exploitation of multiple sensor arrays in electronic nose

Exploitation of Multiple Sensor Arrays in Electronic Nose Nor Hayati Saad, Carl J. Anthony, Raya Al-Dadah, Michael C.L.Ward School of Mechanical Engineering University of Birmingham Birmingham, United Kingdom [email protected] Abstract—The Coupled Micro Resonator Array (CMRA) is a new type chemical sensor that has been developed to improve the performance of the electronic nose by increasing the number of sensors that can be used to detect specific odours. In the CMRA, an array of mechanically coupled micro mass balances, the mass of each micro mass balance can be determined by measuring the eigenfrequencies of the coupled array, with just a single input and output electrode. If the mass of each resonator is to be uniquely identified it is important that the changes in the eigenfrequencies are distinctive and that the eigenvectors of the system are stable against resonator mass changes. This paper models and evaluates the performance of an unsymmetrical yet balanced CMRA for individual resonator mass determination.

I.

INTRODUCTION

The exploitation of multiple sensor arrays in the electronic nose, in areas such as food monitoring and environmental monitoring [1, 2] has led to a demand for improved sensitivity and reliability. This improvement in performance can be achieved by increasing the number of sensors in the array [1, 2, 3, 4, and 5]. However any increase in sensor number necessarily leads to an increase in complexity and cost of the sensor array. We have previously shown that an array of Coupled Micro Resonant Mass balances (CMRA) [6, 7, and 8] can significantly reduce the complexity of the sensor arrays. Since each sensor is mechanically coupled to its neighbour, the array may be interrogated by simply driving one end of the array and monitoring the output at the other end. This greatly reduces the complexity and cost of the system. This paper briefly reviews the overall performance parameters of the CMRA. We show how the performance of an array of coupled micro resonators can be significantly improved by staggering the mass of the resonators. We analyzed the performance of the staggered mass array using both a simple lumped mass approach and finite element analysis (FEA) to determine the accuracy with which any mass changes should be able to be detected. II.

structure to be fabricated on a single substrate. By measuring the frequency response of the system, we can trace the type and amount of masses absorbed by the single or multiple sensors. The performance of the CMRA depends on the measurability (measurable for readout), uniqueness of the output signal and stability of the system’s eigenvector of the structure [8]. The measurability of the output signal of the CMRA sensor structure relies on the balanced effective mass and stiffness of the coupled resonators and the effective mass and stiffness of the mechanical coupling spring. Fig. 1 shows the first version of the CMRA which was fabricated using 5 micron thickness SOI (silicon on insulator) wafer. Since the structure used electrostatic excitation and a capacitive detection method to drive and readout the output signal respectively, it is important to ensure the balanced effective mass of the comb drive actuator and the fixed-fixed beam resonators for the measurable output signal. If the mass of the actuator is too large compared to the resonator, it may create a node boundary between the actuator and the resonator. Therefore, we are unable to measure the response of the resonators. Fig. 2 illustrates the second version of the CMRA with constant mass design of the coupled resonators. The coupled resonators which were in the form of coupled constant mass comb drives ensure the balanced effective mass of the structure array. .

Comb drive Actuator Fixed-fixed beam resonator Butterfly shape coupling spring

PERFORMANCE OF CMRA

The CMRA with multiple resonators or sensors are coupled together using mechanical springs which allow the

Figure 1. SEM image of the CMRA (version1) sensor structure

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2(a)

2(b)

2(c) Figure 2. CMRA with constant resonator mass design: (a) 5 coupled resonators; (b) Scanning electron microscope (SEM) image of a single resonator; (c) A coupling spring

The Constant CMRA provides measurable output signals. However, it does not have a distinctive output signal for all the sensors in the array. The output signals of the sensors in the first half of the array always mirror the output signal of the sensors in the second half of the array when the sensors absorbs the mass [8]. Furthermore, the eigenmodes of the perturbed constant CMRA are always changed or unstable compared to the unperturbed structure. The unstable eigenvectors cause errors when estimating any changes of mass absorbed by the sensors [8].

III.

In order to improve the performance of the CMRA, the effective mass and stiffness of the constant mass resonators was modified (Fig.2). Several design alternatives were modelled and analyzed to examine the performance of the structure in terms of the measurability and distinguishability of the output signal and the stability of the system’s eigenvector of the structure. Fig. 3 depicts a schematic diagram and the SEM images of an alternative of the staggered mass design of the CMRA (staggered CMRA). To

R2

mi = ki / (2 π fi)2

(1)

The parameters from the FEA analysis were used in the lumped parameter model for further analysis.

