5. PROBABILISTIC INTELLIGENT ANALYSIS
5.4. Training and Testing of Classifier
The generated data for various simulated conditions using FEM were split into 80% for training the classifier and 20% to test the functionality of the classifier. These simulated and experimental conditions are given in table 5.1. The NBC was successfully trained with the simulated data. The results indicate that the probabilistic intelligence method is suited for both voltage and current signatures application. Although an accuracy of approximately 69% for VSA, 65% for CSA (stator) and 61% for CSA (rotor) is achieved on the simulated result. However, when all the data is combine that is induced voltage, stator current and rotor current then the accuracy becomes 86%. This means that the addition of all investigated features yield the best classification results. One incorrectly predicted classification occurred where the instance of healthy was classified as rotor winding inter-turn fault for both the voltage and the stator currents. For the rotor current, there were two misclassifications found where stator and rotor faults were classified as healthy. This may be improved through the addition of training instances at different levels of this fault type.
Tables 5.2, 5.3, 5.4 and 5.5 show the distribution of the posterior probability (see (2.6) determined by Bayes classifier) of the test instances used for the simulated results with load. The presented distributions indicate that each prediction is obtained with a high degree of certainty and precision. The posterior probability distribution for rotor current signature with the inter-turn fault on the rotor winding indicates that Bayes classifier relatively less accurate.
Table 5.2. Simulated posterior probability distribution of test instances for stator voltage with load, over predicted classes
Stator Voltage with Load Predicted Class Probabilities
Actual Class Label Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 0 0 1 0 Healthy 2 0 1 1.94151070119015e-54 0 Brush 3 0.697402783057586 0 7.96357781654809e-301 0.302597216942407 Inter-turn-rotor 4 0.585606727562263 0 1.50066111900894e-310 0.414393272437749 Inter-turn-rotor 5 0.985207967481771 0 7.85961532919385e-298 0.0147920325182170 Healthy 6 0.988688023427211 0 9.48630768368528e-297 0.0113119765727780 Inter-turn-rotor 7 0.178190049696098 0 5.88919971427500e-312 0.821809950303916 Inter-turn-rotor 8 0 0 1 0 Inter-turn-stator 9 0 0 1 0 Inter-turn-stator 10 0 1 4.76744634685221e-56 0 Brush 11 0 0 1 0 Inter-turn-stator 12 0 0 1 0 Inter-turn-stator
Table 5.3. Simulated posterior probability distribution of test instances for rotor current with load, over predicted classes
Rotor Currents with Load Predicted Class Probabilities
Actual Class Label Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 0 1 0 0 Inter-turn-rotor 2 0 0 1 0 Inter-turn-stator 3 0 0 1 0 Inter-turn-stator 4 0 0 1 0 Inter-turn-rotor 5 0 1 0 0 Brush 6 0 0 1 0 Inter-turn-rotor 7 0.386835845225849 0 0 0.613164154774143 Healthy 8 0.905783500544679 0 0 0.0942164994553245 Inter-turn-stator 9 0.903313479060403 0 0 0.0966865209396009 Inter-turn-stator 10 0 0 1 0 Brush 11 0.0169046401266314 0 0 0.983095359873369 Healthy 12 0.892525833722726 0 0 0.107474166277276 Inter-turn-rotor
Table 5.4. Simulated posterior probability distribution of test instances for stator current with load, over predicted classes
Stator Currents with Load Predicted Class Probabilities
