atestprocedureoptimizationmethodforanindustrialrobot...

Research ArticleA Test Procedure Optimization Method for an Industrial RobotServo System on an Integrated Testing Platform

Shaomin Tang 1 Guixiong Liu 1 Zhiyu Lin1 Xiaobing Li2 and Minqiang Pan 1

1School of Mechanical and Automotive Engineering South China University of Technology Guangzhou 510640 China2CEPREI Guangzhou 510610 China

Correspondence should be addressed to Guixiong Liu megxliuscuteducn and Minqiang Pan mqpanscuteducn

Received 3 August 2020 Revised 18 September 2020 Accepted 19 October 2020 Published 21 November 2020

Academic Editor Kang Li

Copyright copy 2020 Shaomin Tang 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

A test procedure optimization method was proposed in this paper to improve the test efficiency of the industrial robot servosystem (IRSS) to be tested on the IRSS integrated testing platform (IITP) First an ordered sequence was used to define the IRSStest project when tested on the IITP -e ordered sequence consisted of execution subelements which were a combination ofcontrol variable parameters of the IITP Second the optimization relationships among the IRSS test projects were dug outaccording to the IRSS test project sequences Finally by using the traveling salesmen problem (TSP) an optimization model wasestablished based on the optimization relationships of the IRSS test projects and the optimal test order of the IRSS test projects tobe tested on the IITP was obtained by solving the model A case analysis showed that the proposed method optimized the testprocedure on the IITP effectively and the test time when implementing the test on the IITP according to the optimized order wasnearly 50 shorter than before optimization -e optimization effect was thus found to be significant

1 Introduction

-e industrial robot servo system (IRSS) is the executionunit that enables industrial robots to complete their assignedtasks and constitutes the core component of industrial ro-bots [1]-emovement speed positioning accuracy bearingcapacity and operation performance of industrial robots aredirectly affected by the IRSS [2] Moreover accurate rapidand reliable testing of the performance of the IRSS is ex-tremely important for improving the performance of in-dustrial robots In recent years IRSS testing technology hasgradually become mature and it becomes a major trend todesign an integrated testing platform for various testingprojects Zhu et al [3] designed a test platform to accomplishthe IRSS operating characteristics including both steadystate and dynamic state Guo et al [4] developed a platformto test the performance of IRSS accurately reliably as well asconveniently In addition with the IRSS specific perfor-mance testing requirements the functions of the test plat-form are further enriched Yang et al [5] designed dynamictracking performance test on the test platform Wang et al

[6] introduced an accelerated degradation test on the IRSStest platform George et al [7] designed and developed anautomated test platform for IRSS at room temperature aswell as at elevated temperatures With the improvement ofthe integration of the IRSS test platform problems related tothe integration become more and more prominent Sidhomet al [8] proposed a higher-order sliding mode differentiatorwith dynamic gains to increase the test accuracy of the testplatform Zhang et al [9] and Luo et al [10] addressed toautomation of the IRSS platform Cheng et al [11] propose asimulation platform to address the complex costly andtedious test process of servo systems

In the previous research we combed the existing IRSStest standards and technical requirements according to thetest requirements of the IRSS and formed the IRSS testprojects as shown in Figure 1 We then built an integratedtesting platform on which to realize all the IRSS test projectsas shown in Figure 2 -e IRSS integrated testing platform(IITP) can be used to conduct a comprehensive test for theIRSS and address the inefficiency caused bymultiple projectsbeing tested on different platforms However due to the

HindawiComplexityVolume 2020 Article ID 7906019 12 pageshttpsdoiorg10115520207906019

large number of IRSS test projects being tested on the IITPas well as the time-consuming nature of doing so low testingefficiency remains an issue Modular experimental designs[12] have been applied to parts of the IRSS test projects basedon the IRSS test standard and technical requirement as seenin Figure 1 as a modular test For example the no-load test ofa modular test on the IITP can test four test projects no-loadcurrent no-load voltage no-load power and no-load speedHowever the efficiency remains nonideal for there are stilltoo many IRSS test projects that cannot be tested modularly

We found that the test process of IRSS test projects onthe IITP involves changing the control variables of the IITPand that some steps of the test process of IRSS test projectsshared the same control variable parameters on the IITPBased on this finding we propose a test procedure opti-mization method for the IRSS being tested on the IITP -enovelty of the proposed method is that we find out a methodto dig out the optimization relationships between IRSS testprojects when tested on the IITP and then we establish anoptimization model based on this finding to get the optimaltest order of the IRSS test projects to be tested on the IITPwhich results in shortening the test time on the IITP

-e main contributions of this paper are the following

(i) A method that uses an ordered sequence to define theIRSS test project is proposed according to the rela-tionship between IRSS test projects and the control

variable parameters on the IITP -e ordered se-quence defining the IRSS test projects is formed by theexecution subelements of IITP which is the combi-nation of IITP control variable parameters

(ii) A method to shorten the test time by sharing thesame IITP execution subelements among the IRSStest project sequences is discussed -e directedoperation symbol ldquocaprdquo is proposed to perform in twoIRSS test project sequences while they were testedone after another Two optimization relationshipsbetween IRSS test projects when tested on the IITPare identified by the ldquocaprdquo operation namely themerger optimization relationship and the sequenceoptimization relationship

(iii) -e optimization problem of the test order of theIRSS test projects on the IITP is considered in theframework of the TSP with a fixed starting pointand ending point whose aim is to seek the shortestpath through all cities An optimization model isestablished and the optimal test order with theshortest test time of the IRSS tested on the IITP isobtained by solving the model

-e remainder of this paper is organized as follows InSection 2 an overview of the TSP and its applications andsolutions is presented In Section 3 the method of using anordered sequence to define the IRSS test projects is proposedIn Section 4 the optimization relationships of the IRSS testprojects based on the ordered sequence definition are pre-sented In Section 5 the IRSS test procedure optimizationmethod including the establishment of and solution to themodel are introduced In Section 6 an application case is usedto verify the effectiveness of the proposed optimizationmethod In Section 7 the conclusion is presented

2 An Overview of the TSP and Its Applicationsand Solutions

-e TSP is based on a scenario including a salesman and ncities in which the salesman must find the shortest paththrough all the cities [13] Given a set of n cities C1 C2

