Academic literature on the topic 'Algebraic estimation method'
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Journal articles on the topic "Algebraic estimation method"
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Beltran-Carbajal, F., R. Tapia-Olvera, A. Valderrabano-Gonzalez, and H. Yanez-Badillo. "An asymptotic and algebraic estimation method of harmonics." Electric Power Systems Research 206 (May 2022): 107771. http://dx.doi.org/10.1016/j.epsr.2022.107771.
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Abouaïssa, H., and V. Iordanova. "Algebraic Methods for Traffic Flow Densities Estimation." Cybernetics and Information Technologies 13, no. 4 (December 1, 2013): 5–17. http://dx.doi.org/10.2478/cait-2013-0049.
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Abstract An estimation approach that allows recovering of the traffic state is proposed in this paper. The method used is based on numerical differentiation, which does not need any integration of differential equations and turns out to be quite robust with respect to perturbations and measurements noises. Numerical simulations, carried-out by using the so-called Cell Transmission Model (CTM) demonstrate the relevance of the proposed on-line estimation scheme.
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Kastoris, Dimitris, Kostas Giotopoulos, and Dimitris Papadopoulos. "Neural Network-Based Parameter Estimation in Dynamical Systems." Information 15, no. 12 (December 16, 2024): 809. https://doi.org/10.3390/info15120809.
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Mathematical models are designed to assist decision-making processes across various scientific fields. These models typically contain numerous parameters, the values’ estimation of which often comes under analysis when evaluating the strength of these models as management tools. Advanced artificial intelligence software has proven to be highly effective in estimating these parameters. In this research work, we use the Lotka–Volterra model to describe the dynamics of a telecommunication sector in Greece, and then we propose a methodology that employs a feed-forward neural network (NN). The NN is used to estimate the parameter’s values of the Lotka–Volterra system, which are later applied to solve the system using a fourth-algebraic-order Runge–Kutta method. The application of the proposed architecture to the specific case study reveals that the model fits well to the experiential data. Furthermore, the results of our method surpassed the other three methods used for comparison, demonstrating its higher accuracy and effectiveness. The implementation of the proposed feed-forward neural network and the fourth-algebraic-order Runge–Kutta method was accomplished using MATLAB.
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Salmi, Tapio, Esko Tirronen, Johan Wärnå, Jyri-Pekka Mikkola, Dmitry Murzin, and Valerie Eta. "A Robust Method for the Estimation of Kinetic Parameters for Systems Including Slow and Rapid Reactions—From Differential-Algebraic Model to Differential Model." Processes 8, no. 12 (November 27, 2020): 1552. http://dx.doi.org/10.3390/pr8121552.
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Reliable estimation of kinetic parameters in chemical systems comprising both slow and rapid reaction steps and rapidly reacting intermediate species is a difficult differential-algebraic problem. Consequently, any conventional approach easily leads to serious convergence and stability problems during the parameter estimation. A robust method is proposed to surmount this dilemma: the system of ordinary differential equations and nonlinear algebraic equations is converted to ordinary differential equations, which are solved in-situ during the parameter estimation. The approach was illustrated with two generic examples and an example from green chemistry: synthesis of dimethyl carbonate from carbon dioxide and methanol.
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Qi, Naixin, Shengxiu Zhang, Lijia Cao, Xiaogang Yang, Chuanxiang Li, and Chuan He. "Fast and robust homography estimation method with algebraic outlier rejection." IET Image Processing 12, no. 4 (April 1, 2018): 552–62. http://dx.doi.org/10.1049/iet-ipr.2017.0254.
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Delpoux, R., and T. Floquet. "On-line Parameter Estimation via Algebraic Method: An Experimental Illustration." Asian Journal of Control 17, no. 1 (May 6, 2014): 315–26. http://dx.doi.org/10.1002/asjc.870.
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BALAMETOV, Ashraf B., Elman D. KHALILOV, Afaq K. SALIMOVA, and Tarana M. ISAYEVA. "State Estimation of an AC Overhead Power Line Using the Relinearization Method." Elektrichestvo 4, no. 4 (2021): 17–24. http://dx.doi.org/10.24160/0013-5380-2021-4-17-24.
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As is well known, dispatch control centers receive information about the electric power system operation mode from a supervisory control and data acquisition system (SCADA) and phasor measurement units (PMU) in the form of remote measurements and remote signals. The remote measurements contain information on the power system operating parameters, and remote signals contain information on the positions of switching equipment. The controlled facility state estimation problem is conventionally solved using iteration methods because the system of state equations is nonlinear in nature. The application of the Kipnis-Shamir method makes it possible to transform the nonlinear system of algebraic equations into a linear system in a non-iterative manner by replacing quadratic state variables, after which the obtained linear system is solved parametrically. By applying a second transformation of variables, the system of algebraic equations is transformed into a second system of linear equations, after which the solution of this system and the quadratic system of linear equations, and, hence, also the initial system of nonlinear equations are found. The application of the non-iterative approach is considered on the example of estimating the state of a 500 kV overhead power line.
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Garba, Bashir Danladi, and Sirajo Lawan Bichi. "A hybrid method for solution of linear Volterra integro-differential equations (LVIDES) via finite difference and Simpson’s numerical methods (FDSM)." Open Journal of Mathematical Analysis 5, no. 1 (May 27, 2021): 69–75. http://dx.doi.org/10.30538/psrp-oma2021.0084.
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In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.
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SIRA-RAMÍREZ, HEBERTT, and MICHEL FLIESS. "AN ALGEBRAIC STATE ESTIMATION APPROACH FOR THE RECOVERY OF CHAOTICALLY ENCRYPTED MESSAGES." International Journal of Bifurcation and Chaos 16, no. 02 (February 2006): 295–309. http://dx.doi.org/10.1142/s0218127406014812.
