Impact of Modeling Simplifications on Lightning Strike Simulation …downloads.hindawi.com/journals/mpe/2019/5176560.pdf · matrixmethod(TLM)isusedtosimulatetheelectromag-netic eﬀect

Research ArticleImpact of Modeling Simplifications on Lightning StrikeSimulation for Aeroengine

Yi-fan Qian Zhi-feng Ye and Hai-bo Zhang

Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

Correspondence should be addressed to Zhi-feng Ye yzfnuaaeducn

Received 3 July 2019 Accepted 19 September 2019 Published 10 October 2019

Academic Editor Rafał Stanisławski

Copyright copy 2019 Yi-fan Qian et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With the development of electromagnetic simulation software and affordable hardware it is allowed for us to complete sim-ulations for EMC purposes However simulation demands will be immense when simulations for models with complexstructures especially aircraft components have to be solved Hence it is meaningful to investigate how to minimize thecomputational demands One of the solutions to reduce the simulation expense is the simplification for the simulated model Butthe simplified model should be guaranteed to provide credible simulation results which do not deviate from the original modelapparently Generally the difference between the simulation results and experimental data is estimated or if the experimentalconditions are not achieved the comparison between the simplified model and the original one has to be analyzed at least -ispaper explores the electromagnetic simulation of a turbofan engine encountering lightning strike With the simplifications ofdifferent components on the turbofan engine the influences on induced currents of engine controller cables are simulated andanalyzed based on the transmission-line matrix method A combining method of components removal and geometric structuresimplification is proposed to simplify the whole engine model Simplified components include compressor combustion chamberturbine and nozzle -e effects of different simplification methods are quantified and the rationality of the simplified model isverified by simulation analysis

1 Introduction

A commercial aircraft suffers lightning strike once a year onaverage in the world -e lightning impact can be dividedinto two categories direct and indirect Direct impact causesphysical damage to the structure due to the direct contact oflightning Indirect effects mainly refer to the transientchanges of induced currents in cables of aircraft caused byelectromagnetic effect of lightning strikes -ese transientchanges are caused by electromagnetic fields generated bylightning currents which diffuse along the surface of aircraftthrough components such as windows or composites In theinterior of aircraft these transients can exceed the immunitylimit of the equipment cause malfunction or damage andendanger flight safety [1] In order to solve the problem oflightning protection electromagnetic simulation technologyis increasingly applied to aircraft designs Considering thelightning protection problem in the development stage ofaircraft it can reduce the cost of development and shorten

the development cycle -erefore relevant research in-stitutions have devoted large amount of manpower andmaterial resources in the electromagnetic simulation tech-nology of aircraft [2]

Aeroengine is the most significant part of aircraft Oncestruck by lightning if the shielding protection is weak it willcause a devastating impact In recent years in order toinvestigate the electromagnetic protection problems oftenencountered by aeroengines in flight various algorithmshave been applied to such large-scale simulation Da Silvaand Bastos used the finite element method (FEM) to sim-ulate and analyze large-scale electronic devices and sim-plified the simulation model [3] Guiffaut and Reineixapplied the finite-difference time domainmethod (FDTD) inthe simulation of electromagnetic compatibility (EMC) for asmall aircraft and they analyzed the distribution of elec-tromagnetic field for the aircraft under high-intensity ra-diation [4] High-precision simulation can provide guidancefor the design certification and life cycle prediction of

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 5176560 11 pageshttpsdoiorg10115520195176560

aeroengine thus improving flight safety At the same timewith the increasing computing power of calculating ma-chine it is possible to simulate the electromagnetic effect forthe whole aeroengine structure However the electromag-netic simulation of such large complex structures is a time-consuming process and the calculation process is arduousFor the lightning strike simulation of aeroengine the cal-culation time of the simulation can be even up to severalweeks It is definitely meaningful to reduce the cost of suchsimulations so that the development cycle can be shortened[5] Recently the development of electromagnetic simula-tion software and affordable hardware allows scholars tocomplete simulations for large-scale structures But elec-tromagnetic simulation demands are still enormous for amodel with complex structures especially aeroengineHence the need to minimize the computational demands isworthy of investigation One of the feasible methods toreduce the computational expense is the simplification forthe original model But the simplified model should beguaranteed to provide credible results of simulation Gen-erally the comparison of the simulation results with ex-perimental data is estimated Actually if there are noexperimental data it is necessary to analyze the difference ofsimulations between the simplified model and the originalone-erefore a simplificationmethod is urgently needed toreduce the overall cost and the required time of simulationIn the past 10 years a few scholars began to discuss thesimplification methods of such kinds of simulation grad-ually -e existing simplification methods mainly focus onthe details and parts of the electromagnetic simulationmodel Arnaud Christophe of Fiat Automobile Companys inBrazil has roughly classified the structural components of anautomobile model the components were removed andsimulated one by one and comparison between the effects ofdifferent simplified classifications on the electromagneticfield intensity in the vehicle was obtained [6] but the modelis simple so the revivification is low Reznicek and Raida ofEVEKTOR Aircraft Manufacturing Company in Czechsimulated the electromagnetic field of its small-sized tur-boprop aircraft taking the electromagnetic field intensity inthe cabin as the simulation target some parts of the aircraftwere removed and simplified -e simulation results afterremoval and simplification were compared and the ratio-nality of geometric simplification in electromagnetic sim-ulation was verified [7] However effects of induced currentsin cables caused by lightning strike were not studied En-gineer Guadalupe Gutierrez et al of Airbus simplified thethree components in the structure of a turboprop loaded byA400M transporter ie the air particulate separator the oilcooler and the electric contact -e effects of simplificationon the induced currents in the internal cables of turbopropwere studied in detail to prove the rationality of simplifi-cation [8] -e peak values of the induced currents weretaken as the judgment in this paper with the overall error ofcurrents

