The world demand for electrical power increasescontinuously, requiring efficient and low-cost methods forpower generation. This thesis investigates two advanced powercycles with mixtures as the working fluid: the Kalina cycle,alternatively called the ammonia-water cycle, and theevaporative gas turbine cycle. These cycles have the potentialof improved performance regarding electrical efficiency,specific power output, specific investment cost and cost ofelectricity compared with the conventional technology, sincethe mixture working fluids enable efficient energyrecovery. This thesis shows that the ammonia-water cycle has a betterthermodynamic performance than the steam Rankine cycle as abottoming process for natural gas-fired gas and gas-dieselengines, since the majority of the ammonia-water cycleconfigurations investigated generated more power than steamcycles. The best ammonia-water cycle produced approximately40-50 % more power than a single-pressure steam cycle and 20-24% more power than a dual-pressure steam cycle. The investmentcost for an ammonia-water bottoming cycle is probably higherthan for a steam cycle; however, the specific investment costmay be lower due to the higher power output. A comparison between combined cycles with ammonia-waterbottoming processes and evaporative gas turbine cycles showedthat the ammonia-water cycle could recover the exhaust gasenergy of a high pressure ratio gas turbine more efficientlythan a part-flow evaporative gas turbine cycle. For a mediumpressure ratio gas turbine, the situation was the opposite,except when a complex ammonia-water cycle configuration withreheat was used. An exergy analysis showed that evaporativecycles with part-flow humidification could recover energy asefficiently as, or more efficiently than, full-flow cycles. Aneconomic analysis confirmed that the specific investment costfor part-flow cycles was lower than for full-flow cycles, sincepart-flow humidification reduces the heat exchanger area andhumidification tower volume. In addition, the part-flow cycleshad lower or similar costs of electricity compared with thefull-flow cycles. Compared with combined cycles, the part-flowevaporative cycles had significantly lower total and specificinvestment costs and lower or almost equal costs ofelectricity; thus, part-flow evaporative cycles could competewith the combined cycle for mid-size power generation. <b>Keywords:</b>power cycle, mixture working fluid, Kalinacycle, ammonia-water mixture, reciprocating internal combustionengine, bottoming cycle, gas turbine, evaporative gas turbine,air-water mixture, exergy

<p>The world demand for electrical power increasescontinuously, requiring efficient and low-cost methods forpower generation. This thesis investigates two advanced powercycles with mixtures as the working fluid: the Kalina cycle,alternatively called the ammonia-water cycle, and theevaporative gas turbine cycle. These cycles have the potentialof improved performance regarding electrical efficiency,specific power output, specific investment cost and cost ofelectricity compared with the conventional technology, sincethe mixture working fluids enable efficient energyrecovery.</p><p>This thesis shows that the ammonia-water cycle has a betterthermodynamic performance than the steam Rankine cycle as abottoming process for natural gas-fired gas and gas-dieselengines, since the majority of the ammonia-water cycleconfigurations investigated generated more power than steamcycles. The best ammonia-water cycle produced approximately40-50 % more power than a single-pressure steam cycle and 20-24% more power than a dual-pressure steam cycle. The investmentcost for an ammonia-water bottoming cycle is probably higherthan for a steam cycle; however, the specific investment costmay be lower due to the higher power output.</p><p>A comparison between combined cycles with ammonia-waterbottoming processes and evaporative gas turbine cycles showedthat the ammonia-water cycle could recover the exhaust gasenergy of a high pressure ratio gas turbine more efficientlythan a part-flow evaporative gas turbine cycle. For a mediumpressure ratio gas turbine, the situation was the opposite,except when a complex ammonia-water cycle configuration withreheat was used. An exergy analysis showed that evaporativecycles with part-flow humidification could recover energy asefficiently as, or more efficiently than, full-flow cycles. Aneconomic analysis confirmed that the specific investment costfor part-flow cycles was lower than for full-flow cycles, sincepart-flow humidification reduces the heat exchanger area andhumidification tower volume. In addition, the part-flow cycleshad lower or similar costs of electricity compared with thefull-flow cycles. Compared with combined cycles, the part-flowevaporative cycles had significantly lower total and specificinvestment costs and lower or almost equal costs ofelectricity; thus, part-flow evaporative cycles could competewith the combined cycle for mid-size power generation.</p><p><b>Keywords:</b>power cycle, mixture working fluid, Kalinacycle, ammonia-water mixture, reciprocating internal combustionengine, bottoming cycle, gas turbine, evaporative gas turbine,air-water mixture, exergy</p>