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In this article, we use a variant of a recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear systems description (basically, module theory and non-commutative algebra). Here, we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. nonasymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The proposed state estimation method can then be used in a coding–decoding process of a secret message transmission using the message-modulated chaotic system states and the reliable transmission of the chaotic system observable output. Simulation examples, using Chen's chaotic system and the Rossler system, demonstrate the important features of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted messages. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner.
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Haddar, Maroua, S. Caglar Baslamisli, Riadh Chaari, Fakher Chaari, and Mohamed Haddar. "Road profile identification with an algebraic estimator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 4 (April 4, 2018): 1139–55. http://dx.doi.org/10.1177/0954406218767470.
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In order to isolate the propagation of unwanted vibrations to passengers and improve vehicle maneuverability, it is common practice to predict road profile roughness in the scope of active suspension design. An algebraic estimator designed for the estimation of the road profile excitation has been investigated in this study based on vehicle dynamics responses. An approximation of road profile excitation by a piecewise constant function has been proposed using the operational calculus method and the differential algebraic theory. The proposed technique allows for the usage of cheap instrumentation with a small number of sensors and employs a straightforward calibration process. Accurate approximation of the road profile was obtained from the measurement of sprung mass and unsprung mass vertical displacements. The performance and robustness of the proposed algebraic predictor is compared with an augmented Kalman estimator. Numerical results are provided to analyze the effectiveness and the limitations of the proposed algorithm for road profile reconstruction. Furthermore, a comparison with real profile was studied.
Dissertations / Theses on the topic "Algebraic estimation method"
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Zhang, Yuqing. "Fixed-time algebraic distributed state estimation for linear systems." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2025. http://www.theses.fr/2025ISAB0001.
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Au cours des dernières décennies, le déploiement massif de capteurs embarqués en réseau dotés des capacités de communication dans des systèmes à grande échelle a suscité un intérêt croissant de la part des chercheurs dans le domaine de l’estimation distribuée. Cette thèse vise à développer une méthode d’estimation d’état distribuée algébrique à temps fixe pour les systèmes linéaires à temps variant d’ordre entier et les systèmes linéaires à temps invariant d’ordre fractionnaire dans des environnements bruités, en concevant un ensemble d’estimateurs locaux d’ordre réduit au niveau des capteurs en réseau.Pour ce faire, nous introduisons d’abord un schéma d’estimation distribuée en définissant un ensemble denoeuds récupérés à chaque noeud de capteur, basé sur un graphe dirigé plus relâché que celui qui est fortement connecté. En utilisant cet ensemble récupéré, nous construisons une transformation inversible pour la décomposition d’observabilité afin d’identifier le sous-système local observable de chaque noeud. De plus, cette transformation permet une représentation distribuée de l’état entier du système à chaque noeud sous forme de combinaison linéaire de son propre état local observable et de ceux des noeuds de son ensemble récupéré. Cela garantit que chaque noeud peut atteindre l’estimation distribuée d’état, à condition que les estimations des états locaux observables soient assurées. En conséquence, ce schéma distribué se concentre sur l’estimation des états locaux observables, permettant une estimation distribuée à travers le réseau de capteurs.En nous appuyant sur cette base, afin de traiter l’estimation algébrique à temps fixe pour chaque sous-système local observable identifié, différentes méthodes d’estimation à fonctions modulatrices sont explorées pour établir des formules algébriques indépendantes des conditions initiales, les rendant efficaces en tant qu’estimateurs locaux de ordre réduit à temps fixe. Pour les systèmes linéaires à temps variant d’ordre entier, la transformation utilisée pour développer le schéma d’estimation distribuée aboutit à une forme normale linéaire partiellement observable à temps variant. La méthode des fonctions modulatrices généralisées est ensuite appliquée pour estimer chaque état local observable à travers des formules intégrales algébriques des sorties du système et de leurs dérivées. Pour les systèmes linéaires à temps invariant d’ordre fractionnaire, une autre transformation est utilisée pour convertir chaque sous-système local observable identifié sous une forme normale observable d’ordre fractionnaire, permettant l’application de la méthode d’estimation à fonctions modulatrices généralisées d’ordre fractionnaire. Cette méthode calcule directement des formules intégrales algébriques pour les variables pseudo-état locales observables.Ensuite, en combinant ces formules algébriques avec la représentation distribuée dérivée, nous réalisons l’estimation d’état distribuée algébrique à temps fixe pour les systèmes étudiés. De plus, une analyse d’erreur est réalisée pour démontrer la robustesse de l’estimateur distribué conçu en présence de bruits continus de processus et de mesure, ainsi que de bruits discrets de mesure. Enfin, plusieurs exemples de simulation sont fournis pour valider l’efficacité du schéma d’estimation distribuée proposéIn recent decades, the widespread deployment of networked embedded sensors with communication capabilities in large-scale systems has drawn significant attentions fromresearchers to the field of distributed estimation. This thesis aims to develop a fixed-time algebraic distributed state estimation method for both integer-order linear time-varying systems and fractional-order linear-invariant systems in noisy environments, by designing a set of reduced-order local estimators at the networked sensors.To achieve this, we first introduce a distributed estimation scheme by defining a recovered node set at each sensor node, based on a digraph assumption that is more relaxed than the strongly connected one. Using this recovered set, we construct an invertible transformation for the observability decomposition to identify each node’s local observable subsystem. Additionally, this transformation allows for a distributed representation of the entire system state at each node by a linear combination of its own local observable state and those of the nodes in its recovered set. This ensures that each node can achieve the distributed state estimation, provided that the estimations for the set of local observable states are ensured. As a result, this distributed scheme focuses on estimating the local observable states, enabling distributed estimation across the sensor network.Building on this foundation, to address the fixed-time algebraic state estimation for each identified local observable subsystem, different modulating functions estimation methods are investigated to derive the initial-condition-independent algebraic formulas, making them effective as reduced-order local fixed-time estimators. For integer-order linear time-varying systems, the transformation used in developing distributed estimation scheme yields a linear time-varying partial observable normal form. The generalized modulating functions method is then applied to estimate each local observable state through algebraic integral formulas of system outputs and their derivatives. For fractional-order linear-invariant systems, another transformation is used to convert each identified local observable subsystem into a fractional-order observable normal form, allowing for the application of the fractional-order generalized modulating functions estimation method. This method directly computes algebraic integral formulas for local observable pseudo-state variables.Subsequently, by combining these algebraic formulas with the derived distributed representation, we achieve the fixed-time algebraic distributed state estimation for the studied systems. Additionally, an error analysis is conducted to demonstrate the robustness of the designed distributed estimator in the presence of both continuous process and measurement noises, as well as discrete measurement noises. Finally, several simulation examples are provided to validate the effectiveness of the proposed distributed estimation scheme
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Wei, Xing. "Non-asymptotic method estimation and applications for fractional order systems." Thesis, Bourges, INSA Centre Val de Loire, 2017. http://www.theses.fr/2017ISAB0003/document.
