In several projects within ABB there is a need of state and parameter estimation for nonlinear dynamic systems. One example is a project investigating optimisation of gas turbine operation. In a gas turbine there are several parameters and states which are not measured, but are crucial for the performance. Such parameters are polytropic efficiencies in compressor and turbine stages, cooling mass flows, friction coefficients and temperatures. Different methods are being tested to solve this problem of system identification or parameter estimation. This thesis describes the implementation of such a method and compares it with previously implemented identification methods. The comparison is carried out in the context of parameter estimation in gas turbine models, a dynamic load model used in power systems as well as models of other dynamic systems. Both simulated and real plant measurements are used in the study.

This masters thesis concerns a modeling project performed at Volvo Technology in Gothenburg, Sweden. The main purpose of the project has been to develop a physical model of the climate in construction vehicles that later on can be used in the development of an electronic climate controller. The focus of the work has been on one type of wheel loader and one type of excavator. The temperature inside the compartment has been set equal to the notion climate. With physical theories about air flow and heat transfer in respect, relations between the components in the climate unit and the compartment has been calculated. Parameters that has had unknown values has been estimated. The relations have then been implemented in the modeling tool Simulink. The validation of the model has been carried out by comparison between measured data and modeled values by calculation of Root Mean Square and correlation. Varying the estimated parameters and identifying the change in the output signal, i.e the temperature of the compartment, have performed a sensitivity analysis. The result of the validation has shown that the factor with the greatest influence on the temperature in the vehicle is the airflow through the climate unit and the outlets. Minor changes of airflow have resulted in major changes in temperature. The validation principally shows that the model gives a good estimation of the temperature in the compartment. The static values of the model differs from the values of the measured data but is regarded being as within an acceptable margin of error. The weakness of the model is mainly its predictions of the dynamics, which does not correlate satisfyingly with the data.

For centuries physicians, scientists, engineers, mathematicians, and many others have been asking: 'what are the forces that drive tissues in an embryo to their final geometric forms?' At the tissue and whole embryo level, a multitude of very different morphogenetic processes, such as gastrulation and neurulation are involved. However, at the cellular level, virtually all of these processes are evidently driven by a relatively small number of internal structures all of whose forces can be resolved into equivalent interfacial tensions γ. Measuring the cell-level forces that drive specific morphogenetic events remains one of the great unsolved problems of biomechanics. Here I present a novel approach that allows these forces to be estimated from time lapse images. In this approach, the motions of all visible triple junctions formed between trios of cells adjacent to each other in epithelia (2D cell sheets) are tracked in time-lapse images. An existing cell-based Finite Element (FE) model is then used to calculate the viscous forces needed to deform each cell in the observed way. A recursive least squares technique with variable forgetting factors is then used to estimate the interfacial tensions that would have to be present along each cell-cell interface to provide those forces, along with the attendant pressures in each cell. The algorithm is tested extensively using synthetic data from an FE model. Emphasis is placed on features likely to be encountered in data from live tissues during morphogenesis and wound healing. Those features include algorithm stability and tracking despite input noise, interfacial tensions that could change slowly or suddenly, and complications from imaging small regions of a larger epithelial tissue (the frayed boundary problem). Although the basic algorithm is highly sensitive to input noise due to the ill-conditioned nature of the system of equations that must be solved to obtain the interfacial tensions, methods are introduced to improve the resulting force and pressure estimates. The final algorithm returns very good estimates for interfacial tensions and intracellular cellular pressures when used with synthetic data, and it holds great promise for calculating the forces that remodel live tissue.

