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Bonfring International Journal of Industrial Engineering and Management Science, Vol. 2, No. 4, December 2012 159

“Qualification of DC Brush Motors used in

Spacecraft Missions using Logistic Regression

Model - An Analytical Approach”

K. Shwetha, Dr.N.S. Narahari and Chandra Shekar Prasad

Abstract--- DC brush motor undergoes rigorous

performance testing to predict the failures occurring.

Acceptance test levels are set with margin expected

flight/operations levels and qualification test levels are set

above the expected operation levels to check for the

survivability of DC brush motor in space. Performance testing

is important to design and integration in a planned test

process in which DC brush motor were tested under actual or

simulated mission profile environments to disclose design

deficiencies and to provide information on failure modes and

mechanisms. Statistical models are helpful in this process. The

Logistic Regression Model is the commonly used parametricstatistical models and is one of the statistical techniques that

are used for analyzing and predicting performance with

binary outputs. The objective was to develop Logistic

Regression Model and is designed to examine the

categorization of dependent variables in the quantitative

analysis for the performance of DC brush motor. The work

carried out demonstrates the development of the Logistic

Regression Model for performance prediction of the DC brush

motors for deploying unfurlable antenna. The methodology

includes performance test data and transforming the

dependent variables into binary digits. And to estimate the

probability of success of DC brush motor. The model

developed is useful in the GO-NO-GO decision making withregard to the DC brush motors which is one of the critical

components in the space module. This paper adds value to the

decision making process through statistical validation using

Logistic Regression Model. This Model helps the decision

makers in qualifying the components based on performance

tests. The Model developed shows the working condition of

motor can said to be good since the model fit is good. The

reliability performance of the DC brush motor in the working

condition is significantly good.

Keywords--- Acceptance Test, DC Brush Motors, Logistic

Regression, Qualification Test, Spacecraft

K. Shwetha, Assistant Professor, Department of Mechanical,

Engineering, R V College of Engineering, Mysore Road, Bangalore-59.

Karnataka, India. E-mail:shwetha.krishna646@gmail

Dr.N.S. Narahari, Professor & Dean, Placement and Training,

Department of Industrial Engineering, R V College of Engineering, Mysore

Road, Bangalore-59 .Karnataka, India. E-mail:[email protected]

Chandra Shekar Prasad, Scientist / Engineer – SE, System Reliability

Group, ISRO-ISAC, RAMD, Bangalore -17.Karnataka, India. E-

mail:[email protected]

DOI: 10.9756/BIJIEMS.1934

I. I NTRODUCTION

PACECRAFT components must withstand the launch

loads and the environmental conditions that are

encountered in the space for successful mission of the

spacecraft. These components are tested rigorously and

performance data analyzed for evaluating them for Acceptancedecision. DC brush motors must withstand vibration and

extreme temperatures during launch and on orbit. The motor is

rigorously tested under simulated environmental conditionsfor performance as part of the acceptance test procedures.

Acceptance tests include vibration tests and thermo vacuumcycling. Speed in rpm is calculated for different settings of

voltage, load (torque) and temperature during performance

tests. Current is also monitored during the test. Four motorunits undergo the acceptance level tests. A motor unit

assembled to fixture is used for vibration test, followed by

thermo vacuum test.

Objective of these tests are to check the performance of the

motors for launch loads and simulated environments. The test

set up consists of a fixture on which the motor is mounted, a

provision to apply the required torque, a DC Power Source, aElectronic driver package and a stop watch to time the period

of the test. Motor Speed is estimated by counting number of

rotations for a given time. The main Objective of this paper isto develop a Logistic Regression Model to predict the

performance of DC brush motors based on test result for space

applications. This model is useful in the GO–NO-GO decision

making with regard to the suitability of the DC brush motors

which is a critical component in the deployment mechanism,

for activating the unfurlable antenna of the spacecraft. The performance data has been effectively utilized in the

development of a Logistic Regression Model which can be

deployed to assist the decision makers in deciding on theAcceptance of the motors based on performance

characterization of the DC brush motors.

S

ISSN 2277-5056 | © 2012 Bonfring



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3.3 Estimating the Logistic Regression Model using

Maximum Likelihood

In this Logistic Regression Model, the maximum

likelihood estimates the values which produce the largest

value for the likelihood equation. In Logistic Regression thelikelihood value measures of parameters fit the model of the

data. The model is estimated after several iterations from the

significance and likelihood value. The log likelihood statistic

is the difference between the two model fits, is 2*[LL (N)-LL(0)] is obtained as 50.843 for Acceptance test and 0.711 for

Qualification test. Since, the value obtained is large it can be

concluded that the model fit is fairly good. This indicates that

the parameters studied are usable to provide adequateinformation to predict the acceptability of the DC brush

motors.

