Approximating Sensors’ Responses of odor mixture on Machine Olfaction

Ekachai Phaisangittisagul Electrical Engineering Department, Faculty of Engineering, Kasetsart University,

Bangkok, Thailand 10900 E-mail: fengecp@ku.ac.th

Abstract—An increasing interest in current research on machine olfaction is to try to approximate or predict the sensor response to odor mixtures. Previously, the aid of special active odor sensing system was proposed. This system is able to produce the target odor recipe based on iteratively adjusting the ingredient from odor palette. Here, a new algorithm solution is proposed by combining the signal decomposition and reconstruction techniques, and Support Vector Machine (SVM). The prediction results of the proposed method are investigated by comparing with the real sensor responses recorded from a commercial e-nose machine. The results demonstrate that the new proposed method provides good approximation when applied to different mixing ratios of some coffees and green tea.

Keywords-e-noses; odor mixture; support vector machine (SVM); wavelet decomposition; wavelet reconstruction

I. INTRODUCTION Recently, an artificial mammalian sensory system has

been developed in many research institutions and commercial organizations around the world. This system is often named electronic nose (e-nose) and has been widely used in many applications: food and beverage quality, perfume and fragrance characterization, hazard detection. One of the current challenging issues in e-nose research is to generate a sensor’s response waveform for a target odor mixture. Some research groups [1-3] proposed a system called odor recorder, that uses an active-sensing system (an e-nose they designed for this purpose) for quantifying the mixing components.

Figure 1. Block diagram of odor recorder system [after 3].

The operation of the odor recorder system displayed in Fig. 1 is based on minimizing the difference between the waveform from the estimated blended odor and the target odor. When the system is converge, the target odor is “quantified” by recording the ratio parameters used in the

odor blender. Hence, an odor recipe is obtained. However, this approach will provide good approximation if one has prior information regarding the target mixture ingredients. In addition, this approach requires intensive computation to reach the convergence.

A different approach to generate a sensor’s response pattern based on an algorithm solution is proposed by [4] which is generalized model of the additive law of mixing which can be expressed as follows:

( ) ( ) ( ) ( )1.,,,,,,, 11111 nnnnn coScoSccooS ⋅++⋅= αα ………

where oi denotes an odor sample i. ci denotes a concentration of an odor sample i. αi is a mixing coefficient of S(oi, ci). S(oi, ci) is the sensor response of an odor sample (oi)

with ci concentration. S(o1,…, on, c1,…, cn) is the sensor response to the

mixture of o1,…, on with c1,…, cn concentrations.

Basically, the additive law model is specifically designed for mixtures of non-interacting compounds. This condition is not feasible in many e-nose applications.

Figure 2 shows a data acquisition process [5] used in many machine olfaction system to measure an odor sensor response. Typically, the features obtained from an odor sensor response are extracted on the reference phase and the sniffing phase. As a result, the approximation of the sensor response proposed in this study is based on those two phases only.

Figure 2. Data acquisition phase of an e-nose sensor[5].

Target odor Array of sensors

Odor Blender Mac/PC

Odor recipe

Solenoid valve

Blended odor

Control signal

1 2 3

2009 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-3816-7/09 $26.00 © 2009 IEEE

DOI 10.1109/AICI.2009.75

60

The objective in this study is to propose a prediction algorithm that can provide good approximation of an odor sensor’s waveform without special apparatus but requires only some pre-measurement of the odor compound. The proposed approach is based on the combination between signal decomposition/reconstruction from wavelet analysis and Support Vector Machine (SVM) to predict the waveform of the odor mixtures. The approximation accuracy between our prediction results and the measured sensor’s waveform is evaluated by the closeness computation.

This paper is organized as follows. In section II, we will review the basic concept of the discrete wavelet analysis and support vector machine for regression. Section III provides a detail of the proposed prediction model. The experimental result is given in section IV. Section V presents a discussion/conclusion of this study.

II. REVIEWS OF BASIC DISCRETE WAVELET ANALYSIS AND SUPPORT VECTOR MACHINE

In this section, brief reviews of discrete wavelet analysis and SVM are provided as necessary to understand the proposed method in this study.

A. Discrete Wavelet Analysis A signal or function f(t) from a space S can be

represented as a linear combination as shown in (2).

