Automated Tool condition monitoring is critical in intelligent manufacturing to improve both productivity and sustainability of manufacturing operations. Estimation of tool wear in real-time for critical machining operations can improve part quality and reduce scrap rates. This paper proposes a probabilistic method based on a Particle Learning (PL) approach by building a linear system transition function whose parameters are updated through online in-process observations of the machining process. By applying PL, the method helps to avoid developing a complex closed form formulation for a specific tool wear model. It increases the robustness of the algorithm and reduces the time complexity of computation. The application of the PL approach is tested using experiments performed on a milling machine. We have demonstrated one-step and two-step look ahead tool wear state prediction using online indirect measurements obtained from vibration signals. Additionally, the study also estimates remaining useful life (RUL) of the cutting tool inserts.

1. Particle Learning in Online Tool Wear
Diagnosis and Prognosis
Zhang, JianLei
Advisor: Starly, Binil
Department of Industrial and Systems Engineering
NC State University
Raleigh, NC, 27695, USA →
For Citation:
Zhang, Jianlei, Binil Starly, Yi Cai, Paul H. Cohen, and Yuan-Shin Lee.
"Particle learning in online tool wear diagnosis and prognosis." Journal of
Manufacturing Processes (2017).

2. Economic Significance of Tool Wear Prediction
• Fail to detect tool wear
Affect the workpiece quality
Damage workpiece, its fixtures, and tool
holder
Lead to extended machine downtime
Undesirable inventory management
2
• The growing demand and wide applications
Assure the surface quality of final parts
Increase machining process uptime
Efficient use of the cutting tools
Cutting Tool – Image Courtesy of Sandvik Coromant →

3. Tool Type and Wear Types
3
• Cutting tool Wear
Crater Wear
Nose radius wear
Notch Wear
Flank Wear
(Astakhov, 2006).
(Yildiz, et al., 2008)
• On relief face, Tool Wears are categorized
by their zones
Zone C, VBC is the Nose Wear
Zone B, VBB is the flank wear
Zone N, VBN is notch wear

4. Overall Research Motivation
4
Monitoring the tool wear Estimate the RULPredict tool wear
http://www.lgam.info/remaining-useful-life
→

5. Summary of the Tool Wear Prognosis Approaches
→

6. Literature Review: Bayesian Updating with Growth
Curves
• Generate a large number of the growth curves
prms, i = at2 + bt + c
• The posterior probabilities of the tool wear
growth curves get updated by the likelihood
P(path = prms growth curve| test result)
∝P(test result|path = true prms growth curve)
×P(path = prms growth curve)
• Likelihood L= exp[-(p-pm)2/k]
• Iteratively updates the posterior probabilities
of the growth curves
6
(Karandikar, et al. 2013a, 2013b, 2013c, 2014a, 2014b)
10 sample prms growth curves
(Karandikar, et al. 2013)

7. Literature Review: Nonlinear Transition
Function with Intrusive Sensors
• Feature extraction and selection from accelerometers and Force
sensors
• Regression analysis for system observation function
• System Transition function, which incorporates the Taylor’
equation, is nonlinear
• Particle filter updates the estimation of the parameters
• Prediction of the tool wear
• RUL get estimated every run 7
(Wang, et al. 2015a, Wang, et al. 2015b, Wang, et al. 2013)

8. Literature Review: Finite Difference as System
Transition Function
• Root mean square (RMS) of the power signal of spindle motor is collected
• Kalman filter and particle filter are applied
• Applied following system model to realize tool wear prediction via online
measurement
• System transition functions: Assume the tool wear process subject to the first
order finite difference
(Niaki, et al. 2015)
8
VB(k) = VB(k-1) + VB’(k-1)×MR×Δt + w1(k)
VB’(k) = VB’(k-1) + w2(k)

9. Research Motivation (Desired Solution)
• Incorporate indirect measurement into model
• Utilize the nonintrusive sensor
• Predict the tool wear and RUL
• Minimize calculation cost
• Algorithm should be robust and accurate
• Applicable to variety of workpiece and tool materials
9

