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Decentralised Adaptive Sampling of Wireless Sensor Networks

Johnsen KhoAlex Rogers

Nicholas R. Jennings{jk05r,acr,nrj}@ecs.soton.ac.uk

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Outline

Background: Wireless Sensor Network. Research Challenge & Aim.

Research: FloodNET Domain. Generic Sampling Problem Formulation. Information Metric. Adaptive Sampling Algorithms. Empirical Evaluations.

Conclusions & Future Work.

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Wireless Sensor Network

WSNs are increasingly being deployed for: Environmental monitoring [deRoure 2005; Martinez et al. 2005;

Cardell-Oliver et al. 2005; Werner-Allen et al. 2006; Mainwaring et al. 2006].

Smart building [Guestrin et al. 2005].

Structural health surveillance [Chintalapudi et al. 2006].

Object tracking [Simon et al. 2004].

Other security and health related applications [Kroc and Delic 2003; Lo and Yang 2005].

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Research Challenge and Aim

Energy management issue. Hardware perspective to tackle this problem:

Using rechargeable battery and energy harvesting technologies.

Designing nodes with discrete transceiving power levels and dynamic radio ranges.

Software perspective to tackle this problem: Effective sampling policies:

Adapt a node’s sampling rate (i.e. how often it is required to sample during a particular time interval).

Adapt a node’s schedule (i.e. when it is required to sample).

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Research Challenge and Aim (Cont.)

Generally, a WSN is characterised by its: Dynamism. Hostile environment deployment Large scale. Imprecise and noisy observations. Redundant sensed events. Limited communication, computational, storage, and

energy resources. Control regime: centralised vs. decentralised? Ultimate aim: maximising the amount of useful

information that can be gathered over the network’s lifetime, given the energy constraints. Gaussian Process (GP) regression techniques as our

principled means of valuing the sensors’ observations.

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Centralised vs. Decentralised Centralised

Single coordinator node: Bottleneck in decision processing. Increases dependence and vulnerability as nodes rely on a single processor. Lack of robustness.

Further aggravated within hostile environments where hardware or battery replacement is typically not an option.

Infeasibly large number of computations in the central node. Able to find optimal solution from global knowledge. Communication difficulties in providing all the relevant systems states to the

central node in a timely manner. Decentralised

No central node. Dispersing each smaller decision into a single node. Increases robustness. Any autonomous nodes may fail without dramatically affecting the overall network

performance. More difficult:

Hard to predict the global system behaviours. Dynamic interactions between the interconnected nodes. No node has a global view.

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Static Sampling vs. Adaptive Sampling Trade-off associated with wanting to gain as much information as

possible by sampling as often as possible, with the constraints of the limited power available to perform these activities.

Devise theoretical, decentralised optimal algorithms using the GP valuation function.

Develop a practical information-based adaptive sampling algorithm: Conserving battery energy to take more samples during most dynamic

events while taking fewer samples during the static ones.

Static events

Dynamic events

Sample more

Sample less

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FloodNET Domain Twelve sensor nodes measuring water-level data on a river for real-

time accurate flood forecasting. Nodes take a sample at five minutes interval (requires 70mW). Nodes transmit collected samples in every two hour period (requires

1910mW amount of power). Centralised control. Decentralised control: autonomous agents and each decides its individual

actions, regarding its adaptive sampling rates adjustment, based on its local states and observations.

Centralised

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Generic Sampling Problem Formulation Set of sensors I={i1,…,in} Each sensor i ∈ I has s sampling actions, denoted Ci={ci

1,…cis}, where Ci ⊆

Z+ and ci1<…< ci

s Daily fixed window size H=1..w such that each element represents a time

slot in a particular day. Each sensor, thus, has its own allocation of actions (i.e. sampling

schedule) per day, denoted Alloci={ai1,…ai

w}, where aiz ∈ Ci, ∀z ∈ H

At the end of a day, sensor i collects sets of observations (Ti={ti1,…ti

w}) at corresponding sampling points (Xi={xi

1,…xiw}), in which ti

z={tiz1

,…tizai

z},

xiz={xi

z1,…xi

zaiz}, where ti

z ∈ Ti, xiz ∈ Xi, ∀z ∈ H

Constraints: A sensor can only select one action at any particular point of time. The sum of all the energy required to do the sampling actions on a day must

not exceed the remaining battery power:

where es represents the amount of energy required to sample an event and Eir

is the remaining battery power left for sensor i at the beginning of that day.

IiwhereEea irs

w

z

iz

,.1

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The Information Metric An agent’s preferences express the satisfaction of its particular

action when faced with a choice between different alternatives: The actions, C, correspond to the different sampling rates a node is

allowed to choose to perform. The preferences express the information values of the data collected by

performing the corresponding actions. A simple cardinal preference structure (that consists of a valuation

function or mathematical function used to calculate the value or goodness of a certain action taken by nodes):

u : V Val where Val is a set of numerical values (typically Z)

Advantage: Interpersonal comparisons of nodes’ observations. For instance,

expressing statements such as sensor i is obtaining greater information value by sampling at rate ci

x than ciy or than sensor j operating at ci

z:

u(cix) < u(ci

y) < u(cjz)

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The Information Metric (Cont.) Several techniques for valuing information:

Kalman Filter [Guestrin et al. 2005; Rogers et al. 2006]. Simple Linear Regression [Padhy et al. 2006].