FINITE ELEMENT ANALYSIS (FEA) OF THE STAGGERED CMRA

R1

break the symmetry of the constant CMRA, the staggered CMRA was designed with a slight unsymmetrical mass distribution between all resonators, resonator 1 (R1), R2, R3, R4 and R5 (refer to Fig. 3). To ensure the structure vibrates efficiently for measurability of output signal, all masses in the first half of the structure array (sum of R1 and R2) and the second half of the array (sum of R4 and R5) remained balanced with the heaviest mass positioned in the middle of the structure. Using FEA (COMSOL Multiphysics 3.4), we performed eigenfrequency analyses [1] to determine the 5 fundamental frequencies, (f1, f2, f3, f4, and f5 [Hz]) and eigenmodes of the structure. The analysis result was compared with the eigenvalue and eigenvector analysis result using lumped mass model analysis (Section IV). The effective stiffness of the 5 resonators (k1, k2, k3, k4 and k5) and the coupling spring constant (kc1, kc2, kc3 and kc4) were determined using static analysis [6, 8]. From the eigenfrequency and static analysis, the effective mass of each resonators (m1, m2, m3, m4 and m5) were determined using an equation to relate between, f (resonant frequency of single resonator), k (effective mass of the resonator) and m (effective mass of the resonator); assuming low damping. The effective mass of the resonator i:-

IV.

LUMPED MASS PARAMETER ANALYSIS

The lumped analysis was accomplished using MATLAB code to determine the eigenvalues and eigenvectors of the coupled structure and the overall frequency response of the staggered CMRA at initial condition (unperturbed structure) and after mass was added to particular resonators (perturbed structure). To examine the stability of the staggered mass CMRA eigenvectors when selected resonators absorb mass, an inverse eigenvalue analysis was carried out and the mass change pattern of the structure was estimated using unperturbed eigenvectors. The stability of the system’s eigenvector was confirmed by computing the error between the estimated mass and the actual mass added to the resonators. The stability of the system’s eigenvectors of the staggered CMRA was compared with the constant CMRA.

R3 A. Eigenvalue and Eigenvectors Analysis R4 The equation of motion for a lightly damped coupled resonator (as shown in Fig. 4) :-

R5

Figure 3. CMRA with staggered mass design

mxn + cx n − k c n −1 x n −1 + (k c n −1 + k n + k c n +1 ) x n .... ....... − k c n +1 x n +1 = F (t ) (2) 1576

Where, m: mass of the resonator, c: damping factor, k: stiffness of the resonator, kc :stiffness of the mechanical coupling, F(t): force used to drive the structure and xn is the displacement of the resonator; Consider a model of mass spring system, with negligible damping (Fig. 4) to represent a 5 resonator CMRA. By assuming the system undergoes harmonic motion, the 5 equations of motion can be simplified into the form of the matrix eigenvalue problem: (ω )2 [X]

[M-1] [K] [X]

=

(3)

ω is the eigenvalue or natural frequencies of the system, [X] is a displacement matrix of the 5 degrees of freedom of the CMRA, [M] is the mass matrix and [K] is the stiffness matrix of the CMRA. F1(t) x2

x1

x3

k1

k2

m1

kc1

m2

x4 k3

kc2

m3

x5 k4

kc3

m4

k5 kc4

m5

simple relationship exists between the eigenfrequencies, ωi and the elements of the generalised mass and stiffness matrices:-

ωi2 =

K Gii

(5)

M G ii

Assuming, a mass Δm1 is added to resonator 1 (R1), then a perturbed set of eigenvalues will be obtained; and since the stiffness matrix is unchanged, we may uniquely identify the generalised mass matrix. We can then transform this back to the real mass matrix, so identifying Δm1, if we have the new eigenvectors or if the unperturbed eigenvectors are sufficiently unchanged. The challenge is to have the CMRA structure design, in which any small change of masses should give insignificant change to the eigenvectors of the unperturbed system. We examined the performance of the staggered CMRA by adding a mass of 1e-24 [Kg], 1e-18 [Kg], 1e-15[Kg], 1e-12 [Kg] and 1e-11 [Kg] separately to each resonators (R1,2 ,3, 4 and R5). We then used the unperturbed eigenvectors to estimate the perturbed mass (epm). Errors of mass estimation, Eest were calculated by comparing the estimated perturbed mass, epm and the actual perturbed mass, apm added to the structure:

Figure 4. A mass spring system model of the 5 CMRA

Eest = | epm - apm|

(6)

To solve for the eigenvalue and eigenvectors of the CMRA, the value of k, kc, and m (from the FEA) were substituted in the equation 3. The analysis was repeated to determine the overall frequency response of the coupled structure, by applying an excitation force F(t) on the structure array (i.e. at R1, F1(t)). From equation (2) and (3), we computed the response of the resonators: -

The performance of the staggered CMRA and constant CMRA was compared by calculating the Eest for both sensor structures when absorbing similar amount of masses.

