application of taguchi-grey method to evaluate …...cycles (rankine or carnot). according to...

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 10, Issue 10, October 2019, pp. 52-63, Article ID: IJMET_10_10_005

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=10

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

APPLICATION OF TAGUCHI-GREY METHOD

TO EVALUATE THE PERFORMANCE OF

ENERGY PRODUCED BY USING TRILATERAL

FLASH CYCLES AND LOW-GRADE

RENEWABLE HEAT

Mohammed Yunus* and Mowaffq M. Oreijah

Mechanical Engineering Department, College of Engineering and Islamic Architecture,

Umm Al-Qura University, Makkah, KSA

*[email protected]

ABSTRACT

Increased in population and automation of process have upsurge the demands of

fossil fuels drastically. Although the solar, bio-mass, geothermal etc. energy

renewable resources are easily available for extraction, the contemporary topics like

very high initial costs and power developing costs have curtailed their progress.

Improvements on current power production methods demand implementing a strong

thermal system to draw energy from low-grade renewable heat sources as most of the

present techniques can only extract high temperature resources and are very

expensive. A proposed binary system having Trilateral-Flash-Cycle (TFC) and a

reaction turbine would tackle the contemporary topics with low operation cost and

widely utilize the available sources to generate direct power by means of a

hydrothermal with the reduced greenhouse gas emissions. The performance

characteristics measured were efficiency, Gross power and nozzle flow area have

been optimized for input factors such as speed, isentropic efficiency, binary working

fluids and turbine diameters using hybrid Taguchi based grey relation analysis (GRA)

where experimental trials carried out with Taguchi L9 orthogonal array. The multiple

response optimization and ranking of input parameters were productively completed

by GRA to find the effect of each of it. Analysis of variance produced the higher

significant factor from selected parameters with percentage of their contribution and

was confirmed with an affirmation (verification) test for the obtained optimal set of

factors. Thus, the hybrid GRA with Taguchi technique design provides the optimal

design parameters affecting multi-performances of TFC system.

Key words: Taguchi-Grey Relation; Trilateral- Flash-Cycle; Geo-thermal energy;

Binary working Fluids; Thermal efficiency and ANOVA

Application of Taguchi-Grey Method to Evaluate the Performance of Energy Produced by using

Trilateral Flash Cycles and Low-Grade Renewable Heat


Cite this Article: Mohammed Yunus and Mowaffq M. Oreijah, Application of

Taguchi-Grey Method to Evaluate the Performance of Energy Produced by using

Trilateral Flash Cycles and Low-Grade Renewable Heat. International Journal of

Mechanical Engineering and Technology 10(10), 2019, pp. 52-63.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=10

1. INTRODUCTION

Energy retrieving from the largely available clean and renewable sources (especially from

low amount of heat) would become the significant solution for meeting demand such as dual

(binary) power system (BPS) to convert into electricity. BPS is successfully applied in geo,

solar-thermal energy and retrieval of waste heat from industries and industrial wherein ORC

(Organic Rankine Cycle) is mature technique employed to retrieve sources of geothermal

energy in various parts of the world (Oreijah et al., 2019). It is high time to investigate other

possible techniques for improving the efficiencies of available BPS using other thermo

principles of cycle such as Trilateral Flash Cycle (TFC). TFCs are employed for retrieving

excess amount of heat present in the low-grade heat resources compared to other conventional

cycles (Rankine or Carnot). According to (DiPippo et al., 2007), the main advantages of TFC

are the employing hot fluid not vapor while entering the expander. Therefore, there is no extra

energy is needed drawing from developed energy for phase transformation (fluid to vapor).

As a result, the net power developed by converting into mechanical from thermal-energy is

larger in contrast to conventional cycles. The main motive for TFC implementation is to

reduce the irreversibility in the heat transfer process occurs between the primary hot source

(low-grade waste heat) and the working fluid (coolants) in binary power system. As the

source temperature increases, recovering capacity of binary working fluid increases and in

turn thermal energy for each unit heat source at a given mass flow rate and temperature

increases power output. As far as the efficiency of TFC remains lesser than other conventional

cycles but in terms of overall efficiency based on full conversion of thermal (from heat

resource) into the mechanical energy is still higher due to utmost capability of TFC for

extracting the sensible heat of hot source in contrast to other conservative cycles. Besides,

various scientists have reported that no appropriate expander (or turbine) was cascaded for

TFC system to exploit the enormous quantity of the obtained thermal energy. Presently

available screw type expander has not proved efficient in TFC based system.