( ) ( )2.∑=i

iitf ϕα

where αi is an expansion coefficient. ϕ i is a set of function of t or an expansion set.

i is an integer index ∈ Z.

Conceptually, a wavelet system is created by simply scaling (j) and shifting (k) a single scaling function and a single wavelet function. The goal is to generate a set of basis function such that any signal or function f (t) ∈ L2 can be expressed by linear combination of the scaling and wavelet functions as shown in (3) and (4) [6].

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( )4.22

22

3.

0

0

00

0

0

00

2/

2/

,,

∑∑

∑

∑∑∑

∞

=

∞

=

−⋅+

−⋅=

+=

k jj

jjj

k

jjj

k jjkjj

kkjj

ktkd

ktka

tkdtkatf

ψ

ϕ

ψϕ

where aj(k) is called scaling coefficients. dj(k) is called wavelet coefficients. j, k, n ∈ Z (integer number)

The relationship between the expansion coefficients from a lower scale to a higher scale or from fine scale to coarse scale, wavelet decomposition, can be expressed by (5) and (6).

( ) [ ] ( ) ( )

( ) [ ] ( ) ( )6.2

5.2

11

10

∑

∑

+

+

−=

−=

mjj

mjj

makmhkd

makmhka

where m = 2k + n

Similarly, the relationship between the expansion coefficients from a higher scale to a lower scale or from coarse scale to fine scale, wavelet reconstruction, can be expressed by (7). The wavelet decomposition and reconstruction can be implemented by filter bank algorithms [7] as illustrated in Fig. 3, respectively.

[ ] ( ) [ ] ( ) ( )7.22 101 ∑∑ −+−=+m

jm

jj mdmkhmamkha

Figure 3. (a) Two-channel filter bank of wavelet decomposition, (b) Two-channel filter bank of wavelet reconstruction.

B. Support Vector Machine (SVM) The foundations of the SVM have been developed by

Vapnik and coworkers [8-9] and are gaining favor in machine learning community due to their attractive properties and promising performance. In this study, the SVM is employed as a regression algorithm to approximate the wavelet coefficients. Consequently, the SVR notation is used as a support vector machine for regression. Suppose we have available in this case a set of training data

( ) ( ){ } RR ⊂⊂ id

iNN yandwhereyy xxx ,,,, 11 …

In ε-SVR, the idea is to find a function f(x) = ⟨w,x⟩ + b that has at most ε deviation from its target yi of all the training data. However, in practice we may allow some errors to relax the complexity of the SVR. Two sets of slack variables ξi and ξi* are introduced for this optimization problem and can be stated as in [10]. So, the Largrangian function of the primal problem can be constructed as follows.

( ) ( )

( ) ( )

( ) .,

8,

21:

1

**

1

1

**

1

*2

∑

∑

∑∑

=

=

==

−−++−

++−+−

+−++=

N

iiiii

N

iiiii

N

iiiii

N

iii

by

by

CJ

xw

xw

w

ξεα

ξεα

ξγξγξξ

where ** ,,, iiii ααγγ > 0 are Lagrange multipliers.

(b)

HPF

h1[-n] 2

h0[-n]aj+1 2 aj

dj

(a)

LPF

dj

aj

2

2 aj+1+h0[n]

h1[n]

LPF

HPF

61

This loss function is called the ε-insensitive loss function. Instead of applying SVR to the original training input features, we can map the input space (X ) to a feature space (F ) using a set of nonlinear transformation φ(x) [11] leading to nonlinear SVR. From linear SVR, the algorithm can be written in terms of the inner product of the input vector x. Hence, we would replace all those inner product in x with ⟨φ(xi),φ(xj)⟩ which allows us to reformulate the SVR optimization problem as follows:

( ) ( ) ( )

( ) ( )

( ) [ ]

( )9

,0,0tosubject

.

