Self-Constructive High-Rate System Energy Modeling for - - PowerPoint PPT Presentation

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Self-Constructive High-Rate System Energy Modeling for - - PowerPoint PPT Presentation

Dec 20, 2023 110 likes •554 views

Self-Constructive High-Rate System Energy Modeling for Battery-Powered Mobile Systems Mian Dong and Lin Zhong Rice University System Energy Model y ( t ) = f ( x 1 ( t ), x 2 ( t ),, x p ( t )) Predictors x i ( t ): Response y ( t ): System

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Self-Constructive High-Rate System Energy Modeling for Battery-Powered Mobile Systems Mian Dong and Lin Zhong Rice University

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System Energy Model

Response y(t): Energy consumed by the system in t

y(t) = f(x1(t), x2(t),…, xp(t))

Predictors xi(t): System status variables in t

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Rate (1/t)

0.01Hz 1Hz 100Hz

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A High-Rate Energy Model

is needed to provide an energy reading at each OS scheduling interval

10ms

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Target System Data Acquisition Equipment Host PC

31,415,926

y(t1) x1(t1) x2(t1) … xp(t1) x1(t2) x2(t2) … xp(t2) x1(tn) x2(tn) … xp(tn) y(t2) y(tn) t=t1=t2=…=tn

Model Construction

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Target System Data Acquisition Equipment Host PC

31,415,926

y(t1) x1(t1) x2(t1) … xp(t1) x1(t2) x2(t2) … xp(t2) x1(tn) x2(tn) … xp(tn) y(t2) y(tn) t=t1=t2=…=tn

X(t) Y(t)

Regression

Model Construction

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Target System Data Acquisition Equipment Host PC

31,415,926

t=t1=t2=…=tn

y(t) = β0+β1x1(t)+…+ βpxp(t) β = argminβ(║Y(t)−[1 X(t)]β║2) ^

Linear Model:

Model Construction

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Target System Data Acquisition Equipment Host PC

31,415,926

t=t1=t2=…=tn

y(ti) − y(ti) err(ti) = y(ti) ^ ^ ^ ^ ^ y(t) = β0+β1x1(t)+…+ βpxp(t)

Linear Model:

Model Construction

Mean Absolute Root-Mean-Square

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What are the limitations?

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External Devices

for energy measurement

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Deep Knowledge

for predictor collection

www.nokia.com

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Exclusive Model

for a specific platform

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Fixed Model for all

instances of the same platform

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Hardware & Usage

suggest “personalized” models be constructed for a mobile system Dependencies of system energy models on

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Self-Constructive

System Energy Modeling

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External Devices Deep Knowledge Exclusive Model Fixed Model

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Battery Interface Statistical Learning

Personalized Model

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Battery

Interface

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State-of-the-art battery Interfaces are

Low-rate/Inaccurate

N85 T61 N900 Max Rate 4Hz 0.5Hz 0.1Hz Accuracy 67% 82% 58%

Accuracy = 100% – Root_Mean_Square(Instant_Relative_Error)

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Errors in battery interface readings are Non-Gaussian

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High-Rate/Accurate System Energy Model Low-Rate/Inaccurate Battery Interface

Statistical Learning

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0% 10% 20% 30% 40% 50% 0.01 0.1 1 10

RMS of Relative Error Rate (Hz)

N900 T61 N85

Averaged battery interface readings

have

Higher Accuracy

but

Even Lower Rate

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y x

Time

y(t) y(T) x(t) x(T)

Time High-rate data points Low-rate data points

High-rate data points Low-rate data points

Linear models are

Independent on Time

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  • 1. Model Molding

0.01Hz 1Hz 100Hz Y(tH) Y(tL) Y(tVL) X(tH) X(tVL) β ^ ^ β ^

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0% 10% 20% 30% 0.01 0.1 1 10 100

RMS of Relative Error Rate (Hz)

Battery Interface

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0% 10% 20% 30% 0.01 0.1 1 10 100

RMS of Relative Error Rate (Hz)

Model Molding improves rate

Battery Interface Molded Model

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  • 2. Predictor Transformation

x1(t), x2(t),…, xp(t) z1(t), z2(t),…, zL(t)

Principle Component Analysis

L L ≤ p

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0% 10% 20% 30% 0.01 0.1 1 10 100

RMS of Relative Error Rate (Hz)

PCA improves accuracy

Battery Interface Molded Model Molded Model + PCA

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x y yj rj y=f(x)

Training data points

dj xj Δxj

  • 3. Total-Least-Square
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0% 10% 20% 30% 0.01 0.1 1 10 100

RMS of Relative Error Rate (Hz)

TLS improves accuracy at high rate

Battery Interface Molded Model Molded Model + PCA Molded Model + PCA + TLS

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Data Collector

Sesame

Model Constructor

Predictor transformation

Model

Model Manager Operating System Bat I/F STATS

Energy readings Stats readings Predictors Responses

Model molding

Application specific predictors

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Implementation

N900 T61

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Sesame is able to generate energy models with a rate up to 100Hz T61 N900 1Hz 95% 86% 100Hz 88% 82%

Accuracy = 100% – Root_Mean_Square(Instant_Relative_Error)

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Field Study

Day 1-5: Model Construction Day 6: Model Evaluation

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Models were generated within 15 hours

0% 10% 20% 30% 7 9 11 13 15

Error Time (hour)

User 1 User 2 User 3 User 4 0% 10% 20% 30% 1 2 3 4

Error Laptop User

Sesame@1Hz Sesame@100Hz

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  • 1. Sophisticated Statistical Methods
  • 2. Capability to Adapt Models

Sesame is able to construct models

  • f high accuracy because of
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Virtual Power Meter

Sesame is a high-rate/accurate

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Energy Optimization & Management

and creates new opportunities in

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y(t) = β0+β1x1(t)+…+ βpxp(t)

Software Optimization

“Knob” provided by target software

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y(t) = β0+β1x1(t)+…+ βpxp(t)

Energy Accounting

n Processes

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y(t) = β0+β1x1(t)+…+ βpxp(t)

Energy Accounting

x1(t) = x1,1(t)+…+ x1,n(t) xp(t) = xp,1(t)+…+ xp,n(t)

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yj(t) = β1x1,j(t)+…+ βpxp,j(t)

Energy Contribution by Process j

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Servers and Workstations

Sesame can be also used for

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Conclusions

  • Self-Modeling is necessary to adapt to the

changes in hardware and usage

  • Statistical methods help to construct high-rate

/accurate models from low-rate/inaccurate battery interfaces

  • Sesame creates new opportunities in system

energy optimization and management