Raunak Bhinge, Nishant Biswas and David DornfeldMechanical EngineeringUC. Berkeley Berkeley, CA, USA

Jinkyoo Park and Kincho H. LawCivil and Environmental EngineeringStanford UniversityStanford, CA, USA

Moneer Helu and Sudarsan RachuriNational Institute of Standards and TechnologyGaithersburg, MD, USA

An Intelligent Machine Monitoring System Using Gaussian Process Regression for Energy Prediction

Industrial: 22% of U.S. use

Mileage for automobiles has greatly increasedWe also understand the energy consumption pattern well

2

Transportation: 28% of U.S. energy use

Industrial: 22% of U.S. energy use

What about manufacturing energy use?

3

Can we predict how much energy the manufacturing machine will consume when machining the part?

4

Designed part NC code Target machine Machined part

Part design NC code Target machine Machined part

Input parameters for the machine

• Feed rate• Spindle speed• Depth of cut

• Cutting direction• Cutting strategy• Dimensions

Output measurements from the machine

• Energy consumption• Part quality, e.g., surface roughness• Machine conditions, e.g., tool wear

XML-based structured data with automatic acquisition

From data to insight: Mapping control parameters to energy consumption

5

Training data set 𝑫

Learning Algorithm

Hypothesisℎ(𝒙)

Predict total energy consumption

𝑫 = 𝒙𝑖 , 𝑦𝑖 ; 𝑖 = 1,… ,𝑚

Using training data set 𝑫, learning algorithm finds the best function ℎ(𝒙) that is believed to accurately predict the output 𝑦 for a given input 𝒙

𝑖=1

𝑚

ℎ 𝒙𝑖

New NC Code

…

6

𝒙 = control parameter 𝑦 = Response

𝑛 control parameters

𝑚NC code

blocks

Procedure for constructing data-driven energy prediction model

• Fanuc Controller : Collect machine control parameters

• System Insights High Speed Power Meter (HSPM):Collect power time series

Hardware Data types

7

Data acquisition & simulator for this study

Step-NC file 1

Step-NC file 2

Step-NC file 18

Level Spindle Speed (RPM)

Chip Load (mm/tooth)

Depth of Cut (mm)

1 1500 0.0254 12 3000 0.0330 1.53 4500 0.0432 34 6000 0.0508

Condensed and contextualized data<Input features – output response>

8

First, one must acquire the training data set

Input:𝑥1 ∈ ℝ Feed rate𝑥2 ∈ ℝ Spindle speed𝑥3 ∈ ℝ Depth of cut𝑥4 ∈ 1, 2, 3, 4 Active tool axis ID (1 for 𝑥-axis, 2 for 𝑦-axis, 3 for 𝑧-axis and 4 for 𝑥-y direction)𝑥5 ∈ 1, 2, 3 Cutting strategy (1 for conventional, 2 for climbing and 3 for both)

Output:𝑦 = 𝐸/𝑙 ∈ ℝ Energy density (energy consumption per unit length of a tool path) in NC code block.

In total, 3,092 pairs of 𝒙 (machine operation feature vector) and 𝑦 (energy density) collected from the experiments.

That is, 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … , 3,092 serve as the basis for this study.

𝑙 ∈ ℝ Length of tool a tool path in NC code block

9

Description of training data set

𝑥1 𝑥2 ⋯ 𝑥𝑛 𝑦

𝑥11 𝑥2

1 ⋯ 𝑥𝑛1 𝑦1

𝑥12 𝑥2

2 ⋯ 𝑥𝑛2 𝑦2

⋮ ⋮ ⋮ ⋮

𝑥1𝑚 𝑥2

𝑚 ⋯ 𝑥𝑛𝑚 𝑦𝑚

𝑛 machine parameters𝑫1 = 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … ,𝑚1 𝑦 = 𝑓1 𝒙

Clustered input and output datafor each machine operation

Energy Prediction models for machine operations

…

Training data

Face milling

Contouring

𝑫2 = 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … ,𝑚2

𝑫𝑞 = 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … ,𝑚𝑞

𝑫𝑄 = 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … ,𝑚𝑄

…

𝑦 = 𝑓2 𝒙

𝑦 = 𝑓𝑞 𝒙

𝑦 = 𝑓𝑄 𝒙

• Cutting operations : Face milling, Contouring, Slotting, Pocketing, Spiraling, Drilling • Non-cutting operations: Air-cut in 𝑥 − 𝑦 direction, Air-cut in 𝑧 direction, Rapid motion

10

Classifying training data set by machine operations

𝑫𝑞 = 𝒙𝑖 , 𝑦𝑖 |𝑖 = 1, … ,𝑚𝑞 𝑦 = 𝑓𝑞 𝒙

How to construct prediction function?

