Sensor Placement and Allocation.pdf

Machine Learning Approach to Sensor Alloca3on and Placement in System-‐

on-‐Chips (SoCs)

Santanu Sarma Centre for Embedded and Cyber-‐Physical Systems (CECS)

University of California, Irvine Spring 2013

Impact of Temperature

•  Elevated temperatures directly impact all key circuit metrics including: life3me and reliability, speed, power, and costs.

•  Hot spots reduce the mean 3me to failure as most failure mechanisms have strong temperature dependencies [Pedram2006].

•  Different thermal expansion coefficients of chip materials cause mechanical stresses that can eventually crack the chip/package interface [Brooks2007]

•  The exponen3al dependency of leakage power on temperature further increases total power and could lead to thermal runaway [Lin2008].

6/1/12 © Santanu Sarma, UCI 2


•  The failure rate due to thermal cycling increases with the increasing magnitude and frequency of the temperature cycles [JEDEC2006].

•  A 10 oC rise in temperature can reduce the chip life-‐3me by half [h\p://www.nanowerk.com].

•  Increasing temperature increases local resistances, and thus circuit delays and IR drop [Santarini2005].

•  Elevated temperatures also slow down devices and interconnects leading to 3ming failures [Cheng1998], [Pileggi2006].



•  Inaccuracies in thermal tracking decreases the processor’s performance and wastes power. In par3cular, it was shown that a 1oC accuracy translates to 2W power savings, and that due to lack of proximity, sensor measurements and hot spot temperatures could differ by up to 10oC [Rotem2006]

•  In mobile computers, 1.5oC accuracy in temperature measurement is equivalent to 1 Wa\ of CPU power [Rotem2006]

•  Inaccuracy 1oC in thermal es3mates can trigger DTM and unwanted performance loss of upto 14.4 % [Zhang 2011].


Thermal Profile Characteris3cs

•  Hot spot loca3ons and temperatures are applica3on dependent [Skadron2005] –  Hot spots will not always remain in the same loca3ons on the chip during execu3on of a single program [Hamann2007, IBM]

–  Various applica3ons running on the same chip will show hot spots in different regions [Hamann2007, IBM]

– Within-‐die temperature varia3on can be up to 50 °C [Borkar2003]. Large number of delay viola3ons would occur if the peak temperature exceeds 85°C [Skadron2003].

– Maximum temperature varies across layers [Im2000]


Thermal Distribu3on During Boo3ng [Hamann2007, IBM]


Thermal Gradient as high as 50oC


Temperatures for gcc benchmark. [Han2007]

Within die temperature varia0on

6/1/12 © Santanu Sarma, UCI 8 Within die maximum temperature varia0on of up to 50 oC [Borkar2003]

Sensor Placement Far Away From Ho\est Block

6/1/12 © Santanu Sarma, UCI 9 Temperature for nbench benchmark [Han2006]

Maximum Temperature Distribu3on Across Layers

6/1/12 © Santanu Sarma, UCI 10 Maximum temperature distribu3on along ver3cal distance from the substrate to the top metal layer [Im2000]

Maximum Temperature Distribu3on Across Benchmarks


[Srinivasan 2004]

Thermal Profile Characteris3cs

Proper0es Magnitude Remarks

Independent Dimensions Spa3al & temporal

In all three dimensions and 3me, Technology & Workload dependent

Maximum Spa3al Varia3ons

Up to 40-‐60 oC across adjacent blocks

In the order of block size,

Maximum Spa3al Gradients

Up to 40-‐60oC per nm^2

Maximum Temporal Varia3ons

Up to 40-‐100oC In Seconds in the same block.

[0.1oC/ 30 us = 3333 oC/S] [Skadron2003]

Maximum Temporal Gradients

?


Sensor Placement Requirements

•  Sensor placement configura3on must suffice for all hot spots that may arise during the execu3on of any program –  It is unlikely that a solu3on op3mized for a single applica3on will be sufficient for other workloads

•  Need to reduce/minimize the overheads of using large number of sensors

•  Placement need to ensure overall reduc3on in error in the thermal profile reconstruc3on


Problem Classifica3on

Placement Techniques

•  Based on Approach –  Sta3c placement –  Dynamic placement

[Buedo2004]

•  Based on Geometry –  Uniform –  Non-‐uniform

•  Based on Transformed Domain

Reconstruc0on Techniques •  Direct Methods •  Inverse Methods

–  Based on Sensing Approach –  Based on Sampling Mechanism –  Based on Transformed domain –  Based on Informa3on Theory