Actual Class Label Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 0 1 8.60640751228794e-52 0 Brush 2 0 0 1 0 Inter-turn-stator 3 0 0 1 0 Inter-turn-stator 4 0 0 1 0 Inter-turn-stator 5 0.657981277653023 0 0 0.342018722346990 Inter-turn-rotor 6 0.000596856621944650 0 0 0.999403143378058 Inter-turn-rotor 7 0.791627396819480 0 0 0.208372603180527 Healthy 8 0.953995774839456 0 0 0.0460042251605525 Inter-turn-rotor 9 0 0 1 0 Healthy 10 0 0 1 0 Inter-turn-stator 11 0 1 7.92246726283388e-46 0 Brush 12 0.00343653677630197 0 0 0.996563463223692 Inter-turn-rotor
Table 5.5. Simulated posterior probability distribution of test instances for combined stator voltage, stator current and rotor current over predicted classes
Combined Predicted Class Probabilities
Actual Class Label Test
Instances Healthy Brush
Inter-turn -
Stator Inter-turn - Rotor
1 0 1 0 0 Brush 2 0.139323960397068 0 0 0.860676039602959 Inter-turn-rotor 3 0 0 1 0 Inter-turn-stator 4 0 1 0 0 Brush 5 0.999440426826103 0 0 0.000559573173864603 Inter-turn-rotor 6 0 0 1 0 Inter-turn-stator 7 0 0 1 0 Inter-turn-stator 8 0.999845370989955 0 0 0.000154629010062992 Inter-turn-rotor 9 8.90651422572818e-06 0 0 0.999991093485719 Inter-turn-rotor 10 0 0 1 0 Healthy 11 0.998436383681025 0 0 0.00156361631897470 Healthy 12 0 0 1 0 Inter-turn-stator
Pattern classification is the act of assigning a class label to an object, physical process or an event, based on some prior information [64]. The performance behaviour displays a specific pattern corresponding to each fault presented in this investigation. The simulated and experimental posterior probability distribution of the voltage and current at each of the harmonics are the features which enable identification of this pattern. The relationship between these features for different instances shows the Bayesian spectrum estimates at three different frequencies of stator
circuited fault (3 and 6 turns), rotor winding short circuited fault (3 and 6 turns) and brush fault conditions. These frequencies cluster in particular regions corresponding to each condition. The scatter plots results obtained from training and testing the classifier, using simulated data with load conditions is given in figures 5.22, 5.23 and 5.24. The instances are in terms of the four different labels predicted by the classifier as per legend respectively.
Fig.5.22: Simulated Scatter plot of instances (with load) illustrating relationship between the predicted class labels and posterior distribution (induced voltages)
Fig.5.23: Simulated Scatter plot of instances (with load) illustrating relationship between the predicted class labels and posterior distribution (stator currents)
Fig.5.24: Simulated Scatter plot of instances (with load) illustrating relationship between the predicted class labels and posterior distribution (rotor currents)
Experimental training and test data are obtained using the experimental generator under the healthy and three faults conditions that are considered in this investigation. The data instances
harmonic data as attributes. The results indicate that the probabilistic intelligence method is suited for this application. Although an accuracy of approximately 99% for VSA, 99% for CSA (stator) and 91% for CSA (rotor) is achieved, when the feature data are combined, an overall accuracy is approximately 99%. This indicates that the classifier works better with experimental data and with the combined feature data.
The applied algorithm determines a posterior probability distribution for every classified instance. The distribution of the posterior probability (see (2.6) determined by Bayes classifier) of the test instances used in the experimental cases with load is given in tables: 5.6, 5.7, 5.8, 5.9, 5.10, 5.11 and 5.12. The presented distributions indicate that each prediction is obtained with a high degree of certainty and precision.
