vibe

Paper Ref: S1146_P0507 3rd International Conference on Integrity, Reliability and Failure, Porto/Portugal, 20-24 July 2009

-1-

IMPROVEMENT IN MEASURED SIGNALS OF MEMS ACCELEROMETER

Abdellatef E. Badri, Jyoti K. Sinha School of Mechanical, Aerospace and Civil Engineering, University of Manchester, P.O. Box 88, Manchester, M60 1QD, UK ([email protected], [email protected])

Alhussein Albarbar Department of Engineering & Technology Manchester Metropolitan University, Manchester, M1 5GD ([email protected]) ABSTRACT

The MEMS accelerometer is relatively new technology in vibration measurement. It has been observed that the measured signals from the MEMS accelerometer deviate when compared with the conventional accelerometer. Hence a method has been proposed to correct the measured MEMS accelerometer signals in the frequency domain.

INTRODUCTION

Vibration measurement and analysis is one of the accepted methods in machinery condition monitoring techniques; it plays a significant role in the dynamic qualification of newly designed structural components, prediction of faults and structural aging-related problems, and several other structural dynamics studies and diagnosis (Sinha, 2008). However, multiple data collection points are generally required in most of the condition monitoring systems which makes the system costly if conventional accelerometers are used. Hence, there is a need for cheaper and reliable alternative for the conventional accelerometers. The MEMS accelerometers are one such options recently receiving attention due to their low cost and small size (Ratcliffe et al., 2008). It is a new technology for an accelerometer and produced in a similar fashion as an integrated circuit manufacturing (Pandiyan et al., 2006). However, the use of MEMS accelerometers is still limited in the field of condition monitoring because of lack of confidence level in their performance. A few earlier researches gave comparison of the performance between the MEMS and conventional accelerometers, mainly related to the frequency content in the spectrum of the measured signals. It has been observed that the frequencies content in the spectrum of the measured signal from the MEMS accelerometer are same as the spectrum obtained from the conventional accelerometer; however the significant deviation has been noticed in the amplitude and phase (Albarbar et al., 2009). This need to be corrected for the reliable vibration based diagnosis using the MEMS accelerometers. This can be done either in frequency domain or in time domain. In practice, many vibration based diagnosis for machines and structures have been utilising the frequency domain data for the system and fault identifications, hence this paper presents a correction method for MEMS accelerometer response in the frequency domain.

-2-

PROPOSED IMPROVEMENT METHOD

It has been proposed that the characteristic function (CF) curve for a MEMS accelerometer signals with respect to the reference conventional accelerometer can be generated and then used for correction purpose (Badri and Sinha, 2008). The CF curve is nothing but the frequency response function over the measured frequency range of the MEMS accelerometer generated from the laboratory test using the sweep-sine excitation.

Fig. 1 The Test Setup

The test setup as shown in Figure 1 consists of a small shaker (M/s GW make) together with a shaker power amplifier, signal generator and a PC based data acquisition for data collection and storage for further signal processing. Two accelerometers (one reference accelerometer and other test accelerometer) were attached back to back on the armature of to the shaker. The collected experimental data have then been analysed to compute the Frequency Response Function (FRF) using the test accelerometer as output and the reference accelerometer as input using the following equation

)(

)()()(

ωω

ωωxx

xy

S

SCFFRF == (1)

where, Sxy(ω)is the cross spectral density and Sxx(ω) is the Power Spectral Density (PSD) at frequency (ω). y(t) is the test accelerometer signal and x(t) is the reference accelerometer signal. The functions Sxy(ω) and Sxx (ω) have been compute as

Ε= ∗

=∑ )().(

1

ωω r

n

rrxy YXS (2)

Ε= ∗

=∑ )().()(

1

ωωω r

n

rrxx XXS (3)

where, Xr(ω) is the Fourier Transformation (FT) of the rth segment of x(t), )(ω∗rX is its

complex conjugate, Yr(ω) is the FT of the rth segment of y(t), )(ω∗rY is its complex conjugate,

and ( ).Ε indicates the mean value.