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Cette thèse vise à concevoir des estimateurs non-asymptotiques et robustes pour les systèmes linéaires d’ordre fractionnaire dans un environnement bruité. Elle traite une classe des systèmes linéaires d’ordre fractionnaire modélisée par la dite pseudo représentation d’état avec des conditions initiales inconnues. Elle suppose également que les systèmes étudiés ici peuvent être transformés sous la forme canonique de Brunovsky. Pour estimer le pseudo-état, la forme précédente est transformée en une équation différentielle linéaire d’ordre fractionnaire en prenant en compte les valeurs initiales des dérivées fractionnaires séquentielles de la sortie. Ensuite, en utilisant la méthode des fonctions modulatrices, les valeurs initiales précédentes et les dérivées fractionnaires avec des ordres commensurables de la sortie sont données par des formules algébriques avec des intégrales à l’aide d’une méthode récursive. Ainsi, ces formules sont utilisés pour calculer le pseudo-état dans le cas continu sans bruit. En outre, elle fournit un algorithme pour construire les fonctions modulatrices requises à l’accomplissement de l’estimation. Deuxièmement, inspiré par la méthode des fonctions modulatrices développée pour l’estimation de pseudo-état, cette méthode algébrique basée sur un opérateur est introduite pour estimer la dérivée fractionnée avec un ordre arbitraire fractionnaire de la sortie pour les systèmes considérés. Cet opérateur sert à annuler les valeurs initiales non désirées, puis permet d’estimer la dérivée fractionnaire souhaitée par une nouvelle formule algébrique à l’aide d’une méthode récursive. Troisièmement, l’estimateur du pseudo-état et le différenciateur d’ordre fractionnaire obtenus précédemment sont étudiés respectivement dans le cas discret et bruité. Chacun d’entre eux contient une erreur numérique due à la méthode d’intégration numérique utilisée et au bruit. En particulier, elle fournit une analyse pour diminuer la contribution du bruit au moyen d’une d’erreur bornée qui permet de sélectionner les degrés optimaux des fonctions de modulation à chaque instant. Ensuite, des exemples numériques sont donnés pour mettre en évidence la précision, la robustesse et la propriété non-asymptotique des estimateurs proposés. En outre, les comparaisons avec certaines méthodes existantes et avec un nouvel observateur d’ordre fractionnaire de typeH1sont montrées. Enfin, elle donne des conclusionsThis thesis aims to design non-asymptotic and robust estimators for a class of fractional order linear systems in noisy environment. It deals with a class of commensurate fractional order linear systems modeled by the so-called pseudo-state space representation with unknown initial conditions. It also assumed that linear systems under study can be transformed into the Brunovsky’s observable canonical form. Firstly, the pseudo-state of the considered systems is estimated. For this purpose, the Brunovsky’s observable canonical form is transformed into a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output. Then, using the modulating functions method, the former initial values and the fractional derivatives with commensurate orders of the output are given by algebraic integral formulae in a recursive way. Thereby, they are used to calculate the pseudo-state in the continuous noise-free case. Moreover, to perform this estimation, it provides an algorithm to build the required modulating functions. Secondly, inspired by the modulating functions method developed for pseudo-state estimation, an operator based algebraic method is introduced to estimate the fractional derivative with an arbitrary fractional order of the output. This operator is applied to cancel the former initial values and then enables to estimate the desired fractional derivative by a new algebraic formula using a recursive way. Thirdly, the pseudo-state estimator and the fractional order differentiator are studied in discrete noisy case. Each of them contains a numerical error due to the used numerical integration method, and the noise error contribution due to a class of stochastic processes. In particular, it provides ananalysis to decrease noise contribution by means of an error bound that enables to select the optimal degrees of the modulating functions at each instant. Then, several numerical examples are given to highlight the accuracy, the robustness and the non-asymptotic property of the proposed estimators. Moreover, the comparisons to some existing methods and a new fractional orderH1-like observer are shown. Finally, conclusions are outlined with some perspectives
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Pribadi, Aaron. "Algebraic Methods for Log-Linear Models." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/41.
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Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case of binary data.
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Kaperick, Bryan James. "Diagonal Estimation with Probing Methods." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/90402.