10. Particle Learning Approach
1. Online Updating of Parameters in System Transition
Function
2. Build System Observation Function via Indirect
Measurement
3. Online System State Estimation and Prediction
4. One-Step and Two-Step Prediction of Tool Wear
10
→

11. Task 1: Online Updating
• System transition function
xt+1 = f(xt) + ωt, ωt subjects to certain distribution
• General Bayesian Updating
xt+1 ∼ p(xt+1|xt, θ)
– it can only use direct or indirect measurement
– a closed form system transition function need to be
developed
11

12. Task 1: Assumption of System Transition Model
• Markovian state transition
The current state only related to the last state
• Linear transition function
The current state have linear relation with the last state
• Assume the System Transition Function is: First Order
Autoregression
xt|xt-1, θ ~ N(α+βxt-1, τ2), here, θ = (α, β, τ2)
(Lopes, et al. 2011)
12

13. Task 2: Incorporate Indirect Measurement
• System observation function
yt = g(xt) +et
here, et ~ Normal(0, σ2)
• Assume the relashionship is linear
𝑉𝐵 = K1 + K2. RMSvibration
here, 𝑉𝐵 is the estimated tool wear
(yt is the VB at time t)
13

14. Task 3: Online System State Estimation and
Prediction
• State filtering probability distribution
Updating:
p(xt, θ|yt) =
p yt xt p(xt|yt−1)
p(yt|yt−1)
(Bayes’ theorem)
• State prediction probability distribution:
Prediction:
p(xt+1|yt) = p(xt+1 |xt)p(xt|yt)dxt (Marginal distribution)
where yt = (y1, …, yt)
How to solve them!?
The integration with respect to xt-1 and implement Bayes’ theorem are
both analytically intractable and/or computationally costly.

15. • Probability Distribution
pN(𝑥) = {𝑥 𝑡
(𝑖)
}𝑖=1
𝑁
=
1
𝑁 𝑖=1
𝑁
𝛿(𝑥)(𝑖) (Dirac
Measure)
Bayes’ theorem for Updating
p(xt, θ|yt+1) ∝ p yt+1 xt, θ p(xt, θ|yt)
𝑥𝑡
(𝑖)
, θ(𝑖)
= sample from 𝑥𝑡
(𝑖)
, θ(𝑖)
with weights ∝p yt+1 𝑥𝑡
(𝑖)
,θ(𝑖)
Marginal distribution for Prediction
p(xt+1|yt) = p(xt+1 |xt)p(xt|yt)dxt
Dirac Measure:
𝛿x(A) = 1A(x) =
0, 𝑥 ∉ 𝐴
1, 𝑥 ∈ 𝐴
Dirac Measure:
Makes an intractable calculation into tractable Robust algorithm
𝑥𝑡+1
(𝑖)
= sample from p(xt+1|𝑥𝑡
(𝑖)
)
Task 3: Online System State Estimation
and Prediction

16. Task 4: Conduct Experiments to Validate
Proposed Method
16
• Install the vibration sensor, the DAQ,
and laptop for data collection
• Install the cutter and workpiece
• Repeatedly execute the cutting
• During every cutting process, the
signal get collected
• After each cut, microscope measure
the flank wear
• Analyze the experiment data
• Try several different cutting
conditions
(Niaki, Wang, Gao, Laine Mears)

17. 17
Task 4: Experiment Conditions
Workpiece material steel 4142
(cold rolled, 40-45HRC)
Each single cutting pass 37.0mm
Spindle speed 500rpm
Surface speed 19.81m/min
chip load 0.05mm
Radial depth of cut 6.5mm
axial depth of cut 0.5mm
3-axis vibration sensor Kistler accelerometers
8762A10
Sensor Sample rate 1652Khz
Feed rate 50 mm/min

