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Wyświetlanie 1-15 z 16
Tytuł:
A generalized fractional calculus of variations
Autorzy:
Odzijewicz, T.
Malinowska, A. B.
Torres, D. F. M.
Powiązania:
https://bibliotekanauki.pl/articles/205955.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
generalized fractional operators fractional variational analysis
Euler-Lagrange equations
natural boundary conditions
Noether's theorem
damped harmonic oscillator
Opis:
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, transversality conditions for free boundary value problems, and a generalized Noether type theorem.
Źródło:
Control and Cybernetics; 2013, 42, 2; 443-458
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of semilinear evolution inclusions via discrete approximations
Autorzy:
Mordukhovich, B. S.
Wang, D.
Powiązania:
https://bibliotekanauki.pl/articles/1839178.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
analiza wariacyjna
różniczkowanie uogólnione
aproksymacja dyskretna
warunek konieczny optymalności
optimal control
variational analysis
generalized differentiation
semilinear evolution inclusions
discrete approximations
necessary optimality conditions
Opis:
This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
Źródło:
Control and Cybernetics; 2005, 34, 3; 849-870
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
Autorzy:
Mordukhovich, B. S.
Wang, D.
Wang, L.
Powiązania:
https://bibliotekanauki.pl/articles/969562.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
discrete approximations
optimal control
variational analysis
endpoint constraints
delay-differential inclusions
multivalued initial conditions
extended Euler-Lagrange formalism
generalized differentiation
Banach and Asplund spaces
necessary optimality conditions
Opis:
This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
Źródło:
Control and Cybernetics; 2008, 37, 2; 393-428
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of constrained delay-differential inclusions with multivalued initial conditions
Autorzy:
Mordukhovich, B. S.
Wang, L.
Powiązania:
https://bibliotekanauki.pl/articles/970519.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
aproksymacja dyskretna
warunek konieczny optymalności
analiza wariacyjna
stabilność
optymalizacja niegładka
różniczkowanie uogólnione
delay-differential inclusions
discrete approximations
necessary optimality conditions
variational analysis
stability
nonsmooth optimization
generalized differentiation
Opis:
This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.
Źródło:
Control and Cybernetics; 2003, 32, 3; 585-609
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape identification via metrics constructed from the oriented distance function
Autorzy:
Delfour, M. C.
Zolesio, J.-P.
Powiązania:
https://bibliotekanauki.pl/articles/970145.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
identyfikacja kształtu
analiza wrażliwości
zagadnienie wariacyjne
przetwarzanie obrazów
metryka
dziedzina Soboleva
metoda prędkości
odległość
shape identification
sensitivity analysis
variational problems
set-valued and variational analysis
image processing
image enhancing
metric
distance
oriented distance function
signed distance function
Sobolev domains
velocity method
cracked sets
Opis:
This paper studies the generic identification problem: to find the best non-parametrized object [Omega] which minimizes some weighted sum of distances to I a priori given objects [Omega]_i for metric distances constructed from the W^1,p-norm on the oriented (resp. signed) distance function which occurs in many different fields of applications. It discusses existence of solution to the generic identification problem and investigates the Eulerian shape semiderivatives with special consideration to the non-differentiable terms occurring in their expressions. A simple example for the new cracked sets recently introduced in Delfour and Zolesio (2004b) is also presented. It can be viewed as an approximation of a cracked set by sets whose boundary is made up of pieces of lines or Bezier curves that are not necessarily connected.
Źródło:
Control and Cybernetics; 2005, 34, 1; 137-164
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic analysis of the steady advection-diffusion problem in axial domains
Autorzy:
Morales, Fernando A.
Powiązania:
https://bibliotekanauki.pl/articles/29519253.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
asymptotic analysis
mixed-type variational formulations
advection-diffusion
Opis:
We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.
Źródło:
Opuscula Mathematica; 2023, 43, 2; 199-220
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stifness operator for boundary problems of structural analysis and several new variational formulations
Autorzy:
Zolotov, A. B.
Sidorov, V. N.
Akimov, P. A.
Mozgaleva, M. L.