Bryson (2007) noticed the work yield is due to the energy change in the course of heating

less than that dissipated in cooling. All Heat engines (ORC and TFC) use this as key principle

as at present, they are most successful equipments to produce electricity from various thermal

sources economically. Using new improved heat engines, cycles, heat sources, working fluids

and plans for power production by employing low amount temperature sources which leads to

redesigning cycle basic factors in BPS would improve solution for existing technology

economically. The basic devices required are condensers, expanders (or turbines), electrical

generators, heat exchanger, and the secondary working fluid.

(Eastop & McConkey, 1993) noticed that standard RC run by a working fluid (WF) water

works only when the thermal source is above 1800C (SKM, 2005) whereas for low amount

temperature thermal resources (LGTR) available below 1500C, therefore water cannot be used

as the WF. RC can be operated employing LGTR with the help of WF other than water

having low saturation temperature at atmospheric pressure. Such WFs are mostly hydrocarbon

organic fluids boil at very low temperatures and few have been effectively employed in BPS.

Therefore, ORC uses organic fluid into RC (Ian K Smith & Marques, 1994) constitutes the

same apparatus of RC but need modification of cycle factors to work with LGTR. In 1960, the

first industrial ORC was developed to use the LGTR (Sawyer & Ichikawa 1980). In 1987,

Mohammed Yunus and Mowaffq M. Oreijah


Tabor and Bronicki studied for using 4 kW solar turbines in ORC and modified to

commercial ORC with Italian company, Ormat (Garg, 1987). Currently, Ormat produces

ORC based systems for geo-thermal and waste heat recovery at high MW thermal energy

level.

TFC involves the expansion of saturated liquid inside the expander instead of saturated

vapor but remains consisting of four processes similar to ORC as shown in figure 1. The

processes start by compressing the WF in a saturated liquid phase by a fluid pump. The

constant pressure WF enters the heat exchanger and heat gets added. The saturated liquid WF

enters the Reaction Turbine with the isentropic expansion where the temperature and pressure

of the WF decrease simultaneously. Finally, the WF gets condensed going into the condenser

before inflowing to the pump to form a fresh cycle. The working theory of TFC was explored

widely in 1992 (Ian K Smith, 1993; I. Smith, 1992). The TFC offers two benefits to use as an

striking thermo principled cycle such as firstly, it corresponds the temperature profiles,

secondly, it get operated at actual pressures to implement them efficiently practicable for the

low-power functions (Zamfirescu & Dincer, 2008). The key output shows that the TFC best

med the considered Kalina and ORC by an increment of 7 % under similar operating

parameters. That was due to the ability of TFC to recover most of the heat from the heat

source.

The efficiency of the BPS can be improved by improving the efficiency of individual

components among several techniques to develop the thermodynamic performance. Each

component has various control parameters and optimum value of these factors will contribute

to improvement of various outputs of TFC based BPS. As the trilateral shows an advantage of

increasing the heat retrieval from heat resource, yet, required to develop an effective expander

to improve the power utilization essentially due to the pressure difference of the WF. The

expander (outflow reaction turbine) is the major unit in the BPS to extract the power and by

thermal efficiency will be increased gradually with design parameters namely, diameters,

speed of rotation. WF in BPS has the vital role in achieving efficiency and the productivity.

Some characteristics of the WF are important for selecting the proper WF such as higher

thermal conductivity, thermodynamically stable, compatible with a wide range of materials,

low toxicity. Another output exit nozzle area to be optimized. In this work, multi optimization

of outputs under various control factors listed in Table 1 are carried out using taguchi based

grey relation analysis to find optimum values of control factors for improving the outputs.

In the present complex and multi response system involving various factors

simultaneously affecting it has to be evaluated for the developing design by knowing which of

the parameters affect the system significantly. On the other hand, the relationship between

various factors remains grey as information or data on them not clear or complete or doubtful

as well as complex to achieve realistic and investigational data from much scattered for

analysis. Various conventional statistical methods such as factor and regression analysis are

commonly used for finding mutual effect of relationship of dependent and independent

parameters between variables need vast data and should match the given characteristic

distribution. It is very hard to attain the data on relationship of parameters using such

methods. Hence, conventional multi output statistical techniques have difficulties in giving a

realistic justification and to overcome these advantages, a new statistical method to be used.