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Probing methods for trace estimation of large, sparse matrices has been studied for several decades. In recent years, there has been some work to extend these techniques to instead estimate the diagonal entries of these systems directly. We extend some analysis of trace estimators to their corresponding diagonal estimators, propose a new class of deterministic diagonal estimators which are well-suited to parallel architectures along with heuristic arguments for the design choices in their construction, and conclude with numerical results on diagonal estimation and ordering problems, demonstrating the strengths of our newly-developed methods alongside existing methods.Master of Science
In the past several decades, as computational resources increase, a recurring problem is that of estimating certain properties very large linear systems (matrices containing real or complex entries). One particularly important quantity is the trace of a matrix, defined as the sum of the entries along its diagonal. In this thesis, we explore a problem that has only recently been studied, in estimating the diagonal entries of a particular matrix explicitly. For these methods to be computationally more efficient than existing methods, and with favorable convergence properties, we require the matrix in question to have a majority of its entries be zero (the matrix is sparse), with the largest-magnitude entries clustered near and on its diagonal, and very large in size. In fact, this thesis focuses on a class of methods called probing methods, which are of particular efficiency when the matrix is not known explicitly, but rather can only be accessed through matrix vector multiplications with arbitrary vectors. Our contribution is new analysis of these diagonal probing methods which extends the heavily-studied trace estimation problem, new applications for which probing methods are a natural choice for diagonal estimation, and a new class of deterministic probing methods which have favorable properties for large parallel computing architectures which are becoming ever-more-necessary as problem sizes continue to increase beyond the scope of single processor architectures.
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Baggio, Giacomo. "Novel Results on the Factorization and Estimation of Spectral Densities." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3421827.
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This dissertation is divided into two main parts. The first part is concerned with one of the most classical and central problems in Systems and Control Theory, namely the factorization of rational matrix-valued spectral densities, commonly known as the spectral factorization problem. Spectral factorization is a fundamental tool for the solution of a variety of problems involving second-order statistics and quadratic cost functions in control, estimation, signal processing and communications. It can be thought of as the frequency-domain counterpart of the ubiquitous Algebraic Riccati Equation and it is intimately connected with the celebrated Kálmán-Yakubovich-Popov Lemma and, therefore, to passivity theory. Here, we provide a rather in-depth and comprehensive analysis of this problem in the discrete-time setting, a scenario which is becoming increasingly pervasive in control applications. The starting point in our analysis is a general spectral factorization result in the same vein of Dante C. Youla. Building on this fundamental result, we then investigate some key issues related to minimality and parametrization of minimal spectral factors of a given spectral density. To conclude, we show how to extend some of the ideas and results to the more general indefinite or J-spectral factorization problem, a technique of paramount importance in robust control and estimation theory.
In the second part of the dissertation, we consider the problem of estimating a spectral density from a finite set of measurements. Following the Byrnes-Georgiou-Lindquist THREE (Tunable High REsolution Estimation) paradigm, we look at spectral estimation as an optimization problem subjected to a generalized moment constraint. In this framework, we examine the global convergence of an efficient algorithm for the estimation of scalar spectral densities that hinges on the Kullback-Leibler criterion. We then move to the multivariate setting by addressing the delicate issue of existence of solutions to a parametric spectral estimation problem. Eventually, we study the geometry of the space of spectral densities by revisiting two natural distances defined in cones for the case of rational spectra. These new distances are used to formulate a "robust" version of THREE-like spectral estimation.La tesi è divisa in due parti. La prima parte riguarda uno dei problemi più importanti e classici della Teoria dei Sistemi e del Controllo, ossia la fattorizzazione di densità spettrali razionali a valori matriciali, meglio conosciuto come problema di fattorizzazione spettrale. Quest’ultimo rappresenta uno strumento fondamentale per la soluzione di una vasta gamma di problemi riguardanti statistiche del secondo ordine e funzioni costo quadratiche nella teoria del controllo, della stima, dell’elaborazione di segnali e delle comunicazioni. Il problema di fattorizzazione spettrale può essere visto come la controparte nel dominio della frequenza della soluzione di un’Equazione Algebrica di Riccati ed è strettamente connesso con il famoso Lemma di Kálmán-Yakubovich-Popov e, di conseguenza, con la teoria dei sistemi passivi. Questa prima parte fornisce un’analisi approfondita e completa del problema di fattorizzazione spettrale nel caso a tempo discreto, uno scenario sempre più diffuso nelle applicazioni del controllo. Il punto di partenza della nostra analisi è un risultato generale sulla fattorizzazione spettrale che si ispira ad un approccio ideato da Dante C. Youla. Basandoci su questo risultato, esaminiamo quindi alcuni aspetti chiave legati alla minimalità e alla parametrizzazione dei fattori spettrali minimi di una data densità spettrale. Per concludere, mostriamo come estendere alcuni idee e risultati al caso più generale di fattorizzazione spettrale indefinita o fattorizzazione J-spettrale, una tecnica di importanza primaria nella teoria del controllo e della stima robusta. Nella seconda parte della tesi, consideriamo il problema della stima di una densità spettrale incognita a partire da un insieme finito di misure. Seguendo l’approccio THREE (Tunable High REsolution Estimation) di Byrnes, Georgiou e Lindquist, interpretiamo il problema di stima spettrale come un problema di ottimizzazione soggetto ad un vincolo sui momenti generalizzato. In questo contesto, studiamo la convergenza globale di un algoritmo efficiente per la stima di densità spettrali scalari basata sul criterio di Kullback-Leibler. Successivamente, ci spostiamo ad analizzare il caso multivariato, considerando un problema estremamente delicato riguardante l’esistenza di una soluzione ad un problema di stima parametrico. Infine, analizziamo la geometria dello spazio delle densità spettrali rivisitando due distanze naturali definite su coni per il caso di spettri razionali. Queste nuove distanze verranno utilizzate per formulare un problema di stima spettrale "robusta" simile all’approccio THREE.
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Пукас, Андрій Васильович. "Методи та засоби побудови математичних моделей характеристик складних об’єктів в умовах інтервальної невизначеності." Diss., Національний університет «Львівська політехніка», 2021. https://ena.lpnu.ua/handle/ntb/56677.
