The Blood Oxygen Level Dependent (BOLD) signal provides indirect estimates of neural activity. The parameters of this BOLD signal can give information about the pathophysiological state of the brain. Most of the models for the BOLD signal are overparameterized which makes the unique identification of these parameters difficult. In this work, we use information from multiple neu- roimaging sources to get better estimates of these parameters instead of relying on the information from the BOLD signal only. The mulitmodal neuroimaging setup consisted of the information from Cerebral Blood Volume (CBV) ( VASO-Fluid-Attenuation-Inversion-Recovery (VASO-FLAIR)), and Cerebral Blood Flow (CBF) (from Arterial Spin Labelling (ASL)) in addition to the BOLD signal and the fusion of this information is achieved in a Particle Filter (PF) framework. The trace plots and the correlation coefficients of the parameter estimates from the PF reflect ill-posedness of the BOLD model. The means of the parameter estimates are much closer to the ground truth compared to the estimates obtained using only the BOLD information. These parameter estimates were also found to be more robust to noise and influence of the prior. / Master of Science

Traditional methods of analyzing functional Magnetic Resonance Images use a linear combination of just a few static regressors. This work demonstrates an alternative approach using a physiologically inspired nonlinear model. By using a particle filter to optimize the model parameters, the computation time is kept below a minute per voxel without requiring a linearization of the noise in the state variables. The activation results show regions similar to those found in Statistical Parametric Mapping; however, there are some notable regions not detected by that technique. Though the parameters selected by the particle filter based approach are more than sufficient to predict the Blood-Oxygen-Level-Dependent signal response, more model constraints are needed to uniquely identify a single set of parameters. This illposed nature explains the large discrepancies found in other research that attempted to characterize the model parameters. For this reason the final distribution of parameters is more medically relevant than a single estimate. Because the output of the particle filter is a full posterior probability, the reliance on the mean to estimate parameters is unnecessary. This work presents not just a viable alternative to the traditional method of detecting activation, but an extensible technique of estimating the joint probability distribution function of the Blood-Oxygen-Level-Dependent Signal parameters. / Master of Science

The thesis presents algorithms based on a linear algebraic solution for the identification of the parameters of the FIR system using only higher order statistics when only the output of the system corrupted by additive Gaussian noise is observed. All the traditional parametric methods of estimating the parameters of the system have been based on the 2nd order statistics of the output of the system. These methods suffer from the deficiency that they do not preserve the phase response of the system and hence cannot identify non-minimum phase systems. To circumvent this problem, higher order statistics which preserve the phase characteristics of a process and hence are able to identify a non-minimum phase system and also are insensitive to additive Gaussian noise have been used in recent years. Existing algorithms for the identification of the FIR parameters based on the higher order cumulants use the autocorrelation sequence as well and give erroneous results in the presence of additive colored Gaussian noise. This problem can be overcome by obtaining algorithms which do not utilize the 2nd order statistics. An existing relationship between the 2nd order and any Ith order cumulants is generalized to a relationship between any two arbitrary k, Ith order cumulants. This new relationship is used to obtain new algorithms for FIR system identification which use only cumulants of order > 2 and with no other restriction than the Gaussian nature of the additive noise sequence. Simulation studies are presented to demonstrate the failure of the existing algorithms when the imposed constraints on the 2nd order statistics of the additive noise are violated while the proposed algorithms perform very well and give consistent results. Recently, a new algebraic approach for parameter estimation method denoted the Linear Combination of Slices (LCS) method was proposed and was based on expressing the FIR parameters as a linear combination of the cumulant slices. The rank deficient cumulant matrix S formed in the LCS method can be expressed as a product of matrices which have a certain structure. The orthogonality property of the subspace orthogonal to S and the range space of S has been exploited to obtain a new class of algorithms for the estimation of the parameters of a FIR system. Numerical simulation studies have been carried out to demonstrate the good behaviour of the proposed algorithms. Analytical expressions for the covariance of the estimates of the FIR parameters of the different algorithms presented in the thesis have been obtained and numerical comparison has been done for specific cases. Numerical examples to demonstrate the application of the proposed algorithms for channel equalization in data communication and as an initial solution to the cumulant matching nonlinear optimization methods have been presented.