Gaussian Process • model complex input and output relationships without the basis functions• update model with new measurement data based on Bayesian framework• estimate uncertainty in prediction

12

Which learning algorithm to choose ? : Gaussian Process (GP) regression

𝒚1:𝑚𝑞

𝑦~𝑁 𝟎,

𝐊 𝒌𝒌𝑇 𝑘(𝒙, 𝒙)

𝑫𝑞 = 𝒙𝑖 , 𝑦𝑖 ; 𝑖 = 1,… ,𝑚𝑞

𝑦 = 𝑓𝑞 𝒙 + 𝜖, 𝜖~ 𝑁(0, 𝜎𝑒𝑟𝑟𝑜𝑟2 )

𝑦 |𝑫𝒒~𝑁 𝜇 𝒙|𝑫𝒒 , 𝜎2 𝒙|𝑫𝒒

𝜇 𝒙|𝑫𝒒 = 𝒌𝑇𝐊−1𝒚1:𝑚𝑞

𝜎2 𝒙|𝑫𝒒 = 𝑘 𝒙, 𝒙 − 𝒌𝑇𝐊−1𝒌𝑘 𝒙𝑖 , 𝒙𝑗 = 𝜏2exp −

1

2𝒙𝑖 − 𝒙𝑗 𝑇

diag 𝝀 −2 𝒙𝑖 − 𝒙𝑗 + 𝜎𝜖2𝛿𝑖𝑗

𝒌𝑇 = 𝑘 𝒙1, , 𝒙 , . . . , 𝑘 𝒙𝑚𝑞 , 𝒙

𝐊𝑖𝑗 = 𝑘 𝒙𝑖 , 𝒙𝑗

Conditionalizationon observed data

(Bayesian updating)

Given training data set for 𝑞th operation

Assumption : measurements are corrupted with noise

Prior on the measured outputs

13

Power of GP comes from Bayesian framework

𝑦1

𝑦2

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )𝑛 = 2

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled without error

14

How GP constructs regression model from data?

𝑦1

𝑦2

𝑦3

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 3

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled without error

15

How GP constructs regression model from data?

𝑦1

𝑦2

𝑦3

𝑦4

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 4

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled without error

Gaussian Process (simple example)

16

𝑦1

𝑦2

𝑦3

𝑦4

𝑦5

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 5

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled without error

17

How GP constructs regression model from data?

𝑦1

𝑦2

𝑦3

𝑦4

𝑦5

𝑦6

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 6

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled without error

18

How GP constructs regression model from data?

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled with error:

𝑓 𝑥 = 𝑥sin 𝑥 + 𝜖,𝜖 ~ 𝑁(0, 12)

𝑦1

𝑦2

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )𝑛 = 2

19

How GP constructs regression model from data?

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled with error:

𝑓 𝑥 = 𝑥sin 𝑥 + 𝜖,𝜖 ~ 𝑁(0, 12)

𝑦1

𝑦2

𝑦3

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 3

20

How GP constructs regression model from data?

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled with error:

𝑓 𝑥 = 𝑥sin 𝑥 + 𝜖,𝜖 ~ 𝑁(0, 12)

𝑦1

𝑦2

𝑦3

𝑦4

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 4

21

How GP constructs regression model from data?

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled with error:

𝑓 𝑥 = 𝑥sin 𝑥 + 𝜖,𝜖 ~ 𝑁(0, 12)

𝑦1

𝑦2

𝑦3

𝑦4

𝑦5

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 5

22

How GP constructs regression model from data?

True 𝑓 𝑥 = 𝑥sin(𝑥)

Sampled with error:

𝑓 𝑥 = 𝑥sin 𝑥 + 𝜖,𝜖 ~ 𝑁(0, 12)

𝑦1

𝑦2

𝑦3

𝑦4

𝑦5

𝑦6

𝑦

~𝑁 𝟎,𝒌

𝒌𝑇 𝑘(𝒙 , 𝒙 )

𝑛 = 6

23

How GP constructs regression model from data?