-is paper is organized as follows Section 2 provides thesimplification method of aeroengine Section 3 shows themodeling process of aeroengines and cables simulationconfigurations are presented in Section 4 and comparison

and analysis are shown in Section 5 Finally simulationscheme and verification are presented in Section 6 InSection 7 we draw the conclusions briefly

2 Simplification Method

-e primary task of geometric simplification is to define thesimulation target For an aeroengine the largest impact ofindirect lightning strike effect is that the transient current inthe cable exceeds the immunity of the aeroengine controllerwhich leads to the malfunction and causes potential safetyhazards Secondly the establishment of simulation model isalso very significant -e higher the accuracy of structureand cable layout the higher the simulation revivificationand the more complex the model details are thus moredetailed grouping and simplification of components can becarried out Although simplification is an important way toreduce simulation cost the rationality of simplification isalso needed to be guaranteed Each simplified simulationshould be compared with the simulation results of theoriginal model and the data should be analyzed in detail-e simplification methods of components are classified(removal detail processing and cannot be removed) so as toguarantee the rationality for simplification For the elec-tromagnetic simulation of a whole aeroengine structurewhether themodel is simplified reasonably or not will greatlyaffect the accuracy of the final results otherwise the sim-ulation will be meaningless -e flow chart is shown inFigure 1

3 Modeling

31 Geometric Structure A certain turbofan engine is builtas the research object -e model structure includes nacelleinlet compressor combustor part of fuel lines turbine andnozzle -e total length is about 4 meters as shown inFigure 2

32 Modeling of Cables Four cables are established in themodel according to the real position of the wiring harnessesin the turbofan engine Different areas are covered by thecables imitating the connection with few major componentsof the aeroengine as shown in Figure 3

In order to show the effect of various types of cables theharnesses include four types of cables which are mostcommonly used in aeroengines [9] namely shielded twistedpair twisted pair double-shielded twisted pair and coaxialline respectively Table 1 lists the details of the cables

33ComponentsGrouping -e influence of induced currentin the cables for different components is the focus of thispaper Because the existence of a nacelle has a great impacton the electromagnetic shielding ability of the engine itcannot be removed and it is not considered when grouping-erefore several main components of the engine are di-vided into nine groups regarding the whole engine model asone group there are ten groups in total and their Englishname and abbreviation are shown in Table 2

2 Mathematical Problems in Engineering

4 Simulation

In this paper CST software based on the transmission-linematrix method (TLM) is used to simulate the electromag-netic effect of lightning strike on a turbofan engine -esimulation conditions are set according to the current

waveform and lightning test method defined in SAE ARP5412 [10] and SAE ARP 5416 standards [11]

41 Transmission-LineMatrix -e transmission-line matrixmethod (TLM) is used to solve the three-dimensional time-domain problem of Maxwell equation in which the trans-mission line is a facility capable of transmitting electro-magnetic energy between two points with minimumradiation In the TLM method firstly the engineeringproblem is simulated through the continuous transmission

Turbofanengine

Figure 2 3D model of turbofan engine

A

C

B

FADEC

D

Figure 3 Diagram of internal cables

Table 1 Information of cables

Cables Areas Types Cross section

A Compressor Shielded twisted pair

B Combustor Twisted pair

C Turbine Double-shieldedtwisted pair

D Nozzle Coaxial line

Start

Define the simulation target

Establishment of simulation model

Divide components into groups

Simulate separately aer removal

Classification according to simulation results

Propose a scheme for simplification

End

Figure 1 Flow chart of simplification

Table 2 Component grouping of aeroengine

Groups AbbreviationsAeroengine model ALLFan FanIntermediate-pressure compressor IPCHigh-pressure compressor HPCFuel nozzle FNCombustor CombustorHigh-pressure turbine HPTIntermediate-pressure turbine IPTLow-pressure turbine LPTNozzle Nozzle

Mathematical Problems in Engineering 3

line network each node in the network is represented by alumped element whose physical parameters correspond tothe actual problem ie spatial discretization -e lumpedelement is simulated by each node of the transmission lineie time discretization One-dimensional transmission lineis taken as an example and its equivalent circuit is shown inFigure 4

According to Kirchhoffrsquos law we have

z2V(z t)

zz2 lcz2V(z t)

zt2

z2I(z t)

zz2 lcz2I(z t)

zt2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)

where V and I stand for the voltage and current in thecircuit z is the position coordinate t is the time coordinateand l and c represent the distributed inductance and ca-pacitance parameters respectively

