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1
Parameters estimation of photovoltaic module using Grey Wolf optimization method
EN
Parameter prediction of a photovoltaic module is fundamental to simulate the photovoltaic generator for correctly reproduce the photovoltaic curves under natural environment. In this work, a new method for solar parameter estimation applying grey wolf algorithm is presented. This technic mimics the mechanism of the chase and the chain of command of wolves in wildlife. In the grey wolf optimizer algorithm four kinds of wolves are used for simulating the control hierarchy. This technique is tested on three different photovoltaic modules. The results showed the effectiveness and validity of the method to find with great precision the parameters of the three photovoltaic modules at various values of temperatures and illuminations.
PL
Przedstawiono nową metodę określania parametrów ogniw fotowoltaicznych wykorzystującą algorytm Grey Wolf. Wykorzystano cter modele zaworów do symulacji. Algorytm przetestowano na różnych modułach. Modele potwierdziły swoją efektywność dla różnych temperatur i naświetleń.
EN
The paper concerns the application of fractional calculus in the modeling of a selected part of a power system generating unit, which is the high frequency AC exciter. The model’s fractional derivative-based generalization is recalled. The basis of the estimation process for the model consists of two sets of measurement waveforms. In order to solve the fractional and nonlinear problem – a numerical solver is applied. The solver and the estimation procedure have been both implemented in GNU Octave. The model parameter susceptibility is examined. The changes of each model parameter value is studied in a way that the influence on the model output is observed.
EN
Computational Intelligence (CI) is a computer science discipline encompassing the theory, design, development and application of biologically and linguistically derived computational paradigms. Traditionally, the main elements of CI are Evolutionary Computation, Swarm Intelligence, Fuzzy Logic, and Neural Networks. CI aims at proposing new algorithms able to solve complex computational problems by taking inspiration from natural phenomena. In an intriguing turn of events, these nature-inspired methods have been widely adopted to investigate a plethora of problems related to nature itself. In this paper we present a variety of CI methods applied to three problems in life sciences, highlighting their effectiveness: we describe how protein folding can be faced by exploiting Genetic Programming, the inference of haplotypes can be tackled using Genetic Algorithms, and the estimation of biochemical kinetic parameters can be performed by means of Swarm Intelligence. We show that CI methods can generate very high quality solutions, providing a sound methodology to solve complex optimization problems in life sciences.
4
Bayesian multidimensional-matrix polynomial empirical regression
EN
The problem of parameter estimation for the polynomial in the input variables regression function is formulated and solved. The input and output variables of the regression function are multidimensional matrices. The parameters of the regression function are assumed to be random independent multidimensional matrices with Gaussian distribution and known mean value and variance matrices. The solution to this problem is a multidimensional-matrix system of the linear algebraic equations in multidimensional-matrix unknown regression function parameters. We consider the particular cases of constant, affine and quadratic regression function, for which we have obtained formulas for parameter calculation. Computer simulation of the quadratic regression function is performed for the two-dimensional matrix input and output variables.
EN
A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
EN
A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.
EN
At present, concentrations of pharmaceuticals in surface and ground waters are low; however, even low concentrations of certain substances may prove very harmful. One of such pharmaceutical drugs is diclofenac, a popular non-steroidal anti-inflammatory drug (NSAID). For this reason, it is important to determine its mobility in groundwater and to estimate parameters of migration. Authors conducted column tests for two porous media: an artificial one, consisting of glass granules, and a natural one, i.e., sandur sand obtained from a site north of the city of Poznań (Poland). During the test, impulse breakthrough curves of chloride ions and diclofenac were recorded. The results were used to identify a specific sorption model and to determine values of migration parameters. Solutions of the inverse problem using optimisation methods and of equations of mathematical migration models were carried out in a MATLAB environment. Based on test results, the mobility of diclofenac is shown to be very high and comparable to that of chloride ions. The tests also revealed a slight and irreversible sorption of diclofenac on grains of both porous media.