GP Regression Technique [Mackay 1998; Seeger 2004]: Inputs:

A set of g training points (X={x1,x2,…,xg}) A set of g noisy observations (T={t1,t2,…,tg})

Outputs: A set of new estimated data points (μ(X)={μ(x1),μ(x2),…,μ(xg)}) The corresponding bounded error (a.k.a. variance or uncertainty error)

(σ2(X)={σ2(x1),σ2(x2),…,σ2(xg)}) Fisher information value [Frieden 2004] contained in this set of observations is:

The bigger the bounded error, the more uncertain we are about this set of observations, hence, the less valuable it is.

g

k kxgFI

12 )(

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The Information Metric (Cont.)

Utilitarian Social Welfare [Chevaleyre 2006]: Measures the quality of an allocation of nodes’ actions from

the view-point system as a whole. The USW for an allocation Alloc is defined as the sum of

each node’s FI valuation:

)()(

Ii

iFI AllocFIAllocUSW

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Theoretical Decentralised Algorithms

The GP valuation function: Covariance function [Rasmussen and Williams 2006] used is the sum

of: Squared exponential or Gaussian covariance function. Periodic covariance function. Independent covariance function.

Whenever target observations are closely related (i.e. they have a small covariance matrix or they are more frequently sampled), the variances of the estimated values, σ2(X), will decrease. The Fisher information value will, on the other hand, increase.

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Gaussian Process Regression & Valuation Function

FI=1.263 . 10-1 FI=0.5168 . 10-1

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The Optimal Adaptive Sampling Algorithm (naïve approach)

Enumerates all of the possible solutions and then to choose the best one:

such that:

Ii

iAllocFIX )(maxargmax

g

k ki

Ii xg 12 )(

11maxarg

HzIiXxua iz

iz u

,,,maxarg max

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The “Greedy” Optimal Adaptive Sampling Algorithm

Approximation algorithm that works by allocating one additional sampling point at a time until there is no more sample to add:

such that:

HzIipreSampxua iz

iz u

,,,maxarg

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Practical Decentralised Algorithm

The valuation function: Standard deviation error of the linear regression line. The uncertainty error is expressed in confidence bands about the

linear regression line:

number of data points

mean value of X

location along the x-axis data points where the distance isbeing calculated

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Practical Decentralised Algorithm (Cont.) Information value, Gaini

u(z), is the reduction in total deviation error, TDE, that sensor i can achieve by taking samples at rate ci

u rather than the minimum sampling rate ci

1 in time slot z. Minimum sampling rate is applied as a basis where sensor gains zero

value/profits.

1

11 ]2[

2

1 n

knkn xTDE

HzIiCwherezTDEzTDEzGain i

cc

iu i

ui ,,c ),()()( i

u1

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Practical Decentralised Algorithm (Cont.)

V as a s x w matrix with s number of actions and w number of time slots.

D is a matrix of binary values and each of the elements corresponds to a decision variable.

such that viuz represents the value that sensor i will get if

it chooses to perform action ciu in hour slot z.

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Problem Solver

Cast into binary integer programming problem.

Function to be maximised.

Second constraint:The total number of samples takenby a sensor must not exceed the maximum number of samples it can take on that day.

First constraint:A sensor can only elect one action atany particular point of time.

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The Information-Based Adaptive Sampling Algorithm

HzIiuca iu

iz ,,1d|{1..s} where, i

uz

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The Information-Based Adaptive Sampling Algorithm (Cont.)

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FloodNET Domain Simulator

High-fidelity models: The battery model The energy harvesting model The node model The network stack model

Assumptions on wireless communication model: Unlimited bandwidth Single transmission level No failure in transmission

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Network and Parameters Initialization

FloodNET data for batteries, tide readings, and cloud cover.

FloodNET actual topology. H=1..24 (such that each element represents a one

hour slot, for instance 1 represents the slot between 00:00am and 01:00am).

Four different sampling actions, Ci={1,3,6,12}, ∀i ∈ I

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Benchmark Algorithms

The Naïve Non-Adaptive Sampling Algorithm. This dictates that each sensor should sample at its maximum rate, whenever there is enough battery energy to do so.

The Uniform Non-Adaptive Sampling Algorithm. This dictates that each sensor should simply choose to divide the total number of samples it can perform in a day (Ni where Ni = Ei

r/es) equally into its time slots.

HzIica is

iz ,,

HzIiw

NcCuua

iiy

iiz ,},|{c where,maxarg i

y

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Empirical Result I (Run-Time Performance)

The optimal adaptive sampling algorithm works only for small problems as it very rapidly becomes infeasible for even small- to medium-sized ones.

The “greedy” optimal adaptive sampling algorithm significantly reduces the number of iterations.

The information-based adaptive sampling algorithm runs in real time on the current configuration.

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Empirical Result II (Information Value Analysis)

FI=1.804 . 10-4FI=3.278 . 10-2

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Empirical Result II (Information Value Analysis)

FI=7.396 . 10-2FI=1.045 . 10-1

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Empirical Result II (Information Value Analysis)

Information Measured Cumulative Information(at the base station per day) Measured

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Empirical Results III(Adaptive Water-Level Samples)

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Empirical Results III(Adaptive Water-Level Samples)

The 2nd Day

Dynamic events

Static events

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Simulator Demonstration

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Conclusion & Future Work Using state-of-the-art GP regression technique as a principled

means of valuing a set of node’s observations, we show how theoretical optimal algorithms can be devised.

We also developed a practical information-based adaptive sampling algorithm that is effective in balancing the trade-offs associated with wanting to gain as much information as possible by sampling as often as possible, with the constraints imposed on these activities by the limited power available.

Future work: Simulator improvements (inc. wireless communication model) Extended mechanisms (inc. adaptive transmitting & adaptive

routing) Real Deployment

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Any Questions?

Thank you