-e two-dimensional TLM is composed of parallel-connected transmission line grids Four pulses incident to anode from four branches scattering first and then incidentto adjacent nodes respectively It can be expressed as

k+1Vi

Ck+1Vr

k+1Vr

SkVi

(2)

where Vi is the excitation voltage matrix Vr is the reflectionvoltage matrix S stands for the impulse scattering matrix ofthe node C is the connection matrix describing the networktopology and subscripts k and k + 1 represent the discretetime interval of scattering -us the scattering formula canbe obtained as follows

k+1Vin

12

1113944

4

m1kV

im

⎡⎣ ⎤⎦ minus kVim (3)

where r stands for scattering i stands for incident and m

and n represent the port numbers respectively-e three-dimensional TLM is based on a symmetrical

condensation node (SCN) algorithm to simulate the elec-tromagnetic propagation in the space unit Each three-di-mensional SCN has six branches one branch is composed oftwo vertical transmission lines to simulate the propagationof electromagnetic field Because the slot model can beregarded as the dual form of a dipole antenna according tothe Babinet theorem the radiation field vector on the slot isthe same as the equivalent dipole but the electric andmagnetic field vectors are interchangeable For the narrowslot model the field along the long edge of the slot forms aninterface through a one-dimensional transmission lineconnected with a symmetrical condensation node and itsynchronizes the slot with the residual pulse and the timestep of the three-dimensional TLM unit through the ca-pacitance and inductance of the slot unit length thus theglobal scattering model is established [12] -e formulationis as follows

YL Δt

LsΔl

Ys 2CsΔlΔt

minus YL1113888 1113889

Cs 0637ε ln0563Δl

ω1113888 1113889 +

εdω

Lminus 1s

πμ2 ln(1591Δlω)

1113890 1113891

minus 1

+μωd

1113874 1113875minus 1

(4)

In the formula YL is the characteristic admittance of thetransmission line YS is the capacitive characteristic ad-mittance ε is the relative permittivity in free space μ is thepermeability and Δl is the distance of electromagnetic wavetransmission

-e TLM can deal with complex nodes simulate wavepropagation in time domain simplify calculation and avoidpossible problems such as convergence stability andpseudosolution -e TLM can also get the main- and high-order mode eigenvalues through the Fourier transformwhich can accurately simulate the physical characteristicsand behavior of waves and can explain the propagationcharacteristics of different states-erefore it is very suitablefor the simulation of three-dimensional time-domainelectromagnetic field [13]

42 Excitation Source In this paper the expression oflightning impulse excitation waveform of airborne elec-tronic and electrical system is I(t) I0[eminus αt minus eminus βt]I0 218810A α 11354 sminus 1 and β 647265 sminus 1 which isgiven by SAE ARP 5412 and SAE ARP 5416 standardsLightning strike point is set at the axle tip of the turbofanengine which is most likely to be struck by lightning [14]and the exit point of lightning strike signal is at the end of thenozzle as shown in Figure 5 -e boundary condition is setto ldquoopenrdquo to simulate the infinite free space which meanselectromagnetic waves will be absorbed completely withoutany reflection when they hit these boundaries-e waveformof the excitation signal is shown in Figure 6 -e peakcurrent is 21881 kA peak time is 64 μs and duration is500 μs frequency is set at 0ndash50MHz and there is almost nocurrent component above 50MHz It can represent the mostextreme lightning strike situation and save time [15]

I (z t) lΔz

cΔz

I (z + Δz t)

V (z + Δz t) V (z t)

Figure 4 Lumped-parameter model of transmission line


-e schematic diagram is shown in Figure 7 in which theyellow part stands for the lightning signal the resistancebetween twisted pairs is 100Ω the matching resistance ofcoaxial cable is 50Ω and the shielding layers are allgrounded

5 Simulation and Analysis

51 Simulation Each cable is equipped with a probe tomeasure the induced current according to the groups di-vided from the components in Section 32 and the simu-lation results of the models after removing each group areobtained Figures 8ndash11 show the simulation results of fourcables -e abscissa is time the unit is μs the longitudinalcoordinate is induced current and the unit is A As can beseen from Figures 8ndash11 compared to the curves of theoriginal model the induced current corresponding to theremoval of some components has changed considerablysuch as fan (Fan) and intermediate-pressure compressor(IPC) -e simulation results of the induced current cor-responding to some simplified models are similar to those ofthe original model such as nozzle (Nozzle) and low-pressureturbine (LPT)

52 Data Analysis In the previous section the inducedcurrent data in each cable of the simplified model has beenobtained after removing different components In order toobtain the quantified results the simulation results of theoriginal model are taken as the standard values -e data ofeach simplified model is compared with the data of theoriginal one Finally the influence of the simplified com-ponents for the induced current in cables is obtained Be-cause the peak value of induction current of various types ofcables differs greatly some scholars have used decibel errorto measure the error in the study of induction current errors-is analysis method is worth for reference [16] -ereforethe decibel error in electronic instrument measurement andthe root mean square error (RMSE) in mathematical sta-tistics are used In numerical calculation the decibel errorrepresents the difference between the accurate value and theapproximation that is the error between the simulationresult Ji of the original model and the simulation result Ii ofthe simplified model For the induced current in a singlecable the expression is as follows

