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This thesis presents simple efficient algorithms to estimate distribution parameters and to construct prediction intervals for location-scale families. Specifically, we study two scenarios: one is a frequentist method for a general location--scale family and then extend to a 3-parameter distribution, another is a Bayesian method for the Gumbel distribution. At the end of the thesis, a generalized bootstrap resampling scheme is proposed to construct prediction intervals for data with an unknown distribution. Our estimator construction begins with the equivariance principle, and then makes use of unbiasedness principle. These two estimates have closed form and are functions of the sample mean, sample standard deviation, sample size, as well as the mean and variance of a corresponding standard distribution. Next, we extend the previous result to estimate a 3-parameter distribution which we call a mixed method. A central idea of the mixed method is to estimate the location and scale parameters as functions of the shape parameter. The sample mean is a popular estimator for the population mean. The mean squared error (MSE) of the sample mean is often large, however, when the sample size is small or the scale parameter is greater than the location parameter. To reduce the MSE of our location estimator, we introduce an adaptive estimator. We will illustrate this by the example of the power Gumbel distribution. The frequentist approach is often criticized as failing to take into account the uncertainty of an unknown parameter, whereas a Bayesian approach incorporates such uncertainty. The present Bayesian analysis for the Gumbel data is achieved numerically as it is hard to obtain an explicit form. We tackle the problem by providing an approximation to the exponential sum of Gumbel random variables. Next, we provide two efficient methods to construct prediction intervals. The first one is a Monte Carlo method for a general location-scale family, based on our previous parameter estimation. Another is the Gibbs sampler, a special case of Markov Chain Monte Carlo. We derive the predictive distribution by making use of an approximation to the exponential sum of Gumbel random variables . Finally, we present a new generalized bootstrap and show that Efron's bootstrap re-sampling is a special case of the new re-sampling scheme. Our result overcomes the issue of the bootstrap of its ``inability to draw samples outside the range of the original dataset.'' We give an applications for constructing prediction intervals, and simulation shows that generalized bootstrap is better than that of the bootstrap when the sample size is small. The last contribution in this thesis is an improved GRS method used in nuclear engineering for construction of non-parametric tolerance intervals for percentiles of an unknown distribution. Our result shows that the required sample size can be reduced by a factor of almost two when the distribution is symmetric. The confidence level is computed for a number of distributions and then compared with the results of applying the generalized bootstrap. We find that the generalized bootstrap approximates the confidence level very well. / Dissertation / Doctor of Philosophy (PhD)

This thesis focuses on utilizing the persistent voltage vector injections by finite control set model predictive control (FCSMPC) to enable simultaneous estimations of both position and parameters in order to realize robust sensorless interior permanent magnet synchronous machine (IPMSM) drives valid at the entire operating region including no-load standstill without any additional signal injection and switchover. The system (here, IPMSM) needs to meet certain observability conditions to identify the parameters and position. Moreover, each combination of the parameters and/or position involves different observability requirements which cannot be accomplished at every operating point. In particular, meeting the observability for parameters and position at no-load standstill is more challenging. This is overcome by generating persistent excitation in the system with high-frequency signal injection. The FCSMPC scheme inherently features the persistent excitation with voltage vector injection and hence no additional signal injection is required. Moreover, the persistent excitation always exists for FCSMPC except at the standstill where the control applies the null vectors when the reference currents are zero. However, introducing a small negative d axis current at the standstill would be sufficient to overcome this situation.The parameter estimations are investigated at first in this thesis. The observability is analyzed for the combinations of two, three and four parameters and experimentally validated by online identification based on recursive least square (RLS) based adaptive observer. The worst case operating points concerning observability are identified and experimentally proved that the online identification of all the parameter combinations could be accomplished with persistent excitation by FCMPC. Moreover, the effect of estimation error in one parameter on the other known as parameter coupling is reduced with the proposed decoupling technique. The persistent voltage vector injections by FCSMPC help to meet the observability conditions for estimating the position, especially at low speeds. However, the arbitrary nature of the switching ripples and absence of PWM modulator void the possibility of applying the standard demodulation based techniques for FCSMPC. Consequently, a nonlinear optimization based observer is proposed to estimate both the position and speed, and experimentally validated from standstill to maximum speed. Furthermore, a compensator is also proposed that prevents converging to saddle and symmetrical ( ambiguity) solutions. The robustness analysis of the proposed nonlinear optimization based observer shows that estimating the position without co-estimating the speed is more robust and the main influencing parameters on the accuracy of the position estimation are d and q inductances. Subsequently, the proposed nonlinear optimization based observer is extended to simultaneously estimate the position, d and q inductances. The experimental results show the substantial improvements in response time, and reduction in both steady and transient state position errors. In summary, this thesis presents the significance of persistent voltage vector injections in estimating both parameter and position, and also shows that nonlinear optimization based technique is an ideal candidate for robust sensorless FCSMPC. / Thesis / Doctor of Philosophy (PhD)