EN
Specific requirements are designed and implemented in electronic and telecommunication systems for received signals, especially high-frequency ones, to examine and control the signal radiation. However, as a serious drawback, no special requirements are considered for the transmitted signals from a subsystem. Different industries have always been struggling with electromagnetic interferences affecting their electronic and telecommunication systems and imposing significant costs. It is thus necessary to specifically investigate this problem as every device is continuously exposed to interferences. Signal processing allows for the decomposition of a signal to its different components to simulate each component. Radiation control has its specific complexities in systems, requiring necessary measures from the very beginning of the design. This study attempted to determine the highest radiation from a subsystem by estimating the radiation fields. The study goal was to investigate the level of radiations received and transmitted from the adjacent systems, respectively, and present methods for control and eliminate the existing radiations. The proposed approach employs an algorithm which is based on multi-component signals, defect, and the radiation shield used in the subsystem. The algorithm flowchart focuses on the separation and of signal components and electromagnetic interference reduction. In this algorithm, the detection process is carried out at the bounds of each component, after which the separation process is performed in the vicinity of the different bounds. The proposed method works based on the Fourier transform of impulse functions for signal components decomposition that was employed to develop an algorithm for separation of the components of the signals input to the subsystem.
EN
The main aim of the paper is to develop a distributed algorithm for optimal node activation in a sensor network whose measurements are used for parameter estimation of the underlying distributed parameter system. Given a fixed partition of the observation horizon into a finite number of consecutive intervals, the problem under consideration is to optimize the percentage of the total number of observations spent at given sensor nodes in such a way as to maximize the accuracy of system parameter estimates. To achieve this, the determinant of the Fisher information matrix related to the covariance matrix of the parameter estimates is used as the qualitative design criterion (the so-called D-optimality). The proposed approach converts the measurement scheduling problem to a convex optimization one, in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gaged sites to the total measurement plan. Then, adopting a pairwise communication scheme, a fully distributed procedure for calculating the percentage of observations spent at given sensor locations is developed, which is a major novelty here. Another significant contribution of this work consists in derivation of necessary and sufficient conditions for the optimality of solutions. As a result, a simple and effective computational scheme is obtained which can be implemented without resorting to sophisticated numerical software. The delineated approach is illustrated by simulation examples of a sensor network design for a two-dimensional convective diffusion process.
EN
We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi–Sugeno (T–S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.
11
Nieobciążone estymatory parametrów rozkładu potęgowego
PL
W pracy sprawdzono właściwości estymatorów parametrów rozkładu potęgowego. Wychodząc z nierówności Rao-Cramera wyznaczono wariancję najefektywniejszego estymatora parametru kształtu. Zaproponowano nową postać nieobciążonego estymatora parametru skali.
EN
The paper examines the qualities of estimators of power distribution parameters. Starting from the Rao-Cramer inequality, the variance of the most efficient estimator of the shape parameter is determined. And a new form of the unbiased estimator of the scale parameter is proposed.
EN
Biofilters are a potential treatment option for removing pollutants from feedlot runoff but little research has been done on their use and design. In this study, two mechanism -based models were developed to simulate biofilter processes: a first-order model and a logistic model. The two models were calibrated and evaluated using nitrogen (N) and phosphorus (P) data collected from rainfall events for an experimental biofilter at Melrose, Minnesota, USA. The first-order model predicted removal efficiencies better than the logistic model. The sensitivity analysis suggested that the predictions of the first-order model are more sensitive to parameter. In addition, the uncertainty analysis suggested that the range in predictive errors could be a consequence of uncertainty of estimating parameter from the limited data set for the first-order model. In contrast, the uncertainty analysis for the logistic model of N suggested that reasons other than the uncertainty in parameter estimation are needed to explain predictive errors. Overall, the study provides a useful tool for assessing biofilter performance that can easily be improved with larger observed data sets. The biofilter model has been implemented in the most recent version of the Minnesota feedlot annualized runoff model (MinnFARM).
