It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errors-in-variables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errors-in-variables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multi-equation model similar to the simultaneous-equations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multi-equation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.

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"This dissertation documents a study on parameter estimation methods for comprehensive pyrolysis modeling. There are four parts to this work, which are (1) evaluating effects of applying different kinetic models to pyrolysis modeling of fiberglass reinforced polymer composites; (2); evaluation of pyrolysis parameters for fiberglass reinforced polymer composites based on multi-objective optimization; (3) parameter estimation for comprehensive pyrolysis modeling: guidance and critical observations; and (4) engineering guide for estimating material pyrolysis properties for fire modeling. In the first section (Section 1), evaluation work is conducted to determine the effects of applying different kinetic models (KMs), developed based on thermal analysis using TGA data, when used in typical 1D pyrolysis models of fiberglass reinforced polymer (FRP) composites. The study shows that that increasing complexity of KMs to be used in pyrolysis modeling is unnecessary for the FRP samples investigated. Additionally, the findings from this research indicates that the basic assumption of considering thermal decomposition of each computational cell in comprehensive pyrolysis modeling as equivalent to that in a TGA experiment becomes inapplicable at depth and higher heating rates. The second part of this dissertation (Section 2) reports the results from a study conducted to investigate the ability of global, multi-objective and multi-variable optimization methods to estimate material parameters for comprehensive pyrolysis models. The research materials are two fiberglass reinforced polymer (FRP) composites that share the same fiberglass mats but with two different resin systems. One resin system is composed of a single component and the other system is composed of two components (resin and fire retardant additive). The results show that for a well-configured parameter estimation exercise using the optimization method described above, (1) estimated results are within ± 100% of the measurements in general; (2) increasing complexity of the kinetic modeling for a single component system has insignificant effect on estimated values; (3) increasing complexity of the kinetic modeling for a multiple component system with each element having different thermal characteristics has positive effect on estimated values; and (4) parameter estimation using an optimization method with appropriate level of complexity in kinetic model and optimization targets can find estimations that can be considered as effective material property values. The third part of this dissertation (Section 3) proposes a process for conducting parameter estimation for comprehensive pyrolysis models. The work describes the underlying concepts considered in the proposed process and gives discussions of its limitations. Additionally, example cases of parameter estimation exercise are shown to illustrate the application of the parameter estimation process. There are four materials considered in the example cases – thermoplastics (PMMA), corrugated cardboard, fiberglass reinforced polymer composites and plywood. In the last part (Section 4), the actual Guide, a standardized procedure for obtaining material parameters for input into a wide range of pyrolysis models is presented. This is a step-by-step process that provides a brief description of modeling approaches and assumptions; a typical mathematical formulation to identify model parameters in the equations; and methods of estimating the model parameters either by independent measurements or optimization in pair with the model. In the Guide, example cases are given to show how the process can be applied to different types of real-world materials. "

This thesis focuses on estimation and inference for a large class of semiparametric estimands: the class of continuous functionals of regression functions. This class includes a number of estimands derived from causal inference problems, among then the average treatment effect for a binary treatment when treatment assignment is unconfounded and many of its generalizations for non-binary treatments and individualized treatment policies. Chapter 2, based on work with Stefan Wager, introduces the augmented minimax linear es- timator (AMLE), a general approach to the problem of estimating a continuous linear functional of a regression function. In this approach, we estimate the regression function, then subtract from a simple plug-in estimator of the functional a weighted combination of the estimated regression function’s residuals. For this, we use weights chosen to minimize the maximum of the mean squared error of the resulting estimator over regression functions in a chosen neighborhood of our estimated regression function. These weights are shown to be a universally consistent estimator our linear functional’s Riesz representer, the use of which would result in an exact bias correction for our plug- in estimator. While this convergence can be slow, especially when the Riesz representer is highly nonsmooth, the action of these weights on functions in the aforementioned neighborhood imitates that of the Riesz representer accurately even when they are slow to converge in other respects. As a result, we show that under no regularity conditions on the Riesz representer and minimal regularity conditions on the regression function, the proposed estimator is semiparametrically efficient. In simulation, it is shown to perform very well in the context of estimating the average partial effect in the conditional linear model, a simultaneous generalization of the average treatment effect to address continuous-valued treatments and of the partial linear model to address treatment effect heterogeneity. Chapter 3, based on work with Arian Maleki and José Zubizarreta, studies the minimax linear estimator, a simplified version of the AMLE in which the estimated regression function is taken to be zero, for a class of estimands generalizing the mean with outcomes missing at random. We show semiparametric efficiency under conditions that are only slightly stronger than those required for the AMLE. In addition, we bound the deviation of our estimator’s error from the averaged efficient influence function, characterizing the degree to which the first order asymptotic characterization of semiparametric efficiency is meaningful in finite samples. In simulation, this estimator is shown to perform well relative to alternatives in high-noise, small-sample settings with limited overlap between the covariate distribution of missing and nonmissing units, a setting that is challenging for approaches reliant on accurate estimation of either or both of the regression function and the propensity score. Chapter 4 discusses an approach to rounding linear estimators for the targeted average treatment effect into matching estimators. The targeted average treatment effect is a generalization of the average treatment effect and the average treatment effect on the treated units.

