A hybrid MCDM approach for parametric optimization of a micro-EDM process

Abstract

In modern day manufacturing industries, micro-electrical discharge machining (micro-EDM) has emerged out as an efficient material removal process to produce miniaturized components having varying industrial applications. To explore its fullest machining potential, it is always required to operate the micro-EDM process while setting its various input parameters at their optimal levels. In this paper, four popular multi-criteria decision making (MCDM) techniques, in the form of weighted aggregated sum product assessment, technique for order of preference by similarity to ideal solution, combinative distance-based assessment and complex proportional assessment are separately hybridized with teaching-learning-based optimization (TLBO) algorithm to solve the parametric optimization problems of a micro-EDM process. The polynomial regression (PR) models are considered here as the inputs to these hybrid optimizers. Their optimization performance is subsequently validated against the conventionally adopted weighted sum multi-objective optimization (WSMO) approach at four different weight scenarios. It is revealed that for the micro-EDM process, all the MCDM-PR-TLBO approaches provide better solutions as compared to PR-WSMO-TLBO method for the considered weight scenarios. The best performance of the MCDM-PR-TLBO approaches is achieved when 50% weight is assigned to material removal rate. Moreover, it is also noticed that MCDM-PR-TLBO approaches are less computationally intensive than PR-WSMO-TLBO with approximately 9.61–26.70% saving in computational time.

Appendix

$$ \begin{aligned} Y\left( {WS_{{1}} } \right) & = {-}0.{84 } + \, 0.{661} \times {\text{T}}_{\rm on} \\ & \quad + { 1}.00{8} \times {\text{I}}_{\rm p} {-}0.0{369} \\ & \quad \times {\text{V}}_{\rm g} {-}{2}.0{4} \times {\text{F}}_{\rm p} {-}0.0{4488} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} {-}0.{4285} \times {\text{I}}_{\rm p}^{{2}} + 0.000{822} \\ & \quad \times {\text{V}}_{\rm g}^{{2}} + { 5}.0{3} \times {\text{F}}_{\rm p}^{{2}} {-}0.0{971} \\ & \quad \times {\text{T}}_{\rm on} \quad \times {\text{I}}_{\rm p} {-}0.0{144} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad + \, 0.{346} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.0{2}0{4} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} {-}0.{95} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} + \, 0.{1}0{1} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.00{233} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + \, 0.00{12}0{3} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + \, 0.0{23} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{4337} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad {-}0.000{79} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + \, 0.0{42} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{2}0{7} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad \times {\text{F}}_{\rm p} {-}0.0{394} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + \, 0.00{24} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(15)

$$ \begin{aligned} Y\left( {WS_{{2}} } \right) & = {-}{2}.{29} + 0.{551} \times {\text{T}}_{\rm on} + {1}.{892} \\ & \quad \times {\text{I}}_{\rm p} + 0.0{152} \times {\text{V}}_{\rm g} + {2}.{74} \\ & \quad \times {\text{F}}_{\rm p} {-}0.0{3262} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad {-}0.{53}00 \times {\text{I}}_{\rm p}^{{2}} + \, 0.000{173} \\ & \quad \times {\text{V}}_{\rm g}^{{2}} + {12}.{77} \times {\text{F}}_{\rm p}^{{2}} {-}0.{1341} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.0{1131} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad + 0.{26} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + 0.0{16} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} {-}{4}.{39} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{79} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.00{178} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.000{842} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + 0.0{141} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{4234} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad + \, 0.000{15} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.0{72} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{128} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad \times {\text{F}}_{\rm p} + \, 0.0{1}0{3} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.00{1}0 \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(16)

$$ \begin{aligned} Y\left( {WS_{{3}} } \right) & = {-}{3}.{37 } + \, 0.{5}0{1} \times {\text{T}}_{\rm on} + { 2}.{5}0{5} \\ & \quad \times {\text{I}}_{\rm p} + 0.0{525} \times {\text{V}}_{\rm g} + {5}.{92} \times {\text{F}}_{\rm p} \\ & \quad {-}0.0{2612} \times {\text{T}}_{\rm on}^{{2}} {-}0.{594} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad {-}0.000{294} \times {\text{V}}_{\rm g}^{{2}} + {18}.{77} \times {\text{F}}_{\rm p}^{{2}} \\ & \quad {-}0.{168} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.00{921} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{\rm g} + \, 0.{191} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.0{14}0 \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{6}.{76} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.{2}0{2} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.000{7} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.000{6}0{6} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + 0.00{98} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{414} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad + 0.000{72} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.0{88} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.00{81} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad \times {\text{F}}_{\rm p} + 0.0{42} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + 0.000{3} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(17)

