Sparse parameter estimation is an important aspect of system identification, as it allows for reducing the order of a model, and also some models in system identification inherently exhibit sparsity in their parameters. The accuracy of the estimated sparse model depends directly on the performance of the sparse estimation methods. It is well known that the accuracy of a sparse estimation method relies on the correlations between the regressors of the model being estimated. Mutual coherence represents the maximum of these correlations. When the parameter vector is known to be sparse, accurate estimation requires a low mutual coherence. However, in system identification, a major challenge arises from the construction of the regressor based on time series data, which often leads to a high mutual coherence. This conflict hinders accurate sparse estimation. To address this issue, the first part of this thesis introduces novel methods that reduce mutual coherence through linear coordinate transformations. These methods can be integrated with any sparse estimation techniques. Our numerical studies demonstrate significant improvements in performance compared to state-of-the-art sparse estimation algorithms. In the second part of the thesis, we shift our focus to optimal input design in system identification, which aims to achieve maximum accuracy in a model based on specific criteria. The original optimal input design techniques lack coherence constraints between the input sequences, often resulting in high mutual coherence and, consequently, increased sparse estimation errors for sparse models. Therefore, the second part of the thesis concentrates on designing optimal input for sparse models. We formulate the proposed methods and propose numerical algorithms using alternating minimization. Additionally, we compare the performance of our proposed methods with state-of-the-art input design algorithms, and we provide theoretical analysis of the proposed methods in both parts of the thesis. / Gles parameterestimering är viktigt inom systemidentifiering eftersom vissa modeller har naturligt förekommande gleshet i dess parametrar, men även för att det kan låta en minska ordningen av icke-glesa modeller. Noggrannheten av en skattad gles modell beror direkt på prestandan av de glesa estimeringsmetoderna. Det ¨ar välkänt att noggrannheten av en gles estimeringsmetod beror på korrelationer mellan regressorerna av den skattade modellen. Ömsesidig koherens (eng: mutual coherence) representerar maximum av dessa korrelationer. Noggrann estimering kräver låg ömsesidig koherens i de fallen då det är känt att parametervektorn är gles. En stor utmaning inom systemidentifiering orsakas av att, när en regressor konstrueras av tidsserie-data, så leder detta ofta till hög ömsesidig koherens. Denna konflikt hindrar noggrann gles estimering. För att åtgärda detta problem så introducerar avhandlingens första del nya metoder som minskar den ömsesidiga koherensen genom linjära koordinattransformationer. Dessa metoder är möjliga att kombinera med godtyckliga glesa estimeringsmetoder. Våra numeriska studier visar märkvärdig förbättring av prestanda jämfört med de bästa tillgängliga algoritmerna för gles parameterestimering. I avhandlingens andra del så ändrar vi vårt fokus till design utav optimala insignaler i systemidentifiering, där målet är att uppnå maximal noggrannhet i en modell, baserat på specifika kriterier. De ursprungliga metoderna för design av insignaler saknar bivillkor för ömsesidig koherens mellan insignalssekvenserna, vilket ofta resulterar i hög ömsesidig koherens och därmed också högre estimeringsfel för glesa modeller. Det är därför avhandlingens andra del fokuserar på att designa optimala insignaler för glesa modeller. Vi formulerar de föreslagna metoderna och erbjuder numeriska algoritmer som använder sig utav alternerande minimering. Vi jämför dessutom prestandan av vår metod med de bästa tillgängliga metoderna för design av insignaler, och vi presenterar även teoretisk analys av de föreslagna metoderna i avhandlingens båda delar. / <p>QC 20230911</p>

In this dissertation, experimental data was used to investigate the influence of a nearby mast structure on the striking distance to a lightning rod. The results of this research helped identify and understand the impact of different factors such as stroke polarity, lightning rod height, striking distance to the ground, lateral distance from the lightning stroke to an adjacent mast, and height of the adjacent mast on the striking distance of a lightning rod. Moreover, a system identification methodology was employed for the development and validation of striking distance models from experimental work performed at the Mississippi State University High Voltage Laboratory. Striking distance models were obtained to represent the striking distance to the ground, striking distance to an isolated lightning rod, and striking distance to a lightning rod in the presence of an adjacent mast. In the case of the striking distance to the ground the system identification approach was used for the extraction of the parameters of the black-box model proposed. From the results the relationship between the striking distance to ground and the leader voltage were obtained for both polarities of the lightning stroke. The system identification approach was then expanded to obtain the models for the striking distance to the lightning rod. The system identification approach was used to evaluate different mathematical models based on the ones found in the literature. The models were trained on experimental data, their quality evaluated, and the best model was selected for both positive and negative polarity. Furthermore, the model for negative polarity was evaluated against data from real lightning conditions in order to corroborate the model extrapolation capability. Building on the success obtained on the cases of the striking distance to the ground and to an isolated lightning rod the focus was turned to expanding the models to incorporate the influence of an adjacent mast. Models for positive and negative polarity were obtained and the quality of the equations was evaluated.