Table 5.6. Experimental posterior probability distribution of test instances for stator voltage at no-load, over predicted classes
Stator Voltage at No-Load Predicted Class Probabilities Actual
Class Label Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 0.000856595426043906 0.999143404573955 2.57444989445387e-27 4.98019886875990e-17 Brush 2 2.29190909090266e-08 6.90689716745318e-49 1.10869123690082e-25 0.999999977080904
Inter-turn- rotor 3 1.62741443898638e-15 1.01416010454325e-61 4.92422498904629e-23 1
Inter-turn- rotor 4 0 0 1 2.86069752905098e-85 Inter-turn- stator 5 1.19064793320661e-265 0 1 7.52567314622202e-80 Inter-turn- stator 6 0.999999999993065 6.94586360245955e-12 5.01635250024981e-24 5.51242952356804e-22 Healthy 7 1.06451399228515e-18 1.53237326463463e-56 2.85078185988593e-26 1
Inter-turn- rotor 8 2.22283929855311e-13 4.73984589501531e-41 3.60895754575886e-25 0.999999999999773
Inter-turn- rotor 9 1 4.57724755399422e-18 2.32542280719804e-22 5.30171153593941e-22 Healthy 10 3.17347814352484e-34 2.17989362802342e-99 4.48565867611622e-23 1
Inter-turn- rotor 11 6.51726280262300e-307 0 1 1.48574614248978e-138
Inter-turn- stator 12 8.49141010955368e-05 0.999915085898919 7.20038702381258e-31 4.49979588431371e-27 Brush 13 0 0 1 2.81017939802074e-163 Inter-turn- stator 14 2.51938615022857e-180 0 1 9.64595599172129e-38 Inter-turn- stator 15 0.999999999790362 2.09634760395448e-10 7.70075029851006e-23 3.63424871779046e-19 Brush 16 0.999784154629090 0.000215845370917164 2.78616877729430e-25 6.40912788430743e-26 Brush 17 2.20383901794477e-277 0 1 8.55730558331086e-126
Inter-turn- stator 18 1.10020423756419e-22 2.97154755141502e-70 8.37012483723588e-23 1
Inter-turn- rotor 19 0.999999999751651 2.48353941592527e-10 6.16422722811456e-23 2.60172361583111e-33 Healthy 20 0.999999999999659 2.61662304041132e-18 1.13888895260792e-24 3.35513738908765e-13 Healthy 21 1.28760481743220e-13 5.32576906936645e-48 6.15107282030077e-29 0.999999999999858
Inter-turn- rotor 22 1.41796105248923e-196 0 1 8.28267632273873e-46
Inter-turn- stator 23 5.50500347268679e-14 6.72661348122215e-105 4.37294999134291e-21 0.999999999999943
Inter-turn- rotor 24 6.38255230005575e-269 0 1 1.83613993840889e-63 Inter-turn- stator 25 0 0 1 1.19169111744813e-245 Inter-turn- stator 26 0.999988663120350 1.13368796479526e-05 9.53761405780369e-20 8.95964819875359e-39 Brush 27 0 0 1 5.52021543257294e-144
Inter-turn- stator 28 0.000327734034915954 0.999672265965077 1.10248701711906e-14 3.16069979283765e-49 Healthy 29 1.54194180139975e-08 2.61388730438862e-29 2.59914519888966e-29 0.999999984580569
Inter-turn- rotor 30 1.27057616620150e-16 1.83977492814508e-47 3.11292864360759e-26 1
Inter-turn- rotor
Table 5.7. Experimental posterior probability distribution of test instances for stator voltage with load, over predicted classes
Stator Voltage with Load Predicted Class Probabilities Actual
Class Label
Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor 1 1.65702106898658e-27 3.53786526920052e-55 1 2.47426807251198e-28
Inter-turn- stator 2 0.999999894463036 1.28999284863302e-27 3.39769306988845e-10 1.05197192904342e-07 Healthy 3 6.37534797073455e-75 7.05441101129343e-122 1 2.92677236829334e-81