The advances in computational and experimental modeling in the area of structural mechanics have stimulated research in a class of hybrid problems that require both of these modeling capabilities to be combined to achieve certain objectives. Real-time substructure (RTS) testing, structural system identification (SSI) and active control techniques fall in the category of hybrid problems that need efficient tools in both computational and experimental phases for their successful implementation. RTS is a hybrid testing method, which aims to overcome the scaling problems associated with the conventional dynamic testing methods (such as shake table test, effective force test and pseudo dynamic test) by testing the critical part of the structure experimentally with minimum compromise on spatio-temporal scaling, while modeling the remaining part numerically. The problem of SSI constitutes an important component within the broader framework of problems of structural health monitoring where, based on the in-situ measurements on the loading and a subset of critical responses of the structure, the system parameters are estimated with a view to detecting damage/degradation. Active control techniques are employed to maintain the functionality of important structures, especially under extreme dynamic loading. The work reported in the present thesis contributes to the areas of RTS, SSI and active control of nonlinear systems, the main focus being the computational aspects, i.e., in developing numerical strategies to address some of the unsolved issues, although limited efforts have also been made to undertake laboratory experimental investigations in the area of nonlinear SSI. The thesis is organized into seven chapters and five appendices. The first chapter contains an overview of the state of the art techniques in dynamic testing, SSI and structural control. The topics covered include effective force test, pseudo dynamic test, RTS test, time and frequency domain methods of nonlinear system identification, dynamic state estimation techniques with emphasis on particle filters, Rao-Blackwellization, structural control methods, control algorithms and active control of nonlinear systems. The review identifies a set of open problems that are subsequently addressed, to an extent, in the thesis. Chapter 2 focuses on the development of a time domain coupling technique, involving combined computational and experimental modeling, for vibration analysis of structures built-up of linear/nonlinear substructures. The numerical and experimental substructures are allowed to interact in real-time. The equation of motion of the numerical substructure is integrated using a step-by-step procedure that is formulated in the state space. For systems with nonlinear substructures, a multi-step transversal linearization method is used to integrate the equations of motion; and, a multi-step extrapolation scheme, based on the reproducing kernel particle method, is employed to handle the time delays that arise while accounting for the interaction between the substructures. Numerical illustrations on a few low dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using RTS testing techniques. The concept of substructuring is extended in Chapter 3 for implementing Rao-Blackwellization, a technique of combining particle filters with analytical computation through Kalman filters, for state and parameter estimations of a class of nonlinear dynamical systems with additive Gaussian process/observation noises. The strategy is based on decomposing the system to be estimated into mutually coupled linear and nonlinear substructures and then putting in place a rational framework to account for coupling between the substructures. While particle filters are applied to the nonlinear substructures, estimation of linear substructures proceeds using a bank of Kalman filters. Numerical illustrations for state/parameter estimations of a few linear and nonlinear oscillators with noise in both the process and measurements are provided to demonstrate the potential of the Rao-Blackwellized particle filter (RBPF) with substructuring. In Chapter 4, the concept of Rao-Blackwellization is extended to handle more general nonlinear systems, using two different schemes of linearization. A semi-analytical filter and a conditionally linearized filter, within the framework of Monte Carlo simulations, are proposed for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. The first filter uses a local linearization of the nonlinear drift fields in the process/observation equations based on explicit Ito-Taylor expansions to transform the given nonlinear system into a family of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. In the second filter, the marginalized posterior distribution of an appropriately chosen subset of the state vector is obtained using a particle filter. Samples of these marginalized states are then used to construct a family of conditionally linearized system of equations to obtain