Vassilis Katsouros, Vassilis Papavassiliou ad Christos Emmaouilidis ATHENA Research & Iovatio Cetre, Greece www.athea-iovatio.gr www.ceti.athea-iovatio.gr/compsys e-mail: christosem AT ieee.org
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Worked with differet modelig approaches Best results obtaied with a Bayesia classificatio approach defie distict problem classes oe for each problem type calculate the posterior probability of a test case for each problem class recommed the problem class that correspods to the maximum a posteriori (MAP) probability
case: cosists of a collectio of evet codes, each of which correspods to a umber of parameters a record of a case ca be defied as a sigle evet code alog with the respective measuremet parameters 30 parameters of oboard measuremets, recorded each time a evet code was geerated 1 dataset of cases with their evet codes ad respective parameters for traiig ad aother 1 for testig/evaluatio The traiig dataset icluded the classificatio of the cases ito uisace or problem for the cases classified as problems, the correspodig problem label/idetifier was also provided.
Traiig dataset: 1.316.653 records that correspod to 10.459 cases of which 10.295 were characterized as uisace ad 164 as problem (13 distict problem IDs) Testig dataset: 1.893.882 records of evet codes measured parameters that correspod to 9.358 distict cases. Groud truth of the testig dataset ivolved 174 problem cases, with the remaiig 9.184 beig uisace cases A recommeder should idetify the problem cases from the 9.358 testig cases ad for each oe of them provide the respective problem idetifier. Evaluatio metric: calculated o a set of cases that ivolved all 174 groud truth problem cases ad a radom selectio of 174 from the total of 9.184 uisace cases.
maximum performace: 348, i.e. sum of 174 groud truth problem cases ad 174 uisace that the traiig dataset icludes oe case with a problem type idetifier (P7940) that is ot foud i the test dataset test dataset icludes cases that have bee categorized i two problem types (P0932 ad P6880) for which there is o available traiig data Problem ID Traiig dataset Test dataset Number of Cases P0159 19 15 P0898 4 6 P0932-2 P1737 2 2 P2584 53 26 P2651 13 13 P3600 17 20 P6559 3 1 P6880-15 P7547 6 4 P7695 17 37 P7940 1 - P9766 14 12 P9965 2 5 P9975 13 16 Total 164 174
Pr P j C k Pr C k P j Pr[ C k Pr[ P ] j ] Bayes rule
P 1 C k P 2 P P C 3 P arg max log Pr Pr C P Pr log P PrP P M k jj j1... MMM j k k k jj j j
C C C C P Pr E E... E P Pr k j 1 2 k k k Nk j C C C E P Pr E P...Pr E P Pr j 1 2 k k k j Nk j Assumig idepedece amog evets
Cosider the case IDs as colums of a matrix NK N N K K K e e e e e e e e e e e e 2 1 3 32 31 2 22 21 1 12 11 Cosider the evet IDs as rows of a matrix The elemets e ij of the matrix is the umber of occurreces of evet i beig observed i case j
Agai case IDs are the colums of the matrix 0 0 1 0 1 0 0 0 0 1 0 0 With the rows beig the problem IDs Ad elemets 0 or 1
C k P 1 C log Pr[ Ck Pj ] log Pr E Pj P i1 2 P 3 P M N k k i
Cosider the problem IDs as colums of a matrix NM N N M M M 2 1 3 32 31 2 22 21 1 12 11 Cosider the evet IDs as rows of a matrix The elemets ij of the matrix is the umber of occurreces of evet i is observed i a case that is classified i problem j
Add a ε term whe ij = 0 to avoid zero probabilities E 1 E 2 P 1 P 2 P M p p p p 11 21 31 N1 p p p p 12 32 22 E PrE 3 i Pj E N N 2 N p p p i1 p 1M 2M ij 3M NM ij
P 1 P 2 P M p p... 1 Pr P j 2 N i1 M N j1 i1 pij M ij
Problem ID Number of Cases Top-1 Top-3 Top-5 P0159 19 15 16 18 P0898 4 4 4 4 P1737 2 1 1 1 P2584 53 49 53 53 P2651 13 13 13 13 P3600 17 15 17 17 P6559 3 1 2 2 P7547 6 2 5 5 P7695 17 15 17 17 P7940 1 1 1 1 P9766 14 14 14 14 P9965 2 2 2 2 P9975 13 10 11 12 Total 164 142 156 159 Overall (%) 86.59 95.12 96.95
Problem ID Number of Cases Top-1 Top-2 Top- 3 Top-4 Top-5 P0159 15 1 2 4 7 10 P0898 6 0 1 1 5 6 P1737 2 0 0 0 0 0 P2584 26 12 19 21 24 25 P2651 13 6 7 7 7 11 P3600 20 9 15 18 19 19 P6559 1 0 0 0 0 0 P7547 4 1 1 1 1 1 P7695 37 24 30 32 35 37 P9766 12 5 5 5 8 9 P9965 5 0 0 0 1 1 P9975 16 2 3 4 7 7 Total 157 60 83 93 114 126 Overall (%) 38.22 52.87 59.24 72.61 80.25
Gaussia Mixture Models (GMMs) for each problem ID traied o the case to evets parameters Diagoal covariace type No. of Gaussia mixtures 10 Best score: 18 Support Vector Machies (SVM) classifiers with features the case to evets parameters Radial Basis Kerel Best score: 35
A hybrid techique comprisig: (a) A recommeder for problem type ID (b) A classifier for uisace / problem Tried the proposed (a) approach with a SVM-based (b) approach but the gai i uisace rate detectio was balaced by the loss i problem ID idetificatio ad there was o time left for further improvemets
A Bayesia Approach for the Maiteace Actio Recommedatio 2013 PHM Data Challege was proposed A hybrid techique could achieve improved results The defiitio of evaluatio metrics for differet PHM problems is a key issue How about data challeges with multiple objectives?
Vassilis Katsouros, Vassilis Papavassiliou ad Christos Emmaouilidis ATHENA Research & Iovatio Cetre, Greece www.athea-iovatio.gr www.ceti.athea-iovatio.gr/compsys e-mail: christosem AT ieee.org