NIDAQ Card

Signal Generator

Shaker

S.C

Test Accelerometer

Reference Accelerometer

Power Amplifier

Signal Processing & Data display

-3-

This FRF will give both the amplitude ratio and phase relation between two signals, which has been referred as the CF for the Test accelerometer and used for MEMS signals correction. CORRECTION IN FREQUENCY DOMAIN

Now it is assumed that test accelerometer has been used in the field, the measured data is ym(t). Let Ym,r(ω) is the FT for rth segment of ym(t), this Ym,r(ω) will have error in both amplitude and phase. Hence, the corrected FT for rth segment can be calculated as:

)(,,

12

1

2

)(

)()( θθ

θ

θ

ωω

ω −=== j

j

jrmC

rm eA

B

Ae

Be

CF

YY (4)

Equation (4) will be repeated for all segments of )(tym data, say r=1,2,3,……..,n segments.

Finally the corrected PSD of the test accelerometer data can be computed as

Ε= ∗

=∑ )().()( ,

1, ωωω

C

rm

n

r

Crm

Cyy YYS (5)

TEST EXAMPLE 1

Here the PCB accelerometer has been used as a Reference accelerometer and MEMS accelerometer as the Test accelerometer. The PCB accelerometer is an ICP type with the technical specifications – Sensitivity 100mV/g, Linear frequency range up to 2 kHz, 50 g level. The MEMS accelerometer is of technical specifications – 250mV/g, Frequency range 1.5 kHz, ±2 g level. The experiments were conducted using the chirp-sine excitation up to 1 kHz with linear chip rate of 2.5 kHz/s.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.5

0

0.5

Time, s

Acc

eler

atio

n, g

MEMS 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-10

-5

0

5

10

Time, s

Acc

eler

atio

n, g

PCB Accelerometer

Fig. 2 Measured acceleration responses of the MEMS and Reference Accelerometers

The time domain signals for both Test and Reference accelerometers are shown in Figure 2. The spectra and the FRF of the measured acceleration responses up to 400Hz are also shown in Figure 3 as the excitation level was within 1 g. The deviation in the amplitude and phase of the MEMS compared to the Reference Accelerometer has been observed as shown in Figure 3(b). Hence, FRF shown in Figure 3(b) has been referred as the CF for the Test Accelerometer.

-4-

Fig. 3 Acceleration responses in frequency domain for the Test and Reference Accelerometers, (a) Amplitude Spectra, (b) FRF Amplitude and Phase

CORRECTION APPLIED

Now, the corrections have been applied to the measured signals by the Test Accelerometer when the chirp-sine excitation and sinusoidal excitation at the number of frequencies were used. The correction method discussed earlier has been used.

CHIRP-SINE MEASUREMENT

Here the output of the Test accelerometer shown in Figure 3(a) has been chosen for the correction. The corrected amplitude spectrum for the Test Accelerometer is shown in Figure 4, and it is also compared with the amplitude spectrum of the Reference Accelerometer. The FRF between the Test Accelerometer and the Reference Accelerometer after correction has also been computed which is shown in Figure 5. The amplitude ratio is now 1 with 0 degrees phase at all frequencies. The small scatter seen in the phase angle at different frequencies in Figure 5 is almost negligible error. Hence, the example shows the advantages of the proposed method.

0 50 100 150 200 250 300 350 4000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Acc

eler

atio

n, g

*MEMS - PCB

Fig. 4 Comparison Amplitude spectra of the Test accelerometer (after correction, line with star) and the Reference

accelerometer (solid line) for the linear chirp-sine excitation

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency, Hz

Acc

eler

atio

n, g

MEMSPCB

(a)

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

Frequency, Hz

FR

F A

mp

litu

de

MEMS /PCB Accelerometer

0 50 100 150 200 250 300 350 400-200

-100

0

100

200

Frequency, Hz

FR

F P

has

e, d

eg.


(b)

-5-

0 50 100 150 200 250 300 350 4000

0.5

1

1.5

2

Frequency, HzF

RF

Am

plit

ud

e


0 50 100 150 200 250 300 350 400-2

-1

0

1

2x 10

-14

Frequency, Hz

FR

F P

has

e, d

eg.


Fig. 5 FRF plot between the Test accelerometer (after correction) and the Reference accelerometers for the linear

chirp-sine excitation.