Anaerobic digestion (AD) is widely used in wastewater treatment plants for stabilisation of primary and waste activated sludges. Increasingly energy prices as well as stringent environmental and public health regulations ensure the ongoing popularity of anaerobic digestion. Reduction of volatile solids, methane production and pathogen reduction are the major objectives of anaerobic digestion. Phased anaerobic digestion is a promising technology that may allow improved volatile solids destruction and methane gas production. In AD models, microbially-mediated processes are described by functionally-grouped microorganisms. Ignoring the presence of functionally-different species in the separate phases may influence the output of AD modeling. The objective of this research was to thoroughly investigate the kinetics of hydrolysis, acetogenesis (i.e., propionate oxidation) and methanogenesis (i.e., acetoclastic) in phased anaerobic digestion systems. Using a denaturing gradient gel electrophoresis (DGGE) technique, bacterial and archaeal communities were compared to complement kinetics studies. Four phased digesters including Mesophilic-Mesophilic, Thermophilic-Mesophilic, Thermophilic-Thermophilic and Mesophilic-Thermophilic were employed to investigate the influence of phase separation and temperature on the microbial activity of the digestion systems. Two more digesters were used as control, one at mesophilic 35 0C (C1) and one at thermophilic 55 0C (C2) temperatures. The HRTs in the first-phase, second-phase and single-phase digesters were approximately 3.5, 14, and 17 days, respectively. All the digesters were fed a mixture of primary and secondary sludges. Following achievement of steady-state in the digesters, a series of batch experiments were conducted off-line to study the impact of the digester conditions on the kinetics of above-mentioned processes. A Monod-type equation was used to study the kinetics of acetoclastic methanogens and POB in the digesters, while a first-order model was used for the investigation of hydrolysis kinetics. Application of an elevated temperature (55 0C) in the first-phase was found to be effective in enhancing solubilisation of particulate organics. This improvement was more significant for nitrogen-containing material (28%) as compared to the PCOD removal (5%) when the M1 and T1 digesters were compared. Among all the configurations, the highest PCOD removal was achieved in the T1T2 system (pvalue<0.05). In contrast to the solubilisation efficiencies, the mesophilic digesters (C1, M1M2 and T1M3) outperformed the thermophilic digesters (C2, T1T2 and M1T3) in COD removal. The highest COD removal was obtained in the T1M3 digestion system, indicating a COD removal efficiency of 50.7±2.1%. The DGGE fingerprints from digesters demonstrated that digester parameters (i.e., phase separation and temperature) influenced the structure of the bacterial and archaeal communities. This resulted in distinct clustering of DGGE profiles from the 1st-phase digesters as compared to the 2nd-phase digesters and from the mesophilic digesters as compared to the thermophilic ones. Based on the bio-kinetic parameters estimated for the various digesters and analysis of the confidence regions of the kinetic sets (kmax and Ks), the batch experiment studies revealed that the kinetic characteristics of the acetoclastic methanogens and POB developed in the heavily loaded digesters (M1 and T1) were different from those species developed in the remaining mesophilic digesters (M2, M3 and C1). As with the results from the mesophilic digesters, a similar observation was made for the thermophilic digesters. The species of acetoclastic methanogens and POB within the T1 digester had greater kmax and Ks values in comparison to the values of the T3 and C2 digesters. However, the bio-kinetic parameters of the T2 digester showed a confidence region that overlapped with both the T1 and T3 digesters. The acetate and propionate concentrations in the digesters supported these results. The acetate and propionate concentrations in the M1 digesters were, respectively, 338±48 and 219±17 mgCOD/L, while those of the M2, M3 and C1 digesters were less than 60 mg/L as COD. The acetate and propionate concentrations were, respectively, 872±38 and 1220±66 in T1 digester, whereas their concentrations ranged 140-184 and 209-309 mg/L as COD in the T2, T3 and C2 digesters. In addition, the DGGE results displayed further evidence on the differing microbial community in the 1st- and 2nd-phase digesters. Two first-order hydrolysis models (single- and dual-pathway) were employed to study the hydrolysis process in the phased and single-stage digesters. The results demonstrated that the dual-pathway hydrolysis model better fit the particulate COD solubilisation as compared to the single-pathway model. The slowly (F0,s) and rapidly (F0,r) hydrolysable fractions of the raw sludge were 36% and 25%, respectively. A comparison of the estimated coefficients for the mesophilic digesters revealed that the hydrolysis coefficients (both Khyd,s and Khyd,r) of the M1 digester were greater than those of the M2 and M3 digesters. In the thermophilic digesters it was observed that the Khyd,r value of the T1 digester differed from those of the T2, T3 and C2 digesters; whereas, the hydrolysis rate of slowly hydrolysable matter (i.e., Khyd,s) did not differ significantly among these digesters. The influence of the facultative bacteria, that originated from the WAS fraction of the raw sludge, and/or the presence of hydrolytic biomass with different enzymatic systems may have contributed to the different hydrolysis rates in the M1 and T1 digesters from the corresponding mesophilic (i.e, M2 and M3) and thermophilic (i.e., T2 and T3) 2nd-phase digesters.