Taguchi based Grey relational approach (GRA) considered as well-organized tool which

performs examination by arranging an outline for planning, predicting, and grouping of grey

schemes. GRA offers advantages like miniature models without characteristic distribution,

independent variables and a minimum amount of computation, with little information besides,

being a clear-cut and precise technique for choosing factors with unique settings [4]. Hence,

the GRA is utilized to carry out multi output optimization for developing GRG (grey




relational grade) with various grades to arrange the rank of the grey relationship within

independent and dependent factors. The control factors (refer Table 1.) and the corresponding

levels of each factor are used for optimizing the TFC based BPS generating power from low

amount of temperature resources. Experimental trials were conducted using Taguchi L9

orthogonal array[16]. GRA involve the steps are as shown in Figure 2.

Table 1: Levels of Process factors for performance characteristics of TFC

Process Parameters Notation Unit Levels of Parameters

Level 1 Level 2 Level 3

Reaction Turbine diameter D M 0.4 0.6 0.8

Working fluids F - R134a R11 R113

Rotational speed of Turbine R Rpm 3500 5000 8000

Isentropic Efficiency E % 50 75 100

Figure 2. Steps followed during Taguchi based hybrid GRA

Transformation of measured values into non- dimension factors ranging the results from

zero to one to consider the level of control parameters magnitudes is called as normalising [7,

8]. In order to perform this sequences of data from original set to comparable are to be

converted. This process of generation of grey relationship of grey data uses various available

techniques. In the present work, hybrid Taguchi GRA employed to optimize the performance

outputs of TFC based BPS generating power from low amount of heat resources for their

multi outputs like Thermal efficiency (ηtherm), Gross power (GP) and Exit Nozzle area (Anozzle)

of a reaction turbine to increase the retrieval capacity of excess heat available. Multi output

characteristics depend upon the quality exceptionality of the initial data which correspond to

the sequence of initial (or original) reference and comparability (or normalized) using (x)

(x), y =1, 2, 3, ..… p; x = 1, 2, 3, ..., q, where p and q are the experimentation runs and

responses of data correspondingly. Also, depending upon its data quality, the main groupings

recognized for normalizing the initial sequence by means of either “smaller-the-better” or

“larger-the-better” referring Eq. (1) or Eq. (2) respectively [9]:

( )

( )

( )

( ) (1)

( )

( )

( )

( ) (2)



Where, ( )

( ) are the maxima and minima values of ( ). But

( ) represent normalized or compatibility and

( ) is the initial sequences of the objective value. In this investigation, p = 9 and q = 3 are employed.

Next step is to evaluate of coefficients such as deviation and grey relational using Eq. (3)

and Eq. (4).

( )

( ) ( ) (3)

Where, ( )

( ) ( ) are the reference (or ideal) sequence, compatible

sequence and the . The grey relational (or distinguishing) coefficient lies in the range of 0 to 1) is evaluated using:

( ( )

( ))) ( )

(4)

Third step is to evaluate the GRGs, (

) acquired by the weighted summation of the ζ grey relational coefficients to signify the of correlation level between primary and

compatible sequences estimated employing Eq. (5):

(

)

(

( ) ( ( ))) (5)

Finally, the GRGs are then ranked in descending order to attain the maximum value of it

for signifying the well-built agreement occur connecting the ideal and the compatible

sequences. The highest GRG value indicates the optimum set of combined control parameters

to achieve the desired outputs.

