<p><h1>Abstract</h1></p> <p>As a compact, robust, and reliable power distribution method, hydraulic systems have been used for flight surface control for decades. Electro-hydrostatic Actuator (EHA) is increasingly replacing the conventional valve-controlled system for better performance, lighter weight and higher energy efficiency. The EHA is increasingly being used for flight control. As such its reliability is thereby critical important for flight safety. This research focuses on fault detection and diagnosis (FDD) for the EHA to enable predictive unscheduled maintenance when fault detected at its inception.</p> <p>An EHA prototype previously built at McMaster University is studied in this research and modified to physically simulate two faults conditions pertaining to leakage and friction. Nine different working conditions including normal running and eight fault conditions are simulated. Physical model has been derived mathematically capable of numerically simulating the fault conditions. Furthermore, for comparison, parametric model was obtained through system identification for each fault condition. This comparison revealed that parametric models are not suitable for fault detection and diagnosis due to the computation complexity.</p> <p>The FDD approach in this research uses model-based state estimation using filters. The filter based combined with the Interacting Multiple Model fault detection and diagnosis algorithm is introduced. Based on this algorithm, three FDD strategies are developed using a combination of the Extended Kalman Filter and IMM (IMM-EKF), the Smooth Variable Structure Filter with Varying Boundary and IMM (IMM-SVSF (VBL)), and the Smooth Variable Structure Filter with Fixed Boundary and IMM (IMM-SVSF (FBL)). All the three FDD strategies were implemented on the EHA prototype. Based on the results, the IMM-SVSF (VBL) provided the best performance. It detected and diagnosed faults correctly at high mode probabilities with excellent robustness to modeling uncertainties. It also was able to detect slow growing leakage fault, and predicted the changing trend of fault conditions.</p> / Master of Applied Science (MASc)

This thesis addresses the problem of tracking multiple ground targets whose motion is dependent on one another. Multiple approaches which integrate the social force based motion model into different filtering algorithms are proposed. The social force concept has previously been used to model pedestrian motion where the interactions among pedestrians are described using social forces. First, the social force based motion model integrated into the Probability Hypothesis Density (PHD) framework is proposed. Two different implementations, namely, the Sequential Monte Carlo (SMC) technique and the Gaussian Mixture (GM) technique, are derived to implement the proposed Social Force PHD (SF-PHD) filter in ground target tracking scenarios. Next, a social-force-based motion model integrated into the stacked Kalman filter (stacked SF-KF) is developed and its multiple model (stacked IMM-SF-KF) variant is derived. Then, the assumption used in the proposed algorithms, that the actual values of the social force parameters are known, is not valid at all times and the assumption is relaxed. Hence, simultaneous parameter estimation techniques for the social force parameters during the tracking are proposed. Three approaches based on the state augmentation method, the Expectation Maximization (EM) method and the maximum likelihood method are derived. The maximum likelihood method can be implemented offline or online, depending on the requirement. The traditional Posterior Cramer Rao Lower Bound (PCRLB), which is the inverse of the Fisher information matrix, gives a bound on the optimal achievable accuracy of the estimated state of a target with independent motion. Subsequently, a modified performance measure based on the PCRLB for targets whose motion is dependent on each other is derived to validate the performance of the proposed algorithms. Finally, the PCRLB that accounts for unknown interactions is derived to validate the proposed simultaneous parameter estimation techniques. Simulated and real data are used to show the performance of the proposed algorithms and simultaneous parameter estimation techniques compared to the algorithms in the literature. / Thesis / Doctor of Philosophy (PhD) / This thesis addresses the problem of tracking multiple ground targets whose motion is dependent on one another. In target tracking literature, it is commonly assumed that a target’s motion follows a nearly constant velocity, constant turn or a constant acceleration model independent of the motion of other targets. But the actual behavior of a ground target may be more intricate than that and it is often affected by the motion of other targets, obstacles in the surrounding and its intended destination. Hence, a more sophisticated motion modeling technique, which integrates the various factors that affect the motion of ground targets, is needed. In this thesis, multiple approaches which integrate the social force based motion model into different filtering algorithms are proposed. The social force concept has previously been used to model pedestrian motion where the interactions among pedestrians are described using social forces. First, the social force based motion model integrated into the Probability Hypothesis Density (PHD) framework is proposed. Two different implementations, namely, the Sequential Monte Carlo (SMC) technique and the Gaussian Mixture (GM) technique, are derived to implement the proposed Social Force PHD (SF-PHD) filter in ground target tracking scenarios. Next, a social-force-based motion model integrated into the stacked Kalman filter (stacked SF-KF) is developed and its multiple model (stacked IMM-SF-KF) variant is derived. Then, the assumption used in the proposed algorithms, that the actual values of the social force parameters are known, is not valid at all times and the assumption is relaxed. Hence, simultaneous parameter estimation techniques for the social force parameters during the tracking are proposed. Three approaches based on the state augmentation method, the Expectation Maximization (EM) method and the maximum likelihood method are derived. The maximum likelihood method can be implemented offline or online, depending on the requirement. The traditional Posterior Cramer Rao Lower Bound (PCRLB), which is the inverse of the Fisher information matrix, gives a bound on the optimal achievable accuracy of the estimated state of a target with independent motion. Subsequently, a modified performance measure based on the PCRLB for targets whose motion is dependent on each other is derived to validate the performance of the proposed algorithms. Finally, the PCRLB that accounts for unknown interactions is derived to validate the proposed simultaneous parameter estimation techniques. Simulated and real data are used to show the performance of the proposed algorithms and simultaneous parameter estimation techniques compared to the algorithms in the literature.