Test projects of IRSS integratedtesting platform

Mechanical properties andcharacteristic parameters

Modular test Control performance

Freq

uenc

y ba

ndw

idth

-torq

ue

Freq

uenc

y ba

ndw

idth

-pos

ition

Freq

uenc

y ba

ndw

idth

-spe

ed

Posit

ion

trac

king

erro

r

Torq

ue tr

acki

ng er

ror

Torq

ue re

spon

se

Posit

ion

resp

onse

Spee

d re

spon

se

Spee

d re

spon

se

Min

imum

bra

king

torq

ue

Min

imum

star

ting

torq

ue

Elec

tric

al ti

me c

onsta

nt

Mom

ent o

f ine

rtia

of t

he ro

tor

Spee

d tr

acki

ng er

ror

Torq

ue co

nsta

nt

Back

elec

trom

otiv

e for

ce co

nsta

nt

Posit

ive a

nd n

egat

ive s

lip

Spee

d flu

ctua

tion

coef

ficie

nt

Ripp

le to

rque

coef

ficie

nt

Cog

ging

torq

ue

Fric

tion

torq

ue

Max

imum

wor

king

spee

d

Dec

eler

atio

n ch

arac

teris

tics

Acce

lera

tion

char

acte

ristic

s

Rate

d sp

eed

Rate

d to

rque

Safe

ty te

st

Effic

ienc

y te

st

Ove

rspe

ed te

st

Tem

pera

ture

-rise

test

Lock

ed-r

otor

test

Load

test

No-

load

test

Figure 1 IRSS test projects of the IITP

Figure 2 IRSS integrated testing platform (IITP)

2 Complexity

Cn with dij denoting the distance between city Ci and Cj theTSP requires the Hamilton circle with the shortest distancethrough all the cities to be found -e decision variables areintroduced as follows

hij 1 if the salemen travelCj after Ci

0 others1113896 (1)

-e objective functions can be derived as follows

minZ 1113944n

ij1hijdij (2)

-e TSP is a classical combinatorial optimizationproblem which is often used as a reference to modelpractical problems Yang et al [14] formulated the path-planning problem of goods transportation as a TSP Weiet al [15] established the mathematical model of image-stitching based on the TSP In addition to the basic modeldescribed above there are many variants of the TSP such asthe TSP with drone [16] asymmetric TSP [17] multiple TSP[18] and colored TSP [19] On the basis of the originalmodel some constraints were added to the variants to makethem more suitable for modeling the practical problemsShahmanzari et al [20] referred to the election logisticalproblem as the roaming salesman problem which can becharacterized as a combination of the traditional periodicTSP and the prize-collecting TSP with static arc costs andtime-dependent node rewards Aifadopoulou et al [21]transformed the route optimization problem of the reba-lancing vehicle into the one-commodity pickup and deliverycapacitated TSP Delle et al [22] modeled the track routes forleaf collecting in the city as an asymmetric TSP and bysolving the model 10ndash15 of the cost was cut down with theconsequence of reduced time vehicle use and fuelconsumption

-e TSP and its variants are well-known NP-hardproblems whose difficulty to solve increases exponentiallywith the increase in the number of cities [23] Solving theTSP and its variants has thus received attention fromthousands since they were first proposed -e solutions tothe TSP and its variants can be divided into deterministicand approximate solutions Deterministic solutions to theTSP and its variants such as cutting plane [24] branch andbound [25] and branch and cut [26] solutions are unat-tractive due to the large amount of computation that theyrequire-e approximate solutions to the TSP have attractedmore attention due to their high solving efficiency and easyimplementation Intelligent search algorithms one class ofapproximate solution to the TSP have become a hotspot ofresearch on TSP solutions in recent years as part of thegrowing interest in artificial intelligence Kucukoglu et al[27] introduced a new and effective hybrid simulatedannealingtabu search algorithm to solve the ETSPTW-MCR problem and the proposed algorithm was capable offinding efficient and more realistic route plans for electricvehicles in computational studies Liu et al [28] proposed aniching particle swarm optimization algorithm based on

Euclidean distance and hierarchical clustering for multi-modal optimization and applied it to solve the TSP Mitraet al [29] reinterpreted the data compression problem as aTSP and introduced a modified ant colony algorithm incombination with a mutation operator to resolve theproblem Moreover new intelligent search algorithms suchas the spider algorithm [30] chicken swarm optimization[31] and whale optimization algorithm [32] have also beenused to solve the TSP and its variants

3 An Ordered Sequence Description of IRSSTest Projects on the IITP

In our previous research we found that the test of the IRSStest projects on the IITP are implemented by changing theparameters of the IITP control variables -e key IITPcontrol variables relating to the IRSS testing are state of theIRSS being tested state of the loading system state runningtime and acquisition of instrumentsensor signal For ex-ample when implementing load test the operation processon IITP is as follows

(i) -e IITP starts the instrumentsensor to sample at acertain sampling frequency controls the state of theIRSS being tested to reach its rated speed andcontrols the state of the loading system to reach therated load of the IRSS being tested

(ii) -e IITP then triggers the state running time whenthe state of the IRSS being tested and the state of theloading system are satisfied for testing the timing is30min

(iii) -e corresponding instrumentsensor signal valuesare obtained by the time node of the completion ofthe state running time and the performance indexesof the IRSS test projects are calculated in thebackground

-e process above shows that the test process of the loadtest can be defined by the combination of three controlvariables including the state of the IRSS being tested thestate of the loading system and the state running time Inorder to determine the optimization relationship we usecode to define different parameters of the two controlvariables the state of the IRSS being tested and the state ofthe loading system respectively as shown in Table 1 Hencethe test process of each IRSS test project can be defined bythe combination of the parameter codes of the IITP controlvariable In addition some of the test process of the IRSS testprojects have one step and only one combination should beused to define this kind of IRSS test project such as a no-loadtest is defined by (I1 L0 30) and a load test by (I1 L1 30) Bycontrast some of the test process of the IRSS test projectshave more than one step and more than one combinationshould be used to define them for example the locked-rotortest is defined by (I2 L3 5) (I2 L4 1) orderly Moreover wetake the combination of IITP control variable parameters asexecution subelements of the IITP and use the orderedsequence of these subelements to define the test process ofeach IRSS test project on the IITP

Complexity 3

Let xi be the subelement of the IITP and it is thecombination of three control variable parameters that is xsirepresenting the state of IRSS being tested xli representingthe state of loading system and xti representing the staterunning time Let X be the set of m IITP executionsubelements

X xi|xi xsi xli xti( 1113857 i isin (1 m)1113864 1113865 (3)

where xsi and xli are the code of the IITP control variableparameters as shown in Table 1 xti which represents thestate running time is defined as the greatest commondivisor of the time of the combinations that have the samexsi and xli -at is the combinations with the same xsi andxli are treated as one IITP execution subelement and xti ofthis element is the greatest common divisor of the time ofall these combinations For example the efficiency testcan be defined by the combination of (I1 L1 60) and thespeed fluctuation coefficient can be defined by (I1 L1 10)-erefore we can form an IITP execution subelementxj = (I1 L1 10) where xtj = 10 and the value 10 of xtj is thegreatest common divisor of 10 and 60 Consequently theefficiency test consists of six IITP execution subelementxj and then it can be defined by the ordered sequence ofxjxjxjxjxjxj Similarly the speed fluctuation coefficientconsists of one IITP execution subelement xj and then itis defined by sequence of xj