the posterior distribution of the states using a bank of Kalman filters. The potential of the proposed filters in state/parameter estimations is demonstrated through numerical illustrations on a few nonlinear oscillators. The problem of active control of nonlinear structural dynamical systems, in the presence of both process and measurement noises, is considered in Chapter 5. The focus of the study is on the exploitability of particle filters for state estimation in feedback control algorithms for nonlinear structures, when a limited number of noisy output measurements are available. The control design is done using the state dependent Riccati equation (SDRE) method. The Bayesian bootstrap filter and another based on sequential importance sampling are employed for state estimation. Numerical illustrations are provided for a few typically nonlinear oscillators of interest in structural engineering. The experimental validation of the RBPF using substructuring (developed in Chapter 3) and the conditionally linearized Monte Carlo filter (developed in Chapter 4), for parameter estimation, is reported in Chapter 6. Measured data available through laboratory experiments on simple building frame models subjected to harmonic base motions is processed using the proposed algorithms to identify the unknown parameters of the model. A brief summary of the contributions made in this thesis, together with a few suggestions for future research, are presented in Chapter 7. Appendix A provides an account of the multi-step transversal linearization method. The derivation of the reproducing kernel shape functions are presented in Appendix B. Appendix C provides the details of the stochastic Taylor expansion and derivation of the covariance structure of Gaussian MSI-s. The performance of a particle filtering algorithm (bootstrap filter) and Kalman filter in the state estimation of a linear system is provided in Appendix D and Appendix E contains the theoretical details of the Rao-Blackwellized particle filter.

The present work focuses on the two areas of investigation: system identification of helicopter and design of controller for the helicopter. Helicopter system identification, the first subject of investigation in this thesis, can be described as the extraction of system characteristics/dynamics from measured flight test data. Wind tunnel experimental data suffers from scale effects and model deficiencies. The increasing need for accurate models for the design of high bandwidth control system for helicopters has initiated a renewed interest in and a more active use of system identification. Besides, system identification is likely to become mandatory in the future for model validation of ground based helicopter simulators. Such simulators require accurate models in order to be accepted by pilots and regulatory authorities like Federal Aviation Regulation for realistic complementary helicopter mission training. Two approaches are widely used for system identification, namely, black box and gray box approach. In the black-box approach, the relationship between input-output data is approximated using nonparametric methods such as neural networks and in such a case, internal details of the system and model structure may not be known. In the gray box approach, parameters are estimated after defining the model structure. In this thesis, both black box and gray box approaches are investigated. In the black box approach, in this thesis, a comparative study and analysis of different Recurrent Neural Networks(RNN) for the identification of helicopter dynamics using flight data is investigated. Three different RNN architectures namely, Nonlinear Auto Regressive eXogenous input(NARX) model, neural network with internal memory known as Memory Neuron Networks(MNN)and Recurrent MultiLayer perceptron (RMLP) networks are used to identify dynamics of the helicopter at various flight conditions. Based on the results, the practical utility, advantages and limitations of the three models are critically appraised and it is found that the NARX model is most suitable for the identification of helicopter dynamics. In the gray box approach, helicopter model parameters are estimated after defining the model structure. The identification process becomes more difficult as the number of degrees-of-freedom and model parameters increase. To avoid the drawbacks of conventional methods, neural network based techniques, called the delta method is investigated in this thesis. This method does not require initial estimates of the parameters and the parameters can be directly extracted from the flight data. The Radial Basis Function Network(RBFN)is used for the purpose of estimation of parameters. It is shown that RBFN is able to satisfactorily estimate stability and control derivatives using the delta method. The second area of investigation addressed in this thesis is the control of helicopter in flight. Helicopter requires use of a control system to achieve satisfactory flight. Designing