Enhancing Battery Efficiency for Pervasive Health-Monitoring Systems Based on Electronic Textiles

350 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 14, NO. 2, MARCH 2010

Enhancing Battery Efficiency for PervasiveHealth-Monitoring Systems Based

on Electronic TextilesNenggan Zheng, Zhaohui Wu, Senior Member, IEEE, Man Lin, Member, IEEE,

and Laurence Tianruo Yang, Member, IEEE

Abstract—Electronic textiles are regarded as one of the mostimportant computation platforms for future computer-assistedhealth-monitoring applications. In these novel systems, multiplebatteries are used in order to prolong their operational lifetime,which is a significant metric for system usability. However, due tothe nonlinear features of batteries, computing systems with mul-tiple batteries cannot achieve the same battery efficiency as thosepowered by a monolithic battery of equal capacity. In this paper,we propose an algorithm aiming to maximize battery efficiencyglobally for the computer-assisted health-care systems with multi-ple batteries. Based on an accurate analytical battery model, theconcept of weighted battery fatigue degree is introduced and thenovel battery-scheduling algorithm called predicted weighted fa-tigue degree least first (PWFDLF) is developed. Besides, we alsodiscuss our attempts during search PWFDLF: a weighted round-robin (WRR) and a greedy algorithm achieving highest local bat-tery efficiency, which reduces to the sequential discharging policy.Evaluation results show that a considerable improvement in bat-tery efficiency can be obtained by PWFDLF under various batteryconfigurations and current profiles compared to conventional se-quential and WRR discharging policies.

Index Terms—Battery-scheduling policies, electronic textiles(e-textiles), health monitoring.

I. INTRODUCTION

E LECTRONIC technology has been following the Moore’slaw for several decades, resulting in the exponential growth

of speed, performance, and complexity in computation, commu-nication, and storage ability. Due to the advances in IC electron-ics, the weight of computing devices is becoming lighter and thesize is growing smaller. And interconnection technologies, espe-cially wireless communication and next-generation techniquesbased on IPV6 are another driving force to a new computationparadigm [1]. The vision of ambient intelligence (i.e., ubiqui-

Manuscript received December 26, 2008; revised July 6, 2009. First pub-lished November 3, 2009; current version published March 17, 2010. This workwas supported in part by the National Science Fund for Distinguished YoungScholars of China under Grant 60525202 and in part by a key Program of NaturalScience Foundation of China under Grant 60533040. The work of M. Lin andL. T. Yang was supported by the National Sciences and Engineering ResearchCouncil, Canada and Canada Foundation for Innovation.

N. Zheng and Z. Wu are with the College of Computer Science and Tech-nology, Zhejiang University, Hangzhou 310027, China (e-mail: [email protected]; [email protected]).

M. Lin and L. T. Yang are with the Department of Computer Science, St. Fran-cis Xavier University, Antigonish, NS B2G 2W5, Canada (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITB.2009.2034972

tous computing or pervasive computing) predicted by Weiserare being realized gradually. Tiny, low-cost, and power-efficientelectronic systems are attached to real objects in the ambientphysical environment, bringing us into a computerized physicalreal world [2]–[4]. Novel pervasive embedded computing sys-tems flush into our world that are digitally enhanced with littlechanges in their physical properties. For example, researchershave designed smart dust [5], uPart [6], media cup [7], and even,electronic textiles (e-textiles) [8]. In an ambient intelligent worldof the near future, clothes is designed for more functions thanwarm and fashion. The novel idea of integrating computationinto clothes brings us a new unobtrusive computing platform:fabrics are computers.

E-textiles are fabrics with computing nodes, flexible inter-connections, and power supplies woven into them. Fabrics aredigitally enhanced with the ability of sensing, computation, andcommunication. Researchers from several disciplines proposemany enabling techniques. New fibers are invented, used as sen-sors [9], [10], actuators [11], energy generators/storage [12],and textile patch antennas [13]. Ongoing miniaturization ofchips give permission to utilize off-the-shelf electronic mod-ules in manufacturing e-textiles. Meanwhile, communicationschemes, weaving machines, design methodologies, and per-formance evaluation methods are being explored by differentresearch groups [14]–[18]. Results and prototypes are reviewedin detail [8].

As an emerging computing platform for ambient intelli-gence, e-textiles providing an “invisible” computing mother-board for diverse applications, such as military, sports, publicsecurity/safety, even as an alternative platform for personal areanetwork or body area network [19], [20]. Of the many potentialapplications, health-care monitoring is the original function ofthe first e-textiles prototype developed by Georgia Tech [21].Based on the vision of “fabrics are computers”, various sensorscan be attached to collect behavioral and physiological signals(gesture, temperature, blood pressure, respiratory or heart rate,and ECG) for health-monitoring applications [22]–[24]. Exam-ples are a wearable ECG system [23], a full-body-motion cap-ture system [25], a smart jacket for an arctic environment [26],and a sensorized glove capable of detecting posture and move-ments of the fingers [27].