Pour un terminal mobile alimenté sur batterie, le rendement de l’amplificateur de puissance (AP) doit êtreoptimisé. Cette optimisation peut rendre non-linéaire la fonction d’amplification de l’AP. Pour compenser lesdistorsions introduites par le caractère non-linéaire de l’AP, un détecteur numérique fondé sur un modèle deVolterra peut être utilisé. Le comportement de l’AP et le canal étant modélisé par le modèle de Volterra, uneapproche par filtrage de Kalman (FK) permet d’estimer conjointement les noyaux de Volterra et les symbolestransmis. Dans ce travail, nous proposons de traiter cette problématique dans le cadre d’une liaison montantedans un contexte radio intelligente (RI). Dans ce cas, des contraintes supplémentaires doivent être prises encompte. En effet, étant donné que la RI peut changer de bande de fréquence de fonctionnement, les nonlinéaritésde l’AP peuvent varier en fonction du temps. Par conséquent, nous proposons de concevoir une postdistorsionnumérique fondée sur une modélisation par modèles multiples combinant plusieurs estimateurs àbase de FK. Les différents FK permettant de prendre en compte les différentes dynamiques du modèle.Ainsi, les variations temporelles des noyaux de Volterra peuvent être suivies tout en gardant des estimationsprécises lorsque ces noyaux sont statiques. Le cas d’un signal monoporteuse est adressé et validé par desrésultats de simulation. Enfin, la pertinence de l’approche proposée est confirmée par des mesures effectuéessur un AP large bande (300-3000) MHz. / For a battery driven terminal, the power amplifier (PA) efficiency must be optimized. Consequently,non-linearities may appear at the PA output in the transmission chain. To compensatethese distortions, one solution consists in using a digital post-distorter based on aVolterra model of both the PA and the channel and a Kalman filter (KF) based algorithm tojointly estimate the Volterra kernels and the transmitted symbols. Here, we suggest addressingthis issue when dealing with uplink cognitive radio (CR) system. In this case, additionalconstraints must be taken into account. Since the CR terminal may switch from one subbandto another, the PA non-linearities may vary over time. Therefore, we propose to designa digital post-distorter based on an interacting multiple model combining various KF basedestimators using different model parameter dynamics. This makes it possible to track thetime variations of the Volterra kernels while keeping accurate estimates when those parametersare static. Furthermore, the single carrier case is addressed and validated by simulationresults. In addition, the relevance of the proposed approach is confirmed by measurementscarried on a (300-3000) MHz broadband PA.

A promising line of research attempts to bridge the gap between detector and tracker by means of considering jointly optimal parameter settings for both of these subsystems. Along this fruitful path, this thesis study focuses on the problem of detection threshold optimization in a tracker-aware manner so that a feedback from the tracker to the detector is established to maximize the overall system performance. Special emphasis is given to the optimization schemes based on two non-simulation performance prediction (NSPP) methodologies for the probabilistic data association filter (PDAF), namely, the modified Riccati equation (MRE) and the hybrid conditional averaging (HYCA) algorithm. The possible improvements are presented in two domains: Non-maneuvering and maneuvering target tracking. In the first domain, a number of algorithmic and experimental evaluation gaps are identified and newly proposed methods are compared with the existing ones in a unified theoretical and experimental framework. Furthermore, for the MRE based dynamic threshold optimization problem, a closed-form solution is proposed. This solution brings a theoretical lower bound on the operating signal-to-noise ratio (SNR) concerning when the tracking system should be switched to the track before detect (TBD) mode. As the improvements of the second domain, some of the ideas used in the first domain are extended to the maneuvering target tracking case. The primary contribution is made by extending the dynamic optimization schemes applicable to the PDAF to the interacting multiple model probabilistic data association filter (IMM-PDAF). Resulting in an online feedback from the filter to the detector, this extension makes the tracking system robust against track losses under low SNR values.