2. EXPERIMENTAL PROCEDURES

Experiments were initiated by decreasing the flow rate of the WF (either R1341, R11 or

R113) in a reaction turbine operated using TFC and WF flow rate is controlled by feed pump

to increase it till it reaches the sensible heat. Before entering the turbine, WF remains in the

saturated liquid phase. The experiments were carried out with certain factors at different

levels values listed in Table 1. Hot source temperature of low amount heat renewable energy

sources (solar or geo thermal) lies in the range of 125 to 75 ºC with constant flow rate of 0.56

L/sec was maintained during simulation for all set of experiments. Whereas on the cooling

section of the condenser, the temperature range of 19 to 26 ºC with a constant flow rate of

0.52L/sec were maintained. Necessary measuring devices were used in the BPS test rig to

measure the required responses (or thermal characteristics) and using data accumulator or

acquisition system, temperatures and flow rate at all accessible points of cool and hot water

were collected. Moreover, the electric DC generator was coupled to an electronic load device

(having voltmeter and ammeter) capable of varying the magnitude of electric generator load

to record the voltage and the current as the output (power). Accordingly, the developed power

is noted down accurately from experimentation. Using digital strain display, the value of the

output force is recorded as it can be changed into the torque of the turbine. Different control

parameters having numerical values at three levels with the interaction effect were selected as

shown in Table 1. In multi-response optimization, some quality characteristic loss is

anticipated in comparison to an optimization of a single-response but always the total quality

improves depending on appropriate method of choosing factors and their levels that affect




these quality characteristics for improving performance outputs of TFC based BPS. The

output characteristics optimized were GP, ηtherm and Anozzle. The Taguchi process is employed

for the carrying out of the experiment’s plan as per orthogonal array (OA) available for four

factors at three levels.

Four columns and nine rows of L9 OA is used in the present study to carry out the

experiments for collecting responses of TFC based BPS (refer Table 2).

3. MULTIPLE OUTPUT OPTIMIZATION OF CONTROL FACTORS BY

GRA

The estimation of performance based output characteristics is judged using greatest values of

GP, TE and NA of BPS. The “higher-the-better” approach for responses is applied to perform

normalization of GRA process by using Eq. (2) [yunus et al., 2015]. Taguchi method was

used for optimization of the multiple-response of performance characteristics to recommend

the field of higher heat withdrawal application. The pre-processed data of responses are listed

in Table 3. The coefficient of grey relation (refer Table 4) of multiple responses estimated

employing using Eq. (4) with the help of coefficients of deviation attained from Eq. (3). All

the input factors considered for equal weight setting at a value of 0.5 were employed to

estimate the GRG from Eq. (5). GRG of each experiment is presented in Table 4 [yunus et al.,

2016]. Thorough investigations of data from Table 4 and Figure 3, signifies that experiment

No. 3 is the best response from the set of all trials as it has large value of GRG, it means

comparable and initial sequences are demonstrating a well-built relationship with each other

[yunus et al., 2017]. GRA finds the most important factor depending on the theory; a

combination of the different levels of input factors afford the largest mean output and is the

optimum factors set for improving heat retrieval effect of TFC based BPS.

Table 2. Experimental trials and data processing of output characteristics of TFC based BPS

TFC performance

Factors

Isen

trop

ic E

ffic

ien

cy

Experimental Results Normalized Data

Ru

n n

o.

Rea

ctio

n

Turb

ine

Dia

met

er

Work

ing F

luid

s

Rota

tional

Spee

d o

f R

T

Outp

ut

pow

er

(KW

)

Ther

mal

Eff

icie

ncy

(%

)

Nozz

le E

xit

area

(mm

2)

Outp

ut

pow

er

Ther

mal

Eff

icie

ncy

Nozz

le E

xit

are

a

Ideal

Sequence

1 1 1

1 0.4 R13

4a

3000 50 339.7 3.4 44.77813

7

0 0 0.3004

2 0.4 R11 5000 75 800.5 8 40.22282 0.5677 0.5672 0.245

3 0.4 R11

3

8000 100 1151.4 11.5

1

70.91513

4

1 1 0.6203

4 0.6 R13

4a

5000 100 939.4 9.39 26.38628

4

0.73882 0.7386 0.0753

5 0.6 R11 8000 50 677.6 6.78 26.4006 0.4163 0.4168 0.0755

6 0.6 R11

3

3000 75 740.8 7.41 101.9404 0.494 0.4945 1

7 0.8 R13

4a

8000 75 924.5 9.25 20.2307 0.721 0.7213 0

8 0.8 R11 3000 100 1083.5 10.8

4

32.9899 0.9163 0.92 0.1562

9 0.8 R11

3

5000 50 641.9 6.42 74.4596 0.3723 0.3724 0.6637



Table 3. Coefficients of deviation and grey relational of output characteristics of TFC based BPS