Inter-turn- stator 4 1.08177004247827e-07 6.18940467168777e-40 0.999999891355407 4.67575726594750e-10
Inter-turn- stator 5 0.241616887918201 2.10696548572568e-30 0.758382075186593 1.03689520801698e-06
Inter-turn- stator 6 1.55167107925036e-09 2.16774072558384e-32 1.02882199679537e-15 0.999999998448317
Inter-turn- rotor 7 0.998415360709025 1.48911260952490e-19 0.00158463890991490 3.81046563968971e-10 Healthy 8 3.57662528472703e-132 9.78801121056835e-199 1 9.07355912251748e-144
Inter-turn- stator 9 2.17376802978139e-16 6.48567374892938e-34 8.11749550239733e-17 1
Inter-turn- rotor 10 1.59232748895083e-09 3.50113968159969e-15 1.23872307428739e-08 0.999999986020441
Inter-turn- rotor 11 8.89549625733526e-15 5.43850334009738e-35 3.38815716190502e-16 1
Inter-turn- rotor 12 1.67089984609606e-12 3.91975296632506e-35 4.74136480318448e-15 0.999999999998323
Inter-turn- rotor 13 3.63507203229774e-08 1.16634333897441e-21 3.13888177368377e-09 0.999999960510395
Inter-turn- rotor 14 5.96716538354055e-131 1 1.07927177953747e-67 1.27419983325660e-70 Brush 15 3.74775990380695e-09 9.43011901866371e-26 1.08218344203673e-08 0.999999985430407
Inter-turn- rotor 16 9.12917310924351e-15 3.64649152825758e-36 2.59573245577895e-15 1
Inter-turn- rotor 17 3.82552544335764e-78 6.56177839804368e-124 1 2.63372397467897e-83
Inter-turn- stator 18 4.50589038048575e-07 1.06942800708252e-27 0.999999549410960 9.83038057105704e-15
Inter-turn- stator 19 5.66594510530414e-16 3.35933067315539e-28 1 7.01226452344186e-25
Inter-turn- stator 20 6.16116813339381e-233 1 2.07737386915202e-127 2.59062219240918e-135 Brush 21 1.02780207514094e-05 7.74201990817835e-23 1.98255292985889e-07 0.999989523723963
Inter-turn- rotor 22 6.63038946598022e-95 1.99247033011101e-124 1 3.34926851236730e-102
Inter-turn- stator 23 1.81963329072342e-287 1 7.75653177621852e-152 5.23619106736195e-157 Brush 24 0.999999999378844 4.28927134408524e-22 6.21147711791355e-10 1.07938256514598e-16 Healthy 25 2.31434265659837e-115 1 3.27513859253202e-67 2.89800295168734e-62 Brush 26 3.05789982044369e-06 9.63222914588489e-23 2.59843560494801e-12 0.999996942097582
Inter-turn- rotor 27 0.999999995491862 5.36337119162068e-25 4.43286240352418e-09 7.52806331755948e-11 Healthy 28 0.907226384286931 7.02062041602603e-26 0.0927715854776948 2.03023537774375e-06 Healthy 29 0 1 1.24402123272382e-214 4.30671954616669e-211 Brush 30 9.08035571559159e-144 7.72324742147434e-207 1 2.89652445677081e-117
Inter-turn- stator
Table 5.8. Experimental posterior probability distribution of test instances for rotor current at no-load, over predicted classes
Rotor Currents at No-Load Predicted Class Probabilities Actual
Class Label
Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 1.91327455047050e-10 0.999999885560651 2.11360564365779e-33 1.14248021554261e-07 Brush 2 0.988562347140265 1.16826844041971e-16 8.34513375076350e-27 0.0114376528597339 Healthy 3 0.991911934592317 1.67679542689754e-17 8.13487896487088e-28 0.00808806540768162 Healthy 4 0 0 1 1.55253451320780e-310 Inter-turn- stator 5 2.91593701046380e-307 0 1 1.37788535179031e-198 Inter-turn- stator 6 0 0 1 0 Inter-turn- stator 7 0.183959913587344 1.23816622492537e-20 3.88066400534381e-33 0.816040086412658 Inter-turn- rotor 8 4.49184082134450e-16 9.79323998893268e-54 1.38745417450184e-58 1