Let Y be the set of n IRSS test projects Each IRSS testproject yi can be described by the ordered sequenceconsisting of IITP execution subelements in the set X-erefore it can be derived from above that the test timeof each IRSS test project can be determined by the staterunning time parameter of the subelements in the or-dered sequence Let N (yi xj) represent the number ofIITP execution subelements xj in the ordered sequence yiWe can thus obtain the test time of yi by the followingformula

t yi( 1113857 1113944m

j1N yi xj1113872 1113873xtj (4)

4 Optimization Relationships of the IRSS TestProjects on the IITP

Describing the IRSS projects with an ordered sequence ofIITP execution subelements intuitively demonstrates thatsome of the IRSS test project sequences have the same IITPexecution subelements When testing multiple IRSS testprojects on the IITP if these same execution subelements ofthe IRSS test project sequences can be shared the test time ofthe IRSS on the IITP can be optimized which is the basis ofthe optimization method proposed in this paper First itmust be decided whether the same execution subelements ofthe IRSS test project sequences can be shared when tested onthe IITP Since the IRSS test project sequence is ordered theexecution subelements of the sequence should be imple-mented on the IITP in a strict order determined by thesequence so as to fulfill the test process of the IRSS testproject -erefore although the IRSS test projects have thesame IITP execution subelements those execution subele-ments may not necessarily be shared Figure 3 shows anexample for those who have the same execution subelementsin the IRSS test project sequences but the same executionsubelements cannot be shared in the test procedure on theIITP -e IRSS test projects in Figure 3 have the same ex-ecution subelement x2 but to test yi the execution sub-element x3 should be implemented after x2 to complete thetest of yi and no other execution subelement can be insertedin the middle of the test sequence of yi -is is similar for thetesting of yj -erefore the IRSS test project yi and yj cannotshare the execution subelement x2 even though it is the sameexecution subelement in their test project sequences

Based on the analysis above we introduce a directedoperation symbol ldquocaprdquo by which yicap yj means searching forthe same execution subelement sequence as the sequence ofyi from the beginning of the sequence of yj such that the endof the sequence must cover the last execution subelement ofyi or yj otherwise yicap yj=empty -e ordered sequence obtainedfrom the operation ldquocaprdquo of the two test project sequences isthat whose execution subelements can be shared in the testprocedure of these two test projects tested on the IITP Twooptimization relationships between the IRSS test project

Table 1 -e codes and definitions of the parameters of control variables on the IITP

Controlvariables -e codes and definitions of the parameters of control variables

State of IRSSbeing tested

I0 I1 I2 I3 I4 I5

Stop Ratedspeech

Rated speech(reverse rotation)

Maximumallowable speed

120

Linear increaseto rated speed

Rated speechdecreases linearly to

0I6 I7 I8 I9 I10 I11

Maximum workingspeed

Stop afterrated speed

Linear increase tostart-up Step signal Chirp signal Sine wave frequency

conversion signalI12

Linear increase to speedchange of load system

State ofloading system

L0 L1 L2 L3 L4 L5No-load output Rated

torqueContinuous locked

torque Peak locked torque Linear load torated torque

Linear increase tomaximum torque

4 Complexity

sequences are determined according to the operation ldquocaprdquothe merger optimization relationship and the sequenceoptimization relationship respectively as shown in Figure 4

41 -e Merger Optimization Relationship -e mergeroptimization relationship means that one IRSS test projectsequence contains the sequence of another IRSS test projectAs is shown in Figure 4(a) the IRSS test project sequence ykcontains the sequence of yl Let yk be the containing testproject and yl be the contained test project -e calculationresult of ldquocaprdquo of yk and yl is thus as follows

yk capyl x2x2x3 yl

yl capyk empty(5)

As can be seen from formula (5) when two IRSS testproject sequences yi and yj have the calculation result ofyicap yj= yj we say that yi and yj have the merger optimizationrelationship and that yi is the containing test project while yjis the contained test project When two IRSS test projectshave the merger optimization relationship the performanceindexes of these two test projects can be obtained from onecontaining test project implemented on the IITP Hence thetest time of these two test projects on the IITP can beshortened to that of the containing test project

42 -e Sequence Optimization Relationship -e sequenceoptimization relationship means that there are the samesequences between the end of one IRSS test project sequenceand the front of another IRSS test project sequence Asshown in Figure 4(b) the execution subelement sequencex3x4 at the end of IRSS test project sequence yg is the same asthat at the front of yh Let yg be the front test project and yhbe the end test project-e calculation result of ldquocaprdquo of yg andyh is thus as follows

yg capyh x3x4

yh capyg empty(6)

As can be seen from formula (5) when two IRSS test projectsequences yi and yj have the calculation result of yicap yjneempty wesay that yi and yj have the sequence optimization relationshipand that yi is the front test project while yj is the end test projectWhen two IRSS test project sequences have the sequence op-timization relationship the execution subelement sequence

obtained by the calculation of ldquocaprdquo of these two test projectsequences can be shared when implementing the test of thefront test project first and then the end test project on the IITP-erefore the test time of these two IRSS test projects on theIITP can be reduced by the test time of that of the executionsubelement sequence they shared

5 IRSS Test Procedure Optimization Methodon the IITP

-e IRSS test procedure optimization method on the IITPproposed in this paper is to establish an optimization modelbased on the optimization relationships of the IRSS testproject sequences introduced above and to obtain an optimaltest order of the IRSS test projects to be tested on the IITP bysolving the model

51-e Establishment of the OptimizationModel of IRSS TestProcedure on the IITP For an IRSS with n test projects to betested on IITP there are n test orders In additionaccording to the optimization relationships derived from lastsection for a certain test order L the test time is calculated asfollows

t(L) 1113944n

i1t yi( 1113857 minus 1113944

nminus1

i1t[L(i)capL(i + 1)] (7)

where L (i) represents the IRSS test project ranking i in thetest order L As can be seen from formula (7) when thetest order is determined the test time on the IITP is thetotal test time of all the IRSS test projects minus the sum ofthe optimized test time of every two ordered test projectsin the test order -erefore the aim of the optimization ofIRSS test procedure on the IITP is to find a test order toobtain the shortest test time that is to minimize formula(7)

In order to further explore the relationship between thetest order and the test time a sequential test time expressionis defined to express the test time of the test project yj afterthe execution of another test project yi as follows

sij t yi⟶ yj1113872 1113873 t yj1113872 1113873 minus t yi capyj1113872 1113873 (8)

As can be seen from formula (8) when testing yj after yion the IITP the test time of yj is the original test time of yjminus the test time of the sharing execution subelementsequence of the two test projects

Here a virtual test project y0 is introduced as the startingand ending test project of the test procedure that is it ranksfirst and last in the test order -e test project sequence of y0is empty Hence according to the definition of operationldquocaprdquo for every arbitrary test project sequence yk there areexpressions as follows

t y0( 1113857 0

t y0 capyk( 1113857 t yk capy0( 1113857 0(9)