Run No. Deviation Coefficient Grey Relational Coefficient

GP ηtherm Anozzle GP ηtherm Anozzle

Ideal Sequence 1 1 1 1 1

1 1 1 0.6996 0.33333 0.3333 0.4168

2 0.4323 0.4328 0.755 0.5363 0.536 0.3984

3 0 0 0.3797 1 1 0.5684

4 0.2612 0.2614 0.9247 0.6586 0.6567 0.351

5 0.5837 0.5832 0.9245 0.4614 0.4616 0.351

6 0.506 0.5055 0 0.497 0.4972 1

7 0.279 0.2787 1 0.642 0.6421 0.3333

8 0.0837 0.08 0.8438 0.8566 0.8621 0.3721

9 0.6277 0.6276 0.3363 0.4434 0.44342 0.53

Table 4. Grey relational grades and their order

Run No. Grey Grade Order

1 0.3611 1

2 0.4902 4

3 0.8561 9

4 0.5554 6

5 0.4247 2

6 0.6647 7

7 0.5390 5

8 0.6969 8

9 0.4723 3

From greater average of GRG, optimum parameter level has been found as D1F3R3E3,

i.e., Diameter of 0.4m, working fluid of isopentane, speed of 8000 rpm and isentropic

efficiency of 100%. Output tables were produced employing the Taguchi method to estimate

the average GRG for every level of input factor for performance characteristics of TFC based

BPS (refer Table 6).

Table 5. Mean grey relational grade at each level

Input Parameters Grey Relational Grade

Max.-Min. Rank Level 1 Level 2 Level 3

Reaction Turbine Diameter 0.5691 0.5483 0.5694 0.0211 4

Working fluids 0.5373 0.6644 0.4852 0.1792 2

Rotational speed of RT 0.5742 0.5060 0.6066 0.1006 3

Isentropic Efficiency 0.4194 0.5646 0.7028 0.2834 1

Total mean grey relational grade = 0.5623

The highest GRG values shown in Table 5 for a set of input factors are D1-F2-R3-E3. It

represents the optimum set of TFC input parameters for the multi-outputs of performance

measurements during assessment of extraction of high heat. D1-F2-R3-E3 combination

indicates the Rotor diameter of 0.4m, the working fluid type of isopentane (R113), at a speed

of 8000 rpm and isentropic efficiency of 100%. The main influence of averages of GRG vs

levels is plotted in Figure 3. The dotted lines stand for the total GRG average.




Figure 3. Plot of total average of GRG vs. input parameters



0.080.040.00-0.04-0.08

99

90

50

10

1

Residual

Pe

rce

nt

1.00.80.60.4

0.04

0.02

0.00

-0.02

-0.04

Fitted Value

Re

sid

ua

l0.040.020.00-0.02-0.04

4

3

2

1

0

Residual

Fre

qu

en

cy

16151413121110987654321

0.04

0.02

0.00

-0.02

-0.04

Observation OrderR

esid

ua

l

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Grey Relational Grade

Figure 4. Residual plots of GRG

4. ANOVA (ANALYSIS OF VARIANCE) APPLIED FOR GRG

Analysis of Variance has been used to find out the ranking or grading of GRG at 95%

probability interval for examining the importance level of input parameters on multiple

response of TFC using Minitab® 19 statistical software [yunus et al., 2016]. A total sum of

squared deviations (SST) can be calculated using Eq. (6):

∑(yj ym)

j

(6)

where, N = number of trials in OA, yj = average of GRG for jth

trial and ym = total average

of GRG. Average square (MS) is achieved by using Eq. (7) as follows

(7)

The most influential input factor on the multiple responses is having a large value of F (or

small value of P). The % contribution of an input parameter can be estimated using an Eq. (8)

and corresponding residual plot of GRG is shown in Figure 4 [15].

(8)

The ANOVA GRG results for of BPS have been determined (refer Table 6) and shows the

isentropic efficiency is the only significant control factor multi-outputs considered

simultaneously during high extraction of heat. The % contribution of input factor for

isentropic efficiency in the multi-response performance is 25.96.