𝑦 = 𝑓1 𝒙𝜇 𝒙|𝑫1mean function

𝜎 𝒙|𝑫1Standard deviation

Prediction can be represented with bound:

𝜇 𝒙|𝑫1 − 𝜎 𝒙|𝑫1 , 𝜇 𝒙|𝑫1 + 𝜎 𝒙|𝑫1

(5D function)

(5D function)

𝑥3

Depthof cut(mm)

𝑥2

SpindleSpeed(RPM)

Energy density prediction functionfor face milling

24

Constructed energy density prediction function

𝜇 𝒙|𝑫𝑞

𝑦 = 𝑓𝑞 𝒙

𝜎 𝒙|𝑫𝑞mean functionstandard deviation

function

𝐸𝑖 = 𝜇𝑞 𝒙𝑖|𝑫𝑞 × 𝑙𝑖 𝑆𝑖 = 𝜎𝑞(𝒙𝑖|𝑫𝑞) × 𝑙𝑖

• Energy consumption for 𝑖th NC code block performing machine operation type 𝑞 :

𝐸𝑞 = 𝒙𝑖,𝑦𝑖 ∈𝑫𝑞

𝜇𝑞 𝒙𝑖|𝑫𝑞 × 𝑙𝑖 𝑆𝑞 = 𝒙𝑖,𝑦𝑖 ∈𝑫𝑞

𝜎𝑞(𝒙𝑖|𝑫𝑞) × 𝑙𝑖

2

• Energy consumption for NC code blocks performing machine operation type 𝑞:

𝐸 = 𝑞=1

𝑄 𝐸𝑞 𝑆 =

𝑞=1

𝑄

𝑆𝑞2

• Energy consumption for the entire operations:

: Probabilistic prediction𝐸~𝑁( 𝐸, 𝑆)

• Energy density prediction model for machine operation type 𝑞

25

From density prediction to energy prediction

Used spindle speeds (RPM)Training parts 1~18 1,500, 3,000, 4,500, 6,000Test part 1 1,500, 3,000, 4,500Test part 2 1,700, 2,800, 4,300Test part 3 2,125, 2,400, 3,750

We test whether the prediction model prediction energy consumptions for machining parts• with different geometry • with different machine control parameters (in this case study, varying spindle speeds)

?

Energy consumption

𝐸~𝑁( 𝐸, 𝑆)

Level of generalization

26

Can we predict how much energy the manufacturing machine will consume when machining the part? YES

Energy density prediction for face milling 𝑦 = 𝑓1 𝒙

27

Prediction results for test parts

Energy consumptions for each NC code blockTotal Energy consumption

Error rates

No. of data

Averagedblock

duration (sec)

RAE(%)

Predictedtotal energy

(KJ)

Measured total energy

(KJ)

Standard deviation

(KJ)

RTE(%)

Test 1 188 10.27 13.004 22.492 21.689 0.434 3.702

Test 2 188 9.82 15.210 21.928 21.864 0.441 0.290

Test 3 188 9.70 23.143 21.747 21.074 0.477 3.192

𝐸~𝑁( 𝐸, 𝑆)

28

Prediction results for test parts

• RAE = {𝑖∈ NC blocks}

𝐸𝑖−𝐸𝑖

{𝑖∈ NC blocks } 𝐸𝑖

• RTE =𝐸− 𝐸

𝐸

29

Future work and Conclusion

TargetMachine Tool

External sensors

MTConnectAgent

DataProcessor

DataBuffer

KnowledgeExtraction Agent

KnowledgeArchive

PastExperience

Process Parameters

OptimizationProcess Parameters

Real time data acquisition and processor

AdaptiveMachine learning

Real time data acquisition

Adaptive machine learning

Continuous machine monitoring and control without saving big data

• The authors acknowledge the support in part of the Smart Manufacturing Systems Design and Analysis Program at the National Institute of Standards and Technology (NIST), Grant Numbers 70NANB12H225 and 70NANB12H273 awarded to University of California, Berkeley, and to Stanford University respectively. In addition, the authors appreciate the support of the Machine Tool Technologies Research Foundation (MTTRF) and System Insights for the equipment used in this research.

• Certain commercial systems are identified in this paper. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology (NIST); nor does it imply that the products identified are necessarily the best available for the purpose. Further, any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NIST or any other supporting U.S. government or corporate organizations.

30

Acknowledgements and disclaimer

Supplementary slides

31

Requirements:

• The amount of data storage should be minimized while maximizing the knowledge extraction

The extracted knowledge should be updated with new measurement data to account for the time varying characteristics of a target machine, i.e., tool wear or aging.

Time

Knowledge

Stored data• The amount of monitoring data increases with time.

