Hidden Markov Model based Hierarchal Clustering for Autonomous Diagnostics

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Hidden Markov Model based Hierarchal Clustering
for Autonomous Diagnostics

• Akhilesh Kumar, Doctoral Candidate
• Dr. R. B. Chinnam, Associate Professor
• Department of Industrial Engineering
• Wayne State University
• Detroit, MI 48202, USA

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Outline

• Maintenance Techniques
• Research Motivation
• Research Objectives
• Modeling Framework
• Diagnostic Hierarchal clustering with similarity
  measure as Hidden Markov Model
• Research Contribution and Future Research

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Maintenance Techniques

• Corrective Maintenance (CM) Action after failure
• Preventive Maintenance (PM) Time based action
• Conditioned Based Maintenance (CBM) Action if
  needed
• CBM is a philosophy of monitoring the condition
  of machinery and performing the maintenance only
  when there is objective evidence of impending
  failure

Optimal Strategy!
CBM
1-5
Criticality
PM
15-25
CM
70-80
Equipment
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Motivation

• Annual DoD maintenance activities consumes over
  40 Billion
• DoD Maintenance Policy, Programs Resources
  FACT BOOK, 2000
• Maintenance costs at medium-sized power utility
  companies exceed operating profit
  Geibig, 1999
• Annual saving potentials from large-scale
  deployment of effective CBM technology in US 35
  Billion Lee, 2003
• Technical barrier to CBM's widespread
  implementation
• (NIST-ATP CBM Workshop Report, 1998)
• Inability of maintenance systems to learn
  identify impending failures

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CBM Architecture
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Research Objective

• To develop generic yet robust methods for
  autonomous diagnostics
• Scope Incipient Failures
• Occur slowly
• Possible to track development
• Health state estimation

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Diagnostics

• Challenges
• Most of the real world data are
• Non stationary time series
• Not enough examples to label the data
• Multidimensional inputs and outputs
• Solution
• Hidden Markov Model based hierarchal clustering

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Why HMM based Hierarchal Clustering?

• State space models are better than classical
  methods
• Do not suffer from finite window effects
• Handles discrete and multi variate inputs and
  outputs with ease Murphy, 2002
• Data
• Problem Mostly not labeled
• Solution Hierarchal Clustering
• ( of cluster not needed as input)
• Reduces computation of unneeded clusters
• Weakness of distance based similarity measures
• Problem Hard to find clusters with irregular
  shapes (Signature )
• Problem Length of time window needs to be equal
• Solution HMM based likelihood estimation

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Hierarchal Clustering

• Uses distance matrix as clustering criteria
• Does not require the number of clusters as an
  input

a
a b
b
a b c d e
c
c d e
d
d e
e
Divisive (DIANA)
Step 3
Step 2
Step 1
Step 0
Step 4

• Distance Measures
• Minimum distance
• Maximum distance
• Mean distance
• Average distance

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Hidden Markov Model

• An HMM is a stochastic finite automaton, where
  each state generates (emits) an observation
  Murphy, 2002
• HMM is parameterized as
• Initial state distribution
• The state transition matrix
• The observation model
• Models are first-order Markov
• The goal computing of the belief state

Xt Hidden state at time t X1, X2, X3, X4 Yt
Observation at time t Y1, Y2, Y3 aij  State
transition matrix bij  Output model
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Proposed Algorithm

• Step 1
• Initialize
• Select initial subsequence as training data
• Step 2
• Construct a node with 1 HMM
• Train HMM with training data
• Step 3
• Calculate Log-likelihood for training data from
  trained HMM
• Based on distribution of log-likelihoods
  construct mean-k sigma threshold
• Step 4
• Pass whole dataset through trained HMM and
  calculate log-likelihood
• Step 5
• Compare log- likelihoods with threshold and
  collect data points cutting the threshold
• Step 6
• Set subsequences cutting threshold as training
  data
• Repeat step 2-5 until all data is exhausted

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Experimental Test-bed

• Experiment Setup
• HAAS VF-1 CNC Machining Center
• Kistler 9257B piezo-dynamometer
• Signals
• Thrust Torque Data (12 drill-bits)
• 200-260 data points per hole
• Initialization
• of hidden states 6 (fixed)
• of health state HMM 1 (fixed)
• of observations 2 (Thrust and Torque)
• Training data All 2nd holes for 12 drill-bits
• State transition matrix 2nd hole of 1st
  drill-bit
• K2 (Chebyshevs Rule)

Hole
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Intermediary Results Log-likelihood (LL) Curves
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Results 1st Health State Based on LL
HOLES
1st HMM
2nd HMM
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Results Health States
HOLES
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Conclusions and Future Research

• Proposed algorithm is promising
• Better computational performance owing to the
  fact
• Less number of parameters to be initialized
• Reduces computation of unneeded clusters
• Time-window is not a problem

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Future Work

• Future Research Goals
• Validating the model
• Prognostics Remaining Useful Life estimation
  based on log-likelihood

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Thank You!