•  Adap3ve Methods –  Direct/Indirect [Sharif 2010] –  Phase based [Reda 2012] –  Predic3ve Model based [Coskun

2009]


Problem Classifica3on


THERMAL CHARACTERIZATION

SENSOR PLACEMENT RECONSTRUCTION

APPROACH GEOMETRY XFORMS DIRECT INVERSE ADAPTIVE

HYBRID (IR Imaging)

Thermal Characteriza0on

•  Design-‐Time Technique –  allocate sensors near poten3al hot spot loca3ons –  Sensor placement algorithms fall into two main categories:

•  Uniform Sensor Placement •  Nonuniform Sensor Placement •  Hybrid

•  Run-‐3me Technique –  full thermal map characteriza3on & hot spot detec3on –  Categories:

•  Direct Method •  Inverse/Indirect Method •  Hybrid


Thermal Sensor Placement Techniques

•  Approach: – Sta3c Placement Technique

•  Dynamic Selec3on & Scheduling [Forte 2013] – Dynamic Placement Technique [Buedo2004]

•  Geometric Sensor Placement – Uniform – Non-‐Uniform

•  Transformed Domain Placement •  Informa3on Theore3c Sensor Placement


Uniform Sensor Placement

•  Intended for use with chips that have an unknown typical thermal pa\ern

•  Sensors are placed in a uniform sta3c grid throughout the en3re chip

•  Only a finely-‐grained grid of sensors is capable of achieving near-‐perfect accuracy

•  Significant cost restric3ons associated with sensor overheads



6/1/12 © Santanu Sarma, UCI 19 [Skadron 2005, Sankaranarayanan2009 ]

Actual Sensed


6/1/12 © Santanu Sarma, UCI 20 [Sankaranarayanan2009 ]


Advantages •  Does not rely on thermal

profiling data •  No knowledge of hot spot

loca3ons and temperatures needs to be acquired prior to implemen3ng a technique of this type

Disadvantages •  limits the accuracy of the

uniform grid model •  distances between the

sensor loca3ons and the hot spots cannot be minimized

•  Not always be able to detect hot spots as accurately as the same number of sensors located near common hot spots


Interpola0on-‐Based Sensing [Memic 2008]

•  Uniform Sensor Placement •  A straight-‐forward linear

interpola3on approach •  accounts for fine-‐grain grid

restric3on and refine the temperature measurements

•  Interpola3on scheme with a 4 x4 grid of sensors improve upon a sta3c uniform grid of the same size with no interpola3on by an average of 1.59◦C

6/1/12 © Santanu Sarma, UCI 22 [Memic 2008]

Interpola0on-‐Based Sensing

6/1/12 © Santanu Sarma, UCI 23 [Sankaranarayanan2009 ]

Non-‐uniform Sensor Placement

•  Intended for use where thermal maps from typical chip execu3on across several applica3ons are available

•  Take advantage of the known hot spots to determine the most advantageous loca3ons

•  Methods: –  Hot Spots based Placement –  Analy3cal Model based Non-‐Uniform Placement [Skadron2005a]

–  Quality-‐Threshold Clustering [Yun 2008] –  K-‐Means Clustering [Mukherjee 2006] –  Power-‐Driven Correla3on Clustering Based[Wang 2013]


Hot Spots Based Placement

•  HotSpot based Placement: place a sensor on each hot spot found through thermal profiling across several applica3ons


Hot Spots Based Placement

Advantages •  Easy to detect hotspots for

a given thermal maps •  Can detect thermal

viola3ons with a limited number of sensors (less than uniform)

•  Temperatures found via thermal profiling of several applica3ons can provide good es3mates

Disadvantages •  Hot spot loca3ons and

temperatures are applica3on dependent

•  Solu3on op3mized for a single applica3on will not be sufficient for other workloads

•  Can have too many hot spots points and hence many sensors


Analytical Model based Non-Uniform Placement [Skadron2005a]

•  Non-‐uniform sensor placement based on hot spot loca3ons and temperatures found via thermal profiling

•  Describe the maximum radius R between a hot spot and a poten3al thermal sensor loca3on, while capping the error to a degree ΔT


ΔT denotes the difference between the maximum and minimum temperature value in the chip

Analy0cal Model based Non-‐Uniform Placement [Skadron2005a]


R

Quality-‐Threshold Clustering [Yun 2008]

•  Hot spot groupings and corresponding sensor loca3ons are determined based on the values of Tmax

•  Incorporates analy3cal model of sensor placement radius with the quality threshold (QT) clustering algorithm commonly used in gene clustering

•  Itera3ve technique that assigns hot spots to clusters –  based on their physical loca3ons on the chip rela3ve to the other hot spots.



