Fourth Texas Educators Conference on Machining
Change Detection in Precision Manufacturing
Processes under Transient Conditions
Zimo (Robin) Wang, Satish T.S. Bukkapatnam
School of Industrial Engineering and Management,
Oklahoma State University
Outline
• Introduction of change detection in precision manufacturing
processes
• Change detection in UPM & CMP
• DPGSM-based detection in sensor-based monitoring system
during precision manufacturing
• Conclusions
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2
Introduction
• Ultra-Precision Machining (UPM)
Ultra-precision machining are those
technologies by which the
highest possible dimensional accuracy is,
or has been achieved (Taniguchi, 1983 )
Triangular microprisms
Aspheric IR optics
Freeform surfaces
Off-axis Mirrors
1960
1970
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1980
1990
2000
2010
3
Introduction
• Challenges for UPM quality assurance
– Limited metrology and methodology for quality control (Dornfeld, 2006)
– Sensor-based in-process monitoring system of process monitoring and
quality control (Abellan-Nebot, 2010)
Demand
• Suitable sensor based monitoring system
for precision machining processes
• Effective incipient change detection
analyzing weak signal of UPM compared
with conventional machining processes
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Surface defects in ultra-precision machining
Most common surface defects (e.g. surface scratches and variations) are
due to abnormal vibration (e.g. chatters) and built-up edge (BUE)
• System vibrations
– Chatter: tool, toolholder and spindle together vibrate at some natural
frequency
– Scratches on the surface, ruining the geometric acquirement of product
Rippled surface finish
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Scratch
6
Surface defects in ultra-precision machining
• Built-up edge (BUE)
– Causing deeper depth of cut and degrading surface finish
– In UPM, surface sometimes rubs against built-up edge, leading to
surface quality deterioration
Deteriorated surface due
to BUE
BUE
Scratch
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CMP experiment setup
XBee wireless sensor
Buehler CMP machine
20
Vibration signal
Time Index
10
0
-10
-20
-30
Wafer with nanometric roughness
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-40
1000
2000
3000 4000
Amplitude
8
5000
6000
UPM experiment setup
• Sensor setup
– Vibration sensor (3-axis)
– Force sensor (3-axis)
– Acoustic emission (AE) sensor
Surface variation
20
0
-20
Scratch
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-40
2000 4000 6000 8000 1000012000140001600018000
9
Application in ultra precision machining
• UPM experiment
Sample 18
Sample 30
1000 rev/min
2000 rev/min
4
Amplitude
– Depth of cut (5, 10, 20, 25 μm)
– RPM (500, 1000, 2000 rev/min)
– Feed rate (1.5, 3, 6 mm/min)
6
2
0
-2
-4
-6
2000
4000 6000
Time Index
8000 10000
1000-2000
ARL1 of CUSUM
160
ARL1 of EWMA
5000
SPC methods are reticent to
intermittent pattern changes in
UPM
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UPM & CMP
Experiments
DPGSM-based change detection in UPM
Data acquisition
Surface scratches
Feature extraction
1
Finish roughness
variations
In-process surface
deterioration
0
40
-1
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
15
20
10
5
0
6
4
2
-20
0.5
0
-0.5
-40
1
2
3
4
5
4
x 10
DPGSM-based change detection
Non-linear time series analysis
Change detection
DP-based Gaussian mixture
Transient behavior quantification
Decision for quality
improvement
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Weighted multivariate process
control
11
Limitations of traditional detection methods
• Traditional statistical change detection involves testing a
hypothesis
– Ho: θ = θo against Ho: θ ≠ θo
– On parameters θ of the distribution or a representation of a stochastic
process, such as x(t+1)=f(x(t), θ)
• For most detection methods, a stable operation implies
stationarity, i.e., θ is time-invariant
• However, most real-world processes are highly
nonstationary, i.e., θ varies over time
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Limitations of traditional detection methods
• Autocorrelation structure change
– Shifting trends (first order) (De Oca, 2010)
– Volatility (second order) (Killick, 2013)
– Eigenstructure of state space model (Basseville, 1987)
• Frequency and spectrum analysis
– Spectral-based change detection (Choi et al., 2008)
– Wavelet based control chart (Guo, 2012)
Few methods reported for change detection in transient
processes because of the difficulty to capture the complex
nonstationary behaviors
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Dynamic intermittency
Window 1
Window 2
Amplitude
5
0
-5
-10
2
4
6
8
Time Index
10 12
4
x 10
State space reconstructed intermittent signal
Intermittency is a common nonstationary (transient) behavior,
consisting of intervals of regularity interrupted at random by bursts as
the trajectory is re-injected into the chaotic part of the phase space.
