Builtin Fault Diagnosis for Tunable Analog Systems Using an Ensemble Method

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Built-in Fault Diagnosis for Tunable Analog
Systems Using an Ensemble Method
Part I
Specification-driven Embedded Self-Testfor
Mixed-Signal Circuits using loopback
Hongjoong Shin, Byoungho Kim and Jacob A.
Abraham VTS 2006
Part II

• Hongjoong Shin, Joonsung Park and Jacob A.
  Abraham
• Submitted to ITC 2006

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Built-in Fault Diagnosis for Tunable Analog
Systems Using an Ensemble Method

• Hongjoong Shin, Joonsung Park and
• Jacob A. Abraham
• Submitted to ITC 2006

Computer Engineering Research Center Department
of Electrical and Computer Engineering University
of Texas at Austin
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Analog fault diagnosis

• Fault diagnosis is important process to improve
  yield and reduce time-to-market slamani ITC92
• Identification of design weak spots and problems
  in manufacturing process
• Increasingly important due to parametric yield
  loss

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Conventional fault diagnosis approach

• Apply a set of test inputs
• Test input is selected to highlight a fault
• However, it may be difficult to find test inputs
• which effectively isolate a fault
• Various observations are used
• Internal nodes as well as primary outputs
• Magnitude of current and voltage, and phase
• Performance parameters are insufficient to
  provide accurate diagnosis
• Number of measurements gtgt number of unknown
  parameters
• Limitations
• Long diagnosis time
• Requires broad range of off-chip measurements
  which usually demand different setups and stimuli
• Use of expensive measurements

Measure- ments
Sensitivity matrix
Compo- nents
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Motivation

• Tackles problems of diagnosis in a more smart way
• Co-operation with Self-Test and Self-Repair
  designs
• Development of an efficient low-cost fault
  diagnosis methodology for analog and mixed-signal
  circuits
• Replacing conventional methods which use
  expensive measurement
• Can be extended to solve problems of
  diagnosis/self-repair/testing simultaneously

How?
Fault Diagnosis
Self-Test
Self-Repair
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Proposed fault diagnosis scheme
Error
Digital Cores
Low-cost Signatures
DUT
Performance parameters
DFT

Mapping Functions
Signatures
Pass/Fail
Parameter tuning
Ensemble Method
Faults identification
Self-Repair

• Based on a specification-based alternate test
• Supplemental signatures (signatures) are
  generated from a re-configured DUT by parameter
  tuning (self-repair circuits)
• Ensemble Method is used to overcome diagnosis
  inaccuracy caused by imperfect signatures
• Widely studied in Data Mining

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Diagnosability enhancement using parameter tuning

• Parameter tuning is widely used to tune
  performance parameters
• Redundant components
• EX) Programmable Capacitor Arrays (PCAs),
  Resistor Arrays
• Analog filters and various types of ADCs and DACs

Digital Code
CU
2CU
4CU
8CU
CA
Programmable Capacitor Array
Analog filter with parameter tuning
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Supplemental signature generation using parameter
tuning

• Re-configured DUT has different
• sensitivities to same input
• Higher-order sensitivity effects
• Changes of operating point
• Can be extended to other tuning
• mechanisms
• Variable biasing current/voltage

Sensitivity
Deviation of C1 ()
Deviation of C1 ()
(b) Sensitivity of R3 to 3dB
(a) Sensitivity of R3 to gain
Tuning cycle 0
DUT
P1 0.2CP 0.1R1
Tuning cycle 1
P2 0.18(CP?C) 0.13R1
Tuning cycle 2
P3 0.15(CP2?C) 0.15R1
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Supplemental signature generation

• Large number of signatures can be achieved using
  parameter tuning
• Typical tuning circuitry in a practical
  implementation uses 4-8 bit PCA ( signatures
  measurements x tuning cycles)
• Possible to identify faults with few measurements
  (performance parameters)

Tuning cycle 0
DUT
P1 0.2CP 0.1R1
Tuning cycle 1
P2 0.16(CP2?C) 0.17R1
CP
R1
Tuning cycle N
PN 0.15(CPN?C) 0.15R1
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Issues low-cost signature generation