a classical controller involves developing a nonlinear model of the helicopter and extracting linearized state space matrices from the nonlinear model at various flight conditions. After examining the stability characteristics of the helicopter, the desired response is obtained using a feedback control system. The scheduling of controller gains over the entire envelope is used to obtain the desired response. In the present work, a helicopter having a soft inplane four bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is considered. For this helicopter, a mathematical model and also a model based on neural network (using flight data) has been developed. As a precursor, a feed back controller, the Stability Augmentation System(SAS), is designed using linear quadratic regulator control with full state feedback and LQR with out put feedback approaches. SAS is designed to meet the handling qualities specification known as Aeronautical Design Standard ADS-33E-PRF. The control gains have been tuned with respect to forward speed and gain scheduling has been arrived at. The SAS in the longitudinal axis meets the requirement of the Level1 handling quality specifications in hover and low speed as well as for forward speed flight conditions. The SAS in the lateral axis meets the requirement of the Level2 handling quality specifications in both hover and low speed as well as for forward speed flight conditions. Such conventional design of control has served useful purposes, however, it requires considerable flight testing which is time consuming, to demonstrate and tune these control law gains. In modern helicopters, the stringent requirements and non-linear maneuvers make the controller design further complicated. Hence, new design tools have to be explored to control such helicopters. Among the many approaches in adaptive control, neural networks present a potential alternative for modeling and control of nonlinear dynamical systems due to their approximating capabilities and inherent adaptive features. Furthermore, from a practical perspective, the massive parallelism and fast adaptability of neural network implementations provide more incentive for further investigation in problems involving dynamical systems with unknown non-linearity. Therefore, adaptive control approach based on neural networks is proposed in this thesis. A neural network based Feedback Error Neural adaptive Controller(FENC) is designed for a helicopter. The proposed controller scheme is based on feedback error learning strategy in which the outer loop neural controller enhances the inner loop conventional controller by compensating for unknown non-linearity and parameter un-certainties. Nonlinear Auto Regressive eXogenous input(NARX)neural network architecture is used to approximate the control law and the controller network parameters are adapted using updated rules Lyapunov synthesis. An offline (finite time interval)and on-line adaptation strategy is used to approximate system uncertainties. The results are validated using simulation studies on helicopter undergoing an agile maneuver. The study shows that the neuro-controller meets the requirements of ADS-33 handling quality specifications. Even though the tracking error is less in FENC scheme, the control effort required to follow the command is very high. To overcome these problems, a Direct Adaptive Neural Control(DANC)scheme to track the rate command signal is presented. The neural controller is designed to track rate command signal generated using the reference model. For the simulation study, a linearized helicopter model at different straight and level flight conditions is considered. A neural network with a linear filter architecture trained using back propagation through time is used to approximate the control law. The controller network parameters are adapted using updated rules Lyapunov synthesis. The off-line trained (for finite time interval)network provides the necessary stability and tracking performance. The on-line learning is used to adapt the network under varying flight conditions. The on-line learning ability is demonstrated through parameter uncertainties. The performance of the proposed direct adaptive neural controller is compared with feedback error learning neural controller. The performance of the controller has been validated at various flight conditions. The theoretical results are validated using simulation studies based on a nonlinear six degree-of-freedom helicopter undergoing an agile maneuver. Realistic gust and sensor noise are added to the system to study the disturbance rejection properties of the neural controllers. To investigate the on-line learning ability of the proposed neural controller, different fault scenarios representing large model error and control surface loss are considered. The performances of the proposed DANC scheme is compared with the FENC scheme. The study shows that the neuro-controller meets the requirements of ADS-33 handling quality specifications.