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Dirichlet Process-based Gaussian State Machines
(DPGSM)
Reconstructed state space
trajectories
Y-AXIS
Window 1 Window 2
5
5
𝜋11(1)
⋮
𝜋51(1)
⋮
0
0
-5
-5
0
X-AXIS
2
4
6 0 8
Time Index
Transition matrix 2
10
12
4
x 10
𝜋11(2)
⋮
𝜋51(2)
⋮
𝜋81(2)
-5
-5
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⋯ 𝜋15(1) . . . 0
⋱
⋮
(1)
𝜋55
… 0
⋯
⋱ ⋮
0
… 0
5
5
Y-AXIS
10
Transition matrix 1
-5
0
Dirichlet process based transition
matrix generation
0
X-AXIS
⋯
⋱
⋯
𝜋15(2)
𝜋55(2)
𝜋85(2)
5
16
. . . 𝜋18(2)
⋮
… 𝜋58(2)
⋱
⋮
… 𝜋88(2)
Dirichlet process-based Gaussian mixture
0
-5
5-
Amplitude
5
0
-10
𝑃 𝑐𝑖 = 𝑘 ≤ 𝐶|𝑐−𝑖 =
𝑃 𝑐𝑖 = 𝐶 + 1|𝑐−𝑖 =
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𝑛𝑘
𝑛−1+𝜗
𝜗
𝑛−1+𝜗
θci|θ−ci~
𝑖−1
𝜏=1 𝛿θci +
𝜗𝐺0
𝑛−1+𝜗
if data belongs to existing cluster
if data belongs to new cluster
17
41.0
- Tables represent infinite clusters
- Customer i represents data 𝑥𝑖
xi~F (•|θci)
21.0
300
Time Index
1.0
250
80.0
200
60.0
150
40.0
100
20.0
50
0
51-
-15
0
01-
Cluster 2
10
5
Cluster 1
𝜗
𝜗+𝑛−1
Clusters & pdf
01
𝑛𝑘
𝜗+𝑛−1
Time series
15
51
• Chinese restaurant process
Amplitude
DPGSM change detection
Simulated Data
15
𝜋11(𝑖)
П(i) ={πjk (i) }=
10
-15
0
…
⋮
, t0≤i ≤ T
𝜋𝐾𝐾 (𝑖)
Track the process change in
terms of distribution of
transition matrix
-5
-10
⋮
𝜋𝐾1
0
𝜋1𝐾 (𝑖)
⋱
(𝑖)
5
⋯
Out of control
Normal condition
1000
2000
Time Index
(t0=1000)
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3000
4000
(T=4000)
18
DPGSM change detection
• Distribution of transition element
– Proposition 1: The Bayesian posterior distribution of the vector πj,
(𝑖)
given the counts 𝒁𝑗 = 𝒛𝑗 (multinomial distributed), follows a
Dirichlet distribution
𝑓
(𝑖)
𝝅𝑗 |𝒛𝑗
=
(𝑖)
𝑖−1
(𝑖)
𝑧𝑗𝑘 −1
𝐾
;
𝑘=1 𝜋𝑗𝑘
𝐵(𝒛𝑗 )
• Calculation of
𝑧𝑗𝑘 =
(𝑖)
1
𝐵
(𝑖)
𝒛𝑗
=
𝑖
𝐾
𝑘=1 Г(𝑧𝑗𝑘 )
(𝑖)
Г( 𝐾
𝑘=1 𝑧𝑗𝑘 )
(𝑖)
𝒛𝑗
𝑃 𝑐𝑡 = 𝑗 𝑥𝑡 , 𝜣 × 𝑃 𝑐𝑡+1 = 𝑘 𝑥𝑡+1 , 𝜣 + 1
𝑡=𝑖−𝐿+1
where
𝑃 𝑐𝑡 = 𝑘 𝑥𝑡 , 𝜣 = 𝑏𝑓(𝑥𝑡 |𝜃𝑘 ) , b is an appropriate normalized constant
𝐾
which makes
𝑏𝑓(𝑥𝑡 |𝜃𝑘 ) = 1
𝑘=1
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Multivariate control chart
• Confidential level
– In DPGSM change detection, we have K control charts (K as cluster
number)
𝑤𝑗
𝐾
– 𝛼𝑗 = 1 − 1 − 𝛼
is the significance level of row j, set by the familywise error rate (FWER), i.e. FWER= Pr(rejecting at least one Hj|
Hj ∈ Ho) = α, where Ho={H1, H2,… HK}
• Measurement in multivariate control chart
(𝑖)
– 𝜋𝑗𝑘 = 𝜋𝑗𝑘 |𝒛(𝑖) =
𝑗
– 𝑑𝑗2 = (𝝅𝑗 − 𝝅𝑗0 ) 𝑺𝑗
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𝑧𝑗𝑘
(𝑖)
𝐾
𝑧
𝑘=1 𝑗𝑘
−1
(𝝅𝑗 − 𝝅𝑗0 )𝑇 ~ 𝜒2K distribution
20
Multivariate control chart
The overall on-line change detection, after consistent estimation of 𝜣,
{𝑈𝐶𝐿𝑗 } and 𝜶 based on a training set, may be summarized as follows:
Step 1: Estimate transition matrix:
(𝑖)
𝜋𝑗𝑘 |𝒛𝑗