$$ \begin{aligned} Y\left( {WS_{{4}} } \right) & = {-}{3}.{91} + 0.{485} \times {\text{T}}_{\rm on} + {2}.{8} \times {\text{I}}_{\rm p} \\ & \quad + 0.0{7}0{8} \times {\text{V}}_{\rm g} + {7}.{44} \times {\text{F}}_{\rm p} \\ & \quad {-}0.0{235} \times {\text{T}}_{\rm on}^{{2}} {-}0.{623} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad {-}0.000{521} \times {\text{V}}_{\rm g}^{{2}} + { 21}.{87} \times {\text{F}}_{\rm p}^{{2}} \\ & \quad {-}0.{187} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.00{824} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{\rm g} + 0.{15} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.0{132} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{7}.{89} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.{261} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.0000{3} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.000{497} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + \, 0.00{85} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{F}}_{\rm p} + \, 0.0{4}0{9} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} + \, 0.000{98} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + \, 0.0{97} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.00{6}0 \\ & \quad \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + 0.0{57} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad {-}0.0000 \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(18)

$$ \begin{aligned} Y\left( {TS_{{1}} } \right) & = {-}{1}.{39 } + \, 0.{3}0{9} \times {\text{T}}_{\rm on} + { 1}.{921} \times {\text{I}}_{\rm p} \\ & \quad + 0.000{8} \times {\text{V}}_{\rm g} {-}{ 2}.{26} \times {\text{F}}_{\rm p} {-} \, 0.0{1746} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} {-} \, 0.{556} \times {\text{I}}_{\rm p}^{{2}} {-} \, 0.000{139} \times {\text{V}}_{\rm g}^{{2}} \\ & \quad + {9}.{22} \times {\text{F}}_{\rm p}^{{2}} {-}0.{228} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.00{311} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + {1}.{113} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.0{2}0{4} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} {-}{ 1}.{66} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{11} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.00{227} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + \, 0.000{335} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{V}}_{\rm g} {-} \, 0.0{178} \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{5}0{6} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} + 0.000{35} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-} \, 0.0{89} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{189} \times {\text{T}}_{\rm on} \times {\text{Vg}} \times {\text{F}}_{\rm p} {-} \, 0.0{41} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.00{48} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(19)

$$ \begin{aligned} Y\left( {TS_{{2}} } \right) & = {-}{4}.{84 } + \, 0.{383} \times {\text{T}}_{\rm on} + { 3}.{61} \times {\text{I}}_{\rm p} \\ & \quad + 0.{1}0{6}0 \times {\text{V}}_{\rm g} + { 8}.{31} \times {\text{F}}_{\rm p} {-}0.0{158} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} {-} \, 0.{664} \times {\text{I}}_{\rm p}^{{2}} {-} \, 0.000{994} \times {\text{V}}_{\rm g}^{{2}} \\ & \quad + {23}.{99} \times {\text{F}}_{\rm p}^{{2}} {-} \, 0.{3}0{7} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.00{469} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + \, 0.{95} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.00{86} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} {-}{ 9}.{83} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-} \, 0.{362} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.00{568} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + \, 0.000{245} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{V}}_{\rm g} {-} \, 0.0{372} \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{448} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} + \, 0.00{143} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.0{82} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-} \, 0.00{7}0 \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.0{88} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.000{3} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(20)

$$ \begin{aligned} Y\left( {TS_{{3}} } \right) & = {-}{5}.{57} + 0.{422} \times {\text{T}}_{\rm on} + {3}.{85} \times {\text{I}}_{\rm p} + 0.{1265} \\ & \quad \times {\text{V}}_{\rm g} + {1}0.{8} \times {\text{F}}_{\rm p} {-}0.0{16}0 \times {\text{T}}_{\rm on}^{{2}} {-}0.{696} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} {-}0.00{12}0{8} \times {\text{V}}_{\rm g}^{{2}} + {29}.0{2} \times {\text{F}}_{\rm p}^{{2}} {-}0.{3}0{3} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-} \, 0.00{513} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + \, 0.{63} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{F}}_{\rm p} + \, 0.0{1}0{7} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{11}.{3}0 \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} \\ & \quad {-}0.{434} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.00{547} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.000{2} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} {-} \, 0.0{27}0 \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} \\ & \quad + 0.0{418} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} + \, 0.00{164} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} + \, 0.{1}0{8} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.00{26} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.{1}0{1} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.000{3} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(21)