Degradation of components and structures is a major threat to the safety and reliability of large engineering systems, such as the railway networks or the nuclear power plants. Periodic inspection and maintenance are thus required to ensure that the system is in good condition for continued service. A key element for the optimal inspection and maintenance is to accurately model and forecast the degradation progress, such that inspection and preventive maintenance can be scheduled accordingly. In recently years, probabilistic models based on stochastic process have become increasingly popular in degradation modelling, due to their flexibility in modelling both the temporal and sample uncertainties of the degradation. However, because of the often complex structure of stochastic degradation models, accurate estimate of the model parameters can be quite difficult, especially when the inspection data are noisy or incomplete. Not considering the effect of uncertain inspection data is likely to result in biased parameter estimates and therefore erroneous predictions of future degradation. The main objective of the thesis is to develop formal methods for the parameter estimation of stochastic degradation models using uncertain inspection data. Three typical stochastic models are considered. They are the random rate model, the gamma process model and the Poisson process model, among which the random rate model and the gamma process model are used to model the flaw growth, and the Poisson process model is used to model the flaw generation. Likelihood functions of the three stochastic models given noisy or incomplete inspection data are derived, from which maximum likelihood estimates can be obtained. The thesis also investigates Bayesian inference of the stochastic degradation models. The most notable advantage of Bayesian inference over classical point estimates is its ability to incorporate background information in the estimation process, which is especially useful when inspection data are scarce. A major obstacle for accurate parameter inference of stochastic models from uncertain inspection data is the computational difficulties of the likelihood evaluation, as it often involves calculation of high dimensional integrals or large number of convolutions. To overcome the computational difficulties, a number of numerical methods are developed in the thesis. For example, for the gamma process model subject to sizing error, an efficient maximum likelihood method is developed using the Genz's transform and quasi-Monte Carlo simulation. A Markov Chain Monte Carlo simulation with sizing error as auxiliary variables is developed for the Poisson flaw generation model, A sequential Bayesian updating using approximate Bayesian computation and weighted samples is also developed for Bayesian inference of the gamma process subject to sizing error. Examples on the degradation of nuclear power plant components are presented to illustrate the use of the stochastic degradation models using practical uncertain inspection data. It is shown from the examples that the proposed methods are very effective in terms of accuracy and computational efficiency.

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6).<br /><br /> Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of <em>H₂</em> and <em>H_∞</em> norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed <em>H₂/H_&infin;</em> control problem is solved under the framework of LMIs. <br /><br /> To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. <br /><br /> Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The <em>l₂-l_&infin;</em> filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. <br /><br /> Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. <br /><br /> Finally, several open problems are listed as the future research directions.

