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Interval Type-2 Fuzzy T-S Modeling For A
Heat Exchange Process On CE117 Process
Trainer
Proceedings of 2011 International Conference on Modelling, Identification
and Control, Shanghai, China, p.p. 457-462, June 26-29, 2011
Outline
• Abstract
• Introduction
• Ce117 process trainer and heat exchange process
• The proposed interval type-2 fuzzy modeling
method
• The experiment and its results
• Conclusions
• References
Abstract
• In this paper, a modified interval type-2 fuzzy T-S modeling
method is applied to a heat exchange process on the equipment
CE117 Process Trainer. First, subtractive clustering method
combined with least square method is employed to build the
type-1 fuzzy T-S model. Then the type-2 fuzzy T-S model is
obtained from the type-1 model through unconstrained
optimization where the Nelder-Mead Simplex method is
utilized.Finally, the results of the experiment prove the
efficiency of the proposed algorithm.
Introduction
• Type fuzzy sets, originally introduced by Zadeh [1], provide
additional degree of freedom in both Mamdani and T-S fuzzy logic
systems. This grants the type-2 fuzzy logic systems the potential to
perform better than type-1 fuzzy logic systems especially when
serious nonlinearity and uncertainty exist.
• In this paper, we build a type-1 T-S fuzzy model using subtractive
clustering method [7]-[8] and least square method to get the premises
and the consequences respectively. Then the Nelder-Mead Simplex
method [9]-[10] is adopted to obtain the type-2 model by varying the
parameters of the premises and consequences in the type-1 model. By
making no distinction between the left and right ends of the type-2
fuzzy premise and consequence parameters, the computation of the
type-2 model output has been simplified
Introduction
• The rest of this paper is arranged as follows. In Section II, some
background knowledge about the CE117 Process Trainer and
the law of heat exchange process is introduced. In Section III,
the algorithm proposed to obtain the type-1 and type-2 model is
presented in detail with an example included to illustrate its
efficiency. A type-1 and a type-2 fuzzy T-S model are
constructed with their accuracy being compared for a heat
exchange process on CE117 Process Trainer in Section IV.
Finally conclusions are drawn in Section V.
Ce117 process trainer and heat exchange
process
Ce117 process trainer and heat exchange
process
• According to the knowledge of heat transfer [11], the
mechanism of heat transfer between TT5 (water temperature in
Process Vessel) and TT1 (water temperature in Heater Tank)
through the Heat Exchanger Coil surfaces is one kind of
convection. This is because water in Heater Tank is in motion
through Heat Exchanger Coil, and so is water in Process Vessel
because of the rotary stirrer. According to Newton’s law of
cooling [11],
Ce117 process trainer and heat exchange
process
• And the convection heat transfer coefficient is not a property of
the fluid. It is an experimentally determined parameter, which
depends on all the variables influencing convection such as the
surface geometry, the nature of fluid motion, the properties of
the fluid and the bulk fluid velcocity. And
• For simplicity, 1/cm is regarded as a part of h, and (1) and (2)
can be combined as follows:
The proposed interval type-2 fuzzy modeling
method
• A. The Proposed Algorithm :
• In this paper, a type-1 fuzzy T-S model is first constructed with subtractive
clustering and least squares method to obtain the premises and the
consequences respectively. Then the Nelder-Mead Simplex Method is
applied to determine the variance of the parameters of both premises and
consequences to build the type-2 fuzzy T-S model.
The proposed interval type-2 fuzzy modeling
method
• There are many methods to compute the output of a type-2
fuzzy T-S model [12]-[14]. Some are based on the theoretical
defuzzification of type-2 fuzzy sets but suffer a lot from
computation complexity. Others are linear combinations of the
right and left boundaries of FOU (footprint of uncertainty) [15]
of type-2 fuzzy sets as listed bellow, which reduce the cost of
computation to some extent.The model output was formulated
as follows:
The proposed interval type-2 fuzzy modeling
method
• The output of type-2 T-S fuzzy model is computed as follows
The proposed interval type-2 fuzzy modeling
method
• The steps to construct the type-1 and type-2 fuzzy T-S models
are as follows:
The proposed interval type-2 fuzzy modeling
method
The experiment and its results
The experiment and its results
Conclusions
• This paper built a type-1 fuzzy T-S model and a type-2 fuzzy T-
S model for a heat exchange process on CE117 Process Trainer.
And some comparisons were given of the ability to approximate
the real process between the two models. When obtaining the
type-2 model from the type-1 model, some trivial restrictions
were removed. Then an unconstrained optimization algorithm
named Nelder-Mead simplex method was introduced to build
the type-2 model. At last, the experiment results showed that the
type-2 fuzzy model was more effective than the type-1 one
when there existed uncertainties in real-time circumstances and
thus could be better.
References
References