,21

maximize

*

1

*

1 1

**

1,

**

Cand

y

k

ii

N

iii

N

i

N

iiiiii

N

jijijjii

∈=−

⎪⎪⎩

⎪⎪⎨

⎧

−++−

−−−

∑

∑ ∑

∑

=

= =

=

αααα

ααααε

αααα xx

( ) ( ) ( ) ""called,:,where ctionKernel funk jiji xxxx φφ=

Likewise, the optimum weight vector w and f(x) may be

written as

( ) ( ) ( ) ( ) ( )∑∑==

+−=−=N

iiii

N

iiii bkfthus

1

*

1

* ,xxxxw ααφαα

Note that the optimization problem solved in nonlinear SVR corresponds to finding the linear function in the feature space (F ) but nonlinear in the input space (X ). Moreover, the kernel function k(xi,xj) can be evaluated without explicitly mapping φ: X → F .

III. A PROPOSED PREDICTION MODEL In discrete wavelet analysis, the low frequency

component, (a) of DWT represents the identity of the original signal and the high frequency component, (d) refers to a detail of the original signal. Based on this result, if we can properly find the low frequency component (a) and the high frequency component (d), any signal which has similar characteristic could be approximated by using wavelet reconstruction.

Based on experimental results of our dataset, we found that a 5-level of wavelet analysis provides a good approximation of our odor mixtures with different mixing ratios. The processes for modeling the prediction algorithm of odor mixture are performed as follows: Step 1: For an odor mixture training dataset, a DWT is applied to each training sensor response (S) to decompose it into 5 levels as shown in Fig. 4. The output of each level in DWT is saved as the box structure illustrated in Fig. 5 and they are called wavelet coefficients.

Figure 4. Five levels of two-channel filter bank of wavelet decomposition.

Step 2: The wavelet coefficient for each particular mixing ratio are subdivided into an approximation and a detail wavelet coefficient.

Figure 5. Wavelet coefficient structure of 5 levels of wavelet decomposition.

Step 3: A SVR as described in section II part B is created as shown in Fig. 6 to model the relationship of training data set between the mixing ratios of three odor types (X-Y-Z) and the corresponding approximation (A′5) and detail (D′5) wavelet coefficients.

Figure 6. Support Vector Regression (SVR) for computing approximation, (A′5) and detail wavelet coefficient, (D′5).

Step 4: A testing mixing ratio’s data set is supplied to the trained SVR implemented in step 3. The output from the SVR, which is a predicted wavelet coefficient (A′5 and D′5), is used to compute an approximation wavelet coefficient (A′4). Then, the result is sequentially forwarded to the wavelet reconstruction in the prior level as illustrated in Fig. 7. Note that the detail wavelet coefficient (D′1-D′4) in wavelet reconstruction comes from the best suited detail wavelet coefficient of the available training dataset. The

5th-Level reconstruction

A′5

D′5

h0[n]2 +SVR A′4

h1[n]2SVR

XYZ

Wavelet Coefficient

1st-Level

5th-Level

A1 D1

S

A5 D5

D5 D1A5 D2

S

1st-Level

h0[-n] 2 A1

h1[-n] 2 D1

5th-Level

h0[-n] 2 A5

h1[-n] 2 D5

62

output (S′) from the wavelet reconstruction is a predicted sensor response.

Figure 7. Wavelet reconstruction using five levels of two-channel filter banks.

IV. EXPERIMENTAL RESULTS In this study, odor mixture datasets were collected using

NST 3320 e-nose system which consists of 11 MOSFET sensors and MOS sensors with different sensitivities. Three types of odor samples used in evaluating our proposed algorithm are a common coffee blend, pure Sumatra coffee, and pure green tea. The mixture of the odor samples are encoded as follows:

Let’s define X – Regular coffee

Y – Sumatra coffee Z – Green tea

The mixed odor sample is denoted as: X-Y-Z in which each numeric number of X, Y, and Z represents the amount of each in the mixture. Example of MOS sensor responses of mixed odor samples is illustrated in Fig. 8. Each sensor’s waveform corresponds to different ratios of odor mixture.

Figure 8. Example of MOS sensor responses with different odor mixture

ratios.

The descriptions of mixed odor dataset used in this study are shown in Table I. One table spoon of mixed odor samples was put in vials of the e-nose device and each vial was heated at 40 ˚C for 30 seconds before starting the acquisition process. The acquisition parameters were set as follows:

Baseline phase: 10 Seconds. Sniffing phase: 60 Seconds. Recovery phase: 260 Seconds. Flow rate: 60 ml/minute. Sampling rate: 1 Sample/Sec.