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У дисертаційній роботі вирішено науково-прикладну проблему зниження обчислювальної складності процесів побудови математичних моделей характеристик складних об’єктів в умовах інтервальної невизначеності з одночасним забезпеченням гарантованої точності цих моделей у межах необхідних для розв’язування задач прийняття рішень. Розроблено метод параметричної ідентифікації інтервальних
моделей характеристик статичних та динамічних об’єктів на основі аналізу інтервальних даних, який грунтується на процедурах самоорганізації та самоадаптації обчислювальних процедур за аналогією з поведінковими моделями бджолиної колонії. Розроблено метод структурної ідентифікації інтервальних моделей характеристик статичних та динамічних об’єктів на основі аналізу інтервальних даних з процедурами самоорганізації та самоадаптації структур моделей. Удосконалено метод еліпсоїдного оцінювання множини значень параметрів інтервальних моделей характеристик статичних об’єктів на основі ітераційної обчислювальної схеми оптимального насиченого планування експерименту, який
грунтується на розпаралеленні процедур обчислень. Створено програмну систему для побудови інтервальних моделей характеристик статичних та динамічних об’єктів, яка об’єднує методи структурної та параметричної ідентифікації, реалізовані на основі поведінкових моделей бджолиної колонії, що забезпечило цілісний підхід до побудови моделей з гарантованою точністю в умовах інтервальної невизначеності та суттєво спростило використання засобів моделювання. Апробовано нові й
удосконалені методи та розроблену програмну систему для розв’язування прикладних задач побудови моделей характеристик статичних та динамічних об’єктів в умовах інтервальної невизначеності, зокрема для моніторингу забруднень атмосфери автотранспортом на прикладі м. Тернополя; ідентифікації зворотного гортанного нерва в процесі хірургічної операції на щитоподібній залозі; моделювання
і прогнозування потужності малої гідроелектростанції «Топольки»; моделювання відвідування веб-сервісів надання адміністративних послуг. В диссертационной работе решена научно-прикладная проблема снижения вычислительной сложности процессов построения математических моделей
характеристик сложных объектов в условиях интервальной неопределенности с одновременным обеспечением гарантированной точности этих моделей в пределах необходимых для решения задач принятия решений. Разработан метод параметрической идентификации интервальных моделей характеристик статических и динамических объектов на основе анализа интервальных данных, основанный на процедурах самоорганизации и самоадаптации вычислительных процедур по аналогии
с поведенческими моделями пчелиной колонии. Разработан метод структурной идентификации интервальных моделей характеристик статических и динамических объектов на основе анализа интервальных данных с процедурами самоорганизации и самоадаптации структур моделей. Усовершенствован метод эллипсоидного оценивания множества значений параметров интервальных моделей характеристик статических объектов на основе итерационной вычислительной схемы оптимального насыщенного планирования эксперимента, основанный на распараллеливании
процедур вычислений. Создано программную систему для построения интервальных моделей характеристик статических и динамических объектов, которая объединяет методы структурной и параметрической идентификации, реализованные на основе поведенческих моделей пчелиной колонии, что обеспечило целостный подход к построению моделей с гарантированной точностью в условиях интервальной неопределенности и существенно упростило использование средств моделирования.
Апробированы новые и усовершенствованные методы и разработанная программная среда для решения прикладных задач построения моделей характеристик статических и динамических объектов в условиях интервальной неопределенности, в частности для мониторинга загрязнения атмосферы автотранспортом на примере г. Тернополя; идентификации обратного гортанного нерва в процессе хирургической операции на щитовидной железе; моделирования и прогнозирования мощности малой
гидроэлектростанции «Топольки»; моделирования посещения веб-сервисов предоставления административных услуг. In the thesis, the scientific and applied problem of reduction the computational
complexity of processes for construction the mathematical models of complex objects characteristics in the conditions of interval uncertainty with simultaneous maintenance of guaranteed accuracy of these models within the limits necessary for decision making is solved. A method of parametric identification of interval models of characteristics of static and dynamic objects based on the analysis of interval data based on procedures of selforganization and self-adaptation of computational procedures by analogy with behavioral
models of bee colony is created. The method of structural identification of interval models of characteristics of static and dynamic objects on the basis of the analysis of interval data with procedures of selforganization and self-adaptation of structures of models is developed. The method of ellipsoid estimation of the set of values of parameters of interval models of characteristics of static objects on the basis of the iterative computational scheme of optimum saturated planning of experiment based on parallelization of computational procedures is improved. A software system for constructing interval models of static and dynamic object characteristics has been created, which combines structural and parametric identification methods based on behavioral models of the bee colony, which provided a holistic approach to building models with guaranteed accuracy in interval uncertainty and greatly simplified the use of modeling tools. New and improved methods and the developed software environment for solving the applied problems of construction the models of characteristics of static and dynamic objects in the interval uncertainty conditions, in particular for monitoring the pollution of the
atmosphere by motor transport on an example of Ternopil; identification of the reverse laryngeal nerve during thyroid surgery; modeling and forecasting the capacity of the small hydroelectric power station "Topolki"; modeling the visiting web services of providing administrative services, were approved.
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Santos, João Paulo Martins dos. "Método multigrid algébrico: reutilização das estruturas multigrid no transporte de contaminantes." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/18/18138/tde-10052016-145452/.