To build practical e-textile health-monitoring systems, theresearch community focuses on the design metrics includingcost-efficiency, durability, lifetime, and the properties of natu-ral textiles (hand feeling, etc.). Limited by the capacity of thebatteries, the utility of health-monitoring systems are directly

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ZHENG et al.: ENHANCING BATTERY EFFICIENCY FOR PERVASIVE HEALTH-MONITORING SYSTEMS BASED ON ELECTRONIC TEXTILES 351

impacted by the battery lifetime. Thus, similar to otherbattery-powered systems, the design considerations related tothe batteries play increasingly important role in developingsystems for future health-monitoring applications based one-textiles [28]. With the help of the new shapes and flexibil-ities of the novel batteries [12], multiple batteries will be usedwidely in e-textiles to increase the total capacity and provideusers more flexibility in the design metrics of weight, operationallifetime, and system reliability. A flexible power networks fore-textiles is proposed, which provides multiple candidate bat-teries to power-consuming nodes in the electric network forenhancing their fault-tolerance ability and extending the opera-tional lifetime [29].

However, it should be noted that a battery efficiency dropexists between the multiple batteries and the monolithic batteryof equal capacity. For example, with the same system config-uration, a battery of four-unit capacity will outperform fourbatteries of one unit capacity because of the nonlinear charac-teristics of the battery [30]. For ambient intelligent systems withmultiple batteries, we are challenged with the problem: do thereexist some battery management approaches which can extendthe ambient intelligent systems’ lifetime as long as possible? Inthis paper, we aim to answer this question and propose somebattery management policies to enhance the battery efficiencyfor pervasive embedded systems.

Some related works are proposed in previous publications[30], [31]. Benini et al. first introduce the concept of batteryscheduling and classified the existing battery-scheduling poli-cies into three classes. The most commonly used and basicpolicy is the sequential discharging. Batteries are connectedto the load in sequence. Once a battery is connected to theload, it remains connected until exhausted. The second battery-scheduling policy is static scheduling, where the batteries areconnected to the load by a round-robin (RR) scheme. The thirdtype of policy, dynamic-scheduling policy, selects a battery fromthe candidates based on specific battery information such as theoutput voltage, the residual capacity or the recovery time. Pro-portional current steering methods are proposed in [32] andcompared with the uniform current steering counterparts witha special battery converter. The authors formulated the staticbattery-scheduling problem as an optimization problem basedon the Peukert’s equation [33]. Their work outperforms the se-quential discharging with a large lifetime extension. In addition,the performance of the sequential, ideal parallel, fast-switched,and threshold discharging in the case of identical batteries arecompared and discussed in [31]. However, the research on bat-tery modeling shows that the Peukert’s law is not accurate inpredicting the nonlinear behavior of the battery [31]. Because ofthe limitation of the Peukert’s equation, the works proposed byBenini et al. were not able to consider the recovery effect on thecapacity lost due to the battery’s nonlinear behavior. Moreover,their work did not take into account the temporal sequence of thecurrents, treating variable loads as a set of current levels and thesum of their corresponding distribution time. In their scheme,an ideal battery switcher is necessary, so that the batteries canbe scheduled at a high frequency as if the current is split toevery battery in an optimized method according to the Peukert’slaw.

Research advances in modeling battery behaviors providemore accurate approaches to grasp the behavior of the batter-ies [34]–[36]. Our multibattery-scheduling algorithms are basedon an analytical battery model, which models the rate-capacityeffect and recovery effect sufficiently well [34]. Essentially, abattery-scheduling technique distributes the load among the bat-teries. All the battery discharging polices distribute slices of theload profiles in some order. Each policy has its own way ofdefining the size of the slices and the discharge order of thebatteries. In this paper, the effect of discharging slice on thebattery-scheduling policies is studied first. We use a weightedfactor to scale the slice of RR and get a battery-scheduling pol-icy, weighted RR (WRR). Then, we study the discharging orderand try to find an optimized policy by achieving local highestbattery efficiency predicted at each schedule instant, which, infact, is proved reducing to the sequential discharging. With thislook-ahead greedy policy, the battery closest to an ideal powersource is discharged first until it is exhausted. To prevent theideal batteries from being exhausted too early and enhance thebattery efficiency ratio globally, the concept of the weighted fa-tigue degree of batteries is defined and used as a cost function toschedule the batteries through a novel algorithm called predictedweighted fatigue degree least first (PWFDLF). Simulation ex-periments are performed to compare the different schedulingpolicies on series of constant current and time-varying cur-rent profiles of synthetic examples. Evaluation results showthat PWFDLF outperforms other polices with a considerableimprovement in battery efficiency. Consequently, PWFDLF isproposed as the solution for extending the lifetime of pervasiveembedded computing systems with multiple batteries.

The remainder of the paper is organized as follows. Section IIdiscusses the background of the accurate analytical batterymodel used in this paper. In Section III, the battery-schedulingalgorithms are described. Simulation results are presented inSection IV. Finally, Section V summarizes the contributions ofour work.

