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Sensors and Actuators A 161 (2010) 278287

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

j ou rna l homepage : www.e l sev i e r. com/ loca t e / sna

Fluid level measurement in dynamic environments using a single ultrasonicsensor and Support Vector Machine (SVM)

Jenny Terzic a,, C.R. Nagarajah b ,1 , Muhammad Alamgir a, 2a Delphi Corporation, 86 Fairbank Road, Clayton Sth, VIC 3169, Melbourne, Australiab Swinburne University, Burwood Hwy, Hawthorn, VIC 3122, Melbourne, Australia

a r t i c l e i n f o

Article history:Received 13 August 2009Received in revised form 19 March 2010Accepted 11 May 2010Available online 1 June 2010

Keywords:Intelligent level measurementLiquid sloshRadial Basis FunctionSupport Vector Machine

a b s t r a c t

A uid level measurement systemto accuratelydetermine uid levelsin dynamic environments hasbeendescribed. The measurement system is based on a single ultrasonic sensor and Support Vector Machine(SVM) basedsignal processingand classicationscheme. For exemplication of the measurementsystemin dynamic environments, the novel measurement system is experimented and veried on a fuel tank of a runningvehicle. Theeffects of slosh and temperature variations on the acoustic sensor based measure-ment system are reduced using the novel approach. The novel approach is based on -SVM classicationmethod with the Radial Basis Function (RBF) to compensate for the measurement error induced by thesloshing effects in the tank due to the motion of the moving vehicle. In this approach, raw sensor sig-nals are differentiated after smoothing with some selected pre-processing lters, namely, Moving Mean,Moving Median, and Wavelet lter. The derivative signal is then transformed into Frequency Domain toreduce the size of input features before performing the signal classication with SVM. Field trials wereperformedon actual vehicle under normal driving conditions at various fuel volumes ranging from 5 L to50 L to acquire sample data from the ultrasonic sensor for the training of SVM model. Further drive trialswere conducted to obtain data to verify the SVM results. A comparison of the accuracy of the predicteduid level obtained using SVM and the pre-processing lters is provided. It is demonstrated that the -SVM model using the RBF kernel function and the Moving Median lter has produced the most accurate

outcome compared with the other signal ltration methods in terms of uid level measurement. 2010 Elsevier B.V. All rights reserved.

1. Introduction

Modern automotive vehicles are equipped with digital gaugesas well as with additional functionalities that inform drivers abouttheir vehicles fuel consumption and the remaining distance thatthe vehicle can travel without refueling. However, the high preci-siondigitaldisplaysand these additional utilitieshave to relyon theaccuracy of the level sensoritself. Thereliabilityand accuracyof theuid level measurement system in a dynamic environment, whichprimarily depends on the level sensor, is increasingly becoming aconcern for automotive industries as well as the everyday vehicleuser.

Conventional uid level measurement systems determine theuid level with the use of oat that is linked with a variableresistorwhose resistance is a functionof theuid level. These conventional

Corresponding author. Tel.: +61 3 9239 2148; fax: +61 3 9551 8764.E-mail addresses: [email protected] (J. Terzic), [email protected]

(C.R. Nagarajah), [email protected] (M. Alamgir).1 Tel.: +61 3 9214 8530.2 Tel.: +61 4 2301 7656.

mechanical level sensors need to occupy a large space and sufferfrom the frictional wear-out over a period of time [1] . The impor-tance of level sensor reliability in hostile environments over longperiods of time has lead to the introduction of various forms of motionless level sensors. Ultrasonic devices can be used in con-tainers with pressures up to 2 mega Pascal (MPa), temperatures upto100 C, anddepths upto 30m, with anaccuracy of approximately2% [2] . The ultrasonic sensor is one such example of a compact aswell as contact-less proximity sensor that is being investigated todetermine the uid level in automotive fuel tanks. The ultrasonicsensor determines the uid level by transmitting echo pulses andmeasuring the return time of the reected echoes. If the speed of soundin the mediumis knownthenthe uid level can be calculatedusing the following equation:

level = levelref 12

v (1)

where level ref is the height of the tank, v is the speed of the soundand is the time-of-ight of the ultrasonic echo ( Fig. 1).