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A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas.The need for solving large linear systems arising from the discretization of partial differential equations modelling physical phenomena motivates the search for scalable numerical techniques. Multigrid algorithms are instances of such techniques.In order to provide a suitable assessment of the solution obtained by such algorithms, an error estimator must be associated to the numerical solution of the discretized problem. In this context, this thesis proposes the reutilization of the hierarchical matrix structures of transfer operators and the restriction to algebraic multigrid methods to speed up the process of solving the linear systems associated with the contaminant transport equation in saturated porous media. In addition, it features the implementation of residual estimates for problems involving constant or non-constant data, the regimes of small- or large-scale advection and the proposal of employing the residual estimates associated to the source term and to the initial condition to build adaptive procedures for the problem data. The development of the computer codes of the finite element method, residual estimator and adaptive procedures were based on the FEniCS project, using the programming language PYTHONR and developed on the Eclipse platform. The implementation of the algebraic methods with reutilization relied upon the libray PyAMG. Grounding on the idea of reutilizing the hierarchical structures, fixed and automatic parameters multigrid methods were proposed and extended to non-stationary iterative methods such as GMRES and BICGSTAB. The numerical results demonstrate that the residual estimator captures the behavior of the real error of the numerical solution, and provide adaptive algorithms for the data whose output mesh yields a numerical solution alike to that obtained from a uniform mesh with more elements. Moreover, the methods with reutilization are faster than those that do not reuse the structures. Besides, the efficiency of such methods can also be observed in the solution of an auxiliary problem, which is necessary for deriving the residual estimates in the regime of large-scale advection. These results encompass both the type SA algebraic multigrid method and those pre-conditioned by them. Moreover, they involve the transport of contaminants in regime of small- and large-scale advection, structured and non-structured meshes, bi- and tridimensional problems and domains with different scales.
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DiPaolo, Conner. "Randomized Algorithms for Preconditioner Selection with Applications to Kernel Regression." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/230.
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The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M-1A ||F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which suggests the quantity is impractical to compute, and a proof we give that ensures the quantity could not possibly be approximated in a useful amount of time by a deterministic algorithm. Using our estimator, we provide a method which can provably select a quality preconditioner among n candidates using floating operations commensurate with running about n log(n) steps of the conjugate gradients algorithm. In the absence of such a preconditioner among the candidates, our method can advise the practitioner to use no preconditioner at all. The algorithm is extremely easy to implement and trivially parallelizable, and along the way we provide theoretical improvements to the literature on trace estimation. In empirical experiments, we show the selection method can be quite helpful. For example, it allows us to create to the best of our knowledge the first preconditioning method for kernel regression which never uses more iterations over the non-preconditioned analog in standard settings.
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Ahmed, Bacha Rekia Meriem. "Sur un problème inverse en pressage de matériaux biologiques à structure cellulaire." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2439.
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Cette thèse, proposée dans le cadre du projet W2P1-DECOL (SAS PIVERT), financée par le ministère de l’enseignement supérieur est consacrée à l’étude d’un problème inverse de pressage des matériaux biologiques à structure cellulaire. Le but est d’identifier connaissant les mesures du flux d’huile sortant, le coefficient de consolidation du gâteau de pressage et l’inverse du temps caractéristique de consolidation sur deux niveaux : au niveau de la graine de colza et au niveau du gâteau de pressage. Dans un premier temps, nous présentons un système d’équations paraboliques modélisant le problème de pressage des matériaux biologiques à structure cellulaire, il découle de l’équation de continuité de la loi de Darcy et d’autres hypothèses simplificatrices. Puis l’analyse théorique et numérique du modèle direct est faite dans le cas linéaire. Enfin la méthode des différences finies est utilisée pour le discrétiser. Dans un second temps, nous introduisons le problème inverse du pressage où l’étude de l’identifiabilité de ce problème est résolue par une méthode spectrale. Par la suite, nous nous intéressons à l’étude de stabilité lipschitzienne locale et globale. De plus une estimation de stabilité lipschitzienne globale, pour le problème inverse de paramètres, dans le cas du système d’équations paraboliques, à partir des mesures sur ]0,T[ est établie. Enfin l’identification des paramètres est résolue par deux méthodes, l’une basée sur l’adaptation de la méthode algébrique et l’autre formulée comme la minimisation au sens des moindres carrés d’une fonctionnelle évaluant l’écart entre les mesures et les résultats du modèle direct, la résolution de ce problème inverse se fait en utilisant un algorithme itératif BFGS, l’algorithme est validé puis testé numériquement dans le cas des graines de colza, en utilisant des mesures synthétiques. Il donne des résultats très satisfaisants, malgré les difficultés rencontrés à manipuler et exploiter les données expérimentalesThis thesis, proposed in the framework of the W2P1-DECOL project (SAS PIVERT) and funded by the Ministry of Higher Education, is devoted to the study an inverse problem of pressing biological materials with a cellular structure. The aim is to identify, of the outgoing oil flow, the coefficient of consolidation of the pressing cake and the inverse of the characteristic time of consolidation on two levels : at the level of the rapeseed and at the level of the pressing cake. First, we present a system of parabolic equations modeling the pressing problem of biological materials with cellular structure; it follows from the continuity equation of Darcy’s law and other simplifying hypotheses. Then a theoretical and numerical analysis of a direct model is made in the linear case. Finally the finite difference method is usedt o discretize it. In a second step, we introduce the inverse problem of the pressing where the study of the identifiability of this problem is solved by a spectral method. Later we are interested in the study of local and global Lipschitizian stability. Moreover, global Lipschitz stability estimate for the inverse problem of parameters in the case of the system of parabolic equations from the measures on ]0,T[ is established. Finally, the identification of the parameters is solved by two methods; one based on the adaptation of the algebraic method and the other formulated as the minimization in the least squares sense of a functional evaluating the difference between measurements and the results of the direct model; the resolution of this inverse problem is done using an iterative algorithm BFGS, the algorithm is validated and then tested numerically in the case of rapeseeds, using synthetic measures. It gives very satisfactory results, despite the difficulties encountered in handling and exploiting the experimental data
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Grosdos, Koutsoumpelias Alexandros. "Algebraic Methods for the Estimation of Statistical Distributions." Doctoral thesis, 2021. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202107155198.
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This thesis deals with the problem of estimating statistical distributions from data. In the first part, the method of moments is used in combination with computational algebraic techniques in order to estimate parameters coming from local Dirac mixtures and their convolutions. The second part focuses on the nonparametric setting, in particular on combinatorial and algebraic aspects of the estimation of log-concave distributions.