II. ANALYTICAL BATTERY MODEL

Batteries produce power energy by electrochemical reactionstaking place between the electrodes and the electroactive speciesin the electrolyte. The dynamics of the concentration gradient ofelectroatctive species at the electrode surfaces leads to the non-linear outer electrical characteristics of the battery [37], [38].This is the reason for the chemical energy stored in a battery notbeing able to be extracted to full extent (i.e., the ideal capac-ity). The analytical model proposed in [34] describes the majorelectrochemical principles of 1-D diffusion in the batteries withlow computational complexity, small number of parameters, andhigh accuracy. This model has simple analytical structure thatcan be used as a cost function when designing battery-awaretask-scheduling policies. The apparent capacity consumed bythe tasks can be calculated as follows:

C(t) = l(t) + u(t) (1)

l(t) =∫ t

0i(τ)dτ, u(t) = 2

+∞∑n=1

∫ t

0i(τ) · e−n2 β 2 (L−τ )dτ

(2)


where C(t) is the apparent lost capacity of the battery for theload profile i(t), the time function of the current drained bythe tasks running in the system. In the analytical structure men-tioned earlier, a battery is modeled by a parameter pair (α, β). αis the initial capacity of a battery. β is the parameter describingthe nonlinear characteristics responding for the rate-dependenteffect (i.e., higher discharging current leads to less output ca-pacity and more unavailable capacity in the battery). L is thecutoff time of a battery, denoting the instant when C(L) = α.That is, L is the time instance when the battery is exhausted.

Rao et al. [39] gave explanations to the two parts of the right-hand side in (1). The first part l(t) is the capacity consumed bythe external circuit, while the second part u(t) is the unavailablecharge during the discharge process due to the nonlinear featureof the battery itself. If the battery is not exhausted, the unavail-able capacity can be recovered to some extent (partly or totally)during the subsequent discharge time.

III. BATTERY-SCHEDULING ALGORITHMS

Recent research works show that a good battery-schedulingpolicy can help a given system to drain less capacity from themultiple batteries [40]. As mentioned in Section I, we searchthe solution for the problem of enhancing battery efficiency bytwo means.

1) Scaling the discharging slice by a weighted factor. WRR isproposed, utilizing the battery characteristics to enhancebattery efficiency over RR.

2) Determining an optimized battery discharging order. First,predicted battery efficiency maximum first (PBEMF) pro-duces the discharging order in a greedy way that achievesthe highest battery efficiency at each scheduling instant.As the proof given in Section III-B, it reduces to the worstcase, sequential battery discharging in the nonincreasingorder of the nonlinear parameter, β. Then, we considerthe load history, residual capacity, and battery nonlinearparameters in a new cost function, called weighted fatiguedegree to discharge the batteries for enhancing the batteryefficiency globally.

A. Weighted RR

The simplest RR discharging policy schedules each batteryfor an identical time slice [30]. After all survival batteries are dis-charged once, another discharging cycle restarts. The fixed dis-charging order is the reason why this kind of battery-schedulingtechnique is defined as “static scheduling”.

The drawback of RR policy is that it does not consider thebattery characteristics at all. We introduce the WRR policy,which takes the battery characteristic into account. The WRRstill uses the fixed discharging order and the fixed time slices.Different from RR, the fixed time slice for each battery is notidentical. Fig. 1 shows a discharging instance of the WRR policy.The discharging slices (i.e., S1, S2-S1, S3-S2, or S4-S3) arefixed in the different discharging cycle but may be of variouslengths, i.e., each slice has a fixed percentage in the dischargingcycle, which is regarded as the weighted factor.

According to (2), nonlinear parameters are quadratic in theexponent of u(t). We determine the weighted factor Wi for

Fig. 1. RR discharging techniques: weighted slices.

WRR policy, as shown in the following equation, where Si isdefined as the slice size for battery i in one discharging cycle,respectively

Wi =β2

i∑mi=1 β2

i

,

Si = Wi · Cycle = Wi · m · slice =β2

i∑mi=1 β2

i

· m · slice.

(3)

The fixed percentage of the slices distributed to a battery isdetermined by the ratio of the square of its nonlinear parametersto the quadratic sum of all the nonlinear parameters. The fixeddischarging slice Si for the battery i is set by multiplying thedischarging cycle with the weighted factor Wi .

B. Predicted Battery Efficiency Maximum First

In this section, we describe a battery-scheduling techniquethat does not follow a fixed discharge order by predicting thebattery discharge efficiency. Here, we base our work on thedefinition of battery efficiency proposed in [41], which measuresthe ability of a system to drain charge from a battery. Let µdenote the efficiency factor of a battery, and let I represent theoutput current required by the discharge circuits. If C0 is theactual capacity that can be used by the circuits and C is theideal/apparent battery capacity, then we have

C0 = C · µ. (4)

Referring to the illustration of the apparent capacity lost,C(t) in (1) and the actual capacity lost, l(t) in (2), the batteryefficiency at the instant t can be written as

µ(t) =l(t)C(t)

. (5)

As far as the multiple battery systems are concerned, our aim isto reduce the capacity lost, u(t), which is due to the nonlinearcharacteristics of the battery, as much as possible. Considersome time point tρ in the task profile. During the past dischargeperiod (0, tρ), the apparent capacity lost C(tρ) consists of thecapacity drained by the circuit l(tρ) and the unavailable capacitylost u(tρ).

l(tρ) =∫ tρ

0i(τ)dτ, u(tρ) = 2

+∞∑n=1

∫ tρ

0i(τ) · e−n2 β 2 (tρ −τ )dτ.

