Diesel engines pollution and functional-constructive performances compromise optimization, using fuzzy sets.

Dragomir, George ; Beles, Horia ; Blaga, Vasile 等

1. INTRODUCTION

1.1 Creating the fuzzy study model of the diesel engine thermo-gaseo-dynamic

By means of Diesel engines thermo-gaseo-dynamic model, we studied how the variations of the distribution phases and of the valves lift moving laws affect the traction, fuel consumption and NOx gases emission performances. The steps that we followed in order to elaborate the fuzzy-systems-based calculus model are described next.

Setting of the input quantities (criteria) according to which the determination of the technical, economic and NOx gases performances will be carried out. The input quantities are the following:

1. Opening advance of the admission valve (DSA);

2. Closing delay of the admission valve (ISA);

3. Opening advance of the exhaust valve (DSE);

4. Closing delay of the exhaust valve (ISE).

A variation range is associated to each input quantity, within which its specific values can be found. These variation ranges are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where: [L.sup.inf], [L.sup.sup] are respectively the inferior and the superior limit of the variation range associated to the input quantity.

A linguistic variable is associated to each input quantity. Thus the input quantities become the input linguistic variables.

Setting of the linguistic degrees associated to each input linguistic variable

Linguistic degrees (Sofron et al., 1998) or linguistic terms (Preitl & Precup, 1997) are defined for each output linguistic variable. These will "vaguely" characterize the firm information. The sets of linguistic degrees associated to each input linguistic variable will be:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Definition of the evaluation process output quantities The decisional process output quantities are:

1. The effective power (Pe);

2. The effective fuel consumption (Ce);

3. The nitric oxides concentration (NOx).

Setting the value range of the output quantities The value ranges of the output quantities are the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Definition of the linguistic variables corresponding to the output quantities

A linguistic value (Pe, Ce, NOx) is associated to each output quantity.

Setting the linguistic degrees associated to each output linguistic variable

The linguistic degrees or linguistic terms are defined for each linguistic variable associated to the output quantities. These will "vaguely" characterize the firm pieces of information that result from the inference procedures. The sets of linguistic degrees associated to each output linguistic variable are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

An appurtenance function is associated to each linguistic degree that corresponds to an input linguistic variable.

The linguistic variables and linguistic degrees sets, to which appurtenance functions were associated, "vaguely" characterize the firm values of the input and output quantities. The inference machine is formed by a set of rules like the following:

IF (premise) THEN (conclusion) (5)

By "de-fuzzy-ing" we mean the operation of getting a "crisp" value of the output quantity, based on the appurtenance function resulted from the fuzzy inferences. From the multitude of existing de-fuzzy-ing methods (Abate & Dosio, 1990), we will use the "gravity-centre" method, which is the most widely used in practice.

1.2 Implementing of the D118 diesel engine fuzzy model

In order to apply the fuzzy model, several motion laws for the valves were previously created, which differ by means of opening advances, closing delays, process durations and the speeds and accelerations of the valves motion. For this purpose, several cam profiles were designed by means of combined polynomial and sinusoidal laws, which assure shock-free and detachment-free motion of the tappet on the cam. After choosing three different moments for each valve opening and closing, nine different motion laws were obtained, which correspond to 81 versions for the engine distribution epures.

The study of the D118 Diesel engine performance variation was carried out for three speed operating conditions: 1400, 1700 and 2000 rpm, and then constructive and functional optimization criteria were established according to the match to the road condition and pollution control.

The determinist values corresponding to the fuzzy system input and output quantities (DSA, ISA, DSE, ISE, Pe, Ce, NOx) were extracted from the output files of the program that simulates the real functioning-cycle of the Diesel engine.

The values of the valves opening advances and closing delays were used in the fuzzy system for expressing the a [sup.0]RA angle, which characterizes the piston position during the engine cycle, due to the clearer visualization of the distribution phases.