Books on the topic "Algebraic estimation method"
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Sira-Ramírez, Hebertt, Carlos García-Rodríguez, John Cortés-Romero, and Alberto Luviano-Juárez. Algebraic Identification and Estimation Methods in Feedback Control Systems. Chichester, UK: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781118730591.
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Bekker, Paul A. Identification, equivalent models, and computer algebra. Boston: Academic Press, 1994.
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service), SpringerLink (Online, ed. L1-Norm and L∞-Norm Estimation: An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.
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Sira-Ramírez, Hebertt, Carlos García Rodríguez, John Cortés Romero, and Alberto Luviano Juárez. Algebraic Identification and Estimation Methods in Feedback Control Systems. Wiley & Sons, Limited, John, 2014.
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Sira-Ramírez, Hebertt, Carlos García Rodríguez, John Cortés Romero, and Alberto Luviano Juárez. Algebraic Identification and Estimation Methods in Feedback Control Systems. Wiley & Sons, Incorporated, John, 2014.
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Sira-Ramírez, Hebertt, Carlos García Rodríguez, John Cortés Romero, and Alberto Luviano Juárez. Algebraic Identification and Estimation Methods in Feedback Control Systems. Wiley & Sons, Incorporated, John, 2014.
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Sira-Ramírez, Hebertt, Carlos García Rodríguez, John Cortés Romero, and Alberto Luviano Juárez. Algebraic Identification and Estimation Methods in Feedback Control Systems. Wiley, 2014.
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Merckens, Arjen, Gerald J. Lieberman, Paul A. Bekker, Tom J. Wansbeek, and Ingram Olkin. Identification, Equivalent Models, and Computer Algebra: Statistical Modeling and Decision Science. Elsevier Science & Technology Books, 2014.
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Witkov, Carey, and Keith Zengel. Chi-Squared Data Analysis and Model Testing for Beginners. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198847144.001.0001.
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This book is the first to make chi-squared model testing, one of the data analysis methods used to discover the Higgs boson and gravitational waves, accessible to undergraduate students in introductory physics laboratory courses. By including uncertainties in the curve fitting, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one- and two-parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics, requiring calculus, are addressed in an advanced topics chapter. This self-contained and student-friendly introduction to chi-squared analysis and model testing includes a glossary, end-of-chapter problems with complete solutions, and software scripts written in several popular programming languages, that the reader can use for chi-squared model testing. In addition to introductory physics lab students, this accessible introduction to chi-squared analysis and model testing will be of interest to all who need to learn chi-squared model testing, e.g. beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences.
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Design of Experiments and Advanced Statistical Techniques in Clinical Research. Singapore: Springer, 2020.
Find full textBook chapters on the topic "Algebraic estimation method"
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Xu, Ling, Feng Ding, and Feng Ding. "Four-Point Algebraic Estimation Method for First-Order Systems via Sine Responses." In Lecture Notes in Electrical Engineering, 620–27. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9698-5_69.
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Kobayashi, Kei, and Henry P. Wynn. "Computational Algebraic Methods in Efficient Estimation." In Geometric Theory of Information, 119–40. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05317-2_6.
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Chorukova, Elena, Sette Diop, and Ivan Simeonov. "On Differential Algebraic Decision Methods for the Estimation of Anaerobic Digestion Models." In Algebraic Biology, 202–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73433-8_15.
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Reid, Greg, Jianliang Tang, Jianping Yu, and Lihong Zhi. "Hybrid Method for Solving New Pose Estimation Equation System." In Computer Algebra and Geometric Algebra with Applications, 44–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11499251_5.
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Lazreg, Sami, Maxime Cordy, and Axel Legay. "Verification of Variability-Intensive Stochastic Systems with Statistical Model Checking." In Leveraging Applications of Formal Methods, Verification and Validation. Adaptation and Learning, 448–71. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19759-8_27.
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AbstractWe propose a simulation-based approach to verify Variability-Intensive Systems (VISs) with stochastic behaviour. Given an LTL formula and a model of the VIS behaviour, our method estimates the probability for each variant to satisfy the formula. This allows us to learn the products of the VIS for which the probability stands above a certain threshold. To achieve this, our method samples VIS executions from all variants at once and keeps track of the occurrence probability of these executions in any given variant. The efficiency of this algorithm relies on Algebraic Decision Diagram (ADD), a dedicated data structure that enables orthogonal treatment of variability, stochasticity and property satisfaction. We implemented our approach as an extension of the ProVeLines model checker. Our experiments validate that our method can produce accurate estimations of the probability for the variants to satisfy the given properties.
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Ushirobira, Rosane, Anja Korporal, and Wilfrid Perruquetti. "Algebraic Estimation in Partial Derivatives Systems: Parameters and Differentiation Problems." In Algebraic and Symbolic Computation Methods in Dynamical Systems, 183–200. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38356-5_7.
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Bloch, Anthony M., and Christopher I. Byrnes. "An Infinite Dimensional Variational Problem Arising in Estimation Theory." In Algebraic and Geometric Methods in Nonlinear Control Theory, 487–98. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4706-1_24.
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Akritas, Alkiviadis G., Adam W. Strzeboński, and Panagiotis S. Vigklas. "Advances on the Continued Fractions Method Using Better Estimations of Positive Root Bounds." In Computer Algebra in Scientific Computing, 24–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75187-8_3.
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Montesinos López, Osval Antonio, Abelardo Montesinos López, and Jose Crossa. "General Elements of Genomic Selection and Statistical Learning." In Multivariate Statistical Machine Learning Methods for Genomic Prediction, 1–34. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-89010-0_1.
