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1

Parameter identification of space manipulator’s flexible joint

Wojtunik Mateusz, Basmadji Fatina Liliana, Granosik Grzegorz, Seweryn Karol

Journal of Automation Mobile Robotics and Intelligent Systems

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2023

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Vol. 17, No. 3

78--87

EN

A manipulator mounted on a satellite is often used to perform active debris removal missions. The space manipulator control system needs to take the dynamic model of the satellite‐manipulator system into account because of the influence of the manipulator motion on the position and attitude of the satellite. Therefore, precise modeling of the space manipulator dynamics as well as parameter identification are needed to improve the credibility of the simulation tools. In this paper, we presented the identification of the flexible‐joint space manipulator model based on dynamic equations of motion. Experiments were performed in an emulated microgravity environment using planar air bearings. The arbitrarily selected joint‐space trajectory was performed by the manipulator’s control system. The experiments were repeated multiple times in order to analyze the identification method sensitivity. The identification is based on the Simulink SimMechanics model. Thus, the procedure can be used for any space manipulator without the need to obtain analytical relations for dynamic equations each time. Including joint flexibility and spring viscous damping in the dynamic model allowed it to reflect the experimental measurements better than the reference model could. Identified parameters of the flexible joint have values of the same magnitude as corresponding real system parameters.

2

Parameter identification of PMSM based on dung beetle optimization algorithm

Yang Xiaollang, Cui Yuyue, Jia Lianhua, Sun Zhihong, Zhang Peng, Zhao Jiane, Wang Rui

Archives of Electrical Engineering

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2023

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Vol. 72, nr 4

1055--1072

EN

In this paper, a creative dung beetle optimization (CDBO) algorithm is proposed and applied to the offline parameter identification of permanent magnet synchronous motors. First, in order to uniformly initialize the population state and increase the population diversity, a strategy to improve the initialization of the dung beetle population using Singer chaotic mapping is proposed to improve the global search performance; second, in order to improve the local search performance and enhance the convergence accuracy of the algorithm, a new dung beetle position update strategy is designed to increase the spatial search range of the algorithm. Simulation results show that the proposed optimization algorithm can quickly and accurately identify parameters such as resistance, inductance, and magnetic chain of the PMSM, with significant improvements in convergence algebra, identification accuracy and stability.

3

Damage behaviour and GTN parameter analysis of TC4 powder metallurgy titanium alloy during hot deformation

Liu Ronge, Wang Baoyu, Hu Shushan

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 3

art. no. e165, 2023

EN

The damage and fracture behaviour of TC4 powder metallurgy titanium alloy were studied by isothermal uniaxial tensile tests. The results show that microcracks formed at grain boundaries, inclusions, initial pores, and adjacent pores and cracks were gathered and perpendicularly linked to the tensile direction, eventually leading to the macroscopic fracture of the material. Increasing the temperature and strain rate promotes the occurrence of dynamic recovery and subgrain merging nucleation, which leads to an increase in the fracture strain and plasticity of the material. Combined with the response surface methodology and genetic optimization algorithm, the GTN damage parameters were obtained by the reverse calibration method. The calculated flow stresses, based on the GTN damage model, are in good agreement with the experimental ones, indicating that the damage parameters can reflect the damage process of the material. In this study, the sensitivity of the damage parameters along with the influence of temperature and strain rate on them was analysed.

4

Tool to identify parameters of insulation system in electrical machines

Kulesz Barbara, Sikora Andrzej, Słota Damian

Przegląd Elektrotechniczny

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2022

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R. 98, nr 11

292--295

EN

The issue of the equivalent scheme parameter identification for the insulation system in an electrical machine is discussed in the paper. The presented method is based upon a recorded voltage waveform, and Artificial Bee Colony algorithm is used in calculations. A numerical example is presented.

PL

W artykule przedstawiono problem identyfikacji parametrów schematu zastępczego układu izolacyjnego maszyny elektrycznej. Zaproponowana metoda identyfikacji wykorzystuje zarejestrowane przebiegi napicia i algorytm roju pszczelego (Artificial Bee Colony Algorithm). Zamieszczono przykład obliczeniowy.