(𝑖)
=
𝑧𝑗𝑘
𝐾 𝑧 (𝑖)
𝑘=1 𝑗𝑘
Step 2: Calculate Hotelling statistics 𝑑𝑗2 for each row 𝑗
Step 3: Monitor the process and estimate 𝐴𝑅𝐿1 based on out-of-control points
Control Chart for transition row πj
Simulated Data
1
20
0.5
0
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
-6
x 10
15
1
0.5
0
1000
Amplitude
10
1
0.5
5
0
1000
1
0
0.5
0
1000
-6
x 10
-5
2
0
1000
-10
1
-15
-20
0
0.5
Normal condition
Out of control
0
1000
-7
x 10
2
1000
2000 3000 4000
Time
Index
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5000
6000
0
1000
21
Benchmark case
Model:
f(x−i;φ(1),ψ(1))
i0<i<i1
…
(𝑚)
(m)
im−1<i<im
xi= f(x−i;φ ,ψ )
…
f(x−i;φ(M),ψ(M)) i𝑀−1<i<iM
20
15
Amplitude
10
5
0
-5
-10
-15
-20
0
Normal
condition
2000
Window
width change
Variance
change
4000
6000
Time Index
8000
where 𝑖𝑚 is the time index of each
breakpoint, 𝑚=1, 2,…,𝑀, 𝑖0 =1,
𝑖𝑀 =N (N is the length of the time
series).
{𝑖0 , 𝑖1 ,… 𝑖𝑚 ,…, 𝑖𝑀 } as a sequence
of order statistics such that each im
follows a uniform distribution
UNIF(0, N).
ARMA(2,1) model at ∼ (N(0, δσ2a ))
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Benchmark case
20
15
Normal
condition
20
Variance change
15
Window width
change
10
Amplitude
10
Amplitude
Normal
condition
5
0
-5
5
0
-5
-10
-10
-15
-15
-20
0
-20
0
1000
2000
3000
4000
5000
6000
Time
Index change
Fault A:
variance
1000
2000
3000
4000
Index
Fault B: Time
sojourn
time change
ARL1 comparisons (expected steps to reveal a change)
EWMA
SD-WCUSUM
RNDP
DPGSM
Fault A
25.6
2.2
6.1
3.5
Fault B
Inf
Inf
Inf
3.8
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5000
23
6000
Detection for surface roughness variation
• Surface variation in three
regions
Region 1
Region 2
Region 3
20
1. Small Ra (~100nm)
2. High Ra (~150nm)
3. High Ra (~ 150nm) with
larger variance
0
-20
-40
2000 4000 6000 8000 1000012000140001600018000
Region 1
Surface Roughness Boxplot
Region 2
Expected delay of detection (ms)
SDEWMA
DPGSM
150
WCUSUM
Region 1-2
10.4
1.5
0.5
100
Region
2-3
21.4
0.4
0.4
200
Ra (nm)
Region 3
1
2
Region
3
Scratch
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Detection for surface scratch
Region 1
Region 2
40
20
0
-20
-40
1
2
3
4
5
4
x 10
Scratch
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Skewness Kurtosis Variance Mean
• Surface scratch and vibration signal
1
0
-1
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
4500
15
10
5
6
4
2
0.5
0
-0.5
25
Detection for surface scratch
18
prediction
observation
16
R2 = 0.7425
Amplitude
14
Output
14
12
10
8
6
4
0
12
Predicted
feature
10
8
6
200
400
600
800
1000
1200
500
Time index
1000 1500
Time Index
Expected delay of detection(ms) comparisons
EWMA
SD-WCUSUM
DPGSM
164
72
24
GP-DPGSM method discovers scratch appearance in 48 ms
ahead of EWMA and 140 ms earlier than SD-WCUSUM.
