Abstract
The article suggests a method of taking into account the instrument errors arising in the solution of inverse heat-conduction problems on specialized analog computers by the method with self-tuned models.
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Abbreviations
- α :
-
thermal diffusivity
- λ :
-
thermal conductivity
- α:
-
heat-transfer coefficient
- Θ:
-
relative temperature
- δ :
-
wall thickness
- τ :
-
time
- C:
-
electrical capacity
- R:
-
electrical resistance
- R′:
-
leakage resistance
- K=R/R′:
-
coefficient
- T=RC:
-
time constant
- n:
-
number of nodal points of the grid
- U:
-
voltage
- p:
-
Laplace operator
- x:
-
coordinate
- Δx:
-
discretization step of the coordinate
- \(\bar X(\tau )\) :
-
vector of state of the object
- y(τ):
-
vector of observation of the object
- \(\bar U(\tau )\) :
-
control vector
- \(\bar \Theta (\tau )\) :
-
vector of the unknown parameters
- \(\bar \varepsilon (\tau ), \bar \xi (\tau )\) :
-
vectors of measurement noise
- Ô:
-
estimate
Literature cited
M. P. Kuz'min, Electrical Modeling of Nonsteady Heat Exchange Processes [in Russian], Énergiya, Moscow (1974).
V. E. Prokof'ev, Inventor's Certificate No. 481043, “Grid integrator for solving non-linear problems,” Byull. Izobret., No. 30 (1975).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 821–825, November, 1983.
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Kuz'min, M.P., Strelyaev, S.I. Taking instrument errors into account in solving inverse heat-conduction problems with specialized analog computers. Journal of Engineering Physics 45, 1312–1315 (1983). https://doi.org/10.1007/BF01254742
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DOI: https://doi.org/10.1007/BF01254742