ξi 20 lgIi

Ji

1113888 1113889dB i 1 2 n (5)

Lightning signal Signal leave path

Figure 5 Lightning strike point

Lightning signal

0 50 100 150 200 250 300 350 400 450 500

20000400006000080000

1e + 00512e + 00514e + 00516e + 00518e + 005

2e + 005

0

Curr

ent (

A)

Time (μs)

Figure 6 Lightning signal waveform


where n stands for the sampling time points-e RMSE is used to measure the overall situation of the

error and its expression is as follows

cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)

where cij represents the RSME of the decibel error in thecable j with the removal of group i in the simulation whichdenotes the effect of i group on the induced current in cablej n stands for the number of samples of the induced currentand ξijk represents the decibel error of the induced currentat the k sampling point on cable j and the corresponding

0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN

CombustorHPTIPTLPTNozzle

Curr

ents

in ca

ble (

A)

A

Figure 8 Comparison of simulation results on Cable (A)

0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A

Figure 9 Comparison of simulation results on Cable (B)

Lightning signal

N2_CG_1_UTP_LIFY_1qmm_1


N2_CG_1_Group1_Screen_1

N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

Figure 7 Schematic diagram


time point for the original model after removing the i groupof components

In this paper the RMSE represents the overall variationof the induced current simulation curve corresponding tothe removal of one group in the model and the inducedcurrent curve of the original one-e larger the RMSE is thegreater the influence of the component on the inducedcurrent of the target cable is -e RMSE is the manifestation

of the comprehensive deviation of induction current so it isthe most reliable basis for judging the influence of com-ponents on the induced current [17]

-e RMSE of the induced current corresponding to thesimplified model can be obtained by taking the simulateddata into formulation (5) and (6) As shown in Table 3 c

represents the RMSE in unit dBFrom Table 3 it can be seen that the error of fuel nozzle

and high-pressure turbine are relatively small which in-dicates that the two components have less influence on theinduced current in the cable and the error of fan andcombustor is relatively large which indicates that the twocomponents have greater influence on the induced currentGuo [18] has studied the influence of small concave-convexstructure in electromagnetic simulation and the corre-sponding model simplification scheme was designedGutierrez et al [19] have studied the evaluation criteria ofthe influence on aeroengine cable induced current Com-bining with the investigation results of various scholarsthis paper will directly judge the evaluation for the influ-ence of components on induced current according to thecombination of investigation results by previous scholarsCombining the above data a simplification method for thesimulation model can be obtained

(1) Groups with RMSE less than or equal to 1 dB can beremoved directly

(2) Groups with RMSE greater than 1 dB and less than5 dB can be adjusted structurally holes with diameterless than 20mm can be filled and microstructurescan be smoothed

(3) Groups with RMSE greater than 5 dB can only beadjusted slightly -e model is fine-tuned to simplifythe structures such as slots bolts bulges andgrooves which are less than 10mm in size andbasically maintain the original structure

6 Simplification Scheme and Simulation

According to the simplification method and the simulationdata for lightning strike simulation in Table 3 the aeroenginemodel is processed as follows

(1) Because the RMSE of induced current for the re-moval of fuel nozzle (FN) or high-pressure turbine(HPT) is less than 1 dB it shows that the effect ofthese two components on induced currents in cablescan be neglected and the corresponding compo-nents can be removed completely

(2) -e RMSE of intermediate-pressure compressor(IPC) high-pressure compressor (HPC) in-termediate-pressure turbine (IPT) and low-pressureturbine (LPT) are all more than 1 dB and less than5 dB So the slots with diameter less than 20mm canbe filled completely and the size of the fine structurewhich is smaller than the mesh size can be flattened

(3) -e RMSE of fan combustor and nozzle are muchlarger than those of other components so their mainstructures are all retained and the fine structures

000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A

Figure 10 Comparison of simulation results on Cable (C)

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A

Figure 11 Comparison of simulation results on Cable (D)


with sizes less than 10mm are smoothed and theholes with diameters less than 10mm can be filled

According to the scheme above the whole model of theturbofan engine in Section 32 is simplified -e inducedcurrent curves obtained by the simulations of simplifiedmodels are compared with the corresponding results of theoriginal one Because the maximum value of the inducedcurrents corresponding to different cables are quite differentthe simulation results of four cables are normalized asshown in Figure 12 It can be seen that the variation trends ofthe curves are the same and the magnitudes are similar -eerror parameters are obtained by processing the simulateddata as shown in Table 4 and the RMSE are very small -ismeans that the induced current of the simplified modelchanges quite little