PL
Metoda największej wiarygodności (MLE) służy do estymacji parametrów modelu statystycznego dla zadanych danych. Metoda ta pozwala na estymację nieznanych parametrów modelu statystycznego. Parametry te otrzymuje się poprzez maksymalizację funkcji wiarygodności rozważanego modelu. Często w praktyce metoda ta może jednak nastręczać trudności związane z wielomodalnością funkcji wiarygodności oraz niemożnością uzyskania jawnych analitycznych rozwiązań równań wiarygodności. Równania takie można jedynie rozwiązywać za pomocą metod numerycznych. Trudności te dobrze ilustruje estymacja parametrów rozkładu Weibulla z wykorzystaniem metody największej wiarygodności wykonywana w oparciu o prawostronnie cenzurowane dane z eksploatacji. Rozwiązanie przedstawione w niniejszej pracy opiera się na zastosowaniu algorytmu maksymalizacji wartości oczekiwanej (EM). Możliwości aplikacyjne proponowanej metodyki badano na przykładzie danych eksploatacyjnych uzyskanych z przedsiębiorstwa petrochemicznego, dotyczących awarii pięciu pomp odśrodkowych.
EN
The maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model for given data. This method allows us to estimate the unknown parameters of a statistical model. These parameters are obtained by maximizing the likelihood function of the model in question. In many practical situations the likelihood function is associated with complex models and the likelihood equation has no explicit analytical solution, it is only possible to have its resolution through numerical methods. The estimation of the parameters of the Weibull distribution by maximum-likelihood method based on information from a historical record with right censored data shows this difficulty. The solution presented in this article entails using the Expectation-Maximization (EM) algorithm. Actual data from the historical record of 5 centrifugal pumps failures of a petrochemical company were analyzed for application of the methodology.
14
EN
The paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.
EN
Joint probability density function of estimation errors of DGD and power split factor, the parameters defining the first order Polarization Mode Dispersion in an optical fibre, is formulated and used as a tool for investigation of influence of uncertainty of the reference signal, required by PMD measurement method, on uncertainty of the estimates. With the application of confidence intervals the uncertainty is evaluated through numerical analysis. Results can be applicable to PMD monitoring in optical fibre communications.
PL
Sformułowano model łącznego rozkładu prawdopodobieństwa błędów estymacji DGD i współczynnika podziału mocy, parametrów opisujących dyspersję polaryzacyjną I rzędu w światłowodzie, który użyto jako narzędzia do zbadania wpływu niepewności sygnału referencyjnego, wymaganego przez metodę pomiaru PMD, na niepewność estymat. Z zastosowaniem przedziałów ufności niepewność estymat została oceniona metodą analizy numerycznej. Rezultaty mogą znaleźć zastosowanie w monitorowaniu PMD w komunikacji światłowodowej.
16
Problems in Modelling Charge Output Accelerometers
EN
The paper presents major issues associated with the problem of modelling change output accelerometers. The presented solutions are based on the weighted least squares (WLS) method using transformation of the complex frequency response of the sensors. The main assumptions of the WLS method and a mathematical model of charge output accelerometers are presented in first two sections of this paper. In the next sections applying the WLS method to estimation of the accelerometer model parameters is discussed and the associated uncertainties are determined. Finally, the results of modelling a PCB357B73 charge output accelerometer are analysed in the last section of this paper. All calculations were executed using the MathCad software program. The main stages of these calculations are presented in Appendices A−E.
EN
Interrupt Timed Automata (ITA) are an expressive timed model, introduced to take into account interruptions according to levels. Due to this feature, this formalism is incomparable with Timed Automata. However several decidability results related to reachability and model checking have been obtained. We add auxiliary clocks to ITA, thereby extending its expressive power while preserving decidability of reachability. Moreover, we define a parametrized version of ITA, with polynomials of parameters appearing in guards and updates. While parametric reasoning is particularly relevant for timed models, it very often leads to undecidability results. We prove that various reachability problems, including robust reachability, are decidable for this model, and we give complexity upper bounds for a fixed or variable number of clocks, levels and parameters.
EN
This paper describes the unknown parameter and reliability function of the Weibull distribution based on hierarchical Bayesian model for the progressively Type-II censored data. The scale parameter of the Weibull distribution is considered with a gamma prior under the shape parameter is known. Furthermore, the scale parameter of the gamma prior is assumed to be three different known hyper prior. Under these assumptions, the Weibull parameter and reliability function estimators are derived based on the squared error loss (SEL) function, which can be easily extended to other loss functions situation. The result from hierarchical Bayesian method is used to compare with Bayes and maximum likelihood estimate (MLE) methods. The simulation shown that the results from Bayes is the best, followed by hierarchical Bayesian method, and then MLE in terms of root mean square error (RMSE). Finally, one real dataset has been analyzed for illustrative purposes.