Real-time monitoring of electromechanical oscillations is of great significance for power system operators; to this aim, software solutions (algorithms) that use synchrophasor measurements have been developed for this purpose. This thesis investigates different approaches for improving mode estimation process by offering new methods and deepening the understanding of different stages in the mode estimation process. One of the problems tackled in this thesis is the selection of synchrophasor signals used as the input for mode estimation. The proposed selection is performed using a quantitative criterion that is based on the variance of the critical mode estimate. The proposed criterion and associated selection method, offer a systematic and quantitative approach for PMU signal selection. The thesis also analyzes methods for model order selection used in mode estimation. Further, negative effects of forced oscillations and non-white noise load random changes on mode estimation results have been addressed by exploiting the intrinsic power system property that the characteristics of electromechanical modes are predominately determined by the power generation and transmission network. An improved accuracy of the mode estimation process can be obtained by intentionally injecting a probing disturbance. The thesis presents an optimization method that finds the optimal spectrum of the probing signals. In addition, the probing signal with the optimal spectrum is generated considering arbitrary time domain signal constraints that can be imposed by various probing signal generating devices. Finally, the thesis provides a comprehensive description of a practical implementation of a real-time mode estimation tool. This includes description of the hardware, software architecture, graphical user interface, as well as details of the most important components such as the Statnett’s SDK that allows easy access to synchrophasor data streams. / <p>The Doctoral Degrees issued upon completion of the programme are issued by Comillas Pontifical University, Delft University of Technology and KTH Royal Institute of Technology. The invested degrees are official in Spain, the Netherlands and Sweden, respectively.</p><p>QC 20160218</p> / FP7 iTesla

<p>Nonlinear systems occur in industrial processes, economical systems, biotechnology and in many other areas. The thesis treats methods for system identification and control of such nonlinear systems, and applies the proposed methods to a solar heating/cooling plant. </p><p>Two applications, an anaerobic digestion process and a domestic solar heating system are first used to illustrate properties of an existing nonlinear recursive prediction error identification algorithm. In both cases, the accuracy of the obtained nonlinear black-box models are comparable to the results of application specific grey-box models. Next a convergence analysis is performed, where conditions for convergence are formulated. The results, together with the examples, indicate the need of a method for providing initial parameters for the nonlinear prediction error algorithm. Such a method is then suggested and shown to increase the usefulness of the prediction error algorithm, significantly decreasing the risk for convergence to suboptimal minimum points. </p><p>Next, the thesis treats model based control of systems with input signal dependent time delays. The approach taken is to develop a controller for systems with constant time delays, and embed it by input signal dependent resampling; the resampling acting as an interface between the system and the controller.</p><p>Finally a solar collector field for combined cooling and heating of office buildings is used to illustrate the system identification and control strategies discussed earlier in the thesis, the control objective being to control the solar collector output temperature. The system has nonlinear dynamic behavior and large flow dependent time delays. The simulated evaluation using measured disturbances confirm that the controller works as intended. A significant reduction of the impact of variations in solar radiation on the collector outlet temperature is achieved, though the limited control range of the system itself prevents full exploitation of the proposed feedforward control. The methods and results contribute to a better utilization of solar power.</p>

Using some form of dynamical model in a visual tracking system is a well-known method for increasing robustness and indeed performance in general. Often, quite simple models are used and can be effective, but prior knowledge of the likely motion of the tracking target can often be exploited by using a specially-tailored model. Specifying such a model by hand, while possible, is a time-consuming and error-prone process. Much more desirable is for an automated system to learn a model from training data. A dynamical model learnt in this manner can also be a source of useful information in its own right, and a set of dynamical models can provide discriminatory power for use in classification problems. Methods exist to perform such learning, but are limited in that they assume the availability of 'ground truth' data. In a visual tracking system, this is rarely the case. A learning system must work from visual data alone, and this thesis develops methods for learning dynamical models while explicitly taking account of the nature of the training data --- they are noisy measurements. The algorithms are developed within two tracking frameworks. The Kalman filter is a simple and fast approach, applicable where the visual clutter is limited. The recently-developed Condensation algorithm is capable of tracking in more demanding situations, and can also employ a wider range of dynamical models than the Kalman filter, for instance multi-mode models. The success of the learning algorithms is demonstrated experimentally. When using a Kalman filter, the dynamical models learnt using the algorithms presented here produce better tracking when compared with those learnt using current methods. Learning directly from training data gathered using Condensation is an entirely new technique, and experiments show that many aspects of a multi-mode system can be successfully identified using very little prior information. Significant computational effort is required by the implementation of the methods, and there is scope for improvement in this regard. Other possibilities for future work include investigation of the strong links this work has with learning problems in other areas. Most notable is the study of the 'graphical models' commonly used in expert systems, where the ideas presented here promise to give insight and perhaps lead to new techniques.