(6)


The derivative of u(tρ) with respect to β is always non-positive. That is, u(tρ) is monotonically decreasing with β. Thelarger the value of β is, the closer the battery is to an ideal powersource [42]. For a dynamic voltage scaling (DVS)-enabled pro-cessor, the current load i(t)|t∈(0,tρ ) is determined by DVS task-scheduling algorithms [36], [43]. The part of l(tρ) is equal forall batteries. The batteries with larger β are prior to be scheduledfor their lower u(tρ).

The unavailable capacity lost u(tρ) during (0, tρ) can be re-covered during the remaining battery lifetime according to thefollowing equation, which can be derived from (2).

u(t|t ≥ tρ) =+∞∑n=1

u(tρ) · e−n2 β 2 (t−tρ ) . (7)

Based on the exponential series of (7), the attenuate rate ofu(tρ) increases with the value of β. Batteries of larger β havethe ability to recover more capacity than the batteries of smallerβ do.

The first nonstatic battery-scheduling technique is calledPBEMF. Before selecting the battery candidate for poweringthe system, the algorithm predicts the battery efficiency ratioat the end instant of the next schedule slice for each battery.The battery with the highest predicted efficiency ratio will beselected and be connected to the load for being discharged. Thealgorithm aims to achieve the highest battery efficiency ratio in agreedy way. Recalling the previous discussion, the battery withthe largest β is the choice for discharging in the multiple sys-tems using PBEMF. This is obvious for systems with constantdischarging profiles.

In the case of variant current profiles, the function of batteryefficiency predicted for each scheduling slice is varied with thetime. It seems that the battery efficiency of a nonideal batteryincreases when the part of the capacity u(t) is attenuated in therecovery state or is increased slowly in the light-load discharg-ing state. With the PBEMF battery-scheduling policy, will thebatteries of smaller β be selected to replace the survival batter-ies of larger β for discharging? The answer is negative. Next,we prove that this greedy algorithm reduces to the sequentialdischarging in the nonincreasing order of β.

Proof: Suppose the current time point is ti , we first evaluatethe local battery efficiency ratio of the ith segment in the profilewith its interval [ti , ti + Ti ]. For the battery scheduling slice Ti ,the time function of the current load, i(t), can be divided intom constant current subsegments Iij for the correspondent sub-period [tij , ti(j+1)], where ti1 = ti and ti(m+1) = ti + Ti . Con-sider sub-segment Iij (1 ≤ j ≤ m) with its duration [tij , ti(j+1)]included in the period [ti , ti + Ti ]. The local battery efficiencyratio for the jth subsegment at instant t can be written as

µij (t)

=ti(j+1)− tij

ti(j+1)− tij+∑+∞

n=12

β 2 n2 [e−β 2 n2 (t−ti ( j + 1))− e−β 2 n2 (t−ti j) ].

(8)

Note that the battery efficiency ratio µij (t) for the jth subseg-ment is independent of its corresponding current Iij . Moreover,

the derivatives of the battery efficiency ratio with respect toeither β or t are nonnegative.

For the total segment [ti , ti + Ti ], the local battery efficiencyratio, can be evaluated as

µsegi =

∑mj=1 lij∑mj=1 Cij

=

∑mj=1 lij∑m

j=1 lij /µij. (9)

The numerator in (9) is given by the current segment and is equalfor each battery for the subsequent scheduling slice [ti , ti + Ti ],while the denominator is smaller for the batteries with larger β.Thus, the battery with the largest β has the highest local batteryefficiency ratio µsegi at the instant ti + Ti .

If the current slice is the first segment, the initial capacity ofthe battery is not influenced by any history discharging process,i.e., if ti = 0, the battery with the largest β will be selectedbecause it has the maximal µsegi .

On the other hand, if ti > 0, then there are i − 1 history dis-charging segments with duration intervals [tk , tk + Tk ], where1 ≤ k ≤ i − 1. During each interval [tk , tk + Tk ], the corre-sponding local battery efficiency is denoted as µsegk (Tk ) andcapacity drained by external circuits is denoted as Ik . Notethat the battery efficiency function µ(t) is monolithically in-creasing with respect to the time variant t. Since battery effi-ciency ratios of the history discharging slices further increasewith the time variant t, the earlier slices have the larger bat-tery efficiency ratio, i.e., at the instant ti + Ti , local batteryefficiency ratio for i − 1 segments have the following relation:µsegk (ti + Ti − tk ) > µsegi(Ti), 1 ≤ k ≤ i − 1.

Thus, we can evaluate the battery efficiency at the instant

µ(ti + Ti) =∑i

k=1 lk∑ik=1 Ck (ti + Ti)

=∑i

k=1 lk∑ik=1 lk /µsegk (ti + Ti − tk )

≥∑i

k=1 lk∑ik=1 lk /µsegi(Ti)

= µsegi(Ti). (10a)

Therefore, a battery with history discharging slices will havea ratio greater than those without any history discharging.