Powiązania:
https://bibliotekanauki.pl/articles/402415.pdf
Data publikacji:
2010
Wydawca:
Politechnika Świętokrzyska w Kielcach. Wydawnictwo PŚw
Tematy:
stiffness operator
boundary problems
structural analysis
variational formulations
Opis:
So-called "stiffness operator" for boundary problems of structural analysis is introduced in the distinctive paper. There is a direct analogy between this stiffness operator and corresponding stiffness matrix of the considering structure in terms of finite element method. Namely we can consider stiffness operator as a limiting (continual) generalization of stiffness matrix. The explicit formulation of stiffness operator is presented. Several new variational formulations are discussed as well.
Źródło:
Structure and Environment; 2010, 2, 2; 9-13
2081-1500
Pojawia się w:
Structure and Environment
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal algorithms for seeking the minimum
Autorzy:
Adamski, A.
Korytowski, A.
Mitkowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/747469.pdf
Data publikacji:
1977
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Mathematical programming methods, Numerical analysis, Mathematical programming, optimization and variational techniques
Opis:
.
The definition of the optimality of an algorithm is modified so that the optimal algorithm satisfies Bellman's principle. The search for a minimum using this technique is compared with J. Kiefer's algorithm
Źródło:
Mathematica Applicanda; 1977, 5, 11
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic analysis of nonlinearly elastic shells with variable thickness
Asymptotyczna analiza nieliniowo sprężystych powłok o zmiennej grubości
Autorzy:
Gratie, L.
Powiązania:
https://bibliotekanauki.pl/articles/280441.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
asymptotic analysis
nonlinearly elastic shells
Koiter's model
variable thickness
energy functional
variational problems
Opis:
P.G.Ciarlet recently proposed, and justified with A.Roquefort through the method of formal asymptotic expansions, a nonlinear shell model for shells with constsnt thickness. This model is analogous in its form to the model formerly proposed by W.T.Koiter, but is more amenable to numerical computations. In the same spitit, we propose and we justify here, again by the method of formal asymptotic expansion, a more general nonlinear model, which is valid for shells with variable thickness.
W pracy odniesiono się do nieliniowego modelu powłoki o stałej grubości, który uprzednio został zweryfikowany za pomocą metody formalnych rozwinięć asymptotycznych. Jego konstrukcja ma właściwości analogiczne do innych modeli spotykanych w literaturze, ale jest bardziej dogodna przy zastosowaniu symulacji numerycznej. W tym samym duchu zaprezentowano w pracy metodę formalnych rozwinięć asymptotycznych do zbudowania bardziej ogólnego modelu o podobnym charakterze, ale dotyczącego powłoki o zmiennej grubości.
Źródło:
Journal of Theoretical and Applied Mechanics; 2003, 41, 3; 487-508
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generative modelling of vibration signals in machine maintenance
Autorzy:
Puchalski, Andrzej Adam
Komorska, Iwona
Powiązania:
https://bibliotekanauki.pl/articles/28086927.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne PAN
Tematy:
time-frequency analysis
condition monitoring
anomalies detection
deep generative models
variational autoencoder
data distribution
Opis:
The exponential development of technologies for the acquisition, collection, and processing of data from real-world objects is creating new perspectives in the field of machine maintenance. The Industrial Internet of Things is the source of a huge collection of measurement data. The performance of classification or regression algorithms needs to take into account the random nature of the process being modelled and any incomplete observability, especially in terms of failure states. The article highlights the practical possibilities of using generative artificial intelligence and deep machine learning systems to create synthetic measurement observations in monitoring the vibrations of rotating machinery to improve unbalanced databases. Variational AutoencoderVAE generative models with latent variables in the form of high-level input features of time-frequency spectra were studied. The mapping and generation algorithm was optimised and its effectiveness was tested in the practical solution of the task of diagnosing the three operating states of a demonstration gearbox.
Źródło:
Eksploatacja i Niezawodność; 2023, 25, 4; art. no. 173488
1507-2711
Pojawia się w:
Eksploatacja i Niezawodność
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological derivative for linear elastic plate bending problems
Autorzy:
Novotny, A. A.