[X]= [F] [(K – M (ω) 2)] -1

Table 1 lists the designed parameters of the 5 staggered mass CMRA which were analysed using FEA. Referring to the stiffness of the resonators; the stiffness of the third resonator, k3, was slightly higher compared to other resonators. The sum of k1 and k2 and the sum of k4 and k5 were more or less similar, which is due to the design of the staggered mass itself.

(4)

Where, [F] is the driving force matrix. The performance of the CMRA was examined when a maximum of 1 percent of mass of the single resonator (R) was added to each resonator separately.

V.

RESULT AND DISCUSSION

Table -1 : Designed Parameter of Staggered CMRA using FEA

B. Estimation of Mass Changes Pattern - Stability of System’s Eigenvector

5 Eigenfrequencies, f [Hz]:-

When one of the resonators of the CMRA absorbs mass, we can identify which mass has changed by using inverse eigenvalue analysis; this requires a knowledge of the perturbed eigenvalues and perturbed eigenvectors. Since the perturbed eigenvectors are complicated to measure, the unperturbed eigenvectors will be used in the estimation of the mass changes pattern of the CMRA. Hence, it is important to ensure that the eigenvectors are stable against mass changes. The eigenvectors of the unperturbed system were used to transform the mass and stiffness matrix into a generalised mass matrix [MG] and generalized stiffness matrix [KG]. A

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f1: 12543.5 f2: 12651.4 f3: 12792.2 f4: 12922.6 f5: 13009.5 Stiffness of coupling sp. kc :-

0.3118 [N/m]

Stiffness of r(s), k [N/M]:-

k1: 24.99 k2: 25.16 k3: 25.21 k4: 25.11 k5: 25.05 Mass of resonators, m [Kg]:-

mR1: 3.87e-9 mR2: 3.99e-9 mR3: 4.03e-9 mR4: 3.95e-9 mR5: 3.91e-9

7(a)

Deformation at Boundary Y- Displacement [m]

Response Amplitude [arbitrary unit]

2.5e-3

Relative displacement: R1 = 1.04

2.0e-3

R2 = 2.90

1.5e-3

R3 = 4.28

0.5e-3

R5 = 1.00

0.0

7(b) Response Amplitude [arbitrary unit]

Figure 5. Example of eigenmode analysis using FEA (mode 1) of unperturbed staggered CMRA

Eigenfrequency Analysis of 4 5 Staggered CMRA-V2 1.3 x 10

Frequency [Hz]

6(a)

1.29

Initial +R1 +R2 +R3 +R4 +R5

1.28 1.27 1.26 1.25 1

2 3 4 5 Eigenfrequencies

Frequency [Hz]

x 10

1.3 1.29 4

5

Stability of Eigenvectors: Constant CMRA (Mode 4, +m = 1e-12Kg) 1 0.5

Initial +m@R1 +m@R2 +m@R3 +m@R4 +m@R5

0 -0.5 2 3 4 Resonator 1 to 5

5

displacement ratio of 4: 1 between R3: R1 and R3: R5, the frequency response of the staggered CMRA are considered measurable if the readout is connected to the R1 or R5; provided that the structure has high Q factor.

Initial +R1 +R2 +R3 +R4 +R5

3

2 3 4 Resonator 1 to 5

Figure 7. Comparison: stability analysis of eigenvectors of the Staggered and constant CMRA (example of mode 4); (a) Stability of eigenvectors of the staggered CMRA, (b) Stability of eigenvectors of the Constant CMRA [8]

4

2

-1 1

5

1.31

1.28 1

Initial md4(+m@R1) md4(+m@R2) md4(+m@R3) md4(+m@R4) md4(+m@R5)

0

-1 1

Eigenfrequency Analysis: Constant CMRA 6(b)

0.5

-0.5

1.0e-3

R4 = 2.16

Stability of Eigenvectors: Staggered CMRA (Mode 4, +m = 1e-12Kg) 1

Figure 6(a) and 6(b) show the result of frequency response analysis of the staggered CMRA and constant CMRA respectively. As portrayed in Fig. 6(a), the staggered CMRA produces a unique output signal when any single sensor absorbs 1 percent of R mass. Comparing Fig. 6(a) and 6(b), by breaking the structure symmetry of the constant CMRA distinctive frequency response patterns can be produced (Fig. 6(a)) for ease of tracing the masses absorbed by the resonators.

