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