Consequently, the battery of the highest β will always achievethe best battery efficiency unless it is exhausted. After the bat-tery of highest β is exhausted, the battery with the next highestβ will be selected to power the system. Thus, the PBEMF al-gorithm performs the battery selection in the same way as thesequential discharging, in the nonincreasing order of the non-linear parameter β. �

C. Predicted Weighted Fatigue Degree Least First

The sequential discharging is usually the worst choice, be-cause once a battery is exhausted, the unavailable part cannot berecovered. Other policies can attenuate the unavailable capacitymore efficiently because the batteries are able to enter the recov-ery state before they are completely drained out. Consequently,sequential discharging or PBEMF policy leads to lower batteryefficiency for this reason. To overcome this disadvantage, wedevelop another novel battery-scheduling technique aiming to


keep all the batteries alive as late as possible, in order to havethe unavailable capacity recovered adequately. Furthermore, weadjust the discharging slice with a weighted factor for eachbattery according to their nonlinear parameter β. In other words,the slice Si for the battery i is scaled by a factor Wi as (3).

Definition 1: We define the fatigue degree (Fd(t)) of a batteryat a time instant t as the unavailable capacity u(t) divided by theapparent remaining capacity α − C(t), i.e., Fd(t) = u(t)/(α −C(t)).

Here, α is the initial apparent capacity of the battery andC(t) is the lost apparent capacity up to time instant t. Thefatigue degree can be regarded as a way of measuring how tireda battery is due to its load history. For batteries of the sameparameter β, the higher the fatigue degree, the heavier historyload the battery has been imposed on. In order to prevent thebatteries from being exhausted too early and allow the batteriesto recover, the scheduling policy keeps the fatigue degrees ofthe batteries as close as possible.

Definition 2: For a battery with the nonlinear parameter asβ, we define its weighted factor of the fatigue degree as anexponential expression e−β 2

.The weighted factor can be used to normalize the fatigue

degrees of the batteries with different nonlinear parameters.For a battery i at time instant t, the weighted fatigue degree iscalculated as follows:

WFdi(t) = e−β 2 · ui(t)αi − Ci(t)

. (11)

Next, we describe the PWFDLF battery-scheduling policy. Theweighted fatigue degree is used as the cost function. Beforeselecting the battery candidate for powering the system, the al-gorithm predicts the weighted fatigue degree of each batteryat the end instant of the next schedule slice. The policy se-lects the battery candidate with the smallest value of the costfunction. The pseudocode of PWFDLF is given by AlgorithmPWFDLF. Its input is the parameters of the batteries 〈αi, βi〉and the current profile i(t). BIP indicates the beginning instantof the task profile and EIP indicates the end instant of the taskprofile.Algorithm PWFDLFInput: Battery parameters table 〈αi, βi〉, Current function i(t),

BIP, EIPOutput: Battery discharging profile1. Calculate the slice(i) for each battery using Equation 3;2. while (current instant ≤ EIP) and (there exists at least a

nonexhausted battery)3. for i ← 1 to (the number of the batteries)4. if the current battery remains unexhausted

during this slice5. then Predict the weighted fatigue degree

at the end instant of the next schedu-ling slice;

6. Search the array of weighted fatigue degree (WFd)and select the battery with the least WFd value;

7. Update the battery discharging profile;8. Update current instant as the end time point of the

next scheduling slice;9. return battery discharging profile.

TABLE ICURRENT VALUES FOR THE REAL-LIFE TASKS RUNNING ON ITSY POCKET

COMPUTER [35]

In a single DVS processor system, at most one task is run-ning on the processor. With the load current function i(t), thebattery-scheduling policy first evaluates the cost function of allthe batteries at the end instant of the subsequent time slice. Ifthe battery of the lowest cost function output survives the nextschedule slice, it is selected and connected to the load for aweighted slice. Otherwise, the battery of next least weighted fa-tigue degree, which can survive this scheduling slice, is selectedas the power provider. Once all batteries cannot run through theirsubsequent weighted slice, the sequential discharging policy, ifnecessary, is used to drain all the capacity left in the batteries.

IV. EXPERIMENTAL RESULTS

To validate the effectiveness of PWFDLF, we compare thebattery efficiency (defined in (4) and (5)) of different algorithmsunder various types of profiles and battery configurations.

A. Experiment Settings

1) Current Profiles: We will test two kinds of currentprofiles.

1) Load type I: Constant/square-wave current load profiles,denoted as CL(I , R, L/P ), where I is the current value,R is the percentage of I (i.e., duty cycle), and L/P is thelength/period of the load. When R = 1, the load of theconstant current load is I with the length of L. Otherwise,the load is a square-wave consisting of two levels, I and0, where R is the percentage of I in the period P .

2) Load type II: Load profiles with real-life tasks whose pa-rameters are sampled from the ITSY pocket computer[35]. The current values of the seven real-life tasks arelisted in Table I. The load profiles are composed of loadsof the real-life tasks and are derived from random taskgraphs by a battery-aware DVS algorithm [36]. We de-note the loads as RL(P ), where P is the period of theloads.