Inter-turn- rotor 9 1.84690761246970e-22 8.22448834496269e-67 2.34542933533776e-56 1
Inter-turn- rotor
10 0 0 1 0
Inter-turn- stator 11 7.75729491551582e-15 0.999999999999844 2.27752999856903e-20 1.46903620752879e-13 Brush 12 0.997388538881814 3.17436664717254e-14 1.65417935792603e-23 0.00261146111815545 Healthy 13 6.27253275405732e-19 5.08582799230461e-64 2.20108682510021e-57 1
Inter-turn- rotor 14 0.585499619994156 9.15580554219489e-18 4.99331354669607e-28 0.414500380005844 Inter-turn- rotor 15 0 0 1 1.00000000000000e-323 Inter-turn- stator 16 0.999519269833063 2.85218989934865e-06 3.20507070254324e-12 0.000477877973832457 Healthy 17 1.11731690606767e-15 4.25629093122353e-51 1.19982209926616e-46 1
Inter-turn- rotor 18 0 0 1 0 Inter-turn- stator 19 0.000441687783067903 2.63295995465527e-29 4.66549462756284e-30 0.999558312216933 Inter-turn- rotor 20 0.985574593104142 6.86869728067365e-17 2.88465579062951e-24 0.0144254068958570 Inter-turn- rotor 21 4.00473436498482e-08 0.999999865214909 3.07736773757575e-24 9.47377462444062e-08 Brush
22 0 0 1 0
Inter-turn- stator 23 0.914715936110826 5.93143461648080e-18 5.40699518676147e-30 0.0852840638891735 Healthy
24 0 0 1 0
Inter-turn- stator 25 1.26234548660354e-220 3.56000000000000e-322 1 5.14551526267692e-147
Inter-turn- stator 26 0.357652903622125 1.84467580096515e-20 1.47202708735667e-32 0.642347096377875 Inter-turn- rotor 27 0.633201649648750 6.92584637034431e-21 3.06475540017835e-31 0.366798350351250 Inter-turn- rotor 28 2.49068426144464e-306 0 1 3.99910268844304e-199 Inter-turn- stator 29 1.13115388622073e-13 0.999999999724688 2.51168888548946e-24 2.75199358866274e-10 Brush 30 1.50416559976563e-12 0.999999996064382 1.47751450148702e-33 3.93411487221160e-09 Brush
Table 5.9. Experimental posterior probability distribution of test instances for rotor current with load, over predicted classes
Rotor Currents with Load Predicted Class Probabilities Actual
Class Label
Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor 1 0 2.38275375975167e-11 0.00256857145734918 0.997431428518822
Inter-turn- rotor 2 0 0.999999998685425 7.10500513641248e-24 1.31457689475457e-09 Brush
3 0 0 1 0
Inter-turn- stator 4 0.999999219609314 1.30288115936031e-15 7.80390684398858e-07 1.85896169206628e-20 Healthy 5 0.999999689588746 7.71206165268544e-17 3.10411255669300e-07 2.01621482736425e-21 Healthy 6 4.54689257673271e-42 4.15023082812447e-07 0.999999584425006 5.51912314361865e-10
Inter-turn- stator 7 0 2.21472800919745e-10 0.000342614328303340 0.999657385450225 Inter-turn- rotor 8 0 0 1 0 Inter-turn- stator 9 0 1.65849546633660e-07 0.000119097462403331 0.999880736688049 Inter-turn- rotor 10 0.999999950888858 3.44445278362637e-18 4.91111417848674e-08 1.27124764440281e-22 Healthy
11 0 0 1 0 Inter-turn- stator 12 0 0 1 0 Inter-turn- stator 13 0 1 3.28508219047711e-133 1.67854892585960e-42 Brush 14 0 1 7.08373220612265e-49 5.60380409073830e-17 Brush 15 5.74650589362173e-142 1.46525775431788e-05 0.999983859080369 1.48834208726468e-06
Inter-turn- stator 16 0 9.25058238138950e-09 0.000226131139679982 0.999773859609738
Inter-turn- rotor 17 0.999999993109270 2.35398100831492e-18 6.89072842493483e-09 2.59733944897758e-22 Healthy