In addition according to formula (8) the followingexpressions can be obtained

IITP execution process x1 x2 x2 x4 x5x3

x2 x4 x5x1 x2 x3

yi

yi

yj

yj

Figure 3 Schematic diagram of two IRSS test projects that cannotshare a test process on the IITP even though they have the sameexecution subelement in their test sequences

Complexity 5

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)

-en introducing the virtual starting and ending testproject y0 to the test order L which consists of n IRSS testprojects and combining formulas (8) and (10) the test timeof the IRSS that is being tested in the test order L on the IITPcan be updated as follows

t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)

As seen from formula (11) when the test order is deter-mined the test time is the sum of the test time of every twoordered test projects in the test order being tested sequentially Iftaking each IRSS test project as a city and the test time of everytwo test projects being tested sequentially on the IITP as thepath cost between two cities the optimization problem of IRSSprocedure on the IITP can be transformed into the TSP withfixed starting and ending points whose aim is to seek theshortest path traversing all the cities Figure 5 shows the cor-responding relation between the TSP and the optimizationproblem of IRSS test procedure on the IITP

After relating the TSP and the optimization problem ofIRSS test procedure on the IITP the optimization model ofIRSS test procedure on the IITP can be established accordingto the objective function of the TSP which formulated as (1)and (2) -en we get the model expressed as follows

min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

where formula (12) means that the aim of the optimizationproblem of IRSS test procedure on the IITP is to find a testorder according to which we tested on the IITP resulting inthe shortest test time Formula (13) means that every IRSStest project should be tested on the IITP and tested onlyonce In formula (13) xij is the decision variables whosevalue is 0 or 1 and its expression is as follows

xij 1 yi⟶ yj

0 else1113896 (14)

52 -e Solution to the Optimization Model of IRSS TestProcedure on the IITP As mentioned above there are n testorders with n IRSS test projects to be tested on the IITP thatis the solving scale of the optimizationmodel of the IRSS testprocedure on the IITP will increase exponentially with thenumber of the IRSS projects to be tested Similar to the TSPit is also an NP-hard problem We use the simulatedannealing (SA) algorithm [33] to solve the optimizationmodel in this paper -e pseudocode of SA algorithm is asfollows (Algorithm 1)

-e pseudocode of the SA algorithm shows that thealgorithm includes two cycles an inner cycle and an outercycle -e inner cycle accepts the new solution according tothe metropolis probability criterion as a result of that eventhe suboptimal solution is likely to be accepted thus ef-fectively breaking out of the local optimal solution More-over the outer cycle simulates the annealing process withwhich the probability of accepting a suboptimal solutiondecreases meaning that the solution obtained in eachannealing process can converge leading to the optimalsolution -e inner and outer cycle solution mechanismsensure that the solution obtained by the SA algorithm has ahigh probability of being the global optimization

-ere are three key design points when using the SAalgorithm to solve the optimization model of IRSS testprocedure on the IITP the generation of an initial solutionand a new solution the determination of the fitness of thesolution and the acceptance rules of the new solution -esethree key design points are introduced as follows

x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3

IITP execution process

ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)

Figure 4 Two optimization relationships between the IRSS test project sequences (a) the merger optimization relationship (b) thesequence optimization relationship

6 Complexity

(i) Generation of an initial solution and a new so-lution the solution of the optimization model ofIRSS test procedure on the IITP is the test order ofIRSS test projects to be tested on the IITP -e SAalgorithm is not sensitive to the initial solutionthat is whether the optimal solution obtained ornot is not related to the initial solution -ereforewhen solving the optimization model the initialsolution L0 is thus the input order of IRSS testprojects to be tested Moreover the generation ofa new solution Lnew is to randomly select two testprojects in the current solution Lcurrent and toexchange their positions in Lcurrent Figure 6shows the generation process of new solutionLnew

(ii) Determination of the fitness of solution the fit-ness of solution refers to whether the solution isgood or bad which is judged in the solvingprocess of the optimization model of IRSS testprocedure on the IITP by whether the test timeobtained by testing according to test order of thesolution is short or long -e shorter test time thesolution gets the better the solution is -ereforethe fitness of the solution can be determined byformula (11)

(iii) Acceptance rules of the new solution when the newsolution Lnew generated it is accepted according tothe metropolis probability criterion -e specificsteps are as follows

(a) If t (Lnew)minus t (Lcurrent)lt 0 that is the new so-lution is better than the current one the newsolution Lnew is accepted and let Lcurrent Lnew

(b) If t (Lnew)minus t (Lcurrent)ge 0 that is the new so-lution is worse than the current one then cal-culate the state transition probability by thefollowing formula

PT Lcurrent⟶ Lnew( 1113857 expminus t Lnew( 1113857 minus t Lcurrent( 1113857( 1113857

Tk

1113888 1113889

(15)

(c) Randomly select a number r from a uniformlydistributed interval of (0 1) If PT lt r the newsolution Lnew is accepted and letLcurrent Lnew Otherwise the new solution is

discarded and the original current solution isretained for the next iteration

-e solution of the optimization model of IRSS testprocedure on the IITP based on the SA algorithm can bedesigned according to the three key design points introducedabove and the optimal test order for IRSS test projects to betested on the IITP would be obtained by solving the opti-mization model Figure 7 shows the flowchart of solving theoptimizationmodel of IRSS test procedure on the IITP basedon the SA algorithm

6 Case Analysis

In this section the method proposed in the paper is appliedto test procedure optimization of an IRSS in the develop-ment phase on the IITP -ere are three IRSSs being testedeach with the same test projects namely a ripple torquecoefficient a speed fluctuation coefficient a positive andnegative slip an electrical time constant a safety test a no-load test a load test a locked-rotor test a temperature-risetest an overspeed test and an efficiency test with total of 11IRSS test projects All the IRSS test projects above can betested on the IITP

First seven execution subelements are constructedaccording to the relationship between the IRSS test projectsto be tested and the control variables on the IITP as follows

X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)

Second the ordered sequence of the IRSS test projectsare defined according to the seven execution subelements asshown in Table 2 In Table 2 if each IRSS test project is testedwithout optimizing the test procedure on the IITP the testtime of one IRSS is 273min and the total test time of thethree IRSSs is 819min -e test time is thus too long to meetthe urgent testing needs in the development phase

Finally the SA algorithm is adopted to solve the opti-mization model -e initialization parameters of the SA

The TSP

Cities

The path costbetween two cities

The optimization problem of the IRSStest procedure on the IITP

IRSS test projects

The time cost when two IRSS testprojects tested on IITP sequentially

Figure 5 Corresponding relation between the TSP and the optimization problem of IRSS test procedure on the IITP