5

Inter-harmonic parameter identification method based on transform with local maximum spectrum

Sun Lin, Song Jing, Jin Yan

Archives of Electrical Engineering

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2022

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Vol. 71, nr 1

189--209

EN

In order to improve the detection accuracy of harmonics/inter-harmonics in power systems, a new method of harmonic/inter-harmonic detection based on synchrosqueezed transform and the Hilbert operator based on local spectrum maximum is proposed. Firstly, the spectrum of inter-harmonic signals is obtained through short-time Fourier transform, and the local maximum value of the spectrum in the frequency direction is detected. Then, based on the maximum frequency of the spectrum, a new frequency redistribution operator and synchronous extraction operator are constructed. It combines the operators with ridge detection for the decomposition of harmonic/inter-harmonic signals, so as to obtain a series of intrinsic mode function (IMF) components. Finally, the instantaneous amplitude and frequency of the IMF components is obtained by using the Hilbert operator. Meanwhile, according to the instantaneous frequency mutation point in the spectrum, the starting and ending time of transient harmonics/inter-harmonics is located accurately. Based on a low signal-to-noise ratio (SNR), the wavelet packet method (WP), Hilbert Marginal Spectrum method (HMS), synchrosqueezing wavelet transform method (SST), the Hybrid SST method (HSST), enhanced empirical wavelet transform (EEWT) and the proposed method are used to identify the harmonic/inter-harmonic parameters, respectively. The experimental results show that the proposed LMSST method can effectively separate the steady-state and transient harmonic/inter-harmonic signals, and has higher detection accuracy and better noise robustness.

6

Dual-mode control magnetically-coupled energy storage inductor boost inverter for renewable energy

Chen Yiwen, Luo Sixu, Huang Zhiliang, Jiang Jiahui

Archives of Electrical Engineering

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2022

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Vol. 71, nr 1

211--225

EN

A novel magnetically-coupled energy storage inductor boost inverter circuit for renewable energy and the dual-mode control strategy with instantaneous value feedback of output voltage are proposed. In-depth research and analysis on the circuit, control strategy, voltage transmission characteristics, etc., providing the parameter design method of magnetically-coupled energy storage inductors and output filter. The circuit topology is cascaded by the input source 𝑉in, the input filter 𝐶in, a single-phase inverter bridge with a magnetically-coupled energy storage inductor, and a CL filter; The control strategy serves the output voltage as a reference to achieve the switch of step-down and step-up modes smoothly. The simulation results of a 1000 VA 100–200 VDC, 220 V 50 Hz AC inverter show that the proposed inverter can realize single-stage boost power conversion, which can adapt to resistive, capacitive and inductive loads, has high power density and low output waveform distortion. It has good application prospects in small and medium-capacity single-phase inverter occasions with low input voltag

7

Digital Predistortion of Wideband Signals with Reduced Complexity Based on Feedback Wiener System

Bouazza Tayeb H. C., Bachir Smail, Duvanaud Claude

Journal of Telecommunications and Information Technology

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2021

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nr 2

1--10

EN

Digital predistortion (DPD) using baseband signals is commonly used for power amplifier linearization. This paper is devoted to this subject and aims to reduce DPD complexity. In this study, we propose a structure that allows to decrease the number of DPD parameters by using multiple blocks, with each one of them dedicated to characterizing the non-linear behavior and/or memory effects. Such a structure is based on the feedback Wiener system, involving a FIR filter used as a feedback path to reproduce the PA inverse dynamics. A memory polynomial block (MP) is inserted as the final element to minimize the modeling errors. A relevant model identification method, based on an iterative algorithm, has been developed as well. The proposed architecture is used for the linearization of a commercial class-AB LDMOS RF PA by NXP Semiconductors, in wideband communication systems. Comparison of performance with the conventional generalized memory polynomial model (GMP) shows that the proposed model offers similar results, with its advantage consisting in the reduced number of parameters.

8

The importance of structural and practical unidentifiability in modeling and testing of agricultural machinery. Identifiability testing of aggregate model parameters tractor-baler wrapper

Kromulski Jacek, Szczepaniak Jan, Mac Jarosław, Wojciechowski Jacek, Zawada Michał, Szulc Tomasz, Rogacki Roman, Jakubowski Łukasz, Aleksandrowicz Roman

Journal of Research and Applications in Agricultural Engineering

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2021

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Vol. 66, nr 1

4--9

EN

New methods of parametric identification are presented in particular tests of identifiability and non-identifiability of model parameters. A definition of the concept of identifiability of model parameters is presented. Methods for testing identifiability using Laplace transform using similarity transformation and using symbolic calculations are described. Available software for testing model identifiability is presented. These are programs for symbolic calculations (MAPLE MATHEMATICA) operating in the form of web applications and in the form of tools for the Matlab environment. The method of introducing the model to the computational environment in the form ordinary differential equations (ODE) is presented. Examples of calculations identifiability of parameters of the complex model of the tractor-single-axle agricultural machine e.g. a balerwrapper are included.