18. Task 4: Vibration Trend vs Time Step
18
Tool Nose Wear Vibration Example Images on right show tool nose wear micrographs.
Table 1. Flank Wear Measurement and Vibration Index
Replication 1 Replication 2
Test
Flank
Wear
Vibration
Index
Test
Flank
Wear
Vibration
Index
# (μm) ×10-3
(g) # (μm) ×10-3
(g)
1.1 159 11.6336 2.1 85 11.5215
1.2 175 13.2887 2.2 94 12.2370
1.3 175 13.7673 2.3 98 11.7758
1.4 179 13.9541 2.4 99 11.9476
1.5 179 13.6441 2.5 106 12.2356
1.6 180 13.5912 2.6 110 12.9962
1.7 180 15.9381 2.7 115 13.7390
1.8 184 18.6700 2.8 142 13.6430
1.9 191 18.7381 2.9 183 17.5361
1.10 199 20.0806 2.10 186 18.0902
1.11 214 20.2440 2.11 287 20.2915
1.12 220 20.9609 2.12 305 22.0541
1.13 248 24.5650 2.13 330 25.8142
1.14 274 27.4840
1.15 299 28.4834
Scale bar 500µm.

19. Task 5: Online Updating with Indirect Measurement
Replication 1
The parameters α, β, τ2, and σ2 is
estimated and updated by the
measurement of the RMS of the
vibration sensor for every cut
• α ∈ (-0.0412 -0.0155 0.0141),
With 95% confidence level,
• β ∈ (0.9702 1.1188 1.2530)
With 95% confidence level
19

20. Task 5: Online Updating with Indirect Measurement
Replication 2
The parameters α, β, τ2, and σ2
get estimated and updated by the
measurement of the RMS of the
vibration sensor for every cut
• α∈(-0.0277, -0.0111, 0.0052),
With 95% confidence level,
• β∈(1.1201, 1.2254 1.3491)
With 95% confidence level
Reject β =1 in first order finite difference method

21. Task 6: Online Tool Wear Diagnosis with Indirect
Measurement
21
Replication 1 Replication 2

22. Task 7: Online Tool Wear One-Step Ahead
Prediction
22
Replication 1 Replication 2

23. Task 8: Online Tool Wear Two-Step Ahead
Prediction
23
For two-step ahead tool wear prediction, following two equations run once
Three-step ahead run twice, and so on.
pN(μ) = pN(α)+ pN(β)pN(x)
where μ is the mean for the normal distribution
pN(x) = resample N particles from Norm(pN(μ), τ2)

24. Task 8: Online Tool Wear Two-Step Ahead
Prediction
24
Replication 1 Replication 2

25. Task 9: Online RUL Prediction
25
pN(μ) = pN(α)+ pN(β)pN(x)
where μ is the mean for the normal distribution
pN(x) = resample N particles from Norm(pN(μ), τ2)
Set criterion of the tool wear as 0.3 mm
Set 90 percentile of the tool wear as the reference
By looping through following equations
until the certain percentile tool wear reaches the tool wear criterion, the
number of loops can be used to predict the RUL.

26. Task 9: Online RUL
26
Replication 1 Replication 2

27. • Incorporated the indirect measurement
• Realized online updating the model parameters
• Realize tool wear online estimation and prediction
• Realize the RUL prediction
• Certify the First Order Regression as System Transition
• Particle Learning as a robust and no closed form formula
is needed
27
Conclusion

28. 28
Limitations of Proposed Method
• Assumption on linearity of the System Transition and
Observation Function
• Assumption on the Markov process in System Transition
Function
System transition function
xt+1 = f(xt) + ωt, ωt subjects to certain distribution
which may not capture all the dynamics of the system

29. • NCSU
29
Acknowledgement
• DMDII 15-16-08 • NSF Travel award
For Citation:
Zhang, Jianlei, Binil Starly, Yi Cai, Paul H. Cohen, and Yuan-Shin
Lee. "Particle learning in online tool wear diagnosis and
prognosis." Journal of Manufacturing Processes (2017).