However,the speedof soundis inuencedby the temperature of the medium through which it travels [3] . Therefore, changes in theambient temperature will create incorrect uid level readings. The

0924-4247/$ see front matter 2010 Elsevier B.V. All rights reserved.

doi: 10.1016/j.sna.2010.05.005
http://dx.doi.org/10.1016/j.sna.2010.05.005http://dx.doi.org/10.1016/j.sna.2010.05.005http://www.sciencedirect.com/science/journal/09244247http://www.elsevier.com/locate/snamailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.sna.2010.05.005http://dx.doi.org/10.1016/j.sna.2010.05.005mailto:[email protected]:[email protected]:[email protected]://www.elsevier.com/locate/snahttp://www.sciencedirect.com/science/journal/09244247http://dx.doi.org/10.1016/j.sna.2010.05.005


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J. Terzic et al. / Sensors and Actuators A 161 (2010) 278287 279

Fig. 1. Fluid level measurement using ultrasonic transducer.

speed of sound in air canbe approximated in terms of temperatureas [4] :

v (T ) = 331 .3 + kT m/s (2)

where T is the ambient temperature in C, k is the rate at which thespeed changes with respect to the temperature, which is approxi-mately 0.607m/s at every change of 1 C in temperature.

Ultrasonic sensors are normally combined with a temperaturesensor to compensate for the effects of temperature variations[58] . Apart from the accuracy of the level sensor itself, the uidlevel measurement system in dynamic environments, such as inautomotive fuel tanks, is inuenced by the sloshing effects causedby acceleration. In automotive fuel tanks, vehicle accelerationinduces slosh waves having natural frequencies whose wave pat-tern is dependent on the magnitude of the acceleration, geometryof the tank and the amount of uid contained in the tank [9] . Theo-retical studies and numerical analysis have been carried out in thepast to describe various sloshing phenomena [1015] .

To compensate for the effects of sloshing in uid level measure-ment systems, various mechanical dampening methods consistingof bafes, electrical dampening techniques, and statistical aver-aging methods have been used in the past. However, all thesemethods follow approaches that lead to higher production cost.

The accuracy of these measurement systems under sloshing con-ditions is also very limited. The electrical dampening techniquesand the statistical averaging methods primarily perform averag-ing on the raw sensor signals over some period of time. Averagingover a variable time frame has also been used in the past [1618]to improve the level sensor accuracy under sloshing conditionsby determining the running state of the vehicle using the vehiclespeed data from the speed sensor. The uid measurement systemsdescribed by Kobayashi and Kita [17] employ a vehicle speed sen-sor to determine the running state of the vehicle. When the vehicleis operating at low speed (i.e. near static condition), the averagingperiod is reduced to small values typically in the range from 5 to25 s, and when the vehicle is operating at a higher speed, the aver-aging period is prolonged up to 90 s. Despite the dependence of

the measurement system on the speed sensor, after analyzing theraw sensor data from a resistive type fuel level sensor in a movingvehicle, it can be observed that the averaging method still pro-duces signicant errors after averaging the raw sensor signal overa longer period of time. Fig. 2 illustrates the raw volume signalobtained from a driven vehicle, and two averaged signals calcu-lated after averaging the raw signal over 20 s, which is the typicalaveraging time used in an automotive instrument cluster; and thesecond curve is the averaged signal averaged over 90 s, which is areasonably long period of time.

Support Vector Machine (SVM) is a newly developed machinelearning algorithm [19] . SVM is based on Statistical Learning The-ory and has the ability to recognise patterns [20] . SVM representsnovel learning techniques in the framework of structural risk mini-mization(SRM)andin thetheoryof VapnikChervonenkis [21] (VC)bounds [2224] . SVM has been successfully used in various appli-cations for solving classication, regression, time series predictionand function estimation problems [25] . SVM has quickly found itsplace in many applications of pattern recognition such as hand-writtencharacterrecognition [26] , image classication [20,27] , f acedetection [28] and signal processing [29] .