5

5 Eigenfrequencies Figure 6. Comparison: eigenfrequency analysis of the Staggered and constant CMRA; (a) Eigenfrequency analysis of 5 staggered CMRA; (b) Eigenfrequency analysis of 5 constant CMRA (referred from [8])

Fig. 5 exemplifies the first mode shape of the unperturbed staggered CMRA, where all the resonators move in similar phase. As shown in Fig.5, the third resonator, R3 has the largest displacement and R1 and R5 have the smallest displacement in y-direction of excitation. Comparing to the eigenvector analysis result using lumped mass model, the ratio of displacement between all resonators (R1, R2, R3, R4 and R5) is 1.04: 2.9: 4.28: 2.16 and 1 respectively. With the

Fig. 7(a) and 7(b) portray a result of stability analysis of the staggered and constant CMRA when each resonator absorbs a mass of 1e-12 [Kg] separately. At a small amount of mass absorbed by the resonator (i.e. less than 0.1% of mass of the single resonator, R), the eigenvectors of the perturbed staggered CMRA (Fig. 7(a)) are seen to be always more or less similar with the eigenvectors of the unperturbed structure (at initial condition). As shown in Fig. 7(b), the eigenvectors of the perturbed Constant CMRA are always changed or unstable compared to the unperturbed structure when each resonators absorbs similar amount of mass of 1e-12 [Kg].

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Errors at each R (Eest )

8(a)

VI.

Mass Changes Pattern of Staggered CMRA ( Error of Mass Estimation: Mass (1e-12 [Kg]) Absorbed at R1) 8.E-13

The staggered CMRA which was designed with an unsymmetrical yet balanced mass distribution had a significantly improved the performance compared to the symmetric array of the coupled resonators. From the analysis result, the arrangement of the staggered mass with the heaviest mass positioned in the middle and balanced masses between the first half and the second half of the structure array improved and maintained the measurability of the output signal of the sensors. The unsymmetrical mass distributed between all the resonators helped to break the symmetry of the constant structure and provided a unique frequency response pattern for any single or multiple sensors of the CMRA. Breaking the symmetry of the structure also stabilised the system’s eigenvectors of the CMRA to be significantly insensitive to any small amount of mass absorbed by the sensors. By having measurable, unique responses and stable eigenvectors, it is possible to unambiguously identify any mass changes absorbed by the single or multiple sensors of the staggered CMRA.

6.E-13 4.E-13 2.E-13 0.E+00 2 3 4 5 Coupled Resonators

5

8(b)

Mass Changes Pattern of Constant CMRA ( Error of Mass Estimation: Mass (1e-12 [Kg]) Absorbed at R1) 6.E-11

Errors at each R (Eest )

1

5.E-11

CONCLUSION

4.E-11 3.E-11

ACKNOWLEDGMENT

2.E-11

Nor Hayati Saad would like to acknowledge the MARA University of Technology (UiTM) Shah Alam and the Malaysian Ministry of Higher Education for sponsoring her PhD study at the University of Birmingham. Grateful thank to individuals who involved directly and indirectly to the success of the research study.

1.E-11 0.E+00 1

2 3 4 5 Coupled Resonators

5

Figure 8. Comparison- stability of eigenvectors of the staggered and constant CMRA (when similar amount of masses were added to the single resonator, R1) ; (a) Error of mass estimation for constant staggered CMRA; (b) Error of mass estimation for constant CMRA

Figure 8(a) and 8(b) compare analysis result of the calculated error when estimating mass using the unperturbed eigenvectors for the staggered and constant CMRA. Comparing the error of mass estimation at R1 between the staggered CMRA and constant CMRA; the error for the staggered CMRA was reduced below than 35% when the resonator absorbs smaller amount of mass (i.e. less than 1e12[Kg] mass). However for the constant CMRA (Fig. 8(b)), the estimations of mass using unperturbed eigenvectors can be considered invalid, since it causes very high error. Further to emphasize, even though the 30% errors may seem quite high for the Staggered CMRA, but we clearly can distinguish the mass changes pattern of the five coupled resonator when only R1 absorbs the mass. Therefore, from the analysis presented above it is clear that staggering the mass of coupled resonators has resulted in the stabilization of the eigenvectors of the structure. As a result, any small amount of mass absorbed by the resonators, will not affect the designed eigenvectors of the structure. Hence, it is then valid to use the unperturbed eigenvectors to estimate any mass changes absorbed by the resonator.

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[4]

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[8]

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