PL

Przedstawiono nowe metody prowadzenia identyfikacji parametrycznej w szczególności badania identyfikowalności oraz nieidentyfikowalności parametrów modelu. Przedstawiono definicję pojęcia identyfikowalności parametrów modelu. Opisano metody badania identyfikowalności za pomocą transformacji Laplace'a z zastosowaniem transformacji podobieństwa oraz za pomocą obliczeń symbolicznych. Przedstawiono dostępne oprogramowanie do badania identyfikowalności modelu. Są to programy do obliczeń symbolicznych (MAPLE MATHEMATICA) działające w formie aplikacji sieciowych oraz w postaci przyborników do środowiska Matlab. Przedstawiono sposób wprowadzenia modelu do środowiska obliczeniowego w postaci równań różniczkowych zwyczajnych. Zamieszczono przykładowe wyniki obliczeń identyfikowalności parametrów złożonego modelu układu ciągnik-jednoosiowa maszyna rolnicza, np. prasoowijarka.

9

Online parameter identification of SPMSM based on improved artificial bee colony algorithm

Wu Chunli, Jiang Shuai, Bian Chunyuan

Archives of Electrical Engineering

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2021

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Vol. 70, nr 4

777--790

EN

The artificial bee colony (ABC) intelligence algorithm is widely applied to solve multi-variable function optimization problems. In order to accurately identify the parameters of the surface-mounted permanent magnet synchronous motor (SPMSM), this paper proposes an improved ABC optimization method based on vector control to solve the multi-parameter identification problem of the PMSM. Because of the shortcomings of the existing parameter identification algorithms, such as high computational complexity and data saturation, the ABC algorithm is applied for the multi-parameter identification of the PMSM for the first time. In order to further improve the search speed of the ABC algorithm and avoid falling into the local optimum, Euclidean distance is introduced into the ABC algorithm to search more efficiently in the feasible region. Applying the improved algorithm to multi-parameter identification of the PMSM, this method only needs to sample the stator current and voltage signals of the motor. Combined with the fitness function, the online identification of the PMSM can be achieved. The simulation and experimental results show that the ABC algorithm can quickly identify the motor stator resistance, inductance and flux linkage. In addition, the ABC algorithm improved by Euclidean distance has faster convergence speed and smaller steady-state error for the identification results of stator resistance, inductance and flux linkage.

10

An inverse procedure for characterization of material parameters of passive skeletal muscle using FEM and experimental data

Liu Shuailong, Sang Jianbing, Zhang Yi, Zhao Luming, Liu Guirong

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 1

247--259

EN

This work develops an inverse procedure which combines an improved niche genetic algorithm, finite element models and experimental data to identify material parameters of biological tissues behaving like hyperelastic materials. A novel objective function is proposed with two coefficients, which controls the contributions in a well-balanced fashion, respectively, for the small deformation stage and the large deformation stage. This allows us to obtain a global minimizer (of material constants) for the error between FEM solutions and experimental data. Moreover, simple uniaxial compression tests at two different angles (0◦ and 90◦) with respect to the muscle fiber orientation are performed on fresh muscle tissues. This enables us to obtain anisotropic properties of the muscle tissue from the present inverse procedure. The result shows that the proposed inverse procedure is stable and reliable to determine material constants in hyperelastic models for soft biological tissues like skeletal muscles considering anisotropy.

11

Optimization of controlled explosion processes parameters using complex analysis methods

Bomba Andrii Ya., Safonyk Andrii P., Malash Kateryna M.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2019

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T. 9, nr 1

29--32

EN

The optimal charge power and position necessary for forming the maximum possible size of the crater along with preservation of the integrity of the two nearby objects with the numerical quasiconformal mapping methods with the alternate parameterization of the of the medium and process character are established. Unambiguously the boundaries of crater, pressed and disturbed soil zones are identified and the corresponding field dynamic grid is built. A number of experiments was held on the basis of the developed algorithm and their results were analyzed.