Physics-based electrochemical models are useful tools for optimizing battery cell and material design, managing battery use, and understanding physical phenomena, all of which are key in enabling adoption of batteries to electrify transportation, grid storage, and other high carbon emission industries. Fitting these models to experiments can be a useful approach to determine missing parameters that may be difficult to identify experimentally. In this dissertation, two use cases of this approach — model parameterization and degradation tracking — are explored. An introduction to the need for batteries and an overview of challenges in the field is presented in Chapter 1. Of these challenges, those that can be addressed by battery modeling solutions are discussed in further detail. An overview of continuum level physics-based electrochemical models is provided, and the case is made for the utility of parameter estimation. In Chapter 2, an extension of a published model for lithium trivandate cathodes for lithiumion batteries is outlined. While the original model described (de)lithiation and phase change in the cathode, the new model describes simultaneous lithiation of the original phase, lithiation of the newly formed phase, and phase change. Parameters associated with the thermodynamics and kinetics of charge transfer and lithium transport in the second phase are estimated directly from experimental data. This study serves as an example of using the model fitting approach to determine model parameters that would be difficult to isolate and measure experimentally. Chapter 3 explores a similar concept of model parameterization, this time focusing on the electrode tortuosity. Tortuosity is a hard to quantify parameter that describes how tortuous of a path lithium ions must travel through an electrode or separator. Because there are several experimental measurement techniques suggested in the literature that do not always provide consistent results, an approach to fit the tortuosity to a standard rate capability experiment is introduced. The Bayesian approach returns uncertainties in tortuosity estimates, which can be used to predict a range of outcomes for high-rate performance. Covariance between parameters in the model and their impact on uncertainties in tortuosity is also discussed. Beyond model parameterization, parameter estimation can also be useful in the context of tracking degradation by fitting a physics-based model over the course of cycling and interpreting the evolution of the parameter estimates. In Chapter 4, this idea is explored by fitting the model developed in Chapter 2 to cycling of an LVO cell. Parameter estimates are interpreted in conjunction with traditional tear down and electrochemical analysis to identify root causes of degradation for this cell. Depending on the number of parameters being simultaneously estimated, it can become an onerous task to fit model parameters, especially if the physics-based model cannot easily be enclosed in an efficient optimization algorithm. To this end, machine learning (ML) can be useful. If a ML model is trained offline on synthetic data generated by a battery model to map the observable electrochemical data to parameters in the battery model, the ML model can be deployed to estimate parameters from experiment. These models can be referred to as inverse ML models, since they perform the inverse task of a "forward" physics based model. The procedure described above is implemented in Chapter 5. Interpretable ML models are trained on published synthetic data generated by equivalent circuit models. Pseudo-OCV (slow charge, C/25) full cell voltage curves are passed into the inverse ML models to estimate degradation modes in lithium ion batteries and classify which electrode limits cell capacity. These models are useful in diagnosing the state of the battery at any given time. Accuracies of the inverse ML models are evaluated on independent test sets also composed of synthetic data and are published to benchmark future diagnostic studies. The insights derived from the trained ML models in terms of which features in the full cell voltage curves are predictive of the degradation modes are compared to expert insights. In chapter 6, the robustness of the inverse ML approach towards model-experiment disagreement is probed. If the experiment does not directly map onto the protocol used to generate the synthetic training data for the ML model, or if the model itself is inherently a poor descriptor of experiment, the inverse ML model will inevitably return inaccurate estimates. In this chapter, a feed forward neural network (NN) is employed as the inverse ML model. In two case studies of model-experiment disagreement, the NN returns biased parameter estimates. A simple data augmentation procedure is introduced to mitigate these biases. Chapter 7 ties together the understanding developed in the previous chapters by applying more robust neural networks to estimate parameters for LVO cells cycled at different rates. This study demonstrates how to interpret parameter estimates in conjunction with cycling data to gain mechanistic insight into degradation. A complex map of coupled degradation hypotheses is reduced to a smaller subset of possible mechanisms for two exemplary LVO cells, and parameter estimates for a larger set of LVO cells are discussed. The framework presented in this study synergistically combines experiment, physics-based modeling, and machine learning to better understand degradation phenomena.