However for the verification of EMC data in modernaeronautical industry RMSE seems to be a humble standardto measure the data In 2006 Duffy et al formally proposedthe Feature Selective Validation (FSV) method [20] and theprinciple of FSV is shown in Figure 13 Subsequently this

method shows a broad application prospect in various fieldsof computational electromagnetics (CEM) [21] In recentyears especially with the introduction of the FSV methodinto the IEEE standard [22] by the working group oncomputer modeling and simulation verification standardsfor CEM the application and expansion of the FSV methodin practical engineering have become a hot spot of wide-spread concern

-e basic principle of the FSV method is to decomposethe original data into DC low-frequency and high-fre-quency and then extract the difference metrics ie am-plitude difference measure (ADM) and feature differencemeasure (FDM) and then form a global difference measure(GDM) [23] -e piecewise approach is shown in Table 5

0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified

Figure 12 Comparison of induced currents between the simplified model and original model

Table 4 Errors of the simplified model relative to the originalmodel

Δ(dB) Cable (A) Cable (B) Cable (C) Cable (D)cOriginalminus simplified 075 030 109 098

Table 3 Induced current error for each simplified model

Δ(dB) Cable (A) Cable (B) Cable (C) Cable (D)cFan 1223 193 296 164cIPC 451 217 209 160cHPC 221 223 181 176cFN 001 032 008 001cCombustor 009 infin 381 138cHPT 011 035 079 020cIPT 017 115 185 099cLPT 010 159 411 061cNozzle 003 151 192 infin


and the ldquoGRADE numberrdquo and ldquoSPREAD numberrdquo areobtained based on the ADM and FDM-eGRADE numbermeans how many agreement categories are required(starting at excellent) before 85 of the data 85 percent ofthe data fall into the top quality categories so lower theGRADE number better the comparison will be -eSPREAD is like a typical standard deviation because it alsodetermines how many categories are needed to include 85of the data but the category is started from the highest ratedcategory (instead of the excellent category as in GRADEnumber) [24]

So the FSV method is applied to the non-normalizeddata of the simplification simulation results and the originalresults -e histogram distribution is shown in Figure 14and the assessments are shown in Table 6 from which it can

be seen that the reliability of the simplified model is morestrongly illustrated by the FSV that is to say in this lightningstrike simulation for induced currents of cables in the

Start

Are there more differences than

similarities

Are there about the same number of similarities and

differences

Many dissimilarities

Some similarities

Many similarities

Virtually no discernable agreement

Minor agreement

Reasonable agreement over many portions

of the data

Generally good agreement across

the data

Minorvariations allowable

Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0

Figure 13 Assessment flow chart

Table 5 Piecewise approach

FSV value Interpretation AssessmentXle 01 1 + 10lowastX Excellent01ltXle 02 2 + 10lowast (X minus 0099) Very good02ltXle 04 3 + 5lowast (X minus 0199) Good04ltXle 08 4 + 25lowast (X minus 0399) Fair08ltXle 16 5 + 125lowast (X minus 0799) PoorXgt 16 6 Very poor

Excellent Very good Good Fair Poor Very poor

07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n

Figure 14 Histogram distribution of the GDM obtained from theFSV analysis of data


turbofan engine the simplification scheme is reasonable andthe original model can be replaced

From Table 7 it can be seen that the number of meshesmemory requirement and computational time are reducedby 535 400 and 698 respectively It is obvious thatthe simplified model not only reduces the requirement ofhardware but also reduces the computing time

7 Conclusion

In this paper the lightning strike simulation task on aturbofan engine is investigated -e induced currents of theaeroengine controller cables are taken as the simulationobjective and the aeroengine model is simplified by re-moving components and simplifying the structures -etransmission-line matrix method (TLM) is used to simulateand analyze the effects of different components on the in-duced currents of cables and the simulation results areobtained -e error of the simplified simulation scheme isless than 13 dB compared with the original -e computingtime and memory requirement are definitely reduced

Once the simulation target is unequivocal some com-ponents of this kind of large-scale complex device will beredundant -erefore the complexity of the model is pro-portional to the effect of simplification Further research onsimplification of EMC simulation for an aeroengine which ismore complex will be needed which will make this tech-nique more meaningful

Data Availability

-e data used to support the findings of this study have notbeen made available because the data in this paper belong toa certain research project which is confidential

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China under Grant no 51876089

References

[1] S Rea D Linton E Orr and J McConnell ldquoElectromagneticmodeling of aircraft air inlet Scooprdquo in Proceedings of the 33rdEuropean Microwave Conference Proceedings (IEEE Cat No03EX723C) pp 17ndash19 Munich Germany October 2003

[2] E Perrin F Tristant C Guiffaut and A Reineix ldquoA nu-merical tool to estimate lightning indirect effects on a com-posite aircraftrdquo in Proceedings of the 2010 30th InternationalConference on Lightning Protection (ICLP) pp 26ndash28Cagliari Italy September 2010

[3] J R Da Silva and J P A Bastos ldquoAnalysis of power trans-former geometry simplifications on electromagnetic andthermodynamic simulationsrdquo IEEE Transactions on Mag-netics vol 51 no 3 pp 1ndash4 2015

[4] C Guiffaut and A Reineix ldquoModeling of different cables typesand their combinations for lightning and HIRF EMC studiesin the FDTDmethodrdquo in Proceedings of the 2015 InternationalConference on Electromagnetics in Advanced Applications(ICEAA) pp 12ndash17 Torino Italy September 2015