2) Battery Configurations: The batteries are simulated us-ing a highly accurate analytical model proposed in [34]. Eachbattery is specified by its initial apparent capacity α and thenonlinear parameter β. During the discharge period, once itsapparent capacity is lower than zero, the battery is cutoff andis no longer able to be selected by the battery schedulingalgorithm.

Four batteries modeled with (1) and (2) are used in our ex-periments. The battery configurations (BCs) are classified intofour categories.

1) BC1: all four batteries are the same.2) BC2: batteries have the same α but different β.3) BC3: batteries have the same β but different α.4) BC4: batteries have different α and different β.The detailed configuration is specified in Table II [44]. For

each combination of the battery configurations and the profiles,


TABLE IIBATTERY CONFIGURATIONS

Fig. 2. Effect of Battery Schedule Slice on Battery Efficiency: CL(400, 1,400).

the sequential, WRR, PBEMF, PWFDLF, and Benini’s methodare evaluated for comparison.

3) Battery Schedule Slice: To explore the role that the bat-tery schedule slice plays, we have designed an experiment thatruns the algorithms of sequential discharging and PWFDLF withdifferent scheduling slices. The load current is 400 mA, and thelength of the load profile is 400 min. Our experimental resultsare consistent with the research results of [30] and [31]. It isfound that shorter slice brings an even larger improvement ofbattery efficiency. Rao et al. used a frequency domain modelto analyze the frequency response of a battery and concludedthat the improvement of efficiency is only significant for batteryoptimization techniques of the order of 10 ms to 28 min (or1000 s) [39]. In Fig. 3, the shortest slice is 0.01 min (i.e., 0.6 s)at which the battery efficiency increase of PWFDLF versus se-quential discharging is 30.13%. However, with a schedule sliceof 30 min, the battery efficiency improvement is only 2.18%.Also note that there are many saw tooth patterns in the Fig. 2(a).The amplitude of the curve vibration increases with the battery-scheduling-slice value. The reason for this is that the dischargingorder of the batteries affects the battery efficiency more whenthe discharge slice becomes larger. Fig. 2(b) demonstrates thedischarging profiles of three slices. Comparing the case of the29.5 min slice and the 29.7 min slice, we can find that the blue

Fig. 3. Effect of parameters on battery efficiency. (a) Period P . (b) Loadcurrent I . (c) Duty cycle R.

curve is almost overlapped by the red one. All the four batteriessurvive in the two discharging cycles and recover some quantityof unavailable capacity [the specific value can be calculated by(7)] to accommodate the next discharging cycle. In our exper-iment, the discharging processes of the 29.5 min and 29.7 minslice terminate at 283.1 min and 283.8 min respectively. Theblack profile of the 30.0 slice is terminates at 247.6 min for thebatteries are exhausted in the second discharging cycle.

The load current and the profile length are arbitrary and ex-periments of other pairs of load current and load length producethe similar tendency of the battery improvement versus scheduleslice. In the following experiments, the scheduling slice is setas 0.1 min.

4) Period P : To explore the effect of period on the batteryefficiency improvements, we also test loads with different peri-ods P (from 10 to 100, step 10), BC4, I = 400 mA and R = 0.3.As shown in Fig. 3(a), the maximum/average improvements ofPWFDLF over sequential and Benini’s method are 19.16/16.53and 17.62/8.62, respectively. It is shown that the improvement ofPWFDLF versus Benini’s method decreases with the increase inP , while that of PWFDLF versus sequential stays at the neigh-borhood of 16.53. In the following experiments, P is set as30 min.

5) Current I: We also tested loads of different current valuesfrom 300 to 800 mA with the step of 100 mA. The other param-eters are BC4, R = 0.55 and P = 50 min. The battery efficiencyimprovements of PWFDLF over sequential and Benini’s methodare illustrated in Fig. 3(b). The maximum/average improve-ments are 18.47/13.55 and 15.65/4.15, respectively. Roughly, itcan be accepted that the improvement increases with the cur-rent loads I . In the following experiments, we use 400 mA and600 mA as the current values.

6) Duty Cycle R: Experiments are conducted for comparingbattery efficiency improvements of PWFDLF versus sequential/


TABLE IIIBATTERY EFFICIENCY VALUES FOR BC1 WITH THE CONSTANT CURRENT

400 MA

Benini’s method with different duty cycles R (from 0.1 to 0.9,step 0.1), BC4, I = 400 mA, and P = 50 min. The maximumand average improvements of PWFDLF over sequential andBenini’s method are 19.54/14.80 and 19.35/5.29, respectively,as shown in Fig. 3(c). In general, the improvements decreasewith the increase in R. In the following experiment, R is set as0.4, near the middle position of its range [0, 1].

