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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
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Bonfring International Journal of Industrial Engineering and Management Science, Vol. 2, No. 4, December 2012 161
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
ParameterOdd-
ratio
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).
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Bonfring International Journal of Industrial Engineering and Management Science, Vol. 2, No. 4, December 2012 162
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
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[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
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N. Ulbrichand T. Volden, Regression Analysis of Experimental Data
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[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.
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ISSN 2277
Science, Vol. 2, o. 4, December 2 12 163
Bangalore, She
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