•  Sensor loca3on for each cluster is refined axer the addi3on of a candidate hot spot to be the centroid of the included hot spots –  obtains the best possible sensor loca3on for the given set of hot spot data points

•  QT Clustering resulted in placing 23 sensors in Alpha 21364 with an average error of 0.2899◦C.

•  To place fewer sensors using QT clustering: –  hot spot to sensor distance value must be increased, – may decrease the accuracy of the en3re model’s results.



Advantages •  algorithm proves to be

sufficient for monitoring thermal events

•  obtains the best possible sensor loca3on for the given set of hot spot data points

Disadvantages •  algorithm does not end

execu3on un3l every hot spot is placed in a cluster

•  Creates new clusters where necessary to include hot spots that are located far away from the others

•  number of sensors required by the QT clustering may be large for prac3cal design


K-‐Means Clustering Based Sensor Placement [Mukherjee 2006]

•  Hot spots are placed into k different clusters, with a temperature sensor placed at the centroid of each cluster

•  cluster assignments are chosen such that the mean squared distance from each hot spot to the nearest cluster center is minimized

•  Algorithm: –  First, the k cluster centers are chosen randomly from the set of known hot

spot points –  Each hot spot is then assigned to a cluster –  Each cluster center is updated at the end of each itera3on –  Euclidean distances between the hot spots and the cluster centers are then

recomputed –  If a new minimum distance between a hot spot and a different cluster center

is found, the hot spot is reassigned to the corresponding cluster. –  process is repeated un3l no hot spot are reassigned to a different cluster


k-‐Means Clustering Sensor Placement [Mukherjee 2006]


Thermal-‐Aware K-‐Means: Place the temperature sensors to hot spots that typically have higher temperatures

Thermal-‐Aware k-‐Means Clustering [Mukherjee 2006]


sensors have been placed closer to the hot spots of higher temperature and further from the hot spots of lower temperature

Clustering results on the same hot spot set

Thermal-‐Aware k-‐Means Clustering [Mukherjee 2006]

Advantages •  Thermal-‐gradient aware k-‐

means clustering is effec3ve for single-‐core processors

•  Works well under many condi3ons

•  Be\er than [Long 2008] for given number of sensors

Disadvantages •  Not appropriate for mul3-‐core

processors with strong inter-‐core thermal interac3on

•  Not always op3mal in complex hot spot distribu3on scenarios and may produce solu3ons worse than the basic k-‐means approach

•  hot spots are oxen sorted into inappropriate clusters due to their common temperature regardless of posi3on


Non-‐uniform Subsampling Method Based Placement [Sabuncu2004]

•  In many-‐core architectures, there is a high likelihood of measuring a very large number of global hot spots

•  No of hotspots can be too large that clustering methods are not able to place a sufficient number of sensors near the ho\est points

•  To reduce the number of points to be clustered while maintaining clear representa3on of thermal data, non-‐uniform subsampling algorithms can be used

•  Obtains a subset of key thermal analysis loca3ons on a chip •  Types Non-‐uniform Subsampling :

–  Determinis3c Subsampling –  Stochas3c Subsampling


Determinis3c Hotspot Subsampling [Sabuncu2004]


Samples are selected more frequently in regions of high gradient

Stochas3c Hotspot Subsampling [Sabuncu2004]


More Samples in the hoYest region than in the coolest region

Correla0on Clustering based Sensor Placement [Wang 2013]

•  Uses direct method (like hotspot) to reconstruct the hotspot using approximate power es3mates of the blocks.

•  Correct the approximates power es3mates of the block by using the o-‐chip thermal measurements

•  Exploits the correla3on between power es3ma3on errors among func3onal blocks to perform sensor placement

•  Applies the correla3on clustering algorithm [Bansal2002] to determine both the loca3ons of sensors and the number of sensors automa3cally


Correla0on Clustering based Sensor Placement [Wang 2013]

•  Reports be\er results than uniform and k-‐mean clustering methods


Thermal Sensor Placement

References Uniform Non Uniform

Interpolated sensing

Accuracy Remarks

[Memic 2008] Yes No Yes 1.59◦C With 16 sensors

Nearest neighbor interpola3on

[Sankaranarayanan2009]

Yes No Yes Be\er than [Memic 2008]