Complexity 7

algorithm are as follows initial temperature Tk= 100 timesof internal cycles res = 20 temperature drop coefficientlam= 095 and cutoff temperature Tf = 10 Table 3 shows theoptimizing schedule of the optimization model of applica-tion case based on the SA algorithm When using the SAalgorithm to solve the optimization model of IRSS testprocedure on the IITP it is with high solving efficiency thatthe optimal solution is obtained in the 20th iteration In the10th iteration and the 15th iteration the current optimalsolution was 148min but by the 20th iteration the SA al-gorithm successfully jumps out from the local optimal so-lution and finally obtains the global optimal solution of138min proving the effectiveness of the SA algorithmFigure 8 shows the schematic diagram of the optimal testprocedure on the IITP of application case -e optimal testorder for the 11 IRSS test projects on the IITP isy5⟶ y9⟶ y11⟶ y7⟶ y1⟶ y4⟶ y8⟶ y10⟶y6⟶ y2⟶ y3 and the total test time is 138min which isonly 5055 of the test time without optimization Whentesting the three IRSSs the total test time is shortened fromthe original 819min to 414min and the total optimizationtime is 405min showing a significant optimization effect ofthe proposed method -erefore the IRSS test procedureoptimization method proposed in this paper can effectivelyshorten the test time of the IRSS on the IITP and improve thetesting efficiency of the IRSS significantly

In fact when the IRSS test project is described by an orderedsequence of IITP execution subelements parallel testing can berealized on the IITP -e purpose of parallel testing is to im-prove test efficiency by integrating the test of test projectsaccording to their test resource [34] In order to furtherdemonstrate the superiority of our proposed method paralleltesting on the IITP is designed according to the IRSS test projectsequences Figure 9 shows the parallel testing result of theapplication case As shown in Figure 9 the test time of the IRSSof application case on the IITP based on parallel testing isequivalent to the test time of sequential test of the IRSS testproject y9 y6 y10 y4 y8 y3 and y5 that is 163min As derivedfrom above the test time of application case on the IITPwithoutoptimization is 273min -erefore the test time of applicationcase based on parallel testing is 110min shorter than thatwithout optimization and the optimization ratio of parallel

testing is 4029 However comparing to our method the testtime of the application case based on parallel testing is 25minlonger than that of our method with 10 lower in the opti-mization ratio -e reason of this phenomenon is that theparallel testing only can deal with the merger optimizationrelationship between the IRSS test project sequences but cannotdeal with the sequence optimization relationship resulting inthe failure to utilize the sequence optimization in the testprocess

In addition we conduct a comparison experiment basedon the solvingmethod to the optimizationmodel of IRSS test

Start

Set the initial temperature Tk maximum number of iterations for the internal cycle rescooling

coefficient lam cutoff temperature Tf

Get the initial solution L0 according to the entrysequence of IRSS test projects

Let Lcurrent = L0 T = Tk k = 1

Let i = 1

Generate the a new solution Lnew and calculate thefitness function t (Lnew) let Δ = t (Lnew) ndash t (Lcurrent)

Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End

T = lamlowastT k = k + 1Record the results of this internal cycle

N

N

N

Y Y

Y

Figure 7 Flowchart of solving the optimization model of IRSS testprocedure on the IITP based on the SA algorithm

y1 y4y3y2 y5

Exchange

Lcurrent

t(Lcurrent) = t(y1rarry2) + t(y2rarry3) + t(y3rarry4) + t(y4rarry5)

y1 y4y2y3 y5Lcurrent


Figure 6 Schematic diagram of the generation process of newsolution Lnew

8 Complexity

procedure on the IITP We use the genetic algorithm (GA)[35] to solve the optimization model of application case andthe solutions obtained from the GA with three differentcombinations of initialization parameters are compared andanalyzed with that of the SA algorithm with the initialization

parameters the same as above Table 4 shows the initiali-zation parameters of the GA and the SA algorithms in thecomparison experiment In the three combinations of ini-tialization parameters of the GA the crossover probability Pcand mutation probability Pm are the same and the

Initialized (Tk Tf lam res S0)Let TTk Scurrent S0If TgtTfRepeatFor k 1 to res doBeginGenerate (Snew from C)If f (Snew)lt f (Scurrent) -en Scurrent SnewElse if expminus[f (Snew)minus f (Scurrent)]Tkgt r -en Scurrent Snew

Endk k+ 1T lamlowastTEnd

End

ALGORITHM 1 Pseudocode for the simulated annealing algorithm

Table 2 -e ordered sequence and the test time of the IRSS test projects of application case

ID IRSS test projects Code of IRSS test projects IRSS test project sequences Test time (min)1 Ripple torque coefficient y1 x5 102 Speed fluctuation coefficient y2 x2 x2 103 Positive and negative slip y3 x2 x3 104 Electrical time constant y4 x6 x6 105 Safety test y5 x1 306 No-load test y6 x2 x2 x2 x2 x2 x2 307 Load test y7 x5 x5 x5 308 Locked-rotor test y8 x6 x7 69 Temperature-rise test y9 x5 x5 x5 x5 x5 x5 6010 Overspeed test y10 x4 x2 x2 x2 1711 Efficiency test y11 x5 x5 x5 x5 x5 x5 60

y5 safety test

y9 temperature-rise test

y11 efficiency test

y1 ripple torque coefficient

y2 speed fluctuation coefficient

y3 positive and negative slip

y4 electrical time constant

y8 locked-rotor test

y10 overspeed test

y6 no-load test

y7 load test

Optimal test procedure

x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7


Figure 8 Schematic diagram of the optimal test procedure of application case

Complexity 9

population size popSize and the number of genetic iterationsGen_iter are different -e reason for the setting of thesecombinations of initialization parameters is that the pop-ulation size and the number of genetic iterations of the GAdetermine the maximum iteration times of one time algo-rithm running where the maximum iteration times of theGA are popSize lowast Gen_iter while the maximum iteration

times of the SA algorithm are 1113880log(TfTk)

lam 1113881 times res In this way

it is easy to compare the performance of these two algo-rithms based on the maximum iteration times We use theGA and the SA algorithms to solve the optimization modelof application case based on the initialization parametersshown in Table 4 As seen from Table 4 four tests areimplemented and the maximum iteration times of test no1are similar to those of test no4 In each test we run 100 timesof the algorithm and the solutions obtained in the 100 times

x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2 x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1

x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1

Test resources on IITP

IRSS test projects

y5safetytest

y9 temperature-risetest

y11 efficiency test

y1 ripple torquecoefficient

y2 speed fluctuationcoefficient

y3 positiveand negative

slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test

Figure 9 Schematic diagram of the parallel testing result of application case

Table 3 Optimizing schedule of the optimization model of application case based on the SA algorithm

Times of cooling Temperature T Times of state transitions Test time (min) Ratio of optimization time ()0 100 mdash 273 mdash5 7738 9 173 633610 5987 6 148 542115 4633 3 148 542120 3584 4 138 5055

Table 4 Initialization parameters of the solving algorithm for comparison experiment