Table 6. Analysis of Variance Results on GRG

Source DF Adj SS Adj MS

F-

Value

P-

Value

Reaction Turbine Diameter 2 0.000882 0.000441 0.00 0.996

Working Fluids 2 0.050981 0.025491 0.61 0.493

Rotational speed of RT 2 0.015835 0.007918 25.96 0.015

Isentropic Efficiency 2 0.120527 0.060263 5.49 0.099

Error 0 0 0

Total 8 0.188225

Regression equation

GRG = 0.5623 + 0.006867 *D1 - 0.01400*D2+ 0.007133*D3 - 0.02500*F1+ 0.1021*F2 –

0.07710*F3 + 0.01197*R1 - 0.05630*R2+ 0.04433*R3 - 0.1429*E1+ 0.002367*E2 + 0.1405*E3

5. VERIFICATION OF RESULTS BY VALIDATING TEST

The optimal set of input factors as D1-F3-R3-E2 for maximizing GP, ηtherm and Anozzle are

optimized using hybrid Taguchi and Grey Relational Approach. A confirmation test was

carried out by using an D1-F1-R1-E1 optimal setting. The results of the verification test were

1151.4 KW for GP, ηthermal of 11.51% and Anozzle of 90.9mm2.The confirmation test result is

observed better than the experiments carried out (refer Table 3). Subsequent to finding the

optimal combination of TFC control factors and the most influential factor, the concluding

stage to verify the feasibility of proposed combined Taguchi based grey method by

conducting some confirmation tests. The optimal grey relational grade, гopt, is calculated as

[15]:

∑ ( )

(9)

where, is the total GRG average, , is the GRG average of the of ith

parameter of

optimum levels, and c is the quantity of most influential as regards to TFC based BPS

parameters[16]. In all outputs such as GP, ηthermal and Anozzle for an optimum set of control

parameters were sufficiently higher as compared to those of initial setting of factors (having

0.80). Three supplementary trials were conducted at various levels of optimum parameter set

and the mean of these is considered in the verification test. The forecast GRG values and the

result of the validation test are provided in Table 7. Performance based outputs such as GP

has been enhanced from 1100 to 1150 KW, ηthermal is from 11.5 to 12% and Anozzle is

improved from 85 to 90 mm2.

Table 7: TFC based BPPS performance results using primary and optimum input factors

Initial Process

Parameters

Optimal process parameters

Prediction Experiment

Level D1-F1-R1-E1 D1-F3-R3-E3 D1-F3-R3-E3

Gross Power 1100 - 1151.4

Thermal Efficiency 12 - 11.51

Nozzle Exit Area 85.008 88.075 90.915134

Grey Relational

Grade 0.80 - 0.8561



6. CONCLUSION

BPS using low amount of heat energy available in of geo-thermal energy are employed

proficiently for extracting least possible available heat derived from secondary WF. Response

characteristics experiments such as Thermal efficiency (ηtherm), Gross power (GP) and Exit

Nozzle area (Anozzle) were carried out using TFC and reaction turbine with various WF. The

multi-responses were collected under L9 OA combination of control factors using Taguchi

design approach. The assessment of GRG enumerates the general performance of input

factors of TFC based BPS for developing power from low amount of heat sources. The

highest GRG value was obtained when the diameter of turbine is 0.4m, WF of isopentane,

Speed of 8000 rpm and isentropic efficiency of 100% for performance characteristics and

these could be recommended levels of TFC based BPS control factors for maximizing

responses measured. GRA Ranking determined by employing ANOVA method discovered

that the speed of RT is the most significant control factor which affects the multi-output

characteristics. The contribution of speed is relatively higher about 25.46% when compared

with the other input factors. The optimal set of input factors upon a verification tests revealed

the GRG enhancement is 0.8561 contrasts to primary combination values of input factors

about 0.80 shows substantial improvement in the performances of TFC such as gross power,

thermal efficiency and nozzle exit area have been validated. This investigation reduced time

as well as cost including production cost to increase the quality. The optimization of

combined multiple responses are significantly simplified with repeatability and

possibility.Hence, the hybrid GRA and Taguchi design used for multiple-output optimization

with set of optimal input factors helps in accomplishing substantial improvement of grey

relation.

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application of taguchi-grey method to evaluate …...cycles (rankine or carnot). according to...

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