Additionally,priorto classifying thesensorsignalswithSVM,thesystem approach described in this paper performs signal ltrationon the raw sensor signals. Three signal lters have been investi-gated through experimentation. These investigated lters consistof Moving Mean, Moving Median, and Wavelet lters. These ltersprovide the following enhancements [30] :

these lters remove impulse noise, these lters smooth the signal, they can be taken over a wider interval so that the lter removes

transients longer than a time instant in duration, and these lters preserve sharp edges of the signal curve.

SVM can also be used to predict the uid level in a dynamicenvironment, especially considering the variations in tempera-ture and the vehicle movement creating slosh waves. This paperdescribes an SVM approach developed to determine the uid levelwithin a dynamic environment without compromising accuracy.The approach described here is also applicable to non-acousticsensors such as capacitive andHall-effect sensors. The existing sta-tistical sloshcompensationmethods are comparedwiththe resultsobtained using the SVM approach.

2. SVM based measurement system

2.1. Concise overview of SVM

The Support Vector Machines (SVMs) construct a system modelusing a set of given training samples for the classication and

Fig. 2. Fuel level signal observed by the level sensor and the calculated average signal in a sample drive trial.


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Fig. 3. Classication of a set of two-class data using hyperplanes.

prediction of the output based on the training samples and inputsamples. The basic idea behind the SVM is to create a distinctionbetween two or more data classes. In principle, SVM constructs ahyperplane between two classes of data and then optimizes theseparation distance between the two classes to provided optimalclassication. For a given datapoints D containing N numberof datapoints such that:

D = (x1 , y 1 ), (x2 , y 2 ), . . . , (xN , y N ) |x i d , y i 1 , + 1N i= 1

(3)

where x i is the feature vector containing d number of features ( d-dimensional), yi is the corresponding class of x i or expected outputvalue. For example, Class A can be assigned the value of yi as 1and Class B as +1. SVM classies the above mentioned data pointsfor the two-class solution (Class A and B) by rst plotting the datapoints D into the feature space. Then, SVM constructs a hyperplanethat separates the data points of one class (i.e. Class A) from otherclass (i.e. Class B).

Fig. 3 shows an illustration of SVM based pattern classicationbetween two classes of data using three hyperplanes (H 1 , H2 , H3 ).There areinnitenumber of ways to createa hyperplane. However,the goal in SVM is to create an optimal hyperplane that creates thebest distinction line between the two classes of data. In Fig. 3, H1does not separate the two classes of data in any way, whereas, H 2and H 3 do separate the two groups of data. However, H 3 providesthe best separation between the two class when compared withH2 . Any hyperplane can be described as set of points x satisfying:

w x b = 0 (4)

where vector w is a normalvector perpendicular to the hyperplane

and b is the bias value of the hyperplane. The offset of the hyper-plane from the origin along the normal vector w can be describedby parameter b/ w .

The goal in SVM is to maximize the margin or separationbetween the two classes of data as far apart as possible while stillseparating the two groups of data. Maximum-margin hyperplanescan be described by the following equations ( Fig. 4):

w x b = 1 (Class A) (5)

w x b = + 1 (Class B) (6)

Hence, eachdata point inbothclasseshas to satisfy thefollowingconditions:

w xi

b 1 for Class A (7)

Fig. 4. Maximum-margin hyperplane between two classes of data.

or

w x b + 1 for Class B (8)

For the optimal SVM classicationsolution, a maximum-marginhyperplane is solved using the mathematical programming solu-tion by minimizing w and b parameters. The optimization can beexpressed in terms of Lagrange multipliers i as [22] :

minw ,b,

12

||w|| 2 N

i= 1

i [yi(w x i b) 1] (9)

This problem can now be solved using any standard quadraticprogramming method. The solutions for w and b can be expressedin the following forms [22] :

w =N

i= 1

iyix i (10)

b =1

N SV

N SV

i= 1

(w x i yi) (11)

where vector x i is the support vector points that lie exactly on themargin hyperplanes, and N SV is the total number of support vectors(SV).