• The extractable knowledge is not necessarily proportional to the amount of data.

• Constructing GP model is computationally expensiveO 𝑚3 , 𝑚 is number of data points.

Issues:

Time

Knowledge

Stored data

Limitations in GP

32

http://www.dailymail.co.uk/sciencetech/article-2020546

• Different types of knowledge are processed and retained by different region of brain.

• The knowledge is updated with new information, i.e., outdated knowledge is replaced with new one.

Online collective GP is composed of

• 𝑝𝑖(𝒙): input feature distribution constructed by Gaussian Mixture Model using local data set. (domain of knowledge).

• ℎ𝑖(𝒙): regression model mapping input to output constructed by GPusing local data set.(content of knowledge).

Collective Gaussian Process

33

Given 𝑁 pairs of energy prediction function and input features’ PDF, { ℎ𝑖 𝒙 , 𝑝𝑖(𝒙) |𝑖 =

𝑦𝑛𝑒𝑤 = ℎ 𝒙𝑛𝑒𝑤 =

𝑖

𝑁

𝑤𝑖 ℎ𝑖 𝒙𝑛𝑒𝑤

𝑤𝑖 =𝑝𝑖 𝒙𝑛𝑒𝑤

𝑗𝑁 𝑝𝑗 𝒙𝑛𝑒𝑤

where the weighting coefficient 𝑤𝑖 for the 𝑖th local energy prediction function is determined as

Prediction by local GPs

Global GP Collective GP

Collective Gaussian Process

34

𝑝 𝒙;𝝋, 𝝁, 𝚺 =

𝑘=1

𝐾

𝑔𝑘(𝒙; 𝝁𝑘 , 𝚺𝑘)𝜑𝑘

𝑔𝑘 𝒙; 𝝁𝑘 , 𝚺𝑘 = 𝑁 𝒙; 𝝁𝑘 , 𝚺𝑘 =1

(2𝜋)𝑛|𝚺𝑘|exp −

1

2𝒙 − 𝝁𝑘

𝑇𝚺𝑘−1 𝒙 − 𝝁𝑘

Modeling a probability density function as a combination of 𝐾 Gaussian components

(Ref: F. Wood, NIPS 1999)

For an feature vector 𝒙 = (𝑥1, 𝑥2, … , 𝑥𝑛), the 𝑘th component density is of a form of Gaussian

𝜑𝑘: (mixture) weight for 𝑘th Gaussian component ( 𝑘=1𝐾 𝜑𝑘 = 1)

𝝁𝑘: mean vector for the 𝑘th Gaussian component𝚺𝑘: covariance matrix for the 𝑘th PDF

𝐾: number of GPDFs𝝋 = 𝜑1, … , 𝜑𝐾 : set of weights𝝁 = 𝝁1, … , 𝝁𝐾 : set of mean vectors 𝚺 = {𝚺1, … , 𝚺𝐾}: set of covariance matrices

Gaussian Mixture Model (GMM)

35

Simple example

Weighted sum of Gaussian PDFs

𝑝 𝒙 =

𝑘=1

𝐾

𝑔𝑘(𝒙)𝜑𝑘

𝑔1(𝒙) 𝑔2(𝒙) 𝑔3(𝒙)

Gaussian Mixture Model (GMM)

36

collective GP

Error histogramEnergy prediction

Global GP

Global GP vs Collective GP

37

Accuracy Computational time RAE (%) RTE (%) Learning (sec) Testing (sec)

Collective GP 15.45 -0.41 102.88 0.20Global GP 17.81 0.72 8.87 0.21

Weighting methods RAE (%) RTE (%)Probability by GMM 17.81 0.72

Variance by GP 18.40 0.14Geometric distance to center 42.41 24.02

Average 48.47 39.50

The comparison of prediction accuracies between the collective GP regression and other local GP regression methods

Numerical results

38

Part design NC code Target machine Machined part

Prediction with blind test parts

𝑓𝑞 𝒙 |𝑞 = 1,… , 𝑄

Simulator

Energy consumption

𝐸~𝑁( 𝐸, 𝑆)

39

Energy prediction on test data set randomly selected from training data set

40

Data acquisition & simulator for this study

• Fanuc Controller : Collect machine control parameters

• System Insights High Speed Power Meter (HSPM):Collect power time series

• Direct data : Directly measured from hardware

• Derived data: Derived through simple calculations, e.g., mean and tool path computation.

• Simulated data : Obtained by simulation, accounting for workpiece geometry

Hardware Data types

41