The value ranges for the input quantities were chosen taking into account their minimal and maximal values, corresponding to Diesel engines with similar characteristics:

DSA = [0, 20] [degrees]RA; ISA = [20, 60] [degrees]RA; DSE = [20, 60] [degrees]RA; ISE = [0, 40] [degrees]RA; Pe = [35, 61] kW, Ce = [245, 265] g/kWh Nox = [595, 900] ppm

The linguistic variables associated to the input and output quantities are DSA, ISA, DSE, ISE, respectively Pe, Ce, NOx. (Wenxiu et al., 1999)The appurtenance function used in the defuzzy-ing process is triangular-shaped. The linguistic degrees associated to the input linguistic variables are: SMALL, MEDIUM and BIG.

The linguistic degrees associated to the output linguistic variables are: VERY SMALL, SMALL, MEDIUM, BIG, VERY BIG (Wolkenhauer, 1999). These were given based on the values that resulted from the evaluation stage of the real engine functioning cycle by means of the calculus program.

The inference machine consists of 81 logic rules, based on the correspondence between the linguistic degrees associated to the input and output variables.

The determinist scalar value associated to the output variable is extracted by means of de fuzzy-ing.

The 3D variation diagrams of the effective power Pe, effective specific fuel consumption Ce and nitric oxides emission NOx in terms of two distribution phase moments, obtained by de-fuzzy-ing the functions by means of MATLAB[R] program, are shown in the next figure.

[FIGURE 1 OMITTED]

2. THE OPTIMIZATION OF THE VALVES MOTION LAWS BY MEANS OF FUZZY SETS

Along with the 3D diagrams shown, other instructions can be written in MATLAB[R] in order to work with the files created by the fuzzy systems and return determinist values corresponding to the output quantities, for each set of input quantities from the value ranges. The values are determined by means of specific methods, using an intrinsic approximated logic and each interpolated numerical value agrees to the physical phenomena evolution logic.

The idea on which this optimization method was based consists of creating a calculus program that generates a very large number of value sets for the input quantities. Processing these value sets with fuzzy systems gives value sets for DSA, ISA, DSE, ISE, Pe, Ce and NOx, which are arranged in a value table or in a seven columns and "[p.sup.4]" rows matrix, where "p" is a number given by the designer, that represents the evaluation points from the value range of an input quantity.

The present paper shows the attempts to set a method for determining the constructive parameters of the distribution epure which would assure the optimal engine functioning at different speed regimes. For this purpose, the following optimization criteria were adopted: getting the highest possible power, getting the lowest possible fuel consumption, getting the lowest nitric oxides NOx emission.

The optimization method took shape into a MATLAB[R] program which processes the data that is obtained by applying the fuzzy system based model.

3. CONCLUSION

The following conclusions can be drawn as a result of the studies concerning the engine performances by means of the above-mentioned calculus programs:

--at high speeds, in order to operate the engine with best power, fuel consumption and NOx emission performances, it is necessary that the cam profiles should assure the admission valve opening at 20[degrees]RA advance in regard to the superior dead point and its closing at 33/40[degrees]RA delay in regard to the inferior dead point, the exhaust valve opening at 40[degrees]RA advance and closing at 20/25[degrees]RA;

--at low speeds, in order to operate the engine with best power, fuel consumption and NOx emission performances, it is necessary that the cam profiles should assure the admission valve opening at 10[degrees]RA advance in regard to the superior dead point and its closing at 20[degrees]RA delay in regard to the inferior dead point, the exhaust valve opening at 20[degrees]RA advance and closing at 10/20[degrees]RA.

The fuzzy functions system makes possible a complex analysis of the simultaneous influences of all the parameters of the distribution upon the engine functioning performances.

4. REFERENCES

Abate M., Dosio N. (1990), Use of Fuzzy Logic for Engine Idle Speed Control, SAE Paper 900594

Preitl, St. & Precup, E. (1997), An introduction to fuzzy control process, Editura Tehnica, ISBN 973-31-1081-1, Bucuresti

Sofron, E.; Bizon, N.; Ionita, S. & Raducu, R. (1998), Fuzzy control systems-Modelling and computer aided design, Editura All, ISBN: 973-9431-32-1, Bucuresti

Wenxiu C., Liguang L. et al. (1999), Design and application of fuzzy control system of engine variable valve timing, Vehicle Electronics Conference, (IVEC apos; 99) Proceedings of the IEEE International Volume, p. 26-29 vol.1

Wolkenhauer O., (1999), Fuzzy Systems Toolbox for Use with Matlab, Control Systems Centre, UMIST, Manchaster,