PL
W prezentowanej pracy opisano metodę estymacji nieznanego parametru oraz funkcji niezawodności rozkładu Weibulla w oparciu o hierarchiczny model Bayesa dla danych uciętych (cenzurowanych) progresywnie typu II. Rozważano parametr skali rozkładu Weibulla o rozkładzie prawdopodobieństwa apriorycznego gamma w sytuacji, gdzie wartość parametru kształtu była znana. Ponadto, przyjęto, że (hiper)parametr skali rozkładu apriorycznego gamma może mieć trzy różne, znane hiper-rozkłady aprioryczne (ang. hyper priors). Przy tych założeniach, estymatory parametru i funkcji niezawodności rozkładu Weibulla wyprowadzono na podstawie kwadratowej funkcji straty (ang. squared error loss, SEL), którą można łatwo rozszerzyć na inne funkcje straty. Wyniki otrzymane z wykorzystaniem hierarchicznej metody Bayesowskiej porównano z wynikami klasycznej estymacji Bayesowskiej oraz estymacji metodą największego prawdopodobieństwa (ang. maximum likelihood estimate, MLE). Symulacja wykazała, że najlepsze wyniki, jeśli chodzi o średnią kwadratową błędów (ang. root mean squared error, RMSE), daje metoda Bayesa, a w dalszej kolejności hierarchiczna metoda Bayesa oraz MLE. W końcowej części pracy rozważane problemy zilustrowano analizując zbiór danych rzeczywistych.
19
Electrothermal Model of Ferromagnetic Cores
EN
This paper presents an electrothermal model of ferromagnetic cores dedicated for SPICE software. The form of this model, dedicated to be used in power electronics applications, is presented and the procedure of estimating magnetic, geometric and thermal parameters of the presented model is proposed. The correctness of the proposed model is verified by comparing the calculated and measured characteristics of the selected ferromagnetic cores operating at different values of flux density, frequency, ambient temperature and cooling conditions. The satisfied agreement between the results of calculations and measurements is obtained.
PL
W pracy zaproponowano elektrotermiczny model rdzeni ferromagnetycznych dla programu SPICE, dedykowany do analizy układów energoelektronicznych. Przedstawiono postać modelu oraz sposób wyznaczania jego parametrów magnetycznych, geometrycznych oraz cieplnych. Poprawność prezentowanego modelu została zweryfikowana przez porównanie obliczonych i zmierzonych charakterystyk wybranych rdzeni wykonanych z różnych materiałów i pracujących przy różnych wartościach indukcji pola magnetycznego, częstotliwości i temperatury otoczenia oraz przy różnych warunkach chłodzenia. We wszystkich przypadkach uzyskano dobrą zgodność między wynikami obliczeń i pomiarów.
EN
In the paper, there are presented the results of parameter estimation of the mathematical model of a synchronous generator operating in a single-machine power system. Noisy dynamic waveforms caused by introducing a disturbance in the form of a step change in the reference voltage or a pseudorandom signal to the generator voltage regulator system were the basis of estimation. It was assumed that the generator load was close to the rated one. Finite and infinite impulse response zero-phase digital filters were used for filtering the waveforms. The least squares method was used for parameter estimation, and the gradient method was applied to minimization of the mean square error.
PL
W artykule przedstawiono wyniki estymacji parametrów modelu matematycznego generatora synchronicznego pracującego w jednomaszynowym systemie elektroenergetycznym. Podstawą estymacji są zaszumione przebiegi dynamiczne wywołane wprowadzeniem do układu regulacji napięcia generatora zakłócenia w postaci skokowej zmiany napięcia zadanego lub sygnału pseudolosowego. Założono, że generator pracuje blisko znamionowego obciążenia. Do filtracji przebiegów wykorzystano filtry cyfrowe o zerowym przesunięciu fazowym o skończonej i nieskończonej odpowiedzi impulsowej. Do estymacji parametrów wykorzystano metodę najmniejszych kwadratów, a do minimalizacji błędu średniokwadratowego metodę gradientową.
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