Bilinear / Cubic Spline

[Long2008] Yes No Yes 3.1◦C with 16 sensors

Non-‐linear Spline

[Skadron2005a] No Yes Yes Analy3cal Model Based

[Yun 2008] No Yes No 0.2899◦C with 23 sensors

QT Clustering + Analy3cal Model

[Mukherjee06] No Yes No 4.58◦C with 16 sensors

Basic K-‐means clustering

[Mukherjee06] No Yes No 2.1◦C with 16 sensors

Thermal-‐aware K-‐means clustering 6/1/12 © Santanu Sarma, UCI 42

Thermal Sensor Placement

References Uniform Non Uniform

Interpolated sensing

Accuracy Remarks

[Long2008] No Yes Yes ~2.0◦C with 16 sensors

Local & Global Hotspots

[Sabuncu2004] No Yes Depends -‐ Sub-‐sampling

[Wang 2013] No Yes Yes 0.26oC with 14 sensors

Correla3on Clustering


Thermal Reconstruc3on Methods

•  Direct Methods –  Hotspot [Skadron et al.] –  Temptor [Koren et al.] –  TILTS [Koren et al.] –  3DICE [A3naza et al.] –  FlowTherm [Mentor Graphics]

–  ANSYS [Commercial FEM]

•  INVERSE Methods –  Based on Sensing Approach

•  Physical / Computa3onal ( Interpolated / Virtual)

•  Hard/ Sox [Reda 2011] •  Dynamic Selec3on [Jong2008]

•  INVERSE Methods –  Based on Sampling Mechanism

•  Uniform Determinis3c Subsampled/ Stochas3c Random Subsampled

–  Based Transformed domain •  FFT/DFT/ DCT/ KLT/ DWT

–  Based on Informa3on Theory •  Eigenmaps based •  Entropy Based •  Bayesian Sta3s3cs based

•  ADAPTIVE Methods –  Direct/Indirect [Sharif 2010] –  Phase based [Reda 2012] –  Predic3ve Model based

[Coskun 2009]


Thermal Reconstruc3on Problem

•  The thermal map of a processor can be es3mated using two dual strategies: – Solu3on of the direct problem, given the heat sources and the physical model of the temperature diffusion (e.g. a nonlinear diffusion equa3on),

– Solu3on of the inverse problem, given the value of the temperature in some loca3ons and some a-‐priori informa3on about the thermal map.


Direct Methods : R-‐C Network Based Thermal Profile Reconstruc0on

•  Direct Problem Formula3on

•  Tools: – Hotspot [Skadron et al.] –  Temptor [Koren et al.] –  TILTS [Koren et al.] –  3DICE [A3naza et al.] –  FlowTherm [Mentor Graphics] – ANSYS [Commercial Tool]


Heat Diffusion through an IC given by Poisson’s PDE Equa0on:

Direct Method Thermal Dissipa3on Model


Direct Methods : R-‐C Network Based Thermal Profile Reconstruc0on


Ti –Temperature of node I Tj-‐ Temperature at node j Pi-‐ Power dissipa0on at node I Ci-‐ thermal Capacitance at node i Gij-‐ lateral conductance between node I and j =1/Rij

RC-‐Network Based Direct Method


Direct Methods

Advantages •  Highly Accurate •  Finite Element Model (FEM)

based automated R-‐C network can be generated

•  Supported by many tools

Disadvantages •  Computa3onally Intensive •  Not feasible as run-‐3me

approach •  Requires power at every

block/grid point


Inverse Methods

•  Inverse methods: given the value of the temperature in some loca3ons and some a-‐priori informa3on about the thermal map, reconstruct the complete map.


Transformed Domain Methods

•  FFT/DFT Based [Chochran 2009] •  DCT Based [Nowroz2010] •  KLT/PCA Based [Juri 2012] •  DWT Based [Cho2009]


FFT Based Reconstruc3on [Cochran2010]

•  Considers temperature as simply a space-‐varying signal and performs Spectral Fourier analysis technique

•  Space domain Convolu3on (interpola3on) is replaced by mul3plica3on in Frequency Domain

•  Proposes methods to handle uniform and non-‐uniform thermal sensor placements




Hot spot es3ma3on full thermal characteriza3on

K-‐LSE : DCT Based Placement [Norwiz 2010]

•  On-‐chip thermal gradients lead to sparse signals in the frequency domain

•  Use DCT based transforma3on to establish the sparsity in frequency domain

•  Exploit this observa3on to – devise thermal sensor alloca3on techniques, – devise signal reconstruc3on techniques that fully characterize the thermal status




placed at the centroids Placed at the center

Eigenmaps (KLT/PCA Based) [Juri 2012]

•  Uses Principal Component Analysis (PCA) to determine the transform

•  Exploits the structural correla3on and temporal varia3ons in the thermal map to achieve very high reconstruc3on accuracy

•  Performs sensor placement and alloca3on to the most important loca3ons corresponding to the principal components

•  Considers non-‐ideal sensors with noise and error. •  Proposes a LSE formula3on for reconstruc3on •  Greedy Algorithm for Placement




The reconstruc3on error as a func3on of the number of sensors used.