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2000
Change detection of surface deterioration
• Chemical Mechanical Planarization
(CMP) process experiment
– Lapped coppers (Ra 10nm~15nm)
were polished on Buehler in 3
minutes of each interval
– Platen speed 250 RPM, head speed
60 RPM and download force 4 lbs
Buehler (model Automet® 250)
with 3-axis accelerometer
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Change detection of surface deterioration
• Pad wear and surface deterioration
– After 3 minutes, the average Ra improved to around 15 nm
– Pad wear was then accelerated worn by soaking the pad in slurry,
followed by air drying
– After 12 minutes polishing, it was noticed that significant glazing of
polishing pad observed (Fig. 2) as well as the scratch on wafer were
observed and finish degrades to Ra~22nm
Ra~9nm
Ra~22nm
Glazed
area
Scratch
After 3 min
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After 12 min
Glazed areas on pad
28
Change detection of surface deterioration
20
Delay for detection (ms)
Time Index
10
EWMA
2941
0
-10
First run
-40
1000
2000
Pad wear
3000 4000
Amplitude
X-vibrend Amplitude spectrum
-3
5
4
4
3
3
|Y(f)|
|Y(f)|
5
2
2
1
1
0
0
DPGSM
34
-20
-30
x 10
SD-WCUSUM
2262
50
100
150 200 250
Frequency(Hz)
300
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5000
x 10
0
0
6000
DPGSM discovers surface deterioration
with an order of magnitude (more than 2
sec) earlier than SPC methods tested
X-vibrend Amplitude spectrum
-3
50
100
150 200 250
Frequency(Hz)
300
29
Change detection for music pattern changes
• Case 1
E5 to D5 Key signature change
Normal condition
• Case 2
1
2
Anomaly condition: 1 1 2 2 1 2
Normal condition: 1 1 1 2 2 2
Comparison of delays for change detection (ms)
EWMA
SD-WCUSUM
DPGSM
Key signature change
90
5
2
Chord progression change in long
period articulation
83
175
15
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Change detection in Ragas
Change detection 1: Sequence
change with ascending and
descending scales
Change detection 2: Scale
change with missing notes
General types of Raga music
Subtle changes in intermittent music signals, namely scores sequence
change and music scale change, are considered.
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Change detection in Ragas
Raga 1
Raga 3
Raga 2
Ascending and descending scales
Raga 4
Scale change with missing notes
Comparison of delays for change detection (ms)
EWMA
SD-WCUSUM
DPGSM
Ascending and
descending scale
24(False alarm)
Inf
17
Descending scale with
missing note
1682
191
151
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Detection of incipient sleep apnea
• Sleep apnea detection using
ECG signal
2
Amplitude
1.5
Monitored ECG signal with
incipient sleep apnea
Normal
Breath
breathing
disorder
1
0.5
Delay for detection (ms) of sleep apnea
0
-0.5
6000
EWMA
SD-WCUSUM
DPGSM
1765
12
11
12000
Time Index
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Conclusions
• We represent nonlinear nonstationary (intermittency) signal within
precision machining processes as a stochastic mixture of Gaussian
clusters with Markov transition matrix
• Intermittent changes in surface uniformity are efficiently identified by
DPGSM, and it could detect surface damage (scratch) almost an order
of magnitude earlier compared to existing change detection methods
(EWMA and SD-WCUSUM)
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Further studies
• Parameters selection
– Selection of window length 𝑳 is crucial to derive consistent estimates of
the transition matrix elements
– Selection of the concentration parameter 𝝑 of Dirichlet process to
ensure generation of proper Gaussian mixtures
• The transition process may be more closely approximated using a
semi-Markov formulation and the representation needs to be
modified to better capture the underlying dynamics
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Q&A
Contact me:
Zimo Wang
Ph.D. candidate
Industrial Engineering
[email protected]
4/1/2014
37
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