[5] X Lu Research on the Technique of Simplifying the EMCSimulation Model Xidian University Xirsquoan China 2009

[6] A N de Satildeo Jose A C P M Colin J F Mologni G M DipU D C Resende and S T M Goncalves ldquoComputationalsavings based on -ree-Dimensional automotive geometriesrsquosimplifications in electromagnetics simulationsrdquo in Pro-ceedings of the 2013 SBMOIEEE MTT-S International Mi-crowave amp Optoelectronics Conference (IMOC) pp 108ndash111Rio de Janeiro Brazil August 2013

[7] Z Reznicek and Z Raida ldquoSimplification methodology ofcomplex EM models of small airplanesrdquo in Proceedings of the2009 International Conference on Electromagnetics in Ad-vanced Applications pp 12ndash19 Torino Italy September 2009

[8] G G Gutierrez D Mateos Romero M R Cabello et al ldquoOnthe design of aircraft electrical structure networksrdquo IEEETransactions on Electromagnetic Compatibility vol 58 no 2pp 401ndash408 2016

[9] Y She N Hou and K Yang ldquoA simulation research of enginecontrol system cables electromagnetic couplingrdquo Aero-nautical Computing Technology vol 2 no 48 pp 66ndash69 2018

[10] Aerospace Recommended Practice SAE ARP 5416 AircraftLightning Test Methods SAE Aerospace Warrendale PAUSA 2005

[11] Aerospace Recommended Practice SAE ARP 5412A AircraftLightning Environment and Related Test Waveform SAEAerospace Warrendale PA USA 2005

[12] L Liu Simulation and Research of Lighting Protection onPower Supply System for Flight Test of C919 Airplane NanjingUniversity of Aeronautics and Astronautics Nanjing China2017

[13] C Sun and M Zhang ldquoSimulation design of harness pro-tection against lightning for aircraftsrdquo in Proceedings of the2014 International Conference on Lightning Protection (ICLP)pp 27ndash34 Shanghai China October 2014

[14] S Song C Gao Y Guo Q Yang and B Zhou ldquoStudy ofnumerical simulation of aircraft lightning zoning based onCSTsoftwarerdquo in Proceedings of the 2011 Second InternationalConference onMechanic Automation and Control Engineeringpp 87ndash90 Inner Mongolia China July 2011

[15] M Zhang and Z Huang ldquoTransient current burst analysisinduced in cable harness due to direct lightning strike onaircraftrdquo in Proceedings of the 2010 Asia-Pacific InternationalSymposium on Electromagnetic Compatibility pp 34ndash39Beijing China April 2010

Table 6 FSV results for the comparison

FSV GDM GRADE SPREADA 0281 3 4B 0349 3 2C 0123 2 3D 0208 3 3

Table 7 Comparison of computing requirements

Model Mesh quantity Memoryrequirement (G)

Computationaltime required (h)

Original 193904740 120 158Simplified 90090975 72 49


[16] B Michielsen F Issac P Aguilera and D Prost ldquoMacro-modelling of lightning strokes on aircraftrdquo in Proceedings of the2014 XXXIth URSI General Assembly and Scientific Symposium(URSI GASS) pp 23ndash29 Beijing China August 2014

[17] J Liu Y Zhang J Lei et al ldquoVehicle model simplifiedmethodof electromagnetic radiation immunity simulationrdquo Safetyand EMC vol 1 no 2 pp 65ndash69 2015

[18] G Guo Research on Simplifying the Stiffeners on Electronic ofElectromagnetic Simulations Xidian University Xirsquoan China2014

[19] G G Gutierrez S F Romero M Gonzaga et al ldquoInfluence ofgeometric simplifications on lightning strike simulationsrdquoProgress in Electromagnetics Research vol 83 pp 15ndash32 2018

[20] A P Duffy A J M Martin A Orlandi G AntoniniTM Benson andM SWoolfson ldquoFeature selective validation(FSV) for validation of computational electromagnetics (CEM)Part Imdashthe FSV methodrdquo IEEE Transactions on Electromag-netic Compatibility vol 48 no 3 pp 449ndash459 2006

[21] G G Gutierrez J Alvarez E Pascual-Gil et al ldquoHIRF virtualtesting on the C-295 aircraft on the application of a passfailcriterion and the FSV methodrdquo IEEE Transactions on Elec-tromagnetic Compatibility vol 56 no 4 pp 854ndash863 2014

[22] IEEE IEEE Standard P1597 Standard for Validation ofComputational Electromagnetics Computer Modeling andSimulationmdashPart 1 2 IEEE Piscataway NJ USA 2008

[23] A Orlandi A P Duffy B Archambeault G AntoniniD E Coleby and S Connor ldquoFeature selective validation(FSV) for validation of computational electromagnetics(CEM) Part II- assessment of FSV performancerdquo IEEETransactions on Electromagnetic Compatibility vol 48 no 3pp 460ndash467 2006