In this dissertation, we introduce novel exponential jump-diffusion models for pricing options. Firstly, the normal convolution gamma mixture jump-diffusion model is presented. This model generalizes Merton's jump-diffusion and Kou's double exponential jump-diffusion. We show that the normal convolution gamma mixture jump-diffusion model captures some economically important features of the asset price, and that it exhibits heavier tails than both Merton jump-diffusion and double exponential jump-diffusion models. Secondly, the normal convolution double gamma jump-diffusion model for pricing options is presented. We show that under certain configurations of both the normal convolution gamma mixture and the normal convolution double gamma jump-diffusion models, the latter exhibits a heavier left or right tail than the former. For both models, the maximum likelihood procedure for estimating the model parameters under the physical measure is fairly straightforward; moreover, the likelihood function is given in closed form thereby eliminating the need to embed a probability density function recovery procedure such as the fast Fourier transform or the Fourier-cosine expansion methods in the parameter estimation procedure. In addition, both models can reproduce the implied volatility surface observed in the options data and provide a good fit to the market-quoted European option prices.

For a numerical or analytical model to be useful it should be ensured that the model outcome matches the observations or field measurements during calibration. This process has been typically done by manual perturbation of the model input parameters. This research investigates a methodology for using non linear parameter estimation technique (the Marquardt-Levenberg technique) with the multi component reactive solute transport model SEAM3D. The reactive multi-component solutes considered in this study are chlorinated ethenes. Previous studies have shown that this class of compounds can be degraded by four different biodegradation mechanisms, and the degradation path is a function of the prevailing oxidation reduction conditions. Tests were performed in three levels; the first level utilized synthetic model-generated data. The idea was to develop a methodology and perform preliminary testing where "observations" can be generated as needed. The second level of testing involved performing the testing on a single redox zone model. The methodology was refined and tested using data from a chlorinated ethenes-contaminated site. The third level involved performing the tests on a multiple redox zone model. The methodology was tested, and statistical validation of the recommended methodology was performed. The results of the tests showed that there is a statistical advantage for choosing a subgroup of the available parameters to optimize instead of the optimizing the whole available group. Therefore, it is recommended to perform a parameter sensitivity study prior to the optimization process to identify the suitable parameters to be chosen. The methodology suggests optimizing the oxidation-reduction species parameters first then calibrating the chlorinated ethenes model. The results of the tests also proved the advantage of the sequential optimization of the model parameters, therefore the parameters of the parent compound are optimized, updated in the daughter compound model, for which the parameters are then optimized so on. The test results suggested considering the concentrations of the daughter compounds when optimizing the parameters of the parent compounds. As for the observation weights, the tests suggest starting the applied observation weights during the optimization process at values of one and changing them if needed. Overall the proposed methodology proved to be very efficient. The optimization methodology yielded sets of model parameters capable of generating concentration profiles with great resemblance to the observed concentration profiles in the two chlorinated ethenes site models considered. / Ph. D.