18 0 0 1 0 Inter-turn- stator 19 0 3.33580789580735e-06 0.00408652932248002 0.995910134869626 Inter-turn- rotor 20 0 7.57460936955278e-09 2.81080866167276e-05 0.999971884338772 Inter-turn- rotor 21 8.85125775724210e-83 4.69864646510964e-06 0.999995260203387 4.11501470542805e-08
Inter-turn- stator 22 0 7.34829395661625e-10 0.00314240886882879 0.996857590396340
Inter-turn- rotor 23 0 1 8.90205596892066e-89 2.82920520301740e-29 Brush 24 0 1 6.37251064454337e-89 4.71171908924296e-29 Brush 25 0 1.88575816899007e-10 2.68667029432736e-05 0.999973133108481 Inter-turn- rotor 26 2.91973041288623e-155 0.000242045494651387 0.999755625326653 2.32917869746618e-06 Inter-turn- stator 27 0 2.75954939662684e-07 0.000107238177121309 0.999892485867938 Inter-turn- rotor 28 0 0.00364035484706013 0.737069281904984 0.259290363247956 Inter-turn- stator 29 0.999999972160801 3.13581630071934e-18 2.78391978552854e-08 1.33150621043222e-22 Healthy 30 0 6.03770483761821e-07 0.000549888289745840 0.999449507939770
Inter-turn- rotor
Table 5.10. Experimental posterior probability distribution of test instances for stator voltage and rotor current over predicted classes
Combined No-Load Predicted Class Probabilities Actual
Class Label
Test
Instances Healthy Brush Inter-turn – Stator Inter-turn - Rotor
1 0 0 1 0
Inter-turn- stator 2 9.40781182149103e-22 8.07292059313433e-85 1.33061846308421e-55 1
Inter-turn- rotor 3 0.999999999902911 9.70797865355870e-11 2.78958864805520e-34 1.26255672084686e-48 Healthy 4 6.90606291872594e-32 6.84207982724303e-168 9.62524261276751e-78 1
Inter-turn- rotor 5 0.477170813370734 0.522829186629277 2.02966135460495e-46 5.17761692669305e-17 Brush 6 0 0 1 2.52999032497077e-261
Inter-turn- stator 7 1 4.19834401719268e-27 2.52770637575493e-50 1.06072475029888e-35 Healthy
8 0 0 1 0
Inter-turn- stator 9 9.69771947569767e-17 1 3.23588043434396e-51 6.85861273673207e-27 Brush 10 1.22516702375099e-22 1.70672270192306e-89 1.91812970813521e-54 1
Inter-turn- rotor 11 0 0 1 3.87234660358054e-226 Inter-turn- stator 12 0 0 1 3.31232731497679e-244 Inter-turn- stator 13 6.96721417575318e-09 0.999999993032787 9.53600427489042e-55 5.84081213879663e-31 Brush
14 0 0 1 0
Inter-turn- stator 15 6.58759662668691e-19 1 8.20024504045774e-51 3.30546222062658e-40 Brush 16 5.32368836692034e-08 9.87102651777476e-49 2.17169569472511e-59 0.999999946763127
Inter-turn- rotor
17 0 0 1 0
Inter-turn- stator 18 8.46588888818377e-30 1.13611393111020e-114 2.60035701045703e-81 1
Inter-turn- rotor 19 1.43079433173566e-34 6.61504430747718e-119 2.13314694394312e-55 1
Inter-turn- rotor 20 1 5.40932382948729e-34 9.81524554788124e-49 3.06703650437121e-24 Healthy 21 3.58948699865664e-16 8.12767480853170e-64 3.75001556471552e-53 1
Inter-turn- rotor 22 1 4.50401421762017e-29 1.48261294864179e-53 2.56977260981519e-23 Healthy 23 0.00352000998550355 0.996479990014509 1.28992437632757e-38 3.73043189078013e-41 Brush
24 0 0 1 0
Inter-turn- stator 25 3.03738251954697e-11 4.51378139195123e-55 7.21685035115740e-47 0.999999999969617
Inter-turn- rotor 26 1.15674317614054e-28 1.04313069243891e-100 8.53433166219245e-87 1
Inter-turn- rotor 27 3.63667533171624e-30 8.63312091155257e-112 5.90819396361649e-69 1
Inter-turn- rotor 28 1 7.46669527193097e-24 1.82598761505852e-36 8.02058702527578e-17 Healthy