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

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In Chapter 1 we give a general introduction and motivate the need for clustering and dimension reduction methods. We continue in Chapther 2 with a review of different types of existing clustering and dimension reduction methods.<br /><br />In Chapter 3 we introduce mixture densities and the expectation-maximization (EM) algorithm to estimate their parameters. Although the EM algorithm has many attractive properties, it is not guaranteed to return optimal parameter estimates. We present greedy EM parameter estimation algorithms which start with a one-component mixture and then iteratively add a component to the mixture and re-estimate the parameters of the current mixture. Experimentally, we demonstrate that our algorithms avoid many of the sub-optimal estimates returned by the EM algorithm. Finally, we present an approach to accelerate mixture densities estimation from many data points. We apply this approach to both the standard EM algorithm and our greedy EM algorithm.<br /><br />In Chapter 4 we present a non-linear dimension reduction method that uses a constrained EM algorithm for parameter estimation. Our approach is similar to Kohonen's self-organizing map, but in contrast to the self-organizing map, our parameter estimation algorithm is guaranteed to converge and optimizes a well-defined objective function. In addition, our method allows data with missing values to be used for parameter estimation and it is readily applied to data that is not specified by real numbers but for example by discrete variables. We present the results of several experiments to demonstrate our method and to compare it with Kohonen's self-organizing map.<br /><br />In Chapter 5 we consider an approach for non-linear dimension reduction which is based on a combination of clustering and linear dimension reduction. This approach forms one global non-linear low dimensional data representation by combining multiple, locally valid, linear low dimensional representations. We derive an improvement of the original parameter estimation algorithm, which requires less computation and leads to better parameter estimates. We experimentally compare this approach to several other dimension reduction methods. We also apply this approach to a setting where high dimensional 'outputs' have to be predicted from high dimensional 'inputs'. Experimentally, we show that the considered non-linear approach leads to better predictions than a similar approach which also combines several local linear representations, but does not combine them into one global non-linear representation.<br /><br />In Chapter 6 we summarize our conclusions and discuss directions for further research.

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Given the rapid population decline and recent petition for listing of the monarch butterfly (Danaus plexippus L.) under the Endangered Species Act, an accurate estimate of the Eastern, migratory population size is needed. Because of difficulty in counting individual monarchs, the number of hectares occupied by monarchs in the overwintering area is commonly used as a proxy for population size, which is then multiplied by the density of individuals per hectare to estimate population size. There is, however, considerable variation in published estimates of overwintering density, ranging from 6.9-60.9 million ha(-1). We develop a probability distribution for overwinter density of monarch butterflies from six published density estimates. The mean density among the mixture of the six published estimates was similar to 27.9 million butterflies ha(-1) (95% CI [2.4-80.7] million ha(-1)); the mixture distribution is approximately log-normal, and as such is better represented by the median (21.1 million butterflies ha(-1)). Based upon assumptions regarding the number of milkweed needed to support monarchs, the amount of milkweed (Asciepias spp.) lost (0.86 billion stems) in the northern US plus the amount of milkweed remaining (1.34 billion stems), we estimate >1.8 billion stems is needed to return monarchs to an average population size of 6 ha. Considerable uncertainty exists in this required amount of milkweed because of the considerable uncertainty occurring in overwinter density estimates. Nevertheless, the estimate is on the same order as other published estimates, The studies included in our synthesis differ substantially by year, location, method, and measures of precision. A better understanding of the factors influencing overwintering density across space and time would be valuable for increasing the precision of conservation recommendations.

Parameter estimation is a long-lasting topic in queueing systems and has attracted considerable attention from both academia and industry. In this thesis, we design a parameter estimation framework for a tandem queueing system that collects end-to-end measurement data and utilizes the finite mixture model for the maximum likelihood (ML) estimation. The likelihood equations produced by ML are then solved by the iterative expectation-maximization (EM) algorithm, a powerful algorithm for parameter estimation in scenarios involving complicated distributions. We carry out a set of experiments with different parameter settings to test the performance of the proposed framework. Experimental results show that our method performs well for tandem queueing systems, in which the constituent nodes' service time follow distributions governed by exponential family. Under this framework, both the Newton-Raphson (NR) algorithm and the EM algorithm could be applied. The EM algorithm, however, is recommended due to its ease of implementation and lower computational overhead. / Graduate / hangli@uvic.ca

Doctor of Philosophy / Department of Statistics / Weixin Yao / This dissertation consists of three parts that are related to semiparametric mixture models. In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm. In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property. In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model.