PL

Optymalna siła wybuchu i położenie ładunku niezbędne do utworzenia maksymalnego rozmiaru uderzenia, o ile zachowana jest integralność dwóch sąsiednich obiektów, są ustalane za pomocą metod odwzorowań quasikonowych z naprzemienną parametryzacją właściwości medium i procesu. Równocześnie ustala się granice dziury, wciśniętych i niezabezpieczonych części ośrodka oraz konstruuje dynamiczną siatkę pola. Na podstawie opracowanego algorytmu przeprowadzono eksperymenty numeryczne i zanalizowano ich wyniki.

12

Optimal input signal design for fractional-order system identification

Jakowluk W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 1

37--44

EN

The optimal design of excitation signal is a procedure of generating an informative input signal to extract the model parameters with maximum pertinence during the identification process. The fractional calculus provides many new possibilities for system modeling based on the definition of a derivative of noninteger-order. A novel optimal input design methodology for fractional-order systems identification is presented in the paper. The Oustaloup recursive approximation (ORA) method is used to obtain the fractional-order differentiation in an integer order state-space representation. Then, the presented methodology is utilized to solve optimal input design problem for fractional-order system identification. The fundamental objective of this approach is to design an input signal that yields maximum information on the value of the fractional-order model parameters to be estimated. The method described in this paper was verified using a numerical example, and the computational results were discussed.

13

Wybór parametrów dla optymalnej strategii sterowania silnikiem synchronicznym z magnesami trwałymi

Sobieraj T.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 3

91--94

PL

W pracy zaproponowano metodę wyboru parametrów silnika (indukcyjności Ld i Lq ) dla metody pozwalającej na wygenerowanie maksymalnej wartości momentu elektromagnetycznego na jednostkę prądu (ang. MTPA) w silniku z magnesami trwałymi. Wartości indukcyjności oraz strumienia od magnesów trwałych są wyznaczone przy użyciu obserwatora. W pracy wykazana została waga poprawnego wyboru parametrów na pracę silnika. Jako platformę sprzętową zastosowano przekształtnik laboratoryjny (własna konstrukcja) ze sterowaniem opartym na module FPGA i karcie dSpace. Praca zawiera rezultaty badań eksperymentalnych na stanowisku laboratoryjnym.

EN

This paper presents method of selection the motor parameters (inductances Ld and Lq) for MTPA method (Maximum Torque Per Ampere) for permanent-magnet synchronous motor. The inductances and magnet flux of the motor are identified using observer method based on mathematical model. Using the technique, performance of the MTPA algorithm can be improved. This paper presents an idea and a procedure of the proposed algorithm. Hardware platform is based on laboratory power inverter with control block using FPGA and dSpace card. Result of experiment are presented to validate the proposed method.

14

The principles of the creation of the control system for the pumping complex variable-frequency electric drive, taking into account the alteration of the current parameters of the hydrosystem

Zagirnyak M., Kovalchuk V., Korenkova T.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 12

38--41

EN

We demonstrated that the alteration of the basic parameters of the pumping and pipeline equipment accompany the pumping complexes functioning in the unsteady operation modes. We considered the special features of the creation of the extreme system of the automatic control of the pumping complex variable-frequency electric drive taking into account the alteration of the current parameters of the electrohydraulic equipment. We presented the algorithm of the operation of the considered extreme system. The algorithm grounds on the identification of the pumping complex parameters based on the equations of the balance of the hydraulic power harmonic components between the power supply and the elements of the hydrosystem.

PL

Wykazano, że zmienność podstawowych parametrów pompowania i wyposażenia rurociągowego wprowadza system pompowania w stan nieustalony. Rozważono specjalne właściwości tworzenia ekstremalnego systemu automatycznego sterowania napędem zespołu pompowego przy zmienności parametru prądowego w urządzeniu elektrohydraulicznym. Zaprezentowany został algorytm działania rozważanego systemu ekstremalnego. Algorytm bazuje na identyfikacji parametrów zespołu pompowego bazujące na równaniu równowagi pomiędzy mocą zasilania i elementów hydrosystemu.

15

Identyfikacja parametrów modelu kondensatora dwiema metodami Monte Carlo

Kubisa S., Warsza Z. L.