The author proposes a novel functional regression method for parameter estimation and adaptive control in this dissertation. In the functional regression method, the regressors and a signal which contains the information of the unknown parameters are either determined from raw measurements or calculated as the functions of the measurements. The novel feature of the method is that the algorithm maps the regressors to the functionals which are represented in terms of customized test functions. The functionals are updated continuously by the evolution laws, and only an infinite number of variables are needed to compute the functionals. These functionals are organized as the entries of a matrix, and the parameter estimates are obtained using either the generalized inverse method or the transpose method. It is shown that the schemes of some conventional adaptive methods are recaptured if certain test function designs are employed. It is proved that the functional regression method guarantees asymptotic convergence of the parameter estimation error to the origin, if the system is persistently excited. More importantly, in contrast to the conventional schemes, the parameter estimation error may be expected to converge to the origin even when the system is not persistently excited. The novel adaptive method are also applied to the Model Reference Adaptive Controller (MRAC) and adaptive observer. It is shown that the functional regression method ensures asymptotic stability of the closed loop systems. Additionally, the studies indicate that the transient performance of the closed loop systems is improved compared to that of the schemes using the conventional adaptive methods. Besides, it is possible to analyze the transient responses a priori of the closed loop systems with the functional regression method. The simulations verify the theoretical analyses and exhibit the improved transient and steady state performances of the closed loop systems. / Ph. D.

Thermophysical characterization of anisotropic composite materials is extremely important in the control of today fabrication processes and in the prediction of structure failure due to thermal stresses. Accuracy in the estimation of the thermal properties can be improved if the experiments are designed carefully. However, on one hand, the typically used parametric study for the design optimization is tedious and time intensive. On the other hand, commonly used gradient-based estimation methods show instabilities resulting in nonconvergence when used with models that contain correlated or nearly correlated parameters. The objectives of this research were to develop systematic and reliable methodologies for both Experimental Design Optimization (EDO) used for the determination of thermal properties, and Simultaneous Parameter Estimation (SPE). Because of their advantageous features, Genetic Algorithms (GAs) were investigated for use as a strategy for both EDO and SPE. The EDO and SPE approaches used involved the maximization of an optimality criterion associated with the sensitivity matrix of the unknown parameters, and the minimization of the ordinary least squares error, respectively. Two versions of a general-purpose genetic-based program were developed: one is designed for the analysis of any EDO / SPE problems for which a mathematical model can be provided, while the other incorporates a control-volume finite difference scheme allowing for the practical analysis of complex problems. The former version was used to illustrate the genetic performance on the optimization of a difficult mathematical test function. Two test cases previously solved in the literature were first analyzed to demonstrate and assess the GA-based {EDO/SPE} methodology. These problems included the optimization of one and two dimensional designs for the estimation at ambient temperature of two and three thermal properties, respectively (effective thermal conductivity parallel and perpendicular to the fibers plane and effective volumetric heat capacity), of anisotropic carbon/epoxy composite materials. The two dimensional case was further investigated to evaluate the effects of the optimality criterion used for the experimental design on the accuracy of the estimated properties. The general-purpose GA-based program was then successively applied to three advanced studies involving the thermal characterization of carbon/epoxy anisotropic composites. These studies included the SPE of successively three, seven and nine thermophysical parameters, with for the latter case, a two dimensional EDO with seven experimental key parameters. In two of the three studies, the parameters were defined to represent the dependence of the thermal properties with temperature. Finally, the kinetic characterization of the curing of three thermosetting materials (an epoxy, a polyester and a rubber compound) was accomplished resulting in the SPE of six kinetic parameters. Overall, the GA method was found to perform extremely well despite the high degree of correlation and low sensitivity of many parameters in all cases studied. This work therefore validates the use of GAs for the thermophysical characterization of anisotropic composite materials. The significance in using such algorithms is not only the solution to ill-conditioned problems but also, a drastically cost savings in both experimental and time expenses as they allow for the EDO and SPE of several parameters at once. / Ph. D.