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In the system identification community a popular framework for the problem of estimating a parametrized model structure given a sequence of input and output pairs is given by the prediction-error method. This method tries to find the parameters which maximize the prediction capability of the corresponding model via the minimization of some chosen cost function that depends on the prediction error. This optimization problem is often quite complex with several local minima and is commonly solved using a local search algorithm. Thus, it is important to find a good initial estimate for the local search algorithm. This is the main topic of this thesis. The first problem considered is the regressor selection problem for estimating the order of dynamical systems. The general problem formulation is difficult to solve and the worst case complexity equals the complexity of the exhaustive search of all possible combinations of regressors. To circumvent this complexity, we propose a relaxation of the general formulation as an extension of the nonnegative garrote regularization method. The proposed method provides means to order the regressors via their time lag and a novel algorithmic approach for the \textsc{arx} and \textsc{lpv-arx} case is given.   Thereafter, the initialization of linear time-invariant polynomial models is considered. Usually, this problem is solved via some multi-step instrumental variables method. For the estimation of state-space models, which are closely related to the polynomial models via canonical forms, the state of the art estimation method is given by the subspace identification method. It turns out that this method can be easily extended to handle the estimation of polynomial models. The modifications are minor and only involve some intermediate calculations where already available tools can be used. Furthermore, with the proposed method other a priori information about the structure can be readily handled, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.   The final topic in this thesis is the initialization of discrete-time systems containing polynomial nonlinearities. In the continuous-time case, the tools of differential algebra, especially Ritt's algorithm, have been used to prove that such a model structure is globally identifiable if and only if it can be written as a linear regression model. In particular, this implies that once Ritt's algorithm has been used to rewrite the nonlinear model structure into a linear regression model, the parameter estimation problem becomes trivial. Motivated by the above and the fact that most system identification problems involve sampled data, a version of Ritt's algorithm for the discrete-time case is provided. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

Yes / This paper presents an investigation into the development of an intelligent active vibration control (AVC) system. Evolutionary Genetic algorithms (GAs) and Adaptive Neuro-Fuzzy Inference system (ANFIS) algorithms are used to develop mechanisms of an AVC system, where the controller is designed on the basis of optimal vibration suppression using the plant model. A simulation platform of a flexible beam system in transverse vibration using finite difference (FD) method is considered to demonstrate the capabilities of the AVC system using GAs and ANFIS. MATLAB GA tool box for GAs and Fuzzy Logic tool box for ANFIS function are used for AVC system design. The system is then implemented, tested and its performance assessed for GAs and ANFIS based design. Finally a comparative performance of the algorithm in implementing AVC system using GAs and ANFIS is presented and discussed through a set of experiments.

Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam. / Master of Science

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the systems. Most of the conventional techniques of system identification, in general, require some amount of a priori knowledge about the structure of the systems. Also, they are only useful either with linear or linearized systems. There are numerous control principles working nicely in industry. However, they are less effective for MIMO systems or complex nonlinear systems. The need to control, in a better way, increasingly complex dynamical systems under significant uncertainty has made the need for new methods quite apparent. This thesis investigates different approaches for identification and control of complex nonlinear systems using neural networks. For system identification and control, ANN properties of generalization and their capability of extracting complex relationships among inputs presented to them are useful. Two different techniques, called whole region method (WRM) and the separate regions method (SRM) technique, have been developed and applied to two classes of nonlinear systems. Different connectionist control techniques such as adaptive control and neuro-PID control have been developed and applied to the robotic manipulators. / Master of Science

Modelling neuronal interactions using a directed network can be used to provide insight into the activity of the brain during experimental tasks. Magnetoencephalography (MEG) allows for the observation of the fast neuronal dynamics necessary to characterize the activity of sources and their interactions. A network representation of these sources and their connections can be formed by mapping them to nodes and their connection strengths to edge weights. Dynamic Causal Modelling (DCM) presents a Bayesian framework to estimate the parameters of these networks, as well as the ability to test hypotheses on the structure of the network itself using Bayesian model comparison. DCM uses a neurologically-informed representation of the active neural sources, which leads to an underdetermined system and increased complexity in estimating the network parameters. This work shows that inform- ing the MEG DCM source location with prior distributions defined using a MEG source localization algorithm improves model selection accuracy. DCM inversion of a group of candidate models shows an enhanced ability to identify a ground-truth network structure when source-localized prior means are used. / Master of Science