Feijoo, R. A.
Padra, C.
Taroco, E.
Powiązania:
https://bibliotekanauki.pl/articles/970132.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pochodna topologiczna
analiza wrażliwości kształtu
sformułowanie wariacyjne
zginanie płyty
topological derivative
shape sensitivity analysis
variational formulation
plate bending
Opis:
This study concerns the application of the Topological-Shape Sensitivity Method as a systematic procedure to determine the Topological Derivative for linear elastic plate bending problems within the framework of Kirchhoff's kinematic approach. This method, based on classical Shape Sensitivity Analysis, leads to a constructive procedure to obtain the Topological Derivative. Utilising the well known terminology of structural optimization, we adopt, the total potential strain energy as the cost function and the equilibrium equation as the constraint. Variational formulation as well as the direct differentiation method are used to perform the shape derivative of the cost function. Finally, in order to obtain a uniform distribution of bending moments in several plate problems, the Topological Derivative was approximated, by the Finite Element Method, and used to find the best place to insert holes. A simple hard-kill like topology algorithm, which furnishes satisfactory qualitative results in agreement with those reported in the literature, is also shown.
Źródło:
Control and Cybernetics; 2005, 34, 1; 339-361
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological derivatives for semilinear elliptic equations
Autorzy:
Iguernane, M.
Nazarov, S. A.
Roche, J. R.
Sokolowski, J.
Szulc, K.
Powiązania:
https://bibliotekanauki.pl/articles/907655.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
optymalizacja kształtu
pochodna topologiczna
nierówność wariacyjna
analiza asymptotyczna
shape optimization
topological derivative
level set method
variational inequality
asymptotic analysis
Opis:
The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L [...] norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 191-205
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A level set method in shape and topology optimization for variational inequalities
Autorzy:
Fulmański, P.
Laurain, A.
Scheid, J. F.
Sokołowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/929713.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
optymalizacja kształtu
pochodna topologiczna
nierówność wariacyjna
analiza asymptotyczna
shape optimization
topological derivative
level set method
variational inequality
asymptotic analysis
Opis:
The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 413-430
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Tool wear condition monitoring in milling process based on data fusion enhanced long short-term memory network under different cutting conditions
Autorzy:
Zheng, Guoxiao
Sun, Weifang
Zhang, Hao
Zhou, Yuqing
Gao, Chen
Powiązania:
https://bibliotekanauki.pl/articles/2038054.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne PAN
Tematy:
tool wear condition monitoring
empirical mode decomposition
variational mode decomposition
fourier synchro squeezed transform
neighborhood component analysis
long short-term memory network
Opis:
Tool wear condition monitoring (TCM) is essential for milling process to ensure the machining quality, and the long short-term memory network (LSTM) is a good choice for predicting tool wear value. However, the robustness of LSTM- based method is poor when cutting condition changes. A novel method based on data fusion enhanced LSTM is proposed to estimate tool wear value under different cutting conditions. Firstly, vibration time series signal collected from milling process are transformed to feature space through empirical mode decomposition, variational mode decomposition and fourier synchro squeezed transform. And then few feature series are selected by neighborhood component analysis to reduce dimension of the signal features. Finally, these selected feature series are input to train the bidirectional LSTM network and estimate tool wear value. Applications of the proposed method to milling TCM experiments demonstrate it outperforms significantly SVR- based and RNN- based methods under different cutting conditions.
Źródło:
Eksploatacja i Niezawodność; 2021, 23, 4; 612-618
1507-2711
Pojawia się w:
Eksploatacja i Niezawodność
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations
Autorzy:
Abdulazeez, Sadeq Taha
Modanli, Mahmut
Husien, Ahmad Muhamad
Powiązania:
https://bibliotekanauki.pl/articles/2202054.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear pseudo-hyperbolic partial differential equation
homotopy analysis method
variational iteration method
approximate solution
nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe
homotopijna metoda analizy
metoda iteracji wariacyjnych
rozwiązanie przybliżone
Opis:
The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 5--15
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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