29 0 0 1 0 Inter-turn- stator 30 0 0 1 0 Inter-turn- stator
Table 5.11. Experimental posterior probability distribution of test instances for stator current with load, over predicted classes
Stator Currents with Load Predicted Class Probabilities Actual Class
Label
Test
Instances Healthy Brush Inter-turn - Stator Inter-turn - Rotor
1 2.12638696451923e-57 0 7.87150669634273e-51 1 Inter-turn-rotor 2 4.43623848379915e-198 1 1.05517654837380e-175 3.06278625685510e-94 Brush 3 0 0 1 4.00370815384803e-217 Inter-turn-stator 4 2.03784026120479e-60 0 3.09606561807320e-53 1 Inter-turn-rotor 5 1.80437594925217e-59 0 3.25202024558998e-53 1 Inter-turn-rotor 6 1.50048357305341e-42 0 7.84147657838705e-06 0.999992158523418 Inter-turn-rotor 7 7.62746989390154e-190 1 1.30468923461635e-216 5.36520798600065e-88 Brush 8 1 0 5.43506618788547e-22 2.58156031236854e-77 Healthy 9 1 0 3.46695298133958e-31 4.13065355722048e-57 Healthy 10 9.32295001042324e-30 0 0.999152568895177 0.000847431104818103 Inter-turn-rotor 11 1 0 7.12267474928018e-22 3.48943773287139e-53 Healthy 12 2.24284586796629e-208 1 2.61632610795730e-222 1.40210037902636e-102 Brush 13 2.77348497949562e-182 0 1 2.40020480456920e-31 Inter-turn-stator 14 0 0 1 5.10802109268173e-182 Inter-turn-stator 15 3.63861146298755e-236 0 1 1.62500496151651e-44 Inter-turn-stator 16 2.87469967018742e-28 0 0.994480352430155 0.00551964756985076 Inter-turn-rotor 17 9.64980810794930e-20 0 0.999998206853407 1.79314659723490e-06 Inter-turn-rotor 18 1.63093631923140e-181 0 1 1.32552504308878e-34 Inter-turn-stator 19 1 0 2.57748076188152e-21 3.96045614648668e-62 Healthy 20 0 0 1 1.62549125661015e-194 Inter-turn-stator 21 0 0 1 1.02599875269330e-250 Inter-turn-stator 22 0 0 1 5.62030228921007e-213 Inter-turn-stator 23 1 0 1.04519629270013e-25 2.79598122676431e-53 Healthy 24 0 1 0 4.88968533888679e-184 Brush 25 2.20146141259192e-59 0 3.25960727102647e-52 1 Inter-turn-rotor 26 0 0 1 2.32994849459985e-66 Inter-turn-stator 27 9.28541963921978e-21 0 0.999999999995254 4.74320961568777e-12 Inter-turn-rotor 28 1.26807503931295e-177 1 6.14373111196585e-183 4.20384836501504e-77 Brush 29 4.19612092067784e-56 0 1.12602831021609e-50 1 Inter-turn-rotor 30 2.80000000000000e-322 0 1 2.90028867064869e-63 Inter-turn-stator
Table 5.12. Experimental posterior probability distribution of test instances for stator voltage, stator current and rotor current over predicted classes
Combined with Load Predicted Class Probabilities Actual Class
Label
Test
Instances Healthy Brush Interturn - Stator Interturn - Rotor
1 0 0 5.01065436244392e-68 1 Inter-turn-rotor 2 0 1 0 6.80638886349187e-247 Brush
3 0 0 1 0 Inter-turn-stator
4 0 0 3.77078366106985e-06 0.999996229216326 Inter-turn-rotor
5 0 0 1 0 Inter-turn-stator
6 1 0 1.40274132179122e-48 8.58106986596907e-87 Healthy 7 1 0 8.41103805260817e-32 5.58505864355991e-94 Healthy 8 0 0 6.11664027601210e-16 1 Inter-turn-rotor 9 0 1 9.34069587226606e-291 7.31898720165010e-173 Brush
10 0 0 1 0 Inter-turn-stator