A measure of the approximation performance applied in this study is defined by [4]:

( )10.'

i

ii

SSS

Closeness−

=

.sensor a of waveformssensor' ofion approximatan is'

.sensor a of waveformssensor' a iswhere

iS

iS

i

i

For the SVR, we used the SVM and Kernel Methods

Matlab Toolbox developed by [12]. The parameters used to fine tune the approximation results are ε-tolerance error, kernel functions and the cost values (C). In this study, the ε-tolerance error is fixed to 1 and the Gaussian kernel function in (11) is employed as a similarity measure between xi and xj as well as the inner product of ϕ (xi) and ϕ (xj).

( ) ( )11.exp,2

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −−=

cK ji

ji

xxxx

where c is used to control the width of the Gaussian kernel function.

TABLE I. DESCRIPTION OF MIXTURE ODOR DATA SET

Mixture detail Dataset no: Mixing ratio

X - Regular coffee Y - Sumatra coffee

Z - Green tea

X-Y-Z

1 0-0-1 2 0-1-0 3 1-0-0 4 1-0-1 5 1-1-0 6 1-1-1 7 1-2-0 8 1-2-2 9 2-0-1

10 2-1-0 11 2-1-1

For performance evaluation, the results of the closeness between the real sensor response waveform and our predicted sensor’s response waveform are computed based on (9). The closeness results are illustrated in Table II. In Fig. 9, the graphical predictions for sensors no.3 on the testing dataset are illustrated together with the real sensor responses for different odor mixing ratios. Note that the real sensor responses and the predicted ones are plotted by solid lines and dots, respectively.

4th-Level

A′4

D′4

h0[n]2 +

h1[n]2

A′3

1st-Level

A′1 h0[n]2 +

h1[n]2D′1

S′

63

TABLE II. THE RESULTS OF CLOSENESS FOR TESTING MIXED ODOR SAMPLES

Sensor no: Odor mixing ratios of testing samples

1-1-1 2-0-1 2-1-0 1 0.0193 0.0222 0.0266 2 0.0433 0.0513 0.0398 3 0.0040 0.0025 0.0041 4 0.0071 0.0144 0.0087 5 0.0216 0.0403 0.0251 6 0.0233 0.0357 0.0309 7 0.0978 0.0094 0.0704 8 0.0407 0.0675 0.0292 9 0.0912 0.0816 0.0549

10 0.0990 0.0500 0.0170 11 0.0182 0.0047 0.0655

In practice, there is no perfect approach to choose the

optimal value C for a given application. As a result, the values of C are determined experimentally via the training error.

Figure 9. Plots of sensor ni. 3’s original responses (lines) vs approximated

responses (dots) for different odor mixing ratios.

V. DISCUSSION AND CONCLUSION The experimental results shown in Table II and in Fig. 9

demonstrate that the proposed prediction algorithm provides good approximation to the waveform of the original mixed odor samples. Although the better approximation could be theoretically obtained by using fewer levels of wavelet decompositions, it not only requires more complexity to compute the parameters (an approximation wavelet coefficient) but also tends to provide poor generalization. For training samples with input dimensionality larger than the number of available training samples (curse of dimensionality), the SVM is a good candidate approach to handle this problem. Specifically, SVR algorithm is independent of the dimensionality of the input space. In addition, it can transform the input space to a higher dimensional feature space that could be simpler to solve the problem.

This study proposes a prediction algorithm to approximate a sensor’s response waveform to an odor mixture using its known responses to individual components of that mixture and a limited set of training mixtures. The difference between this proposed approach and earlier implementation is that we present the algorithm solution rather than using a special hardware solution. Application of this new technique could be in approximating the quantity of the components in the odor sample. Based on the experimental results, this new approach provides a promising method for predicting a sensor’s response in environments in which several odor sources are prevalent in time varying concentrations.

ACKNOWLEDGMENT This work is supported by NSTDA, Thailand under

grant research no. F-31-203-11-01. Also, author wishes to thank to Dr. Susan Schiffman for letting me perform data acquisition of odor mixture on the AppliedSensor NST 3320 electronic nose system.

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