The -Support Vector Machine ( -SVM) [31] is an improvedform of the soft-margin SVM that is also known as C -SVM [32,23] .The -SVM [31] includes two additional cost factors and [33] .The role of these two additional parameters is to improve the clas-sication accuracy. The optimization problem for -SVM can beexpressed as [31,32] :

minw ,b, ,

12

||w|| 2 +1N

N

i= 1i (12)

Subject to

yi((w x i) + b) i, i = 1, 2 , . . . , N ;i 0; and 0

where , , and are tolerance and cost factors that improve

the accuracy of the classication system. The above optimization


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Fig. 5. Mapping of nonlinearly separable data sets into higher dimensional featurespace.

problem can be expressed in the dual form using the Lagrangemultipliers ( , ) as [32] :

L(w , ,b, ,,, ) =12

|| w || 2 +1N

N

i= 1i

N

i= 1

( i(yi(w x i + b) + i) + i i )

(13)

Some variants of the -SVM have been described in Refs.[3436] . The description of the SVM classicationand optimizationprovided so far was related to linearly separable or non-separabledata sets only. In many real-life applications, the data set maynot be linearly separable, especial due to the effects of measure-ment errors and noise [37] . To accurately classify data sets thatare nonlinear, the training data sets are mapped onto higher (orinnite) dimensional space called feature space (Hilbert Space orInner ProductSpace). The intuitionof mappingdatasets intohigherdimensional space is that data can be clearly separated and hencebetter classied in higher dimensional space as illustrated in Fig. 5.

SVM optimization for the data sets that are not linearly separa-blecan be carried outsimply bymappingeach feature vector x witha mapping function such that x (x ) and then carrying out theSVM optimization described earlier [38] . For a set of training sam-ples T = {(x1 ,y1 ), (x2 ,y2 ), . . . , (xn ,yn ) }, where x is an d-dimensionalfeature vector, the mapping of the training data set T is expressedin the feature space as:

(T ) = { ( (x 1 ), y 1 ), ( (x 2 ), y 2 ), . . . , ( (x n ), y n )} (14)

Hence, the decision function D(xk ) for the prediction of the out-put can be given as [37] :

D(x k )= sign[ w (x k ) + b] = signn

i= 1

iyi (x i) (x k ) + b (15)

A famous Radial Basis Function (RBF) Kernel function can beexpressed as [39] :

(x i, x j) = exp( || x i x j || 2 ), > 0 (16)

2.2. SVM classication and measurement system

The observation and analysis of the slosh pattern, producedunder theeffects of acceleration in a closedcontainer, instigatedanapproach that can eliminate the sloshing effects, whereby accurateuid level measurements would be possible in dynamic environ-ments. If theuid quantity in a storage containerremains constant,the instantaneous uid level, L(t ), in a dynamic environmentcan bedened as:

L(t ) = L0

f (17)

Fig. 6. Relationship between the (a) observed level sensor signal and (b) vehicleacceleration.

where L0 is the tank level at still, and f is the unknown sloshingfunction that depends on the acceleration effects exhibited on thetank, the existing uid level, and the tank geometry. The goal isfocused on determining the actual level L0 using the sensor outputL(t ) and the function f . The output of the level sensor was observed(Fig. 6) to have direct relationship with the vehicle acceleration,when the vehicle was driven under normal driving conditions.