[24] G Antonini M D Clerico A Orlandi V RicchiutiM Passacantando and S Santucci ldquoExperimantal charac-terization and equivalent circuit extraction of nanowires forsignal integrity applicationsrdquo Journal of Pharmacy amp Phar-macology vol 17 no 4 pp 256-257 2009


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aeroengine thus improving flight safety At the same timewith the increasing computing power of calculating ma-chine it is possible to simulate the electromagnetic effect forthe whole aeroengine structure However the electromag-netic simulation of such large complex structures is a time-consuming process and the calculation process is arduousFor the lightning strike simulation of aeroengine the cal-culation time of the simulation can be even up to severalweeks It is definitely meaningful to reduce the cost of suchsimulations so that the development cycle can be shortened[5] Recently the development of electromagnetic simula-tion software and affordable hardware allows scholars tocomplete simulations for large-scale structures But elec-tromagnetic simulation demands are still enormous for amodel with complex structures especially aeroengineHence the need to minimize the computational demands isworthy of investigation One of the feasible methods toreduce the computational expense is the simplification forthe original model But the simplified model should beguaranteed to provide credible results of simulation Gen-erally the comparison of the simulation results with ex-perimental data is estimated Actually if there are noexperimental data it is necessary to analyze the difference ofsimulations between the simplified model and the originalone-erefore a simplificationmethod is urgently needed toreduce the overall cost and the required time of simulationIn the past 10 years a few scholars began to discuss thesimplification methods of such kinds of simulation grad-ually -e existing simplification methods mainly focus onthe details and parts of the electromagnetic simulationmodel Arnaud Christophe of Fiat Automobile Companys inBrazil has roughly classified the structural components of anautomobile model the components were removed andsimulated one by one and comparison between the effects ofdifferent simplified classifications on the electromagneticfield intensity in the vehicle was obtained [6] but the modelis simple so the revivification is low Reznicek and Raida ofEVEKTOR Aircraft Manufacturing Company in Czechsimulated the electromagnetic field of its small-sized tur-boprop aircraft taking the electromagnetic field intensity inthe cabin as the simulation target some parts of the aircraftwere removed and simplified -e simulation results afterremoval and simplification were compared and the ratio-nality of geometric simplification in electromagnetic sim-ulation was verified [7] However effects of induced currentsin cables caused by lightning strike were not studied En-gineer Guadalupe Gutierrez et al of Airbus simplified thethree components in the structure of a turboprop loaded byA400M transporter ie the air particulate separator the oilcooler and the electric contact -e effects of simplificationon the induced currents in the internal cables of turbopropwere studied in detail to prove the rationality of simplifi-cation [8] -e peak values of the induced currents weretaken as the judgment in this paper with the overall error ofcurrents

-is paper is organized as follows Section 2 provides thesimplification method of aeroengine Section 3 shows themodeling process of aeroengines and cables simulationconfigurations are presented in Section 4 and comparison

and analysis are shown in Section 5 Finally simulationscheme and verification are presented in Section 6 InSection 7 we draw the conclusions briefly

2 Simplification Method

-e primary task of geometric simplification is to define thesimulation target For an aeroengine the largest impact ofindirect lightning strike effect is that the transient current inthe cable exceeds the immunity of the aeroengine controllerwhich leads to the malfunction and causes potential safetyhazards Secondly the establishment of simulation model isalso very significant -e higher the accuracy of structureand cable layout the higher the simulation revivificationand the more complex the model details are thus moredetailed grouping and simplification of components can becarried out Although simplification is an important way toreduce simulation cost the rationality of simplification isalso needed to be guaranteed Each simplified simulationshould be compared with the simulation results of theoriginal model and the data should be analyzed in detail-e simplification methods of components are classified(removal detail processing and cannot be removed) so as toguarantee the rationality for simplification For the elec-tromagnetic simulation of a whole aeroengine structurewhether themodel is simplified reasonably or not will greatlyaffect the accuracy of the final results otherwise the sim-ulation will be meaningless -e flow chart is shown inFigure 1

3 Modeling

31 Geometric Structure A certain turbofan engine is builtas the research object -e model structure includes nacelleinlet compressor combustor part of fuel lines turbine andnozzle -e total length is about 4 meters as shown inFigure 2

32 Modeling of Cables Four cables are established in themodel according to the real position of the wiring harnessesin the turbofan engine Different areas are covered by thecables imitating the connection with few major componentsof the aeroengine as shown in Figure 3

In order to show the effect of various types of cables theharnesses include four types of cables which are mostcommonly used in aeroengines [9] namely shielded twistedpair twisted pair double-shielded twisted pair and coaxialline respectively Table 1 lists the details of the cables

33ComponentsGrouping -e influence of induced currentin the cables for different components is the focus of thispaper Because the existence of a nacelle has a great impacton the electromagnetic shielding ability of the engine itcannot be removed and it is not considered when grouping-erefore several main components of the engine are di-vided into nine groups regarding the whole engine model asone group there are ten groups in total and their Englishname and abbreviation are shown in Table 2