This thesis focuses on making improvements to time-delayed teleoperation systems, with both direct and semi-autonomous haptic control, by addressing the challenges associated with force-position (F-P) predictive architectures. As the time delay from the communication channel increases, system stability and performance degrade. Previously, solutions focused on communication channel stability and environment force estimation methods that primarily rely on linearization of the Hunt-Crossley (HC) contact model. These result in a loss of transparency in the system and limiting use cases from linearization assumptions. Moreover, semi-autonomous solutions aimed at decreasing user effort and automating subtasks, such as obstacle avoidance and user guidance, require training or singularly focus on joint space tasks. This work addresses the shortcomings of the aforementioned methods by refocusing on system components to achieve more favorable dynamics during environment contact with the use of a series elastic actuator (SEA), investigating alternative HC parameter estimation techniques, and synthesizing an assistive semi-autonomous control framework that predicts user intention recognition and automates gross motion tasks. Experimental results with a remote SEA demonstrate improved performance with stiff environments in delays of up to two seconds round trip time. The coupling of the force and position through the actuator along with simultaneous sensing capabilities also show robustness for contact with soft environments. Further improvements with soft environment contact are achieved through HC parameter estimation, with smooth parameter update switching using a Sigmoid function. A novel application of Chebyshev polynomial approximation for adaptive parameter estimation of the HC model was also proposed. This approach provides control via backstepping with adaptive parameter estimation using Lyapunov methods. Additionally, this method reduces excitation requirements by using nonlinear swapping and the data accumulation concept to guarantee parameter convergence. A simulated teleoperation system demonstrates the effectiveness of this approach and initial results from experiment show promise for this approach in practice. Finally, a user study involving a pick and place task produced favorable results for the proposed semi-autonomous framework which significantly reduced task completion times. / Master of Science / Teleoperated systems are powerful solutions for remotely executing tasks in situations where autonomous solutions are not robust enough and/or user knowledge is desired for a task. However, teleoperation performance and stability is degraded by delays in the communication channel. A common way to deal with time delay is to use a predictive controller on the local side to cancel out the delay by knowing the remote side dynamics. Previous approaches have focused on stabilizing the communication channel or the use of estimators and observers to better capture the remote side dynamics. The drawback of these approaches is that they achieve stability at the expense of system transparency, leading to divergence in the force and position matching between the master and remote side. Many of the methods for environment force estimation involves linearizing contact models, creating limitations in their application. Moreover, semi-autonomous solutions aimed at decreasing user effort and automating subtasks such as obstacle avoidance and user guidance require training data sets for the algorithm or only focus individually on joint space tasks. This thesis addresses the shortcomings of the aforementioned methods by refocusing on system components to achieve more favorable dynamics using a series elastic actuator (SEA) while interacting with the environment, investigating nonlinear and linear contact model estimation methods for identifying parameters of the Hunt-Crossley (HC) model, and synthesising an assistive semi-autonomous control framework that predicts user intention for task execution. Experimental results for the use of an SEA demonstrate improved performance with stiff environments in delays of up to two seconds round trip time (RTT). The coupling of the force and position through the actuator along with simultaneous sensing capabilities also showed robustness for contact with soft environments. Various estimation methods for HC parameter identification was investigated to improve the local side model. A novel application of Chebyshev polynomial approximation of the HC model with adaptive parameter estimation was also proposed to provide control along with decreasing the excitation requirements by using backsteping control with nonlinear swapping and the data accumulation concept. A simulated teleoperation system demonstrated the effectiveness of this approach with a smooth paramater update transition. Initial results from experiment also show promise for this approach in practice. Finally, a user study involving a pick and place task produced favorable results for the proposed semi-autonomous framework which significantly reduced task completion times.

The simultaneous estimation of multi-mode heat transfer properties, conductive and radiative, is investigated for materials that include significant heat transfer by radiation. The focus is on insulative type materials with a relatively large optical thickness. Two basic models were developed for the combined conduction and radiation heat transfer: a diffusion solution and a more exact absorbing and isotropically scattering solution. Both solutions were written for one-dimensional heat transfer in gray, isotropically scattering materials. Different experimental setups were compared through a sensitivity analysis of the parameters to determine the best experiment for estimating the properties. An experiment was performed to collect real data to verify estimation procedures. The material used for the experiment was Styrofoam and the experiment consisted of a heat flux supplied by a thin film heater on one boundary and a constant temperature on the other boundary. The thermal capacitance of the heater proved to have an effect on the temperature measurements at the heated surface and had to be incorporated into the model. The estimation procedure involved the use of two methods, the modified Box Kanemasu algorithm and a genetic algorithm. Difficulties were encountered in simultaneously estimating all the properties due to correlation between the thermal conductivity and the radiation parameters, as well as some correlation between the heat capacity of the Styrofoam and the heat capacity of the heater. However, the genetic algorithm did provide fairly narrow and well-defined property ranges and confirmed that radiation transfer was significant in the Styrofoam. / Ph. D.