15 research outputs found
EXPERIENCES IN EXPERT SYSTEM DEVELOPMENT
Experiences of AI technology application in engineering domain are discussed and illustrated
by several demonstrative examples. Economic aspects of development are also
considered
THE CONVOLUTION OF SERIES AND ITS APPLICATION ON BAR STRUCTURE
The cascade model is widely applied in water-currents flow calculations. The
mathematical background of the cascade models is convolution. The
convolution, especially in the case of continuous functions, is usually
solved by Laplace transformation, which is handled with considerable
difficulty.
This study principally deals with convolution of series, rather than
continuous functions. The convolution is traced back to the multiplication
of the series´ characteristic polynomials. To find a suitable solution for
this task, instead of the traditional definition of the linear space a more
general definition was adopted. According to this adopted definition, the
linear combination created by elements of module from vectors under addition
in a way that the external relationship -instead of multiplying the vectors
with real numbers- is solved by square matrixes. To cast the external
relationship into a matrix multiplication form is possible because the
algebraic structure found in the external relationship sufficient to be
`ring´ according to the general definition of the linear space, and it is
not required to be `field´ (body) as what used to be the common concept in
traditional engineering practice.
The method can be applied on any model that can be described by the linear
differential equations with constant coefficients. To make it easy to follow
each step of implementing the procedure it was demonstrated by application
on one of the most simple bar structures, that is a Kelvin-Voigt type
material model of cantilever
Sorozatok konvolúciójának alkalmazásai
Műszaki folyamatok modellezĂ©sĂ©re (műanyagok deformáciĂłi, Ă©pĂĽletek sĂĽllyedĂ©se, árhullámok követĂ©se, vĂzkivĂ©tel kĂştcsoportokbĂłl, vĂzgyűjtĹ‘terĂĽletek vĂzhozama, folyami vĂzerĹ‘művek teljesĂtmĂ©nyszámĂtása) gyakran használnak elsĹ‘rendű differenciálegyenleteket, ill. -rendszereket. A feladatok megoldására az alkalmazĂłk körĂ©ben a Runge-Kutta-mĂłdszerek valamelyike, vagy a Laplace-fĂ©le transzformáciĂł kĂnálkozik. A munkaigĂ©nyes Laplace-fĂ©le transzformáciĂł használatát azonban a sorozatok konvolĂşciĂłjának karakterisztikus fĂĽggvĂ©nyekkel megoldott kezelĂ©se egyszerű matematikai eszközökkel helyettesĂtheti, amelyre jelen tanulmány mutat be pĂ©ldát az anyagok viszkoelasztikus viselkedĂ©sĂ©nek körĂ©bĹ‘l, majd vázolja az általánosĂtás lehetĹ‘sĂ©geit