Afterobservingthe relationship between the acceleration of thevehicle and the output signal L(t ) from the level sensor, the effectsof slosh can be minimized by predicting the slosh wave once thesloshing function f has been determined. Assuming the amount of uid in the storage tank to be constant, the actual fuel level L0 inthe storage tank under the effects of sloshing can be given as:

L0 = L(t )f = constant (18)

The unknown function f is solved by experimentation with theaid of the SVM based approach. An SVM model was constructedand trained with the actual driving data obtained through severaleld trials. Fig. 7 demonstrates the method adopted to develop anaccurate uid level measurement system.

For the ultrasonic transducer mounted at a height level ref on topof the tank, the instantaneous output of the ultrasonic level sensorat time t and temperature T can be calculated as:

Level(t, T ) = levelref (t )2

v (T ) (19)

where (t ) is the time-of-ight at instant t of the ultrasonic echo,

and v (T ) is the speed of ultrasonic echo at temperature T . Theexpression v (T ) can be obtained using Eq. (2) .

Fig. 7. Block diagram of the proposed system.


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In a dynamic environment, the term (t ) will exhibit variationthat reects an inverted image of the slosh wave produced in theliquidtank.Theterm (t ) willbe invertedsince theultrasonicsensoris facing downmeasuring time-of-ightof ultrasonicecho fromthetopof thetank. Expression / t describesthe change inuidlevelover time.In a dynamicenvironment / t willexhibit the uctu-ation of uid surface (slosh), however during static conditions, theexpression / t will be equal to zero. Fig. 8 shows the variationin (t ) and the actual slosh wave produced in the liquid tank.

The ultrasonic level sensor signal, denoted as s(t ), is typically avoltage signal in the range of 0.54.5 V, which represents the min-imum and maximum of the level range, respectively. The sensorsignal s(t ) is sampled at 100 Hz. The sampled signal is accumu-lated in a -second window frame ( wi). After collecting the sensordata over seconds, the second data is ltered using the threeinvestigated lters: Moving Mean, Moving Median and WaveletTransform. Then the signal features are extracted using the famousFast Fourier Transform (FFT) based feature extraction method. Thecoefcients ( coef ) obtained from the FFT based feature extractionfunction,the medianvalue ( med )ofthe -second ultrasonic sensorsignal, and the temperature readings T are all contained in a vectorforming input features for the SVM model. The median value of theraw signal describes the middle (bias) factor of the slosh wave andhence was decisively added into the input feature vector. The SVMinput vector x i can be represented as:

x i = { coef 1 ,coef 2 , . . . ,coef n ,med,T } (4.4)

Signal classication is performed using the -SVM signal clas-sication technique having the Radial Basis Function (RBF) as thekernel function described earlier.

Fig. 8. Illustration of (a) the time-of-ight signal, (b) the exhibited slosh wave, and(c) the frequency spectrum of the level signal.

Fig. 9. Illustration of the Moving Mean and Moving Median lters.


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Fig. 10. Wavelet lter applied on the raw signal.

2.3. Signal enhancement

The raw sensor signals were smoothened or ltered to removehigh-frequency noise and spikes before processing the sensor sig-nals through the SVM based signal processing method describedpreviously. The Moving Mean and Moving Median lters slideacross the raw signal and calculate the mean/median values inthe neighbouring sampled points. If x is the sampled raw signal of length N , and w is size of the moving window of the lter, then theltered output y usingmean and mediancan be obtained using Eqs.(20) and (21) , respectively. The width of the moving window w isset to 20. Therefore, the sliding windowtakes 20 sampled values of the raw signal and produces a mean or median value at the output:

y[i] = mean (x[i 1] , x[i 2] , . . . , x [i w]), for w i N

y[i] = mean (x[1] , x[2] , . . . , x [i]), for1 i < w (20)

y[i] = median (x[i 1] , x[i 2] , . . . , x [i w]), w i N

y[i] = median (x[1] , x [2] , . . . , x [i]), for1 i < w(21)

Fig. 11. Typical speed and observed during the experiments for each eld trials.