The reconstruc3on error in presence of measurement noise as a func3on of the SNR using 16 sensors

Informa3on Theore3c Approaches

•  Compressive Sensing Based [Candes 2006, Donoho2006, Tropp2007, Zang2011a]

•  Bayesian Sta3s3cs Based [Zang2010, Zang2011a]

•  Entropy Based [Zhou 2012]


Compressive Sensing Based Reconstruc3on [Donoho2006]

•  Key Idea: Thermal Profile is Sparse in Either temporal or spa3al domain

•  Random sampling in 3me or spa3al domain i.e. the sensor placement can be random

•  From few random samples it is possible to reconstruct the complete profile if the thermal signal is Sparse


Bayesian Sta3s3cs Based Reconstruc3on [Zang2010]

•  Uses the idea of Bayesian inference and informa3on theory from sta3s3cs –  to determine an op3mal set of sampling loca3ons where test structures/sensor should be deployed and measured

–  to monitor spa3al varia3ons with maximum accuracy •  Unlike Random Sampling in Compressive Sensing, it used Bayesian inference to select the best loca3ons

•  Can be used characterize and monitor spa3al temperature


Bayesian Sta3s3cs Based Reconstruc3on [Zang2010]


Entropy Based Op0mal Temperature Sensor Alloca0on [Zhou 2012]


Temperature sensor loca3ons are selected by different alloca3on algorithms: (a) the k-‐mean clustering method, (b) the par33on method, (c) the Bayesian method, and (d) the entropy method

[Zhou2012]

Key Idea: Entropy of the Thermal Map Can precisely iden0fy the hotspots and And place them near to them.

Entropy =measure of randomness or varia3ons in the signal

Adap0ve Online Methods

•  Ability to update parameters /model at run3me /on-‐line

•  Model-‐Based Control Centric Approach and System Iden3fica3on

•  Measurement Driven Es3ma3on –  State Es3mators & Observers –  Kalman Filters –  Adap3ve Filters

•  Regression based Predic3on –  AR/ARMA /Other Parametric Models –  PCA


Regressive Model based Predic3on & Reconstruc3on [Coskun2008]


Auto-‐regressive moving average (ARMA) based forcus3ng

Online adapta0on when exis3ng model is not fi{ng the current workload

Full-‐Chip Run-‐3me Thermal Es3ma3on and Predic3on [Wang2011]


correla0on based method for error compensa0on

Phase Predic3on Based Reconstruc3on [Reda 2013]


Other Adap3ve Methods [Noise Compensa3ng]

•  Based on Kalman & Adap3ve Filters: – ZHANG, Y., AND SRIVASTAVA, A. “Adap3ve and autonomous thermal tracking for high performance compu3ng systems,” In DAC, 2010.

– ZHANG, Y., AND SRIVASTAVA, A. “Accurate temperature es3ma3on using noisy thermal sensors,” In DAC, 2009.

•  Sensor Error Compensa3on – Compensa3ng & Calibra3ng Noisy and Erroneous On-‐Chip sensors [Sharif 2010]


Hybrid Method: Infrared (IR) Imaging


References •  [Skadron2003] K. Skadron, M. R. Stan, W. Huang, S. Velusamy, K. Sankaranarayanan, and D. Tarjan,

“Temperature aware microarchitecture,” in Proc. Int. Symp. Comput. Architect., Jun. 2003, pp. 2–13.

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Skadron. Granularity of microprocessor thermal management: a technical report. Technical Report CS-‐2009-‐03, University of Virginia Department of Computer Science, April 2009.

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•  [Zhang2010] Y. Zhang, A. Srivastava, and M. Zahran, “On-‐Chip Sensor-‐Driven Efficient Thermal Profile Es3ma3on Algorithms,” ACM Trans. Design Automa3on of Electronic Systems, vol. 15, no. 3, p. 25:1, 2010.

•  [Zhang2009] ZHANG, Y., AND SRIVASTAVA, A. Adap3ve and autonomous thermal tracking for high performance compu3ng systems. In DAC (2010).References ZHANG, Y., AND SRIVASTAVA, A. Accurate temperature es3ma3on using noisy thermal sensors . In DAC (2009)


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References

•  [Zhang2010] ZHANG, Y., AND SRIVASTAVA, A. “Adap3ve and autonomous thermal tracking for high performance compu3ng systems,” In DAC, 2010.

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