$$ \begin{aligned} Y\left( {TS_{{4}} } \right) & = {-}{5}.{71} + 0.{438} \times {\text{T}}_{\rm on} + {3}.{85} \times {\text{I}}_{\rm p} + 0.{13}00 \\ & \quad \times {\text{V}}_{\rm g} + {11}.{4} \times {\text{F}}_{\rm p} {-}0.0{165} \times {\text{T}}_{\rm on}^{{2}} {-} \, 0.{7}0{6} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} {-} \, 0.00{1253} \times {\text{V}}_{\rm g}^{{2}} + { 3}0.{59} \times {\text{F}}_{\rm p}^{{2}} {-}0.{294} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-} \, 0.00{525} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + \, 0.{46} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{F}}_{\rm p} + \, 0.0{119} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{11}.{51} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.{446} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.00{495} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + \, 0.000{189} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} {-}0.0{189} \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.0{4}0{9} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} + \, 0.00{168} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.{111} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{F}}_{\rm p} {-} \, 0.00{15} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.{1}00 \times {\text{I}}_{\rm p} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.000{4} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(22)

$$ \begin{aligned} Y\left( {COS_{{1}} } \right) & = {-}{12}.{2} + {26}.{55} \times {\text{T}}_{\rm on} + { 1}.{9} \times {\text{I}}_{\rm p} {-}{3}.{14} \\ & \quad \times {\text{V}}_{\rm g} {-}{57}0 \times {\text{F}}_{\rm p} {-}{2}.{8}0{4} \times {\text{T}}_{\rm on}^{{2}} {-}{17}.{93} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} + \, 0.0{2944} \times {\text{V}}_{\rm g}^{{2}} + { 485}.{8} \times {\text{F}}_{\rm p}^{{2}} \\ & \quad + {1}.0{9} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.{4}0{2} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad + {86}.{5} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + { 2}.{538} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \\ & \quad + {182} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} + { 16}.{94} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.0{86} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + 0.0{6781} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{Vg }} + { 1}.{18} \times {\text{T}}_{\rm on}^{{2}} \times {\text{Fp }} + { 1}.{875} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{Ip}}^{{2}} {-}0.{2776} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{37}.{9} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}{3}.0{57} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad {-}{8}.{93} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + { 1}.{222} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(23)

$$ \begin{aligned} Y\left( {COS_{{2}} } \right) & = {-}{155}.{1 } + { 25}.{2} \times {\text{T}}_{\rm on} + { 95}.{8} \times {\text{I}}_{{{\rm p}}} + {1}.{4} \\ & \quad \times {\text{V}}_{\rm g} + { 18} \times {\text{F}}_{{{\rm p}}} {-}{1}.{847} \times {\text{T}}_{\rm on}^{{2}} {-}{26}.{31} \\ & \quad \times {\text{I}}_{{{\rm p}}}^{{2}} {-}0.0{1327} \times {\text{V}}_{{{\rm g}}}^{{2}} + 1001.7 \times {\text{F}}_{{{\rm p}}}^{{2}} \\ & \quad {-}{6}.{82} \times {\text{T}}_{\rm on} \times {\text{I}}_{{{\rm p}}} {-}0.{332} \times {\text{T}}_{\rm on} \times {\text{V}}_{{{\rm g}}} \\ & \quad + {42}.{9} \times {\text{T}}_{\rm on} \times {\text{F}}_{{{\rm p}}} + { 1}.{51} \times {\text{I}}_{{{\rm p}}} \times {\text{V}}_{{{\rm g}}} {-}{2}0{1} \\ & \quad \times {\text{I}}_{{{\rm p}}} \times {\text{F}}_{{{\rm p}}} {-}{2}.{4} \times {\text{V}}_{{{\rm g}}} \times {\text{F}}_{{{\rm p}}} + \, 0.{135} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{I}}_{{{\rm p}}} + \, 0.0{387} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{{{\rm g}}} + \, 0.{59} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad \times {\text{F}}_{{{\rm p}}} + { 1}.{993} \times {\text{T}}_{\rm on} \times {\text{I}}_{{{\rm p}}}^{{2}} {-}0.0{92} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{{{\rm p}}} \times {\text{V}}_{{{\rm g}}} {-}{13} \times {\text{T}}_{\rm on} \times {\text{I}}_{{{\rm p}}} \times {\text{F}}_{{{\rm p}}} {-}{1}.{5} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{{{\rm g}}} \times {\text{F}}_{{{\rm p}}} {-}{1}.{74} \times {\text{I}}_{{{\rm p}}} \times {\text{V}}_{{{\rm g}}} \times {\text{F}}_{{{\rm p}}} + 0.{543} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{{{\rm p}}} \times {\text{V}}_{{{\rm g}}} \times {\text{F}}_{{{\rm p}}} \\ \end{aligned} $$