AlgorithmInitialization parameters

Maximum iteration times Test noPc Pm popSize Gen_iter

GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20

Table 5 Comparative analysis results of the comparison experiment

Algorithm Optimal solution(min) Test no Times of occurrence of optimal solution Average (min) SD Average running time (s)

GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity

of algorithm running of each test are compared and analyzedbased on the times of occurrence of optimal solution av-erage value standard deviation value and the averagerunning time Table 5 shows the comparative analysis resultsof the comparison experiment As can be concluded fromTable 5 the overall performance of the SA algorithm is betterthan that of the GA When the maximum iteration times aresimilar the solving performance of the SA algorithm isobviously superior to the GA Although the performance ofthe GA gets better with the increase of the populationnumber and the number of genetic iterations it needs 10times of maximum iteration times for the GA to achieve theperformance similar to the SA algorithm However thelarger the maximum iteration times is the longer runningtime the algorithm needs And the large population sizewould bring high space complexity of the GA algorithm-erefore the SA algorithm is an ideal solving method to theoptimization model of IRSS test procedure on the IITP

7 Conclusions

In this paper we proposed a test procedure optimizationmethod for the industrial robot servo system on the in-tegrated testing platform In the proposed method firstlywe creatively defined the execution subelements of theintegrated platform as well as the industrial robot servosystem test project ordered sequences In addition wedesigned an ldquocaprdquo operation to dig out the optimizationrelationships between the industrial robot servo system testproject sequences Finally based on these optimizationrelationships we established an optimization model for theindustrial robot servo system test procedure on the inte-grated platform and by solving the model we obtained theoptimal test order of the industrial robot servo system testprojects with shortest test time when testing on the inte-grated testing platform -erefore the test efficiency of theintegrated testing platform improved -e case analysisshowed that the proposed method can shorten the test timeof the industrial robot servo system by 5055 -ecomparative experiment also showed the superiority of theproposed method

Moreover the proposed method can be applied tosimilar scenarios that test samples with multiple testprojects are tested on the integrated testing platformBesides the ideas to apply our proposed method to dealwith the multiple stress combination experiments inbattery aging test [36] and the establishment of newmodels for complex systems based on the process simi-larity [37] are considered in our future work

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported in part by the Guangdong High-End Equipment Manufacturing Plan Project under grant no2017B090914003

References

[1] T Brogardh ldquoRobot control overview an industrial per-spectiverdquo Modeling Identification and Control A NorwegianResearch Bulletin vol 30 no 3 pp 167ndash180 2009

[2] T Yuan D Wang X Wang X Wang and Z Sun ldquoHigh-precision servo control of industrial robot driven by PMSM-DTC utilizing composite active vectorsrdquo IEEE Access vol 7pp 7577ndash7587 2019

[3] D B Zhu J W Han X J Wang Y P Zhu and X B GuoldquoModel and performance study on the PMLSMrdquo in Pro-ceedings of the IECON 2017-43rd Annual Conference of theIEEE Industrial Electronics Society pp 3670ndash3675 New YorkNY USA 2017

[4] H Guo Y F Li and X Zhang ldquoDevelopment of a perfor-mance test platform of direct-drive servo valve linear forcemotorrdquo in Proceedings of the 2018 15th International Con-ference on Ubiquitous Robots pp 781ndash785 New York NYUSA 2018

[5] J Q Yang D Y Wang and W H Zhou ldquoPrecision lasertracking servo control system for moving target positionmeasurementrdquo Optik vol 131 pp 994ndash1002 2017

[6] H Wang Z Y Zhang J Long L Wang and X R YeldquoReliability evaluation method for robot servo system basedon accelerated degradation testrdquo in Proceedings of the 201922nd International Conference on Electrical Machines andSystems pp 1942ndash1947 New York NY USA 2019

[7] S J George K S S Ranjini C Rajagopalan and S MuruganldquoDesign and development of automated high temperaturemotor test facilityrdquo Sadhana vol 45 no 1 p 6 2019

[8] L Sidhom M Smaoui and X Brun ldquoTracking positioncontrol of electrohydraulic system with minimum number ofsensorsrdquo Studies in Informatics and Control vol 25 no 4pp 479ndash488 2016

[9] X Zhang H He J Zheng and H Dong ldquoServo mechanismtest system based on PXIrdquo Ordnance Industry Automationvol 35 no 12 pp 1ndash3 2016

[10] M D Luo Z Q Peng and J Y Li ldquoDesign of a four-channelautomatic test system for servosrdquo in Proceedings of the 2016IEEE Chinese Guidance Navigation and Control Conferencepp 791ndash795 New York NY USA 2016

[11] Z Cheng A Chen and J Li ldquoAnalysis of simulate modelbased on servo mechanism simulation devicerdquo in Proceedingsof the 2019 IEEE 8th International Conference on Fluid Powerand Mechatronics pp 122ndash126 Wuhan China April 2019

[12] M W Ingalls and D R Broussard ldquoModular design of testsystemsrdquo in Proceedings of the 17th Capacitor and ResistorTechnology Symposium CARTSʼ97 pp 251ndash254 Jupiter FLUSA March 1997

[13] N Christofides ldquo-e travelling salesman problemrdquo Combi-natorial Optimization pp 131ndash149 1979

[14] B Yang W Li J Wang J Yang T Wang and X Liu ldquoAnovel path planning algorithm for warehouse robots based ona two-dimensional grid modelrdquo IEEE Access vol 8pp 80347ndash80357 2020

[15] BWei YWei YWang and X-H Cao ldquoImagemosaic basedon TSPrdquo in Proceedings of the International Conference on

Complexity 11

Mechanism Science and Control Engineering pp 364ndash367Changsha China 2014

[16] D Schermer M Moeini and O Wendt ldquoA branch-and-cutapproach and alternative formulations for the travelingsalesman problem with dronerdquo Networks vol 76 no 2pp 164ndash186 2020

[17] G Campuzano C Obreque and M M Aguayo ldquoAcceler-ating the Miller-Tucker-Zemlin model for the asymmetrictraveling salesman problemrdquo Expert Systems with Applica-tions vol 148 2020

[18] T Moyaux and E Marcon ldquoCost of selfishness in the allo-cation of cities in the multiple travelling salesmen problemrdquoEngineering Applications of Artificial Intelligence vol 892020

[19] X Meng J Li X Dai and J Dou ldquoVariable neighborhoodsearch for a colored traveling salesman problemrdquo IEEETransactions on Intelligent Transportation Systems vol 19no 4 pp 1018ndash1026 2018

[20] M Shahmanzari D Aksen and S Salhi ldquoFormulation and atwo-phase matheuristic for the roaming salesman problemapplication to election logisticsrdquo European Journal of Oper-ational Research vol 280 no 2 pp 656ndash670 2020

[21] G Aifadopoulou G Tsaples J M S Grau I Mallidis andN Sariannidis ldquoManagement of resource allocation on ve-hicle-sharing schemes the case of -essalonikiʼs bike-sharingsystemrdquo Operational Research 2020