The value of N for the 20s signal at 100 Hz is calculated as:

N = 100 samples / s 20 s = 2000 samples (22)

Fig. 9 illustrates the signal output when the Moving Mean andMovingMedianlters areappliedto theraw signaldata. Thelteredversions of the raw signal do not contain high-frequency noise.

The third lter investigated in the experiment is the Wavelet

Transform (WT) lter that analyses signals at different frequencybands by de-composing them into coarse information and detailedinformation sets. The coarse information set contains the low-frequency components, and the detailed information set containsthe high-frequency components of the input signal. Only low-frequency components, which reect a smoothened version of therawsignal,are used and the high-frequency components of therawsignal, which usually contain noise, are eliminated. Fig. 10 showsthe high frequency signal (b) and the low-pass ltered signal (c)when the raw sensor signal (a) was processed with the DiscreteWavelet Transform (DWT) function. The Wavelet Transformationwas processed through the MATLAB Wavelet Toolbox [40] usingthe dwt function with Daubechies [41] Wavelet ( db1 ).

3. Experimental setup

A fuel tank was tted with an ultrasonic sensor near the topcenter of the tank. The tank can be approximated as a rectangularcuboid with dimensions 34 cm 34cm 81 cm. The fuel tank was

Fig. 12. Block diagram of the SVM system for training and verication of the experimental data.


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Table 1List of tank volumes investigated in the experiment.

Investigated tank levels5L, 6 L, 7L, 8L, 9 L, 15L, 20L, 25L, 30L, 35L, 36L, 37L, 38L, 39L, 40L, 45L,

46L, 47L, 48L, 49L, 50L

Table 2Techinical details of the ultrasonic transducer used in the experiment.

Ultrasonic sensor specications

Accuracy 0.32cmOutput 0.54.5 V (minmax)Resolution 0.18 cmOperating Temperature 40 to 80 CDesigned for gasoline and diesel liquids

lled with fuel levels ranging from 5 to 50 L in the experiment,which corresponds to 670% of the tank capacity. The fuel tankwas mounted in latitudinal direction, where the longest length of the tank was in parallel to the direction of the vehicle. Table 1 listsall the fuel levels investigated in the experiment.

Eachexperiment was conducted by driving a vehicle containingthe instrumented fuel tank for 3 km in a suburban residential area,where occasional stops were made at some road intersections. Fur-thermore, all eld trials were carried out on the same travel route(Fig. 11 ).

Table 2 lists the technical specications of the ultrasonic sensorused in theexperiments. Thelevelsignal from the ultrasonic sensorwas acquired using the LabVIEW software and a Data AcquisitionCard, which was connected to the ultrasonic sensor in the vehicle.The fuel level signal indicated by the ultrasonic sensor output wassampled and recorded at 100Hz. Fig. 12 illustrates an overview of the experimental setup.

Table 3Training parameters used by the LIBSVM train tool.

Parameter Value

SVM type =1 ( -SVM)Kernel function =2 (RBF)Gamma ( ) =0.125Nu ( ) =0.05Tolerance ( ) =10 5

Fig. 13. SVM training and validation owchart.

4. Validation results

Each investigated lter was applied on a separate SVM model,where the SVM parameters were the same. One half of the data

Fig. 14. Graph of the frequency coefcients obtained from the training data.


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Fig. 15. Validation result generated after training and validating the SVM models for each investigated drive trial.

from the rst eld trials was used to train the SVM model, and half of the samples obtained from the second eld trials were used forverication of the network performance.

The training and validation process is shown in Fig. 13 , whichwas carried out using MATLAB and LIBSVM [42] software appli-cations. LIBSVM [42] is an integrated software for support vectorclassication, regression and distribution estimation. It supportsmulti-class classication, which is required for training the ultra-sonic signals at multiple volume levels. The signal features were

scaled between an optimum range (01) using the LIBSVM scaletool.

Table 3 lists the training parameters used to train theSVM mod-els using the LIBSVM train tool. These parameters were selectedexperimentally using the LIBSVM tool until a higher classicationrate was achieved.