4 Simulation




Turbofanengine


A

C

B

FADEC

D








Start







End







z2V(z t)

zz2 lcz2V(z t)

zt2

z2I(z t)

zz2 lcz2I(z t)

zt2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)



k+1Vi

Ck+1Vr

k+1Vr

SkVi

(2)


k+1Vin

12

1113944

4

m1kV

im





YL Δt

LsΔl

Ys 2CsΔlΔt

minus YL1113888 1113889

Cs 0637ε ln0563Δl

ω1113888 1113889 +

εdω

Lminus 1s

πμ2 ln(1591Δlω)

1113890 1113891

minus 1

+μωd

1113874 1113875minus 1

(4)




I (z t) lΔz

cΔz

I (z + Δz t)








ξi 20 lgIi

Ji

1113888 1113889dB i 1 2 n (5)



Lightning signal

0 50 100 150 200 250 300 350 400 450 500

20000400006000080000

1e + 00512e + 00514e + 00516e + 00518e + 005

2e + 005

0

Curr

ent (

A)

Time (μs)





cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)


0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

A)

A


0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A


Lightning signal




N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018








4 Simulation




Turbofanengine


A

C

B

FADEC

D








Start







End







z2V(z t)

zz2 lcz2V(z t)

zt2

z2I(z t)

zz2 lcz2I(z t)

zt2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)



k+1Vi

Ck+1Vr

k+1Vr

SkVi

(2)


k+1Vin

12

1113944

4

m1kV

im





YL Δt

LsΔl

Ys 2CsΔlΔt

minus YL1113888 1113889

Cs 0637ε ln0563Δl

ω1113888 1113889 +

εdω

Lminus 1s

πμ2 ln(1591Δlω)

1113890 1113891

minus 1

+μωd

1113874 1113875minus 1

(4)




I (z t) lΔz

cΔz

I (z + Δz t)








ξi 20 lgIi

Ji

1113888 1113889dB i 1 2 n (5)



Lightning signal

0 50 100 150 200 250 300 350 400 450 500

20000400006000080000

1e + 00512e + 00514e + 00516e + 00518e + 005

2e + 005

0

Curr

ent (

A)

Time (μs)





cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)


0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

A)

A


0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A


Lightning signal




N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018










z2V(z t)

zz2 lcz2V(z t)

zt2

z2I(z t)

zz2 lcz2I(z t)

zt2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)



k+1Vi

Ck+1Vr

k+1Vr

SkVi

(2)


k+1Vin

12

1113944

4

m1kV

im





YL Δt

LsΔl

Ys 2CsΔlΔt

minus YL1113888 1113889

Cs 0637ε ln0563Δl

ω1113888 1113889 +

εdω

Lminus 1s

πμ2 ln(1591Δlω)

1113890 1113891

minus 1

+μωd

1113874 1113875minus 1

(4)




I (z t) lΔz

cΔz

I (z + Δz t)








ξi 20 lgIi

Ji

1113888 1113889dB i 1 2 n (5)



Lightning signal

0 50 100 150 200 250 300 350 400 450 500

20000400006000080000

1e + 00512e + 00514e + 00516e + 00518e + 005

2e + 005

0

Curr

ent (

A)

Time (μs)





cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)


0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

A)

A


0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A


Lightning signal




N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018












ξi 20 lgIi

Ji

1113888 1113889dB i 1 2 n (5)



Lightning signal

0 50 100 150 200 250 300 350 400 450 500

20000400006000080000

1e + 00512e + 00514e + 00516e + 00518e + 005

2e + 005

0

Curr

ent (

A)

Time (μs)





cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)


0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

A)

A


0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A


Lightning signal




N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018










cij

1n

1113944

n

k1ξijk1113872 1113873

2

11139741113972

(6)


0 100 200 300 400 500t (μs)

00

05

10

15

20

25

30

35

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

A)

A


0

0

1

2

3

4

100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

B)A


Lightning signal




N4_TW_1_1

N4_TW_1_2





N8_CX_1_1

N8_CX_1_Screen




N3_TW_1_1

N3_TW_1_2





N7_CX_1_1

N7_CX_1_Screen

100

50

50

100

50 50

100

50

50

100

1

















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018






















000

002

004

006

008

010

012

014

016

0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


Curr

ents

in ca

ble (

C)A


0 100 200 300 400 500t (μs)

Simplified models

ALLFanIPCHPCFN


00

05

10

15

20

Curr

ents

in ca

ble (

D)

A








0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018













0 100 200 300 400 50000

02

04

06

08

10

Nor

mal

izat

ion

of cu

rren

ts in

cabl

es

t (micros)

AOriginal

BOriginal

ASimplified

BSimplified

COriginal

DOriginal

CSimplified

DSimplified










Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018











Start


similarities


differences


Some similarities

Many similarities


Minor agreement


of the data


the data


Perfect match

Very poor

Poor

Fair

Good

Very good

Excellent

5-6

4-5

3-4

2-3

1-2

0-1

Yes

Yes

No

No

6

5

4

3

2

1

0





07

06

05

04

03

02

01

00

GDM(A)GDM(B)

GDM(C)GDM(D)

GD

M p

ropo

rtio

n





7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018










7 Conclusion



Data Availability




Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018

























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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