Predicting the Remaining Useful Life of Lithium- ion ... · PHM’11, BMS Workshop 9/26/2011 Page 16 • Distributed active learning uses more queries but achieves better prediction

Predicting the Remaining Useful Life of Lithium-ion Batteries with Active Learning and Good-

Turing Usage Profile Estimation

Huimin ChenHuimin Chen

Dept. of Electrical Engineering

University of New Orleans

New Orleans, LA 70148, U.S.A.

Joint work with Brian McClanahan, Norfolk State University

Background Information [Pattipatti et al 11]

Many battery models

Many battery health monitoring techniques

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techniques

Background Information

0 20 40 60 80 100 1200

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historical data prediction

9 5 96 97 9 8 9 9 100 1010

0. 1

0. 2

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0. 9 real failure time

dist of failure time

• Hard to generate run-to-failure data

• Time consuming

• Usage profile may vary

• Environment may change

• Hard to validate prediction methods

• Model may be inaccurate [Saha et al 09]


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• Model may be inaccurate

• No unified criterion for uncertainty characterization

• Treat it as active learning

• Select good examples

• Save the cost of generating labeled training data

[Saha et al 09]

Background Information

?

Start with a pool of unlabeled data

Pick a few samples at random and get their labels

Repeat• Apply a machine learning algorithm to the labels seen so far• Query the unlabeled sample closest to the decision boundary (or most uncertain sample, most likely to decrease overall uncertainty, minimizing the empirical risk, …)

Generic Active Learning Method


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?

Active Learning: Efficient Search in Hypothesis Space

Note that any supervised learning algorithm can be used in learn(•)

Hypotheses in current

Potentially save many training samples

but may introduce sampling bias [Dasgupta et al 07]


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Hypotheses in current version space Region of disagreement

Active Learning: Importance Sampling Based Method

• S={ }

• Take unlabeled point

• Set rejection threshold p

• Draw a random number u ~ U(0,1)

• If u<p, then

• Query label


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• Query label

• Add the example to S with importance weight 1/p

• Learn S and update error rate difference Δ

Can avoid sampling bias!

Active Learning: Importance Sampling Based Method

At k-th unlabeled point, calculate importance weighted error rate

How to set sampling threshold p?


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Error rate difference

Need to make a query when

Otherwise, set

Active Learning: Regression and Prediction

Convert to Multi-Class Active Learning Problem


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Convert to Regression/Prediction Problem

Distributed Active Learning [Chen et al 11]• Each agent performs its own rejection sampling based active

learning• Sample space can be different• Learning algorithm can be different

• Want to combine learning results from multiple agents• Update importance weight on the queried sample• Agents do not need to reach consensus on commonly queried

samples


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samples• Fusion center will learn in the whole sample space (similar to

Boosting)

+

Distributed Active Learning: How Does It Work?

• The method does not have sampling bias

• With high probability, the error rate approaches to that of supervised learning for large sample size k

• If there is a small disagreement coefficient θ, it requires only O(θ[klogk]1/2) queries

• Computationally efficient for optimization-style learning


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• Computationally efficient for optimization-style learning algorithms

• Can have substantial benefit when agents apply different learning algorithms at the price of making more queries

Online Usage Profile Estimation

• Battery RUL prediction depends on the usage profile, e.g., rest time between change and discharge cycles

• Training examples may not well represent testing cases

• Can estimate usage profile online while allowing some prob. of seeing unexpected patterns

• We modified Good-Turing frequency estimator to learn


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• We modified Good-Turing frequency estimator to learn battery rest time vs. capacity fade

• It is more reliable than other ad hoc methods

Orlitsky et al., Always Good Turing: Asymptotically Optimal Probability Estimation, Science, 302 (5644): 427-431

Application to Battery Prognostics

Li-ion battery

run-to-failure data set from NASA Ames Research Centerhttp://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/


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End-of-Discharge Time Prediction: Given the health of the battery, is there enough charge left for anticipated load profile?

End-of-Life Prediction: Given the state of charge of the battery, how many discharge cycles can we use before its full capacity decays below 70% of its initial charge capacity?

UNO Battery Prognostics Test Equipment

Prognostic algorithm on FPGA for real test


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Adjustable load profile using micro-controller

Experimental Study: Prediction Accuracy

• Comparison of End-of-Discharge Time Prediction: Earliest time onwards where the prediction accuracy is above 90%

Good-Turing estimator improves the RUL prediction when battery has irregular rest patterns


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About 100s earlier

Experimental Study: Number of Samples Needed• Discharge cycles needed to learn the regression model

About 13 more cycles on average


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Experimental Study: Centralized vs. Distributed AL

• Predicting battery remaining useful life (RUL) after 40 discharge cycles

• False positive: actual prediction accuracy is above 90% but the predictor declares that it is below 90%

• False negative: actual prediction accuracy is below 90% but the predictor declares that it is above 90%

• Comparison of RUL prediction performance


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• Comparison of RUL prediction performance

• Distributed active learning uses more queries but achieves better prediction accuracy

Concluding Remarks

• Proposed a generic distributed active learning method that can selectively choose examples

• Applied to battery end-of-discharge time and end-of-life prediction and compared with passive learning method

• Active learning achieves comparable prediction accuracy with more than 50% savings of training examples


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with more than 50% savings of training examples

• Distributed active learning combines different active learners to achieve higher prediction accuracy with more examples needed to train than a single active learner

• Good-Turing estimator can update the usage profile online to improve the prediction accuracy

Acknowledgement

• Funding support• Army Research Office• Office of Naval Research (DEPSCoR)• UNO Office of Research & Sponsored Programs• NSF REU Site (B. McClanahan, N. Keller)


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• NSF REU Site (B. McClanahan, N. Keller)

• Stimulating discussions with• B. Saha, K. Goebel (NASA ARC)• G. Liu, X. R. Li, V. P. Jilkov (UNO)

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Predicting the Remaining Useful Life of Lithium- ion ... · PHM’11, BMS Workshop 9/26/2011 Page 16 • Distributed active learning uses more queries but achieves better prediction