrusive measurement with the in-cylinder pressure sensor is expensive and requires special mounting process and engine structure modification. As an alternative method, this work investigated block mounted accelerometers to estimate combustion metrics in a 9L I6 diesel engine. So the transfer path between the accelerometer signal and the in-cylinder pressure signal needs to be modeled. Depending on the transfer path, the in-cylinder pressure signal and the combustion metrics can be accurately estimated - recovered from accelerometer signals. The method and applicability for determining the transfer path is critical in utilizing an accelerometer(s) for feedback. Single-input single-output (SISO) frequency response function (FRF) is the most common transfer path model; however, it is shown here to have low robustness for varying engine operating conditions. This thesis examines mechanisms to improve the robustness of FRF for combustion metrics estimation. First, an adaptation process based on the particle swarm optimization algorithm was developed and added to the single-input single-output model. Second, a multiple-input single-output (MISO) FRF model coupled with principal component analysis and an offset compensation process was investigated and applied. Improvement of the FRF robustness was achieved based on these two approaches. Furthermore a neural network as a nonlinear model of the transfer path between the accelerometer signal and the apparent heat release rate was also investigated. Transfer path between the acoustical emissions and the in-cylinder pressure signal was also investigated in this dissertation on a high pressure common rail (HPCR) 1.9L TDI diesel engine. The acoustical emissions are an important factor in the powertrain development process. In this part of the research a transfer path was developed between the two and then used to predict the engine noise level with the measured in-cylinder pressure as the input. Three methods for transfer path modeling were applied and the method based on the cepstral smoothing technique led to the most accurate results with averaged estimation errors of 2 dBA and a root mean square error of 1.5dBA. Finally, a linear model for engine noise level estimation was proposed with the in-cylinder pressure signal and the engine speed as components.