3.3.1 Logistic Regression Model of the Acceptance Test

The performance test data was analysed using SYSTATsoftware using the structure of a Logistic Regression Model.

The output obtained is summarized in Table 1 and 2.

Table 1: Binary Logit of Acceptance Test

Parameter Estimate

Standard

error t-ratio p-value

Constant 13.713 5.825 2.354 0.019

Torque -1.653 0.662 -2.497 0.013

Current -0.057 0.036 -1.589 0.112

Torque:current 0.012 0.006 1.854 0.064

Table 2: Probability Analysis for the Performance Test Data of

Acceptance Test95.0 % bounds for the parameters

ParameterOdd-

ratio

Upper

Limit

Lower

Limit probability

Torque 0.191 0.701 0.052 0.160

Current 0.945 1.013 0.880 0.485

Torque:

current1.012 1.024 0.999 0.502

3.3.2 The Software Results are

3.3.2.1 The Goodness of Fit Measures as Follows

The measures of likelihood, Mc. Fadden values have been

obtained from the Binary Logit analysis.

Log Likelihood of constants model = LL(0) = -41.756

2*[LL(N)-LL(0)] = 50.546 with 3 degree of Chi-square

p-value = 0.000

McFadden's Rho-Squared = [LL(N)-LL(0)] / LL(0) =

0.605

LL(N) – Log likelihood of full model, LL(0) - Log likelihoodof constant model. For McFadden’s Rho-Squared is always

positive value, since modulus value is considered.

3.3.2.2 Logistic Regression Model of the Qualification Test

The performance test data was analyses using SYSTAT

software using the structure of a Logistic Regression Model.The output obtained is summarized in Table 3 and 4 for the

Qualification test.

Table 3: Binary Logit of Qualification Test

Parameter EstimateStandard

errort-ratio p-value

Constant -1.946 1.069 -1.820 0.069

voltage 0.343 0.073 4.672 0.000

Table 4: Probability Analysis for the Performance Test Data of

Qualification Test

95.0 % bounds for the parameters

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Upper

Limit

Lower

Limit probability

voltage 1.409 1.626 1.220 0.58

3.3.2.3 The goodness of Fit Measures as Follows

Log Likelihood of constants only model = LL(0) = -30.897

2*[LL(N)-LL(0)] = 43.947 with 1 degree of Chi-square p-

value = 0.000

McFadden's Rho-Squared = = [LL(N)-LL(0)] /LL(0) =

0.711

3.4 Assessing the Goodness of Fit of the Estimated Model

This step deals with the assessment of the model fit basedon the performance data as an output to the model

3.4.1.1 Goodness of Fit Measure Obtained are

i. Acceptance Test

Likelihood ratio = 2*[LL (N)-LL (0)] = 50.546 with 3

degree of freedom Chi-square p-value = 0.000

Upper bound = LL (O) = - 41.756

Mc. Fadden’s = 0.605

ii.

Qualification TestLikelihood ratio = 2*[LL (N)-LL (0)] = 43.947 with

1degree of freedom Chi-square p-value = 0.000

Upper bound = LL (O) = - 30.897

Mc. Fadden’s =0.711

LL(N) – Log likelihood of full model, LL(0) - Log

likelihood of constant model

McFadden’s pseudo R 2 is used to measures the overallmodel fit. In the case of the DC brush motor pseudo

R 2obtained is 0.609 for acceptance test and 0.711 for

qualification test, which shows that that the model fit is fairlygood.

The β coefficients, standard errors and p values were

estimated. Also the odds ratio and 95% confidence intervalsfor each of the coefficients were estimated in the study of

Logistic Regression. The odds of an event occurring was the

ratio of the probability that will occur to the probability that it

will not occur. In other words Probability (event) ÷ Probability

(no event).

ISSN 2277-5056 | © 2012 Bonfring




3.5 Testing for Significance of the Coefficients

The Logistic coefficient was statically significant, since

the p-value obtained was closer to 0, the model is significant.

Using the odds ratio approach set 0 at the lower limit and

infinity at the upper limit. The odd ratio shows the probabilityof success rates. Torque, current and voltage were significant

and the interaction between torque and current was found to

be significant. In this case probability of success was higher.

Hence, the chances that motor working condition wassignificantly high.

IV. R ESULTS

The following significant result is obtained from the

analysis using the Logistic Regression Model:

1. The working condition of motor can said to be goodsince the model fit is good, where McFadden's Rho-

Squared = 0.605 for Acceptance test and 0.711 for

Qualification test. The reliability performance of the

DC brush motor in the working condition is

significantly good.2. The larger the maximum likelihood estimates value

estimate model fit can be concluded to be fairly good.

The value obtained from the analysis of DC brushmotor of 50.546 with 3 degree of freedom and Chi-

square p-value = 0.000 for acceptance test and 43.947

with 1 degree of Chi-square p-value = 0.000 for

Qualification test, shows the good fit of model.