Fig. 14 shows the frequency coefcients of the unltered sig-nalsobtainedusing the MATLAB built-in fft function. Trunk [43] hasdemonstrated that data can be detrimental to classication, espe-


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Table 4Relative average error using statistical averaging methods and SVM based system.

Actual volume Statistical averaging Support Vector Machines

MovingMean(withoutSVM)

MovingMedian(withoutSVM)

-SVM(unltered)

-SVM(MovingMean)

-SVM(MovingMedian)

-SVM(Waveletlter)

50 11.5% 10.4% 0.0% 0.0% 0.0% 0.0%49 10.1% 9.3% 1.7% 1.7% 1.7% 1.7%48 2.7% 2.3% 2.1% 1.8% 2.8% 2.2%47 5.3% 5.3% 0.9% 0.6% 0.8% 0.9%46 0.7% 0.9% 0.6% 0.5% 0.5% 0.6%45 2.0% 2.6% 0.5% 0.5% 0.5% 0.5%40 0.1% 0.1% 0.2% 1.1% 0.0% 0.2%39 4.5% 4.6% 0.5% 0.4% 0.5% 0.4%38 0.5% 0.7% 0.9% 0.9% 0.9% 0.9%37 0.9% 0.0% 4.8% 7.1% 4.8% 5.8%36 2.0% 2.5% 1.0% 0.8% 0.6% 1.0%35 1.1% 0.1% 0.6% 0.8% 0.2% 0.6%30 0.4% 0.6% 1.2% 3.6% 2.4% 1.2%25 8.9% 6.0% 6.9% 5.4% 1.4% 6.9%20 14.5% 10.6% 16.1% 16.1% 3.2% 16.1%9 40.6% 35.4% 0.8% 0.8% 0.8% 0.8%8 22.9% 17.1% 1.8% 1.8% 2.7% 2.7%7 4.5% 0.7% 1.0% 1.0% 0.0% 1.0%6 0.1% 1.6% 0.0% 0.0% 0.0% 0.0%

5 6.4% 1.6% 1.4% 2.9% 1.4% 1.4%Abs. average error 7.0% (1.53 L) 5.6% (1.33 L) 2.2% (0.57 L) 2.4% (0.63 L) 1.3% (0.39 L) 2.2% (0.59 L)Max. error 40.6% (5.77 L) 35.4% (5.19 L) 16.1% (3.21 L) 16.1% (3.21 L) 4.8% (1.79 L) 16.1% (3.21 L)

cially if the additional data is highly correlated with previous data[44] . Apartfromthe correlationof data,the size ofinputfeaturedatais also important in signal classication systems. Thus, an increasein the input feature dimension ultimately causes a decrease of per-formance [45] . Hence, the correlation of the input data and thenumber of input features weredecisively selectedduring thedevel-opment of the SVM model. It was observed through experimentsthat only the rst sixty-three frequency coefcients that approxi-mately correspond to the slosh frequency 06.5 Hz has signicantmagnitudeand henceonlythis rangeof data wasusedfor classica-

tion. Thefrequency coefcients,the median value of thesignals,andthe temperature values were all bundled in an array of sixty-veelements, which were nally fed into the -SVM.

After training the SVM models, the models were validated usingthe test samples obtained from the second eld trial. Fig. 15 showstheoutput results forselected(lower andhigher)tank volumes.Theoutput results were obtained afterprocessing the ultrasonic sensorsignals with different processing methods. The time length of eachtrial is indicated as 280s. The graphs in Fig. 15 show fuel volumesaveraged over the whole drive period of 280s, after processing thesignals throughdifferentprocessing methods.To describe thestepsundertaken to obtain the overall averaged volume, a closer look atthe investigated 49 L trial is also shown in Fig. 15 . The raw signalillustratedin Fig. 15 (A) wasdividedinto20-s long signals, as shownin Fig. 15 (B), which were then ltered and processed through theSVM. The overall averaged volume as shown in Fig. 15 (C) was cal-culated by averaging the SVM model outputs for each trial over thewhole 280s period.