[22] D Delle Donne V Di Tomaso and G Duran ldquoOptimizingleaf sweeping and collection in the Argentine city of TrenqueLauquenrdquo Waste Management amp Research 2020

[23] W J Cook In Pursuit of the Traveling Salesman Mathematicsat the Limits of Computation Princeton University PressPrinceton NJ USA 2011

[24] A Ahamdi-Javid and N Ramshe ldquoDesigning flexible loop-based material handling AGV paths with cell-adjacencypriorities an efficient cutting-plane algorithmrdquo QuarterlyJournal of Operations Research vol 17 no 4 pp 373ndash4002019

[25] R Salman F Ekstedt and P Damaschke ldquoBranch-and-boundfor the precedence constrained generalized traveling salesmanproblemrdquo Operations Research Letters vol 48 no 2pp 163ndash166 2020

[26] Y Yuan D Cattaruzza M Ogier and F Semet ldquoA branch-and-cut algorithm for the generalized traveling salesmanproblem with time windowsrdquo European Journal of Opera-tional Research vol 286 no 3 pp 849ndash866 2020

[27] I Kucukoglu R Dewil and D Cattrysse ldquoHybrid simulatedannealing and tabu search method for the electric travellingsalesman problem with time windows and mixed chargingratesrdquo Expert Systems with Applications vol 134 pp 279ndash3032019

[28] Q Liu S Du B J van Wyk and Y Sun ldquoNiching particleswarm optimization based on Euclidean distance and hier-archical clustering for multimodal optimizationrdquo NonlinearDynamics vol 99 no 3 pp 2459ndash2477 2020

[29] S Mitra and D Das ldquoAn efficient VLSI test data compressionscheme for circular scan architecture based on modified antcolony meta-heuristicrdquo Journal of Electronic Testing vol 36no 3 pp 327ndash342 2020

[30] E Bas and E Ulker ldquoDiscrete social spider algorithm for thetraveling salesman problemrdquo Artificial Intelligence Review2020

[31] A G Hussien A E Hassanien E H Houssein M Amin andA T Azar ldquoNew binary whale optimization algorithm for

discrete optimization problemsrdquo Engineering Optimizationvol 52 no 6 pp 945ndash959 2020

[32] Y Hao F Qiang Y Jiaqi and Z Caiming ldquoAn improvedchicken swarm optimization for TSPrdquo in Proceedings of theInternational Conference on Applications and Techniques inCyber Intelligence ATCI 2019 pp 211ndash220 Huainan China2020

[33] V Fabian ldquoSimulated annealing simulatedrdquo Computers ampMathematics with Applications vol 33 no 1-2 pp 81ndash941997

[34] K-W Yeh J-L Huang and L-T Wang ldquoCPP-ATPG acircular pipeline processing based deterministic parallel testpattern generatorrdquo Journal of Electronic Testing vol 32 no 5pp 625ndash638 2016

[35] D Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley Longman Publishing CoBoston MA USA 1989

[36] X Tang K Liu X Wang F Gao J Macro andW D Widanage ldquoModel migration neural network forpredicting battery aging trajectoriesrdquo IEEE Transactions onTransportation Electrification vol 6 no 2 pp 363ndash374 2020

[37] J Lu K Yao and F Gao ldquoProcess similarity and developingnew process models through migrationrdquo AIChE Journalvol 55 no 9 pp 2318ndash2328 2009

12 Complexity

large number of IRSS test projects being tested on the IITPas well as the time-consuming nature of doing so low testingefficiency remains an issue Modular experimental designs[12] have been applied to parts of the IRSS test projects basedon the IRSS test standard and technical requirement as seenin Figure 1 as a modular test For example the no-load test ofa modular test on the IITP can test four test projects no-loadcurrent no-load voltage no-load power and no-load speedHowever the efficiency remains nonideal for there are stilltoo many IRSS test projects that cannot be tested modularly

We found that the test process of IRSS test projects onthe IITP involves changing the control variables of the IITPand that some steps of the test process of IRSS test projectsshared the same control variable parameters on the IITPBased on this finding we propose a test procedure opti-mization method for the IRSS being tested on the IITP -enovelty of the proposed method is that we find out a methodto dig out the optimization relationships between IRSS testprojects when tested on the IITP and then we establish anoptimization model based on this finding to get the optimaltest order of the IRSS test projects to be tested on the IITPwhich results in shortening the test time on the IITP

-e main contributions of this paper are the following

(i) A method that uses an ordered sequence to define theIRSS test project is proposed according to the rela-tionship between IRSS test projects and the control

variable parameters on the IITP -e ordered se-quence defining the IRSS test projects is formed by theexecution subelements of IITP which is the combi-nation of IITP control variable parameters

(ii) A method to shorten the test time by sharing thesame IITP execution subelements among the IRSStest project sequences is discussed -e directedoperation symbol ldquocaprdquo is proposed to perform in twoIRSS test project sequences while they were testedone after another Two optimization relationshipsbetween IRSS test projects when tested on the IITPare identified by the ldquocaprdquo operation namely themerger optimization relationship and the sequenceoptimization relationship

(iii) -e optimization problem of the test order of theIRSS test projects on the IITP is considered in theframework of the TSP with a fixed starting pointand ending point whose aim is to seek the shortestpath through all cities An optimization model isestablished and the optimal test order with theshortest test time of the IRSS tested on the IITP isobtained by solving the model

-e remainder of this paper is organized as follows InSection 2 an overview of the TSP and its applications andsolutions is presented In Section 3 the method of using anordered sequence to define the IRSS test projects is proposedIn Section 4 the optimization relationships of the IRSS testprojects based on the ordered sequence definition are pre-sented In Section 5 the IRSS test procedure optimizationmethod including the establishment of and solution to themodel are introduced In Section 6 an application case is usedto verify the effectiveness of the proposed optimizationmethod In Section 7 the conclusion is presented

2 An Overview of the TSP and Its Applicationsand Solutions

-e TSP is based on a scenario including a salesman and ncities in which the salesman must find the shortest paththrough all the cities [13] Given a set of n cities C1 C2

Test projects of IRSS integratedtesting platform

Mechanical properties andcharacteristic parameters

Modular test Control performance

Freq

uenc

y ba

ndw

idth

-torq

ue

Freq

uenc

y ba

ndw

idth

-pos

ition

Freq

uenc

y ba

ndw

idth

-spe

ed

Posit

ion

trac

king

erro

r

Torq

ue tr

acki

ng er

ror

Torq

ue re

spon

se

Posit

ion

resp

onse

Spee

d re

spon

se

Spee

d re

spon

se

Min

imum

bra

king

torq

ue

Min

imum

star

ting

torq

ue

Elec

tric

al ti

me c

onsta

nt

Mom

ent o

f ine

rtia

of t

he ro

tor

Spee

d tr

acki

ng er

ror

Torq

ue co

nsta

nt

Back

elec

trom

otiv

e for

ce co

nsta

nt

Posit

ive a

nd n

egat

ive s

lip

Spee

d flu

ctua

tion

coef

ficie

nt

Ripp

le to

rque

coef

ficie

nt

Cog

ging

torq

ue

Fric

tion

torq

ue

Max

imum

wor

king

spee

d

Dec

eler

atio

n ch

arac

teris

tics

Acce

lera

tion

char

acte

ristic

s

Rate

d sp

eed

Rate

d to

rque

Safe

ty te

st

Effic

ienc

y te

st

Ove

rspe

ed te

st

Tem

pera

ture

-rise

test

Lock

ed-r

otor

test

Load

test

No-

load

test

Figure 1 IRSS test projects of the IITP

Figure 2 IRSS integrated testing platform (IITP)