Pomiary Automatyka Robotyka

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2018

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R. 22, nr 2

41--48

PL

Omówiono dokładność identyfikacji wartości parametrów modelu kondensatora rzeczywistego przeprowadzoną dwiema metodami Monte Carlo. Jako prosty przykład numeryczny zidentyfikowano parametry pięciu elementów skupionych RC schematu zastępczego kondensatora na podstawie wyników zasymulowanych pomiarów składowych jego impedancji zastępczej przy kilku częstotliwościach. Parametry mierzone i identyfikowane są powiązane układem nieliniowych zależności i ich rozwiązanie analityczne jest bądź bardzo uciążliwe, bądź może nie być znane. Identyfikację wykonano jednokrotną oraz wielokrotną procedurą iteracyjną Monte Carlo. Dla otrzymanych rozkładów wartości zidentyfikowanych parametrów oszacowano przedziały o prawdopodobieństwie 0,95 i 0,99, które charakteryzują poziom obserwowalności tych parametrów. Dokładność parametrów oszacowano na podstawie otrzymanych rozkładów ich zidentyfikowanych wartości. Omówiono skuteczność i użyteczność identyfikacji parametrów modelu obiema metodami Monte Carlo.

EN

The accuracy of identification of internal parameters of the model of capacitor as the physical device carried out by two Monte Carlo methods of simulation is considered. As an simply numerical example are identified parameters of the five RC elements of the equivalent circuit of capacitor based on results of simulated measurements of its equivalent impedance components at several frequencies. The measured and identified parameters are linked by a system of nonlinear relationships and their analytical solution is either very inconvenient, or even non-existing. Identification has been carried by single and by multiple iterative procedure Monte Carlo. From the pdf distributions of identified parameters their achieved coverage rangers of 0,95 and 0,99 probability are estimated. The results demonstrate the efficiency and utility of identifying internal model parameters by both Monte Carlo methods.

16

An identification procedure of electromagnetic parameters for an induction motor equivalent circuit including rotor deep bar effect

Rolek J., Utrata G.

Archives of Electrical Engineering

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2018

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Vol. 67, nr 2

279–-291

EN

The paper presents an identification procedure of electromagnetic parameters for an induction motor equivalent circuit including rotor deep bar effect. The presented procedure employs information obtained from measurement realised under the load curve test, described in the standard PN-EN 60034-28: 2013. In the article, the selected impedance frequency characteristics of the tested induction machines derived from measurement have been compared with the corresponding characteristics calculated with the use of the adopted equivalent circuit with electromagnetic parameters determined according to the presented procedure. Furthermore, the characteristics computed on the basis of the classical machine T-type equivalent circuit, whose electromagnetic parameters had been identified in line with the chosen methodologies reported in the standards PN-EN 60034-28: 2013 and IEEE Std 112TM-2004, have been included in the comparative analysis as well. Additional verification of correctness of identified electromagnetic parameters has been realised through comparison of the steady-state power factor-slip and torque-slip characteristics determined experimentally and through the machine operation simulations carried out with the use of the considered equivalent circuits. The studies concerning induction motors with two types of rotor construction – a conventional single cage rotor and a solid rotor manufactured from magnetic material – have been presented in the paper.

17

Towards intelligent materials testing with reduced experimental effort for hot forming

Bambach M., Imran M., Buhl J., Härtel S., Awiszus B.

Computer Methods in Materials Science

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2017

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Vol. 17, No. 1

44--50

EN

Hot forming processes are typically used to deform metals to the desired shape at lower forming forces and to control the microstructure. During hot deformation, the microstructure evolves by dynamic recrystallization after certain critical conditions are reached. The final recrystallized grain size controls the post-hot forming mechanical properties of metals and components. To predict the evolution of microstructure and flow stress, various material models were developed and implemented in finite element codes. They require a significant number of material-dependent parameters. Currently, experimental designs with a full-factorial approach for a range of temperature and strain rates are utilized to determine the desired parameters, which involve a huge experimental effort. The aim of this paper is to propose a methodology for parameter identification with reduced experimental effort where progression of testing and data evaluation is parallelized. An iterative, sequential approach is presented which optimizes the new testing conditions based upon preceding experimental conditions. The approach is exemplified for the high-temperature material Alloy-800H, using a material model that allows for accurate predictions of the flow stress. The developed strategy allows to achieve the desired accuracy of the material model by utilizing about a half of test matrix representing a full-factorial design. Hence, an efficient cost- and resource-optimized parametrization of models seems possible.