Parameter-Driven Systems (PDS) are widely used in commerce for large-scale applications. Reusability is achieved with a PDS design by relocating implicit control structures in the software and the storage of explicit data in database files. This approach can accommodate various user requirements without tedious modification of the software. In order to specify appropriate parameters in a system, knowledge of both business activities and system behaviour are required. For large, complex software packages, this task becomes time consuming and requires specialist knowledge, yet the consistency and correctness still cannot be guaranteed. My research studied the types of knowledge required and agents involved in the PDS customisation. The work also identified the associated problems and constraints. A solution is proposed and implemented as an Intelligent Assistant prototype than a manual approach. Three areas of achievement have been highlighted: 1. The characteristics and problems of maintaining parameter instances in a PDS are defined. It is found that the verification is not complete with the technical/structural knowledge alone, but a context is necessary to provide semantic information and related business activities (thus the implemented parameters) so that mainline functions can relate with each other. 2. A knowledge-based modelling approach has been proposed and demonstrated via a practical implementation. A Specification Language was designed which can model various types of knowledge in a PDS and encapsulate relationships. The Knowledge-Based System (KBS) developed verifies parameters based on the interpreted model of a given context. 3. The performance of the Intelligent Assistant prototype was well received by the domain specialist from the participating organisation. The modelling and KBS approach developed in my research offers considerable promise in solving practical problems in the software industry.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

In this thesis, three model-based methods are presented for finding the location of a point source with possibly time-varying strength for a class of distributed parameter systems. The first method involves off-line numerical computation of the time-response data at the sensor(s) from all possible source locations and functions of source strength, and comparison of these data with actual measurements. The second method involves approximation of the infinite-dimensional distributed parameter system by a finite-dimensional lumped parameter system: the partial differential and/or integral equations describing the distributed parameter system are replaced by a set of ordinary differential equations, which are obtained through finite difference or finite element methods. The resulting model is used to construct an auto-regressive (AR) filter that takes the sensor data as inputs and produces a scalar output whose value determines the source location. The third method involves off -line steady-state solution of an adjoint problem based on the dual system model. The solutions are used to construct localization functions whose contours, corresponding to a set of sensor data, provide an estimate of the source location. For each method, the sensor data evaluation algorithm is presented, and analysis is given of appropriate sensor placement and the minimal required number of sensors. The robustness of each method to sensor noise and modeling inaccuracies is studied, and techniques to improve robustness are discussed. These techniques include strategic sensor placement to reduce sensitivity to noise and modeling inaccuracies, and prioritization of sensor data in the data evaluation algorithms. In all three methods, a minimal amount of on-line computation is required. The methods are applied to the two-dimensional heat conduction problem with Robin's boundary conditions, and their performances are tested via computer simulations. The thesis concludes with a discussion of the relative strengths and shortcomings of each method and suggestions for future research. / Graduation date: 1999

Methods are presented for parameter identification of an annular gas seal on a flexiblerotor test rig. Dynamic loads are applied by magnetic bearings (MBs) that support the rotor. MB forces are measured using fiber-optic strain gauges that are bonded to the poles of the MBs. In addition to force and position measurements, a finite element (FE) rotor model is required for the identification algorithms. The FE rotor model matches free-free characteristics of the test rotor. The addition of smooth air seals to the system introduces stiffness and damping terms for identification that are representative of reaction forces in turbomachines. Tests are performed to experimentally determine seal stiffness and damping coefficients for different running speeds and preswirl conditions. Stiffness and damping coefficients are determined using a frequency domain identification method. This method uses an iterative approach to minimize error between theoretical and experimental transfer functions. Several time domain approaches are also considered; however, these approaches do not produce valid identification results. Stiffness coefficients are measured using static test results and an MB current and position based model. Test results produce seal coefficients with low uncertainties for the frequency domain identification method. Static test uncertainties are an order of magnitude larger, and time domain attempts fail to produce sealIn addition to the primary identification research, an investigation of the relationships between MB force, strain, and magnetic field is conducted. The magnetic field of an MB is modeled using commercial FE software. The magnetic field model is used to predict strain measurements for quasi-static test conditions. The strain predictions are compared with experimental strain measurements. Strain predictions agree with experimental measurements, although strain is typically over-predicted. coefficient measurements.