A dissertation submitted to the Faculty of Engineering and the Built Environment, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, May 2016 / The present work describes the practical implementation of systems identification techniques to the development of a linear aerodynamic model for a small low-cost UAV equipped with a basic navigational and inertial measurement systems. The assessment of the applicability of the techniques were based on determining whether adequate aerodynamic models could be developed to aid in the reduction of wind tunnel testing when characterising new UAVs. The identification process consisted of postulating a model structure, flight test manoeuvre design, data reconstruction, aerodynamic parameter estimation, and model validation. The estimators that were used for the post-flight identification were the output error maximum likelihood method and an iterated extended Kalman filter with a global smoother. SIDPAC and FVSysID systems identification toolboxes were utilised and modified where appropriate. The instrumentation system on board the UAV consisted of three-axis accelerometers and gyroscopes, a three-axis vector magnetometer and GPS tracking while data was logged at 25 Hz. The angle of attack and angle of sideslip were not measured directly and were estimated using tailored data reconstruction methods. Adequate time domain lateral model correlation with flight data was achieved for the cruise flight condition. Adequacy was assessed against Theil’s inequality coefficients and Theil’s covariance. It was found that the simplified estimation algorithms based on the linearized equations of motion yielded the most promising model matches. Due to the high correlation between the pitch damping derivatives, the longitudinal analysis did not yield valid model parameter estimates. Even though the accuracy of the resulting models was below initial expectations, the detailed data compatibility analysis provided valuable insight into estimator limitations, instrumentation requirements and test procedures for systems identification on low-cost UAVs. / MT2016

A Identificação de Sistemas em Malha Fechada possui considerável apelo prático, uma vez que oferece maior segurança durante a coleta experimental de dados e ao mesmo tempo, em linhas gerais, proporciona a construção de modelos mais adequados para servir de base ao projeto de sistemas de controle. Esta Tese apresenta, como um de seus principais objetivos, a comparação dos Métodos Diretos aplicados à Identificação em Malha Fechada com a classe dos Métodos de Dois-Passos, que se enquadram na abordagem de Identificação Conjunta Entrada/Saída. Complementando esta comparação, propõe-se um novo algoritmo em Dois-Passos, a Dupla Filtragem. As propriedades de convergência deste método são analisadas em detalhe. O desempenho alcançado pelos modelos identificados pelos Métodos Diretos e com o uso dos Métodos de Dois-Passos aqui considerados a saber, Filtragem-u (VAN DEN HOF; SCHRAMA, 1993), Filtragem-y (HUANG; SHAH, 1997) e Dupla Filtragem são comparados em uma abordagem estatística por meio da aplicação de Simulações de Monte Carlo. Também se propõe uma variante ao método da Filtragem-u, proporcionando duas formas distintas de descrever a função de sensibilidade da saída associada ao processo sob estudo (FORSSELL; LJUNG, 1999). Os critérios de comparação de desempenho adotados nesta tese incluem validações dos modelos identificados em simulações livres (operação em malha aberta), em que os objetos de análise são respostas a pulsos retangulares e, com maior ênfase, validações em malha fechada que utilizam o mesmo controlador instalado no sistema sob estudo. Nesta última situação são empregados sinais de excitação de mesma natureza daqueles adotados nos ensaios de identificação, porém com diferentes realizações. Cada uma dessas validações é acompanhada de seu respectivo fit (LJUNG,1999), índice de mérito que mede a proximidade entre as respostas temporais do sistema físico e de seu modelo matemático. Também são consideradas as respostas em frequência do processo, que constituem a base para a determinação do limite máximo para a incerteza associada ao modelo (ZHU, 2001). Tomando como fundamento tais limites