PL

Procesy plastycznej przeróbki na gorąco są zazwyczaj wykorzystywane zarówno do nadawania wymaganego kształtu wyrobom przy zastosowaniu mniejszych sił jak i do kontrolowania ich mikrostruktury. Mikrostruktura w czasie odkształcania na gorąco zmienia się pod wpływem rekrystalizacji dynamicznej, która występuje po osiągnięciu pewnych krytycznych warunków. Wielkość ziarna po rekrystalizacji wyznacza własności mechaniczne wyrobu po kształtowaniu. Aby przewidywać rozwój mikrostruktury i wielkość naprężenia uplastyczniającego opracowane zostały różne modele, które zaimplementowano w programach z metody elementów skończonych. Te modele wymagają wyznaczenia szeregu parametrów charakterystycznych dla danego materiału. Klasycznym podejściem do wyznaczenia tych parametrów jest przeprowadzenie pełnego cyklu badań w szerokim zakresie temperatur i prędkości odkształcenia, co jest to podejściem bardzo kosztownym. Dlatego za cel pracy postawiono sobie opracowanie metodologii identyfikacji parametrów modelu materiału na podstawie zredukowanej liczby doświadczeń, wykorzystując zrównoleglenie oceny danych. W artykule opisano iteracyjną, sekwencyjną procedurę optymalizującą warunki kolejnych prób doświadczalnych na podstawie wyników prób wcześniejszych. Jako przykład zastosowania tej procedury wybrano odkształcanie stopu 80011 w wysokich temperaturach. Identyfikowano model prawidłowo opisujący naprężenie uplastyczniające tego stopu. Zaproponowana strategia pozwoliła uzyskać wymaganą dokładność modelu wykorzystując połowę prób wynikających z pełnego planu eksperymentów. Przeprowadzona analiza potwierdziła możliwość wydajnej kosztowo identyfikacji modeli.

18

Użytkowy model matematyczny quadrocoptera do celów sterowania

Kusalewicz A., Armiński K., Zubowicz T.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2016

|

Nr 51

103--106

PL

Celem pracy jest budowa użytkowego modelu matematycznego quadrocoptera (QC) z uwzględnieniem urządzeń wykonawczych (UW) oraz identyfikacja jego parametrów. Zadanie identyfikacji sprowadzono do rozwiązania trzech zadań optymalizacji. Wynikiem prac jest model QC uwzględniający wpływ zmian napięcia zasilania na działanie UW.

EN

The goal of the paper is to deliver the utility model of quadcopter (QC) dynamics. The focus is on including the information of powersource voltage drop in actuator system model and its parameter identification. The identification problem is initially set up as an optimisation task in function space due to the impact of the actuators. Under the stated assumptions regarding the actuator system model the identification problem is consequently decomposed into three independent optimisation tasks defined in the model parameter space. The designed laboratory experiments deliver inputoutput data sets used to solve the proposed optimisation tasks. Solving the optimisation tasks results in an utility model for control design purposes that encompasses the nonlinearity of the actuator system and the effects of the powersource voltage drop. The latter is obtained by interpolation of the discrete results into the continuous voltage domain by line fitting under the stated assumption. The obtained model features are considered key factors for the control system design to follow in the future work.

19

Analysis of dynamic models of epidemic

Siwek K., Osowski S.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 7

98--102

EN

The paper presents and compared the dynamic models of the epidemic. The spreading of epidemic is described by the set of differential equations. Two models presenting different complexity are analyzed and compared. The simplest one recognizes only three classes of individuals (susceptible, infected and recovering). The second one takes into account also the dynamic changes of the diseased individuals, inoculations and quarantine. The results of numerical experiments concerning both models are presented and discussed. The results of analysis have been used in developing the optimization method of identification of the parameter values of the numerical model.

PL

Praca przedstawia modele rozprzestrzeniania się epidemii przy użyciu układu równań różniczkowych. Dwa rozwiązania o różnej złożoności są poddane analizie i porównaniu. Model najprostszy uwzględnia jedynie 3 klasy osobników: zdrowi, ale wrażliwi na zachorowanie, zakażeni (chorzy) oraz klasa osobników, którzy są odporni na zakażenie po przebytej chorobie. W modelu bardziej złożonym rozróżnieniu podlegają osobnicy zakażeni oraz ci, którzy w wyniku zakażenia zachorowali. Uwzględnia się również kwarantannę oraz szczepienia ochronne. Praca przedstawia wyniki symulacji procesu rozprzestrzeniania się ospy w obu modelach. Na podstawie wyników analizy zaproponowano metodę optymalizacyjną identyfikacji parametrów modelu umożliwiającą przewidywanie z góry przebiegu epidemii.

20

Heating source localization in a reduced time

Beddiaf S., Autrique L., Perez L., Jolly J. C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

623--640

EN

Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.