2 Complexity



0 others1113896 (1)


minZ 1113944n

ij1hijdij (2)










Complexity 3





t yi( 1113857 1113944m

j1N yi xj1113872 1113873xtj (4)







I0 I1 I2 I3 I4 I5

Stop Ratedspeech



120



0I6 I7 I8 I9 I10 I11











4 Complexity



yk capyl x2x2x3 yl

yl capyk empty(5)



yg capyh x3x4

yh capyg empty(6)






t(L) 1113944n

i1t yi( 1113857 minus 1113944

nminus1

i1t[L(i)capL(i + 1)] (7)






t y0( 1113857 0

t y0 capyk( 1113857 t yk capy0( 1113857 0(9)



x2 x4 x5x1 x2 x3

yi

yi

yj

yj


Complexity 5

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)


t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)



min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


xij 1 yi⟶ yj

0 else1113896 (14)




x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3


ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)


6 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity



0 others1113896 (1)


minZ 1113944n

ij1hijdij (2)










Complexity 3





t yi( 1113857 1113944m

j1N yi xj1113872 1113873xtj (4)







I0 I1 I2 I3 I4 I5

Stop Ratedspeech



120



0I6 I7 I8 I9 I10 I11











4 Complexity



yk capyl x2x2x3 yl

yl capyk empty(5)



yg capyh x3x4

yh capyg empty(6)






t(L) 1113944n

i1t yi( 1113857 minus 1113944

nminus1

i1t[L(i)capL(i + 1)] (7)






t y0( 1113857 0

t y0 capyk( 1113857 t yk capy0( 1113857 0(9)



x2 x4 x5x1 x2 x3

yi

yi

yj

yj


Complexity 5

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)


t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)



min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


xij 1 yi⟶ yj

0 else1113896 (14)




x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3


ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)


6 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity





t yi( 1113857 1113944m

j1N yi xj1113872 1113873xtj (4)







I0 I1 I2 I3 I4 I5

Stop Ratedspeech



120



0I6 I7 I8 I9 I10 I11











4 Complexity



yk capyl x2x2x3 yl

yl capyk empty(5)



yg capyh x3x4

yh capyg empty(6)






t(L) 1113944n

i1t yi( 1113857 minus 1113944

nminus1

i1t[L(i)capL(i + 1)] (7)






t y0( 1113857 0

t y0 capyk( 1113857 t yk capy0( 1113857 0(9)



x2 x4 x5x1 x2 x3

yi

yi

yj

yj


Complexity 5

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)


t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)



min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


xij 1 yi⟶ yj

0 else1113896 (14)




x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3


ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)


6 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity



yk capyl x2x2x3 yl

yl capyk empty(5)



yg capyh x3x4

yh capyg empty(6)






t(L) 1113944n

i1t yi( 1113857 minus 1113944

nminus1

i1t[L(i)capL(i + 1)] (7)






t y0( 1113857 0

t y0 capyk( 1113857 t yk capy0( 1113857 0(9)



x2 x4 x5x1 x2 x3

yi

yi

yj

yj


Complexity 5

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)


t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)



min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


xij 1 yi⟶ yj

0 else1113896 (14)




x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3


ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)


6 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity

t y0⟶ yk( 1113857 t yk( 1113857

t yk⟶ y0( 1113857 0(10)


t(L) 1113944n

i0t[L(i)⟶ L(i + 1)] 1113936

n

i0sii+1 (11)



min t(L) 1113944n

ij1xijsij (12)

ST

1113944

n

i1xij 1 j 1 2 n

1113944

n

j1xij 1 i 1 2 n

xij 0 1

i 1 2 n

j 1 2 n

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)


xij 1 yi⟶ yj

0 else1113896 (14)




x1 x1 x2 x2 x3

x1 x1 x2 x2 x3 x4

x4 x2 x2 x3

x2 x2

yk

yk

yl

x3


ykcapyl

yl

(a)

x4

yg

yg

yh

yh

x1 x2 x2 x3

x1 x2 x5 x2 x3x2 x3

x4 x3 x4 x5 x5 x3

x3 x4


ygcapyh

(b)


6 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity







Tk

1113888 1113889

(15)




6 Case Analysis



X

x1

x2

x3

x4

x5

x6

x7

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

I0 L0 30min

I1 L0 5min

I2 L0 5min

I3 L0 2min

I1 L1 10min

I1 L2 5min

I1 L3 1min

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)



The TSP

Cities



IRSS test projects



Complexity 7





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity





Start





Let i = 1


Δ lt 0

i gt res

T gt Tf

exp (ndashΔT)gt r

Let Lcurrent = Lnew

Output Lcurrent

End


N

N

N

Y Y

Y


y1 y4y3y2 y5

Exchange

Lcurrent





8 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity





End




y5 safety test


y11 efficiency test






y10 overspeed test

y6 no-load test

y7 load test


x1

x1

x2 x2 x2

x2 x2 x2 x2 x2 x2

x2 x2

x2 x2 x2 x2 x2 x2

x2 x3

x3

x4

x4

x5 x5 x5 x5 x5 x5

x5 x5 x5 x5 x5 x5

x5

x5 x5 x5

x5 x5 x5 x5 x5 x5

x6

x6 x6

x6

x6 x7

x7



Complexity 9






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity






x5 x5 x5 x5 x5 x5 x2 x2 x2 x2 x2 x2

x5 x5 x5 x5 x5 x5 x2 x2

x5 x5 x5

x5

x4 x2 x2 x2 x6 x6 x6 x7 x2 x3 x1


IRSS test projects

y5safetytest


y11 efficiency test




slip

y4electrical

timeconstant

y8locked-

rotortest

y10 overspeedtest

y6 no-load test

y7 load test







GA 09 0520 50 1000 150 50 2500 2100 100 10000 3

SA Tk Tf lam res 900 4100 10 095 20



GA 138

1 10 1466 48518 00732322 27 1429 36729 01746383 54 14035 25937 0544116

SA 4 73 1395 25981 0031773

10 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity


7 Conclusions



Data Availability




Acknowledgments


References
















Complexity 11

























12 Complexity

























12 Complexity

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