máximos de incerteza, em conjunto com as respostas em frequência dos modelos identificados, é possível associar graduações a esses modelos (A, B, C, ou D). Desta forma, esta tese utiliza índices de mérito fundamentados em ambas as respostas temporais e em frequência. Aspectos relativos à influência da amplitude e do tipo de sinal de excitação aplicado à malha, bem como à relação sinal-ruído estabelecida no sistema, são analisados. Também se investiga a relação entre a qualidade do modelo identificado e o ponto de aplicação do sinal de excitação: no valor de referência da malha de controle ou na saída do controlador. Por fim, verifica-se como a sintonia do controlador afeta o modelo identificado. Todas as simulações realizadas utilizam sinais de perturbação do tipo quase não- estacionário, típicos da indústria de processos (ESMAILI et al., 2000). Os resultados indicam que os Métodos Diretos são mais precisos quando a estrutura de modelo e ordem adotadas são idênticas àquelas do processo real. No entanto, os Métodos de Dois-Passos são capazes de fornecer modelos muito confiáveis mesmo quando a estrutura e ordem do modelo diferem daquelas do processo sob estudo. / Closed-loop System Identification has considerable practical appeal, since it provides increased security during the collection of experimental data and, at the same time, provides the construction of suitable models for the design of high performance control systems. This thesis presents, as one of its main objectives, a thorough comparison between Direct Methods (applied to the closed-loop identification) and Two-Step Methods. The latter ones belong to the Joint Input/Output approach. Complementing this comparison, a new two-step algorithm the Double Filtering is proposed. The convergence properties of this method are analyzed in detail. The performance achieved by the models identified by Direct and Two-Step methods is compared in a statistical approach through Monte Carlo simulations. The Two-Step methods considered in this thesis are the u-Filtering (VAN DEN HOF; SCHRAMA, 1993), the y-Filtering (HUANG; SHAH, 1997) and the Double Filtering. A variant of the u-Filtering method is proposed, providing two distinct ways of describing the output sensitivity function associated with the process under study (FORSSELL; LJUNG, 1999). The performance comparison criteria adopted in this thesis include free-run model validations (open-loop operation), in which rectangular pulses responses are analyzed. Greater emphasis is given to closed loop model validation, which uses the same controller installed in the system under study. This type of validation employs excitation signals similar to those adopted in the identification tests, but with different realizations. Each of these validations is accompanied by its corresponding fit (Ljung, 1999), a merit index that measures the proximity between the time responses of the physical system and its mathematical model. Process frequency responses are also considered, since they form the basis for determining the model uncertainty upper-limit or upper-bound error (ZHU, 2001). The upper- bounds, along with the frequency responses of each identified model, provides ranks (A, B, C, or D) for these models. Therefore, this thesis uses merit indexes based on both time and frequency responses. It is analyzed how the type and magnitude (or equivalently, the signal-to-noise ratio) of the excitation signal applied to the loop impacts the accuracy of the identified models. This work also investigates the relationship between the accuracy of the identified models and the point of application of the excitation signal: the reference of the control loop or the controller output. Finally, it is checked how the controller tuning affects the identified models. All simulations employ quasi non-stationary disturbance signals, typical of the process industries (ESMAILI et al., 2000). The results indicate that Direct Methods are more accurate when the model structure and order adopted in the identification are identical to those of the actual process. However, the Two-Step Methods are capable of providing very reliable models even when the adopted structure and order differ from those of the process under study.