11 0 0 2.56599827439595e-12 0.999999999997442 Inter-turn-rotor 12 1 0 2.64225503550528e-30 3.55610726253431e-104 Healthy 13 8.06028664910563e-291 0 1 4.47864268621153e-76 Inter-turn-stator 14 1.48614055577122e-263 0 1 4.82580710632845e-44 Inter-turn-stator 15 0 0 2.24914672735261e-72 1 Inter-turn-rotor 16 0 0 1 1.89408485889259e-96 Inter-turn-stator 17 0 0 1 0 Inter-turn-stator 18 0 1 0 3.65935669392424e-176 Brush 19 0 0 1 1.04165158887590e-49 Inter-turn-stator 20 0 1 0 0 Brush 21 0 0 1.02224702254943e-71 1 Inter-turn-rotor 22 1 0 3.79754579778529e-37 5.10620443064670e-84 Healthy 23 0 0 1.83921812272684e-09 0.999999998160774 Inter-turn-rotor
24 0 1 0 0 Brush
25 0 0 1.51112010616421e-72 1 Inter-turn-rotor
26 0 0 1 0 Inter-turn-stator
27 1 0 3.00071286602626e-44 3.08425992809514e-91 Healthy 28 0 0 0.439652671991056 0.560347328008972 Inter-turn-rotor 29 0 0 1 9.62916950520261e-81 Inter-turn-stator 30 0 0 4.60140581164705e-69 1 Inter-turn-rotor
The scatter plot results obtained from training and testing the classifier, using experimental data are shown in figures 5.25, 5.26 and 5.27. The instances are presented in terms of the four different labels predicted by the classifier as discussed in the previous section.
Fig.5.25: Experimental Scatter plot of instances (no-load and with load) illustrating relationship between the predicted class labels and posterior distribution (induced voltages)
Fig.5.26: Experimental Scatter plot of instances (with load) illustrating relationship between the predicted class labels and posterior distribution (stator currents)
Fig.5.27: Experimental Scatter plot of instances (no-load and with load) illustrating relationship between the predicted class labels and posterior distribution (rotor currents)
The classification error for the simulated and experimental data as presented in table 5.13 show that the classification works better when the feature data are combined. Errors encountered using the measurement modes – i.e. stator voltage and current, and rotor current, are higher (0.333, 0.25 and 0.37) compared to combined error which is 0.25 for the simulation. An overall error for combined feature data on experimental data is 0.019.
Table 5.13. Simulated and experimental results of the estimated classification error Classification Error
No-Load With Load
Stator Voltage Rotor Current Stator Voltage Stator Current Rotor Current Combined Simulation - - 0,333 0,250 0,370 0,250 Experimental 0,133 0,100 0,0021 0,133 0,0015 0,019
5.5. Conclusion
A fault diagnosis system that utilises the signatures of the machine voltages and currents is presented with two major components namely, signal processing and feature extraction. The NBC was successfully trained with the harmonic data as attributes. The results indicate that the probabilistic intelligence method is suited for both voltage and current signatures application. An accuracy of approximately 69% for VSA, 65% for CSA (stator) and 61% for CSA (rotor) is achieved on the simulated result. However, with all the simulated data combine then an overall accuracy of 86% is achieved. With an experimental data, an accuracy of approximately 99% for VSA, 99% for CSA (stator) and 91% for CSA (rotor) is achieved. With experimental data combined, an overall accuracy of 99% is achieved. This indicates that the classifier works better with the combined feature data as it provides an addition of training instances at different levels of this system.