(24)

$$ \begin{aligned} Y\left( {COS_{{3}} } \right) & = {-}{237} + {24}.{1} \times {\text{T}}_{\rm on} + {144}.{8} \times {\text{I}}_{\rm p} \\ & \quad + {4} \times {\text{V}}_{\rm g} + {315} \times {\text{F}}_{\rm p} {-}{1}.{371} \times {\text{T}}_{\rm on}^{{2}} \\ & \quad {-}{32}.0{5} \times {\text{I}}_{\rm p}^{{2}} {-}0.0{411} \times {\text{V}}_{\rm g}^{{2}} + {1345} \\ & \quad \times {\text{F}}_{\rm p}^{{2}} {-}{1}0.{22} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.{269} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{\rm g} + { 22}.{4} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + { 1}.{14} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \\ & \quad {-}{393} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}{12}.{4} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.{149} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + 0.0{226} \times {\text{T}}_{\rm on}^{{2}} \times {\text{Vg }} + \, 0.{55} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{Fp }} + { 2}.0{87} \times {\text{Ton}} \times {\text{I}}_{\rm p}^{{2}} {-}0.00{7} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{4}.{2} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.{81} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + { 1}.{52} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.{27} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(25)

$$ \begin{aligned} Y\left( {COS_{{4}} } \right) & = {-}{275 } + { 25}.{4} \times {\text{T}}_{\rm on} + { 167}.{3} \times {\text{I}}_{\rm p} + { 5}.0{9} \\ & \quad \times {\text{V}}_{\rm g} + { 436} \times {\text{F}}_{\rm p} {-}{1}.{285} \times {\text{T}}_{\rm on}^{{2}} {-}{34}.{93} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} {-}0.0{5}0{7} \times {\text{V}}_{\rm g}^{{2}} + { 1512} \times {\text{F}}_{\rm p}^{{2}} {-}{11}.{81} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.{287} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + { 14}.{4} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{F}}_{\rm p} + { 1}.00 \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}{477} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}{16}.{6} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.{156} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + \, 0.0{189} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{Vg }} + \, 0.{55} \times {\text{T}}_{\rm on}^{{2}} \times {\text{Fp }} + { 2}.{15} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} + \, 0.0{29} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}0.{5} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.{55} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + {2}.{85} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.{17} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(26)

$$ \begin{aligned} Y\left( {CRS_{{1}} } \right) & = {-}0.0{424 } + \, 0.0{242} \times {\text{T}}_{\rm on} \\ & \quad + \, 0.0{8}0{7} \times {\text{I}}_{\rm p} {-}0.00{1}0{9} \\ & \quad \times {\text{V}}_{\rm g} {-}0.{118} \times {\text{F}}_{\rm p} {-}0.00{1293} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} {-}0.0{2799} \times {\text{I}}_{\rm p}^{{2}} + 0.00000{8} \\ & \quad \times {\text{V}}_{\rm g}^{{2}} + 0.{4444} \times {\text{F}}_{\rm p}^{{2}} {-}0.0{1}0{87} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.000{351} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad + \, 0.0{128} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.00{11} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}0.0{48} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} + \, 0.00{31} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} {-}0.0000{61} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.0000{26} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + 0.00{131} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.00{2717} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad + 0.0000{58} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + \, 0.00{37} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.000{77} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad \times {\text{F}}_{\rm p} {-}0.00{283} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + 0.0000{67} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(27)