Table 4 shows the relative average error gures for all investi-gated volumes computed using the statistical averaging methods,and the SVM based signal classication method having differentpre-processing lters.

A comparison of the accuracy of differentprocessing techniquesinvestigated in the experiment is shown in Fig. 16 . The overallresults obtained from the SVM based system indicate signicantlyless error in fuel volume measurement compared with the simpleaveraging methods under dynamic conditions. The -SVM modelwith theRBF kernelfunctionand applied MovingMedian lter pro-duced the most accurateresults compared with the other methods.

Fig.16. Maximum andaverage error guresof theoverallaveragederror fordiffer-ent signal processing methods.

5. Conclusion

The Support Vector Machines based signal processing and clas-sicationapproachcoupledwitha signal ultrasonicsensorhas beenused to accurately determine the fuel level in an automotive fuel

tank under dynamic conditions. Four identical SVM models weredeveloped and an investigation was carried out by applying threeltrationmethodsandkeeping one unlteredraw signal to analyzethe performance of the -SVM model in improving the accuracy of the level sensor in the presence of liquid slosh. The SVM modelapplied with the Moving Median lter produced a maximum aver-aged error of 1.8L, which is signicantly better than the resultsobtained usingthe statistical and non-SVM network Moving Mean,andMoving Median functions that produced a maximum averagederror of 5.8 L and 5.2 L, respectively. The increased accuracy of thefuel level measurement system in dynamic environment will pro-vide more condence to drivers regarding the actual amount of fuel indicated by the instrument panel. With the accurate fuel levelmeasurement system, the distance-to-empty gures can be accu-

rately computed. In particular the SVM based method is suitable


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for use in a professional car racing where vehicle is subjected toa highly dynamic maneuvers. Drivers of cars equipped with thismeasurement method can condently drive higher number of lapswithout fear of running out of fuel in situations where fuel level inthe tank is low.

6. Future work

An ultrasonic sensor coupled with the Support Vector Machine(SVM) approach to signal processing will be used to address otherinuencing factors such as atmospheric pressure and the tilt thatcauses liquid to shift to one side. With the rapid improvementsin microprocessor technology, it will be possible to automaticallytrain the SVM model in real time, which will further increasethe effectiveness of the measurement system in dynamic environ-ments.

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Biographies

Jenny Terzic Quality/Six Sigma Manager at Delphi Automotive Systems Australia Powertrain Division. Holds Bachelor of Mechanical Engineering (with honours)and Master of Engineering in Computer Integrated Manufacturing. Has extensive

experiencein vehicle fuel system design, development and testing. Area of researchinclude: neural networks,support vector machines, intelligent sensors and applica-tions of articial intelligence in automotive vehicle engineering.

Romesh Nagarajah Professor of Mechanical Engineering at Swinburne Universityof Technology. Graduated with an Honours degree in Mechanical Engineering fromtheUniversity of Ceylonin 1973, M.Phil. in Robotics from theUniversity of Notting-ham in 1985 and a Ph.D. from Swinburne University of Technology in 1994. He hasreceivedseveralnationalcompetitive grants, named in several internationalpatentsand published 75 papers in international journals and conferences.

Muhammad Alamgir Electrical Engineer at Delphi Automotive Systems Australia.Graduated in Computer Systems Engineering from RMIT University in 2008. Areasof research include smart sensors, articial neural networks and support vectormachines.
http://dspace.rice.edu/handle/1911/19831http://www.csie.ntu.edu.tw/~cjlin/libsvmhttp://www.csie.ntu.edu.tw/~cjlin/libsvmhttp://www.csie.ntu.edu.tw/~cjlin/libsvmhttp://www.csie.ntu.edu.tw/~cjlin/libsvmhttp://dspace.rice.edu/handle/1911/19831

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