3. Independent variables torque and current are

significant and the interaction between torque andcurrent is found to be significant in acceptance test

and only voltage was found to be significant in

Qualification test.4. The torque and speed are the dependent variables,

torque is proportional to the current. The deployment

of antenna depends on the speed of the motor for thesuccessful mission of spacecraft. The torque, current

and voltage significantly influences the speed of themotor.

5. The current is approximately 240 mA and the torque

loaded upto 10N/m are the specifications performedon DC brush motor. The torque, current and voltage

variables met these specifications to perform on-orbit

conditions.

V. CONCLUSION

Logistic Regression is used as a tool, which is used to predict the motor working condition in spacecraft by

analyzing dichotomous outcome variables. A LogisticRegression Model for speed performance prediction of DC

brush motors for spacecraft applications has been developed.

This model will enhance the capability of the prediction of the

performance of spacecraft components. Through theinterpretation of the Logistic Regression output can be

inferred that the odds ratio the probability of success is higherand 95% confidence intervals for each of the coefficients are

estimated to study the influence of the dependent variable i.e.

speed. The log likelihood statistic is the difference between

the two model fits, is 2*[LL (N)-LL (0)] is50.843 for

Acceptance test and 43.947 for Qualification test. The valueobtained is large, the model fit to the performance test data is

fairly good. It can be concluded that the Logistic Regression

Model is an useful technique for performance prediction of

spacecraft components and can be used in arriving at thedecisions, regarding acceptability or otherwise of the space

component (in this case of DC brush motors) for conditions of

space based on the ground level performance tests conducted

under simulated conditions. The torque and current parametersmeet the on-orbit conditions for the performance of DC brush

motor with the starting torque and controllability led the

systems acquiring accurate control of speed and position. In a

brush DC Motor, torque control is accomplished easily.Output torque is proportional to current. Therefore, if the

current is limited, the torque can also be limited which the

brush motor achieve.

ACKNOWLEDGEMENT

The authors express sincere gratitude to Sri, Kamesh D,“Division Head”, Sujith Kumar N, Scientist/Engineer, SRG at

ISRO Satellite Centre for their valuable guidance,

encouragement and support. The authors are also thankful toDr.B.S..Satyanarayana, Principal RVCE, & Dr. H.N.

Narasimha Murthy, Dean PG Studies, MechanicalEngineering Department, R.V. College of Engineering for

their valuable guidance.

R EFERENCES

[1]

Dalton S. Rosario, Highly Effective Logistic Regression Model For

Signal (Anomaly) Detection, IEEE, Pp 817-820, ICASSC 2004.[2] Ruibin Xi, Nan Lin, and Yixin Chen, Compression and Aggregation for

Logistic Regression Analysis in Data Cubes, IEEE transactions on

knowledge and data engineering, Vol. 21, No. 4, Pp 479-492, April

2009.[3] F. Zhou1, D. Wu, X. Yang1, and J. Roger Jiao, Ordinal Logistic

Regression for Affective Product Design, IEEE IEEM, Pp 1986-1990,

Proceedings of the 2008.[4] Leif E. Peterson, Maximum Likelihood Logistic Regression Using

Metaheuristics, International Conference on Machine Learning and

Applications, Pp 509-514, 2009.

[5] Alyson G. Wilson, Todd L. Graves, Michael S. Hamada and C. Shane

Reese, Advances in Data Combination, Analysis and Collection for

System Reliability Assessment, Institute of Mathematical Statistics inStatistical Science, Vol. 21, No. 4, Pp 514–531, 2006.

[6] J. Umakant, K. Sudhakar, P.M. Mujumdar and C. Raghavendra Rao,

Customized Regression Model for Improving Low Fidelity Analysis

Tool, 11th AIAA/ISSMO Multidisciplinary Analysis and OptimizationConference, Portsmouth, Virginia. AIAA 2006-7118, Pp 1-13, 6-8

September 2006.

[7] Richard DeLoach, and Iwan Philipsen, Stepwise Regression Analysis of

MDOE Balance Calibration Data Acquired at DNW, 45th AIAA

Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA 2007-144, Pp 1-25, 8-11 January 2007.

[8]

N. Ulbrichand T. Volden, Regression Analysis of Experimental Data

Using an Improved Math Model Search Algorithm, 46th AIAA

Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA 2008-833, Pp 1-21, 7 - 10 January 2008.

[9] N. Ulbrich, Regression Model Optimization for the Analysis of

Experimental Data, 47th AIAA Aerospace Sciences Meeting Including

The New Horizons Forum and Aerospace Exposition, Orlando, Florida,AIAA 2009-1344, Pp 1-31, 5 - 8 January 2009.

ISSN 2277-5056 | © 2012 Bonfring



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ISSN 2277

Science, Vol. 2, o. 4, December 2 12 163

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