B. Load Type I

We conduct experiments with constant current loads first. Theconstant load is applied to the first type of battery configuration(BC1) where the four batteries have the same apparent capacity,40 375 mA·min and nonlinear parameter β, 0.273. Table IIIlists the results for the constant current of 400 mA with BC1.WRR, PWFDLF policies, and Benini’s method achieve betterbattery efficiency than sequential discharging and PBEMF do.Since the batteries have the same nonlinear parameters, WRRand PWFDLF policies have the same scheduling slice for eachbattery. Because all four batteries have the same nonlinear pa-rameter, the accumulating and attenuating rates of the unavail-able capacity are the same for the five approaches even thoughthe discharging orders of the PWFDLF, sequential, weightedRR are different. Only the operational lifetime can affect thebattery efficiency. Since the four batteries are all “alive,” thebattery efficiency of WRR, PWFDLF, and Benini’s method atCL(400, 50) are all 54.98%. After 59.5 min, a battery is ex-hausted in the case of sequential and PBEMF discharging. Con-sequently, it is observed that the battery efficiency of sequentialand PBEMF approaches is inferior to the three counterpart po-lices after 59.5 min. It also can be noted that for a light load thatdoes not result in any exhausted battery, the battery efficiencyresults are the same for the five discharging polices. For a heavyload, since sequential and PBEMF discharging the batteries oneby one, the battery exhausted earlier in the two policies will pulldown the battery efficiency of the four batteries.

With BC2, BC3, and BC4, the battery efficiency are illus-trated in Fig. 4 for various period P and cycle duty R, and themaximum/average battery efficiency improvements of PWFLFover sequential, WRR, and Benini’s method are tabulated inTables IV and V. It can be noted that the variability of β canresult in larger improvements, for example, with BC2. Underequal conditions, Benini’s method is superior to WRR as it usesthe nonlinear optimization function to split the loads. Besides,Benini’s method also has some outliers, such as Fig. 4(d) (R =0.1), (e) (P = 5 min), and (f) (R = 0.1), where it performs evenworse than the base point of the sequential policy. This phe-nomenon can be attributable to the computational error, whichwe will discuss in Section IV-D. And this method also has veryslow convergence rate.

C. Load Type II

In this section, we demonstrate the experiments conductedwith real-life loads. The currents of the seven kinds of real-lifetasks running on ITSY pocket computers are tabulated in Table I.In this experiment, we consider a random task graph whichconsists of eight tasks listed in Table VI and their dependencyis shown Fig. 5.

Table VII collects the experimental results for BC1. With thenonlinear parameter, 0.273, the sum of unavailable capacity forWRR and PWFDLF policy are the same when all four batteriesare still alive. Although the battery discharging schedule ofsequential/PBEMF, WRR, PWFDLF, and Benini’s method aredifferent from each other, the battery efficiency results of the fivepolicies are same at every time point before 569 min. At 569 min,battery I is exhausted by sequential/PBEMF policy, resulting inthe lost of the “unavailable” part that can be recovered fromu1(569) in the subsequent profile. We can observe that after569 min, the battery efficiency of sequential/PBEMF is lowerthan those of WRR, PWFDLF, and Benini’s method at each timepoint.

Fig. 6 shows the battery efficiency values of BC2, BC3, andBC4 with variable period P . Compared with the situations ofload type I, the improvement of PWFDLF over other policiesdecreases (see Table VIII). There are three major reasons. First,the duty cycle of load type II is 1, larger than those in load type I.Second, the period of load type II ranges from 10 to 100, whichis larger than those of load type II. Third, the average currentload of RL(1, *) here is only 72.1 mA. Even with the idealcurrent-splitting device and optimized ratio, Benini’s methodperforms slightly better than the WRR. The maximum/averageimprovements of Benini’s method over WRR is 4.87/0.104,5.13/0.41, and−1.48/−7.73 for the three battery configurations.Compared with the WRR policy, the battery improvements ofBenini’s method is not remarkable. Especially, when the nonlin-ear parameters of the batteries vary considerably such as BC4,Benini’s method is inferior to WRR. And, it should be notedthat in the case of BC4, the difference between the results ofPWFDLF and WRR is trivial. It is shown that using weightedfactor to scale the discharging slice can distribute the load tobatteries in so fair a way to optimize the lifetime in the situationof light load and batteries of great difference.

D. Discussion

Benini’s method is characterized by its ideal current-splittingapproach, which can be used as a static battery-schedulingmethod. Thus, the computation complexity is zero in runtimeand the space complexity is the memory used for storing thecurrent load profiles. When the duty cycle is 1 and the numberof batteries is not larger than three, this method achieves highbattery efficiency by discharging the batteries in a way such thatthe lifetime of all the batteries are equal. However, it has threelimitations. First, the percentage of the load currents should beknown a priori. Second, when the number of batteries is largerthan or equal to 4, the convergence rate is slow. For exam-ple, in our experiments, it takes several weeks using MATLABfor computation using Benini’s method. Third, it is based onPeurkert’s model. This model uses only one exponent item to


Fig. 4. Comparison of Battery Efficiency: BC2-4 and CL(600, R, P ). (a) BC2, CL(600, 0.4, P(5:5:50)). (b) BC2, CL(600, R(0.1:0.1:0.9), 30). (c) BC3, CL(600,0.4, P(5:5:50)). (d) BC3, CL(600, R(0.1:0.1:0.9), 30). (e) BC4, CL(600, 0.4, P(5:5:50)). (f) BC4, CL(600, R(0.1:0.1:0.9), 30).