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AbstractNowadays, huge data quantities are collected and analyzed for delivering deep insights into biological processes and human behavior. This chapter assesses the use of big data for prediction and estimation through statistical machine learning and its applications in agriculture and genetics in general, and specifically, for genome-based prediction and selection. First, we point out the importance of data and how the use of data is reshaping our way of living. We also provide the key elements of genomic selection and its potential for plant improvement. In addition, we analyze elements of modeling with machine learning methods applied to genomic selection and stress their importance as a predictive methodology. Two cultures of model building are analyzed and discussed: prediction and inference; by understanding modeling building, researchers will be able to select the best model/method for each circumstance. Within this context, we explain the differences between nonparametric models (predictors are constructed according to information derived from data) and parametric models (all the predictors take predetermined forms with the response) as well their type of effects: fixed, random, and mixed. Basic elements of linear algebra are provided to facilitate understanding the contents of the book. This chapter also contains examples of the different types of data using supervised, unsupervised, and semi-supervised learning methods.
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Torres Alberto, Nicolas, Lucas Joseph, Vincent Padois, and David Daney. "A Linearization Method Based on Lie Algebra for Pose Estimation in a Time Horizon." In Advances in Robot Kinematics 2022, 47–56. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08140-8_6.
Full textConference papers on the topic "Algebraic estimation method"
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WATANABE, SUMIO. "ALGEBRAIC GEOMETRICAL METHOD IN SINGULAR STATISTICAL ESTIMATION." In Quantum Bio-Informatics — From Quantum Information to Bio-Informatics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793171_0024.
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Delpoux, Romain, Hebertt Sira-Ramirez, and Thierry Floquet. "Acceleration feedback via an algebraic state estimation method." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760788.
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Riachy, Samer, Yara Bachalany, Mamadou Mboup, and Jean-Pierre Richard. "An algebraic method for multi-dimensional derivative estimation." In Automation (MED 2008). IEEE, 2008. http://dx.doi.org/10.1109/med.2008.4602167.
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Qian, Cheng, Xiao Fu, and Nikolaos D. Sidiropoulos. "A Simple Algebraic Channel Estimation Method for FDD Massive MIMO Systems." In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE, 2019. http://dx.doi.org/10.1109/spawc.2019.8815441.
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Wei, Yan-Qiao, Da-Yan Liu, Chang-Chun Hua, YangQuan Chen, and Driss Boutat. "Algebraic Estimation Method of Multiple Disturbances for a Class of Fractional Order Linear Systems*." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153186.
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Mariooryad, Soroosh, Hossein Sameti, and Hadi Veisi. "An algebraic gain estimation method to improve the performance of HMM-based speech enhancement systems." In 2010 18th Iranian Conference on Electrical Engineering (ICEE). IEEE, 2010. http://dx.doi.org/10.1109/iraniancee.2010.5507051.
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Wei, Yan-Qiao, Da-Yan Liu, and Chang-Chun Hua. "Output-based algebraic disturbance estimation method for a class of disturbed fractional order linear systems." In 2022 10th International Conference on Systems and Control (ICSC). IEEE, 2022. http://dx.doi.org/10.1109/icsc57768.2022.9993880.
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Joshi, S., J. Liu, and S. Ananthakrishnan. "Estimation of Clutch Parameters for Online Diagnostics and Control Applications." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82780.
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The primary goal of this research was to identify the role of non-linear parameter estimation in clutch torque estimation for automotive applications. The benefit of this approach in estimating parameters of a system defined by a set of differential algebraic equations (DAEs) that represents, say, clutch torque profile is investigated. In addition, online implementation, albeit at a slow rate compared to control loop rates is demonstrated. This method of analytical DAE based estimation has significant advantages over purely empirical methods in that it directly identifies the relationships between system problem variables, such as, engine speed, cross shaft angle to variable of interest, say, clutch torque, unlike, indirect approaches [1]. In addition, in contrast with time series evolution of discrete system models based on ARMAX models, this approach allows a designer to know the relationship between system parameters such as friction coefficient, clutch engagement angle, etc and the estimation process leading to better design of clutch control algorithms. However, unlike, the direct digital control methods, DAE based approaches are computationally more intensive resulting in a need for additional onboard processing. One of the goals of this initial research is to study this to identify practical analytical and numerical approaches that will lead to onboard implementation of these algorithms for truck applications, specifically in automated mechanical transmissions (AMTs) [2, 3].
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Miranda, R. S., C. B. Jacobina, E. M. Fernandes, A. M. N. Lima, A. C. Oliveira, and M. B. R. Correa. "Parameter and Speed Estimation for Implementing Low Speed Sensorless PMSM Drive System Based on an Algebraic Method." In PEC 07 - Twenty-Second Annual IEEE Applied Power Electronics Conference and Exposition. IEEE, 2007. http://dx.doi.org/10.1109/apex.2007.357700.
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Ghaderi, P., and M. Bankehsaz. "Effects of Material Properties Estimations on the Thermo-Elastic Analysis for Functionally Graded Thick Spheres and Cylinders." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41475.
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In this paper effects of material properties estimations, used for particulate reinforced composites, on the thermo-mechanical response of functionally graded sphere and cylinder are presented. A numerical solution for an arbitrary material gradation is obtained for each geometry independently. With this assumption, the governing partial differential equations are reduced to an ordinary differential equation in each geometry. The thermo-elastic solution for hollow sphere is derived using spherical symmetry. However, plane strain and axial symmetry are assumed for solving hollow cylinder. In the numerical method, radial domain is divided into some finite sub-domains and material properties are assumed to be constant in each sub-domain. With this assumption, the governing thermal and mechanical equations in each sub-domain are an ODE with constant coefficients. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the thermo-elastic responses for the thick-walled FG sphere and cylinder are obtained. Three methods of gradation are used for comparing the effects of different material properties estimations on the results; Rule of Mixtures as a conventional method, Mori-Tanaka estimation and self-consistent scheme. The results show that estimations for material properties could be influential to the thermo-elastic response for some profiles of volume fractions of constituents. However, the effect on elastic response is negligible.