$$ \begin{aligned} Y\left( {CRS_{{2}} } \right) & = {-}0.{1535} + 0.0{26} \times {\text{T}}_{\rm on} + 0.{1362} \\ & \quad \times {\text{I}}_{\rm p} + 0.00{211} \times {\text{V}}_{\rm g} + 0.{171} \\ & \quad \times {\text{F}}_{\rm p} {-}0.00{125} \times {\text{T}}_{\rm on}^{{2}} {-}0.0{35}0{4} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} {-}0.0000{24} \times {\text{V}}_{\rm g}^{{2}} + {1}.0{563} \\ & \quad \times {\text{F}}_{\rm p}^{{2}} {-}0.0{1268} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.000{337} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} + \, 0.0{111} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} \\ & \quad + 0.00{111} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}0.{282} \times {\text{I}}_{\rm p} \\ & \quad \times {\text{F}}_{\rm p} {-}0.00{75} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + 0.0000{17} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} + \, 0.0000{21} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} \\ & \quad + 0.00{1}0{3} \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.00{27} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} + \, 0.0000{7} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.00{38} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.000{58} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad {-}0.0000{3} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.0000{67} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(28)

$$ \begin{aligned} Y\left( {CRS_{{3}} } \right) & = {-}0.{238 } + \, 0.0{282} \times {\text{T}}_{\rm on} \\ & \quad + 0.{178} \times {\text{I}}_{\rm p} + \, 0.00{446} \\ & \quad \times {\text{V}}_{\rm g} + \, 0.{4}0{3} \times {\text{F}}_{\rm p} {-}0.00{1257} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} {-}0.0{4}0{3} \times {\text{I}}_{\rm p}^{{2}} {-}0.0000{45} \\ & \quad \times {\text{V}}_{\rm g}^{{2}} + { 1}.{473} \times {\text{F}}_{\rm p}^{{2}} {-}0.0{1416} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.000{349} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad + 0.00{66} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.00{1}0{5} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}0.{455} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{156} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + \, 0.0000{68} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.0000{18} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + \, 0.000{9} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + 0.00{2742} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad + 0.0000{81} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.00{47} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.000{4} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ & \quad + \, 0.00{225} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + 0.0000{5} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(29)

$$ \begin{aligned} Y\left( {CRS_{{4}} } \right) & = {-}0.{277} + 0.0{292} \times {\text{T}}_{\rm on} + 0.{199} \\ & \quad \times {\text{I}}_{\rm p} + 0.00{564} \times {\text{V}}_{\rm g} + 0.{512} \\ & \quad \times {\text{F}}_{\rm p} {-}0.00{1231} \times {\text{T}}_{\rm on}^{{2}} {-}0.0{4247} \\ & \quad \times {\text{I}}_{\rm p}^{{2}} {-}0.0000{56} \times {\text{V}}_{\rm g}^{{2}} + {1}.{67} \times {\text{F}}_{\rm p}^{{2}} \\ & \quad {-}0.0{1514} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} {-}0.000{36} \times {\text{T}}_{\rm on} \\ & \quad \times {\text{V}}_{\rm g} + \, 0.00{41} \times {\text{T}}_{\rm on} \times {\text{F}}_{\rm p} + \, 0.000{95} \\ & \quad \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} {-}0.{545} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.0{196} \\ & \quad \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} + 0.0000{94} \times {\text{T}}_{\rm on}^{{2}} \times {\text{I}}_{\rm p} \\ & \quad + 0.0000{17} \times {\text{T}}_{\rm on}^{{2}} \times {\text{V}}_{\rm g} + \, 0.000{78} \\ & \quad \times {\text{T}}_{\rm on}^{{2}} \times {\text{F}}_{\rm p} + \, 0.00{273} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p}^{{2}} \\ & \quad + 0.0000{97} \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} + 0.00{63} \\ & \quad \times {\text{T}}_{\rm on} \times {\text{I}}_{\rm p} \times {\text{F}}_{\rm p} {-}0.000{27} \times {\text{T}}_{\rm on} \times {\text{V}}_{\rm g} \\ & \quad \times {\text{F}}_{\rm p} + \, 0.00{36} \times {\text{I}}_{\rm p} \times {\text{V}}_{\rm g} \times {\text{F}}_{\rm p} \\ \end{aligned} $$

(30)