In this thesis, we first present a variance estimation technique based on the standardized time series methodology for steady-state simulations. The proposed variance estimator has competitive bias and variance compared to the existing estimators in the literature. We also present the technique of rebatching to further reduce the bias and variance of our variance estimator. Second, we present two fully sequential indifference-zone procedures to select the best system from a number of competing simulated systems when best is defined by the maximum or minimum expected performance. These two procedures have parabola shaped continuation regions rather than the triangular continuation regions employed in several papers. The rocedures we present accommodate unequal and unknown ariances across systems and the use of common random numbers. However, we assume that basic observations are independent and identically normally distributed. Finally, we present procedures for finding a set of feasible or near-feasible systems among a finite number of simulated systems in the presence of multiple stochastic constraints, especially when the number of systems or constraints is large.

In this paper, we study the parameter estimation of the multiple linear time series regression model with long memory stochastic regressors and innovations. Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) proposed a class of frequency-domain weighted least squares estimates. Their estimates are shown to achieve the Gauss-Markov bound with standard convergence rate. In this study, we proposed a time-domain generalized LSE approach, in which the inverse autocovariance matrix of the innovations is estimated via autoregressive coefficients. Simulation studies are performed to compare the proposed estimates with Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002). The results show the time-domain generalized LSE is comparable to Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) and attains higher efficiencies when the autoregressive or moving average coefficients of the FARIMA models have larger values. A variance reduction estimator, called TF estimator, based on linear combination of the proposed estimator and Hidalgo and Robinson (2002)'s estimator is further proposed to improve the efficiency. Bootstrap method is applied to estimate the weights of the linear combination. Simulation results show the TF estimator outperforms the frequency-domain as well as the time-domain approaches.

The biodegradation kinetics of Geropon TC-42 (trademark) by an acclimated culture was investigated in anoxic batch reactors to determine biokinetic coefficients to be implemented in two biofilm mathematical models. Geropon TC-42 (trademark) is the surfactant commonly used in space habitation. The two biofilm models differ in that one assumes a constant biofilm density and the other allows biofilm density changes based on space occupancy theory. Extant kinetic analysis of a mixed microbial culture using Geropon TC-42 (trademark) as sole carbon source was used to determine cell yield, specific growth rate, and the half-saturation constant for S0/X0 ratios of 4, 12.5, and 34.5. To estimate cell yield, linear regression analysis was performed on data obtained from three sets of simultaneous batch experiments for three S0/X0 ratios. The regressions showed non-zero intercepts, suggesting that cell multiplication is not possible at low substrate concentrations. Non-linear least-squares analysis of the integrated equation was used to estimate the specific growth rate and the half-saturation constant. Net specific growth rate dependence on substrate concentration indicates a self-inhibitory effect of Geropon TC-42 (trademark). The flow rate and the ratio of the concentrations of surfactant to nitrate were the factors that most affected the simulations. Higher flow rates resulted in a shorter hydraulic retention time, shorter startup periods, and faster approach to a steady-state biofilm. At steady-state, higher flow resulted in lower surfactant removal. Higher influent surfactant/nitrate concentration ratios caused a longer startup period, supported more surfactant utilization, and biofilm growth. Both models correlate to the empirical data. A model assuming constant biofilm density is computationally simpler and easier to implement. Therefore, a suitable anoxic packed bed reactor for the removal of the surfactant Geropon TC-42 (trademark) can be designed by using the estimated kinetic values and a model assuming constant biofilm density.

The work presented in this dissertation centers on the theme of regression and computation methodology. Functional data is an important class of longitudinal data, and principal component analysis is an important approach to regression with this type of data. Here we present an additive hierarchical bivariate functional data model employing principal components to identify random e ects. This additive model extends the univariate functional principal component model. These models are implemented in the pfda package for R. To t the curves from this class of models orthogonalized spline basis are used to reduce the dimensionality of the t, but retain exibility. Methods for handing spline basis functions in a purely analytical manner, including the orthogonalizing process and computing of penalty matrices used to t the principal component models are presented. The methods are implemented in the R package orthogonalsplinebasis. The projects discussed involve complicated coding for the implementations in R. To facilitate this I created the NppToR utility to add R functionality to the popular windows code editor Notepad . A brief overview of the use of the utility is also included.