TABLE IVIMPROVEMENTS OF PWFDLF VERSUS OTHER FOUR ALGORITHMS: CL(600,

0.4, P(5:5:50))

TABLE VIMPROVEMENTS OF PWFDLF VERSUS OTHER FOUR ALGORITHMS: CL(600,

R(0.1:0.1:0.9), 30)

simulate the nonlinear behavior of a battery, which leads to highcomputation errors of Benini’s method.

PWFDLF also aims to discharge the batteries in a way thatall the batteries have the same lifetime. It only requires the inputof the current value in the forthcoming slice, not the compo-nents and percentages of the whole load. According to (7), thecapacity lost can be calculated with the ten items from n = 1 to10 [34]. Thus, for each battery in the system, α, β, l(t), and tenitems of u(n, tρ)1≤n≤10 should be stored. The additional com-putation is eleven multiply operations and ten sum operations

TABLE VITASK SET OF REAL-LIFE LOAD

Fig. 5. Dependency relations between the real-life tasks.

TABLE VIIBATTERY EFFICIENCY VALUES FOR BC1 WITH REAL-LIFE LOADS


Fig. 6. Comparison of battery efficiency: BC2-4 and RL(P(10:10:100)).(a) BC2, RL(P(10:10:100)). (b) BC3, RL(P(10:10:100)). (c) BC4, RL(P(10:10:100)).

TABLE VIIIIMPROVEMENTS OF PWFDLF VERSUS OTHER FOUR ALGORITHMS:

RL(P(10:10:100))

for each battery. Both the computational complexity and spacecomplexity are O(m), where m is the number of batteries. Sincethe number of batteries in a system is limited and is usually nota big number, the overhead incurred by PWFDLF is not muchbigger than that of WRR.

Since the batteries are scheduled in a fixed order and slices,sequential and WRR policies requires no extra computationoperation for battery selection. The latter needs additional spacefor storing the nonlinear parameter of each battery. The spacecomplexity of WRR is O(m), while that of sequential policy iszero.

V. CONCLUSION

For future health-monitoring systems based on e-textiles, bat-tery management technique is of increasing importance. In thispaper, several multibattery-discharging-scheduling techniques

for enhancing the battery efficiency are presented to prolongthe system lifetime. WRR discharging policy scales the dis-charging slice with a battery-aware factor and PWFDLF usesthe weighted fatigue degree of the batteries as a cost functionto schedule the batteries. To compare and evaluate differentscheduling policies, experiments are conducted to simulate thedischarging behavior of different battery configurations. The re-sults show that considerable improvement in battery efficiencyis yielded by PWFDLF over other scheduling policies for var-ious battery configurations and current profiles. We have alsoproved that the battery efficiency greedy discharging algorithmreduces to the sequential policy for the nonlinear characteristicsof the battery.

This work can be extended in two ways: 1) extend the algo-rithms to multiprocessor systems by distributing subcurrent atdifferent processors to different batteries, and 2) develop dy-namic battery management with online DVS scheduling andbattery sequencing.

ACKNOWLEDGMENT

The authors greatly appreciate the reviewers’ insightful sug-gestions and comments for improving the quality of this paper.Also, the authors would like to thank Dr. D. Zhu and Dr. H.Aydin for their valuable comments.

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Nenggan Zheng received the B.Sc. degree inbiomedical engineering from Zhejiang University,Hangzhou, China, in 2002, and the Ph.D. degree fromthe College of Computer Science and Technology,Zhejiang University, in 2009.

He is currently with the Academy for AdvancedStudies (QAAS), Zhejiang University. His current re-search interests include real-time systems, wearablecomputing, and brain-computer interface.

Zhaohui Wu (SM’05) received the Ph.D. de-gree in computer science from Zhejiang University,Hangzhou, China, in 1993.

From 1991 to 1993, he was engaged in research onknowledge representation and expert system with theGerman Research Center for Artificial Intelligence(DFKI). He is currently a Professor of computer sci-ence with Zhejiang University, where he is also theDirector of the Institute of Computer System andArchitecture. His current research interests includeintelligent transport systems, distributed artificial in-

telligence, semantic grid, and ubiquitous embedded systems. He has authoredor coauthored four books and more than 100 refereed papers.

Dr. Wu is a Standing Council Member of China Computer Federation (CCF).Since June 2005, he has been the Vice Chair of the CCF Pervasive ComputingCommittee. He is a member of the Editorial Boards of several journals and wasa Program Committee member for various international conferences.

Man Lin (M’08) received the B.E. degree in com-puter science and technology from Tsinghua Univer-sity, Beijing, China, 1994, the Lic. and Ph.D. degreesfrom the Department of Computer Science and Infor-mation, Linkopings University, Linkoping, Sweden,in 1997 and 2000, respectively.

She is currently an Associate Professor of com-puter science with St. Francis Xavier University,Antigonish, NS, Canada. Her current research inter-ests include real-time and embedded system designand analysis, scheduling, power aware computing,

and optimization algorithms.

Laurence Tianruo Yang (M’98) is currently withthe Department of Math and Computer Science, StFrancis Xavier University, Antigonish, NS, Canada.

His current research interests include high-performance computing and networking, embed-ded systems, ubiquitous/pervasive computing andintelligence.

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Enhancing Battery Efficiency for Pervasive Health-Monitoring Systems Based on Electronic Textiles