• Imperfect signatures may cause errors in solving
  the obtained equations
• Measurement errors and prediction errors
  (outliers)
• Significant influence on outcome
• Equations are solved simultaneously
• Obtained equations may not be independent
• Fine tuning (small deviations of coefficients)
• Within tolerance limits of noise redundant
  signatures
• May not be helpful for meeting requirements
• number of measurements gtgt number of unknown
  parameters

Tuning cycle 0
DUT
P1 0.2CP 0.1R1
CP
Tuning cycle 1
P2 0.16(CP2?C) 0.17R1
R1
Tuning cycle N
PN 0.15(CPN?C) 0.15R1
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Example of Issues Imperfect signatures
faulty measurement
h6
Actual solution
h2
h4
over-fitted estimate
h1
h5
h3
Example 1
Example 2

• Estimation error can be dictated by a single
  error
• Estimation is over-fitted to the error

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Ensemble method

• Widely studied in data mining and machine
  learning
• Basic principle
• Develops a system in which the basic
  functionality is re-implemented with a number of
  models
• Pursues an effective combination of various
  models so as to compensate each others weakness
• Thus produces better decisions or predictions

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Proposed ensemble method I

• Measurement space diversified using parameter
  tuning is partitioned into groups of measurements
• Groups of measurements are solved independently
• Individual estimate is evaluated by
  cross-correlation (distance) and uncorrelated
  estimates are pruned from the solution candidates
• K-means Clustering algorithm
• Finally, by averaging the remaining estimates,
  the final estimate is determined

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Proposed ensemble method II

Measurement Partitioning
Clustering and Ensemble Averaging

LSE
Yes
Reject?
LSE
No
Averaging
LSE
LSE Least Square Estimates
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Example - proposed ensemble method

faulty measurement
h6
Actual solution
Estimate of G1
h2
Estimate of G3
h4
h1
h5
h3
Estimate of G2
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Simulation results

• State-variable active filter (ITC benchmark
  circuit)
• 3-bit PCA
• 100 DUTs are generated by introducing statistical
  variations
• Value of passive elements (Resistor and
  Capacitor) are estimated

Analog filter with 3-bit PCA
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Simulation setup I

Measurement Error
4
DUT
HPO
Least Square Estimate (LSE)
D 0
4
LPO
C1
CP(D0)
3
BPO
(a) Parameter Estimation based on 11
specifications and D 0

D 0,17
3
Measurement Error
DUT
HPO
LSE
4
D 0,1,,7
LPO
C1
CP(D)
BPO
(b) Parameter Estimation based on 4
specifications and D 0,1,..7
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Results - Simulation setup I

• Predicts 5 unknown variables with 4
  specifications
• Multiplied by tuning parameters
• Proposed method is as accurate as method which
  uses more measurements (internal node)
• Note Ensemble Method is not applied yet

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Simulation setup II

Measurement Error
4
DUT
HPO
Least Square Estimate (LSE)
D 0
4
LPO
C1
CP(D0)
3
BPO
(a) Parameter Estimation based on 11
specifications and D 0

D 1,2,7
3
Measurement Error
4
DUT
HPO
Ensemble Method
4
D 1,2,,7
LPO
C1
CP(D0)
3
BPO
(b) Parameter Estimation based on 11
specifications and D 1,2,..7
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Results - Simulation setup II

• Estimation Error Versus Total Number of Tuning
  Cycles

Estimation Errors()
Number of Tuning Cycles
Number of Tuning Cycles
Number of Tuning Cycles
No tuning conventional method
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Conclusions and Future work

• Efficient BIST-based fault diagnosis method
  proposed
• Provides fast and low-cost fault identification
  (signature-based)
• Removes expensive off-chip measurements
• Diagnosis accuracy is significantly improved by
  using parameter tuning and ensemble method
• Overcome on-chip limited resources and accuracy
• Also, can be used to facilitate a self-repair
  mechanism by accurately identifying the source of
  errors

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Future work

• Extend the proposed technique to diagnosis of
  device parameters of active elements
• Conjunct with variable biasing
• Develop self-repair algorithm based on proposed
  technique
• Beat conventional adaptive algorithm

DUT
DUT
Adaptive models
Fault diagnosis
performance
Trial
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Thank you!! Any questions?
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Results - Simulation setup II
(a) Estimation Error Versus Total Number of
Tuning Cycles
(b) Estimation Error Versus Injected Measurement
Noise
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Comparison with previous work