System Diagostics usig Kalma Filter Estimatio Error Prof. Seugchul Lee, Seugtae Park, Heechag Kim, Hyusuk Huh ICMR2015 (11/25/2015)
Machie Health Diagostics Desig Desig DNA + + Blue Prit phagocytes lymphocytes Huma Body Egie - Data-drive - Model-based - Expert system Huma Immue System Egieerig Immue System 2
Geeral Methods for Diagostics Geeral framework of data-drive diagostics Time Tred Frequecy Tred Bode plot Orbit Aalysis 3
Model-based Diagostics Possible oly for simple systems Aalytical Computer simulatio But, expesive 4
Assumptios Model-based Diagostics system ca be approximated as state space represetatio If system dyamics are chaged (due to fault) x 1 Ax y Cx Real-time diagostics via estimatig matrix A From x ad y From A x 1 Ax y Cx x x y : state : observatio (measuremet) A: system matrix C : measuremet matrix : system oise : obervatio oise Ax 1 y Cx 5
Kalma Filter for Model-based PHM Widely used i guidace, avigatio ad cotrol of vehicles, particularly aircraft ad spacecraft, trajectory optimizatio Optimally estimate ukow states x usig a series of measuremets y observed over time, cotaiig statistical oise ad ucertaities x늿 x K y C x? 1 1 Kalma gai: T K A C ( C C V ) T t t1 t t1 1 6
Machie Learig vs. Kalma Filter Machie Learig (data-drive): Statistical approach o data Data-drive method Supervised Kalma Filter (model-based) Based o physical model + oise distributio Optimal estimator for White oise Kow covariace Kow model 7
positio Kalma Gai as Features? Questio: Moitorig the Kalma gai for system diagostics? Tested with a sprig ad mass system x(t) k 0 m x k m x x Ac x 1 0 x x Covariace matrix is statioary Kalma Gai is ot a fuctio of observatios Caot be used for system diagostics T K A C ( C C V ) T t t1 t t1 8 1
Estimatio Error: Keep moitorig e Kalma Filter Estimatio Error e y y늿 y Cx 1 Ca be used for a Health Idex (i.e., Coditio Idex) to determie the degree o coditio moitorig 9
Doe? or Ay Problems? Must kow system matrix A to apply the Kalma filter System modelig or System idetificatio problem Difficult to idetify matrix A for complicated systems Equally difficult (PHM System Idetificatio) Pseudo Matrix A p 10
Pseudo Matrix A p Positio ad velocity Real physical system positio 1 dt positio velocity 0 1 velocity k1 k k 0 km A 1 0 x 1 Ax y Cx xk 1 xk vk t k v v k1 k 1 txk 0 1 v k x k Ap v k x 1 AP x y Cx A p 1 t 0 1 11
Simulatio Validatio At time 5 sec Itetioally chaged m ad k Estimatio error x(t) k m Ap 12
System Idetificatio System + + z 1 x c v Aˆ X X ( X X ) T T 1 1 A y  K - z Maximum Likelihood z 1 xˆ 1 + c yˆ 1 ( 1) z A P xˆ 1 z 1 Kalma filter with Pseudo A p System idetificatio with MLE 13
System Dyamics: Pole Locatios System idetificatio via MLE x 1 Ax y Cx x 1 AP x y Cx x ˆ 1 Ax y Cx Compariso of pole locatios 14
Rotatig Machiery: Misaligmet Vibratio measuremet Iduce misaligmet durig operatio Kalma Filter Estimatio error Data-drive ML classificatio (SVM) Cotiuous No traiig step required 15
Bearig Fault Detectio Kalma filter with o a prior kowledge of system dyamics of matrix A Fault bearig itroduced 16
Coclusio Proposed a model-based progostics method usig Kalma filter Does ot require high fidelity models for complex systems Health idex Estimatio error ca be used for a health idex of system deviatio from kow state Future work Observability Diagosability (?) 17
Questios 18
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