In this thesis, the problem of intercepting highly manoeuvrable threats using seeker-less interceptors that operate in the command guidance mode, is addressed. These systems are more prone to estimation errors than standard seeker-based systems. Several non-linear and optimal estimation and guidance concepts are presented in this thesis for interception of randomly maneuvering targets by seeker-less interceptors. The key contributions of the thesis can be broadly categorized into six groups, namely (i) an optimal selection of bank of lters in interactive multiple model (IMM) scheme to cater to various maneuvers that are expected during the end-game, (ii) an innovative algorithm to reduce chattering phenomenon and formulate effective guidance algorithm based on 'differential game guidance law' (modi ed DGL), (iii) IMM/DGL and IMM/modified DGL based integrated estimation/guidance (IEG) strategy, (iv) sensitivity and robustness analysis of Kalman lters and ne tuning of lters in filter bank using innovation covariance, (v) Performance of tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL against various target maneuvers, (vi) Performance comparison with realistic missile model. An innovative generalized state estimation formulation has been proposed in this the-sis for accurately estimating the states of incoming high speed randomly maneuvering targets. The IMM scheme and an optimal selection of lters, to cater to various maneu-vers that are expected during the end-game, is described in detail. The key advantage of this formulation is that it is generic and can capture evasive target maneuver as well as straight moving targets in a uni ed framework without any change of target model and tuning parameters. In this thesis, a game optimal guidance law is described in detail for 2D and 3D engagements. The performance of the differential game based guidance law (DGL) is compared with conventional Proportional Navigation (PN) guidance law, especially for 3D interception scenarios. An innovative chatter removal algorithm is introduced by modifying the differential game based guidance law (modified DGL). In this algorithm, chattering is reduced to the maximum extent possible by introducing a boundary layer around the switching surface and using a continuous control within the boundary layer. The thesis presents performance of the modified DGL algorithm against PN and DGL, through a comparison of miss distances and achieved accelerations. Simulation results are also presented for varying fiight path angle errors. Apart from the guidance logic, two novel ideas have been presented following the evolving "integrated estimation and guidance" philosophy. In the rst approach, an in-tegrated estimation/guidance (IEG) algorithm that integrates IMM estimator with DGL law (IMM/DGL), is proposed for seeker-less interception. In this interception scenario, the target performs an evasive bang-bang maneuver, while the sensor has noisy measure-ments and the interceptor is subject to an acceleration bound. The guidance parameters (i.e., the lateral acceleration commands) are computed with the help of zero e ort miss distance. The thesis presents the performance of the IEG algorithm against combined IMM with PN (IMM/PN), through a comparison of miss distances. In the second ap-proach, a novel modi ed IEG algorithm composed of IMM estimator and modi ed DGL guidance law is introduced to eliminate the chattering phenomenon. Results from both of these integrated approaches are quite promising. Monte Carlo simulation results re-veal that modi ed IEG algorithm achieves better homing performance, even if the target maneuver model is unknown to the estimator. These results and their analysis o er an insight to the interception process and the proposed algorithms. The selection of lter tuning parameters puts forward a major challenge for scien-tists and engineers. Two recently developed metrics, based on innovation covariance, are incorporated for determining the filter tuning parameters. For predicting the proper combination of the lter tuning parameters, the metrics are evaluated for a 3D interception problem. A detailed sensitivity and robustness analysis is carried out for each type of Kalman lters. Optimal and tuned Kalman lters are selected in the IMM con guration to cater to various maneuvers that are expected during the end-game. In the interception scenario examined in this thesis, the target performs various types of maneuvers, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. The tuned IMM serves as a basis for synthesis of e cient lters for tracking maneuvering targets and reducing estimation errors. A numerical study is provided which demonstrates the performance and viability of tuned IMM/modi ed DGL based modi ed IEG strategy. In this thesis, comparison is also performed between tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL in integrated estimation/guidance scheme. The results are illustrated by an extensive Monte Carlo simulation study in the presence of estimation errors. Simulation results are also presented for end game maneuvers and varying light path angle errors . Numerical simulations to study the aerodynamic e ects on integrated estimation/ guidance structure and its e ect on performance of guidance laws are presented. A detailed comparison is also performed between tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL in integrated estimation/guidance scheme with realistically modelled missile against various target maneuvers. Though the time taken to intercept is higher when a realistic model is considered, the integrated estimation/guidance law still performs better. The miss distance is observed to be similar to the one obtained by considering simpli ed kinematic models.

Simultaneous evaluation of the whole set of the model parameters of different orders together with an ability to track unmodeled dynamics are desired features in the tasks of parameter estimation. A technique handling with the factors produced by an augmented covariance (ACM) or information (AIM) matrices is considered to be an appropriate tool for designing multiple model estimation. This is where the name augmented identification (AI) by using the least-squares method was taken. The method AI attains numerical stability of the calculation of the conventional least squares method while in the same time, fully extracts information contained in the observation. In order to track time varying parameters can be found that all the information pertinent to recursive identification and thus to data driven forgetting is concentrated in ACM as well as in AIM. In this thesis will be introduced how to selective forgetting to ACM should be applied in an effective way. It means forget only a portion of accumulated information which will be further modified by the newest data included in the regressor. In the estimation problems the knowledge of the inner states of the identified system is often required. Because the augmented identification belongs within the class so called prediction error method (PEM), some rational requirements can be deduced. As a result, state filter should constitute optimization procedure minimizing the predicted error of given state space model representation with respect to the vector of states. The proposed scheme will considerably extend the family of algorithms based on processing of ACM (AIM) about augmented filtering (AF). This all will establish a comprehensive concept of parametric estimation that compared with conventional approaches is characterized by versatility, low demands on a priori process information and by excellent numerical properties (robust against overparametrization, capable solving the multiple model problem).

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