THE SINUSOIDAL SIGNALS

The number of test experiments conducted when the shaker was excited sinusoidally at different frequencies and then responses were measured by both the Test Accelerometer and Reference Accelerometer. The measured responses by the Test Accelerometer were then corrected using the CF for the Test Accelerometer. Two typical examples at 145Hz and 377Hz (before and after correction) are shown in Figures 6-9.

Fig. 6 Comparison of the amplitude spectra of the Test accelerometer (line with star) and the Reference accelerometer (line with plus) for the sinusoidal signal at 145 Hz, (a) before correction, (b) after correction

120 125 130 135 140 145 150 155 160 165 1700

0.5

1

1.5

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB(a)

120 125 130 135 140 145 150 155 160 165 1700

0.5

1

1.5

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB

(b)

-6-

Fig. 7 FRF plots the MEMS with respect to the Reference Accelerometer for the sinusoidal signal at 145Hz (indicated by circle), (a) before correction, (b) after correction.

Fig. 8 Comparison of the amplitude spectra of the MEMS (line with star) and the Reference Accelerometer (line with plus) for the sinusoidal signal at 377Hz, (a) before correction, (b) after correction

Fig. 9 FRF plots the MEMS with respect to the Reference Accelerometer for the sinusoidal signal at 377Hz

(indicated by circle), (a) before correction, (b) after correction.

130 135 140 145 150 155 1600.1

0.12

0.14

0.16

0.18

Frequency, Hz

FR

F A

mp

litu

de


130 135 140 145 150 155 160-20

-15

-10

-5

0

Frequency, Hz

FR

F P

has

e, d

eg.


(a)

120 125 130 135 140 145 150 155 1600.5

1

1.5

Frequency, Hz

FR

F A

mp

litu

de


120 125 130 135 140 145 150 155 160-10

-5

0

5

10

Frequency, Hz

FR

F P

has

e, d

eg.


(b)

350 355 360 365 370 375 380 385 390 395 4000

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB

(a)

350 355 360 365 370 375 380 385 390 395 400

0

0.2

0.4

0.6

0.8

1

1.2

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB(b)

350 355 360 365 370 375 380 385 390 395 4000.13

0.135

0.14

0.145

0.15

Frequency, Hz

FR

F A

mp

litu

de


350 355 360 365 370 375 380 385 390 395 4006

7

8

9

10

Frequency, Hz

FR

F P

has

e, d

eg.


(a)

350 355 360 365 370 375 380 385 390 395 400

0

1

2

3

4

Frequency, Hz

FR

F A

mp

litu

de


350 355 360 365 370 375 380 385 390 395 400-60

-40

-20

0

20

40

Frequency, Hz

FR

F P

has

e, d

eg.


(b)

-7-

TEST EXAMPLE 2

Similar experiment has been done on another MEMS accelerometer of technical specifications 170mV/g, Frequency range 1.5 kHz, ±1.7 g level. The CF has been estimated for this Test Accelerometer and then used for correcting number of sinusoidal signals measured by this MEMS accelerometer. Two typical examples at 237.5 Hz and 377 Hz. Few typical examples at 237.5Hz and 377Hz (before and after correction) are shown in Figures 10-13. The amplitude spectrum of the Test accelerometer at 237.5 Hz and 377 Hz before correction show significant deviation in the response of the Test accelerometer compared with the spectrum of the Reference accelerometer as shown in Figures 10 (a) and Figure 12 (a) respectively. In fact, this deviation was not only in amplitude but also in phase as can be seen from the FRF plots shown in Figures 11 (a) and 13 (a).

Fig. 10 Comparison of the amplitude spectra of the MEMS (line with star) and the Reference Accelerometer (line with plus) for the sinusoidal signal at 237.5 Hz, (a) before correction, (b) after correction

However, the FRF plots after correction shown in Figures 11(b) and 13(b) indicate amplitude nearly equal to 1 and phase close to 0 degrees.

Fig. 11 FRF plots the MEMS with respect to the Reference Accelerometer for the sinusoidal signal at 237.5 Hz (indicated by circle), (a) before correction, (b) after correction.

230 232 234 236 238 240 242 244 246 248 2500

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency, Hz

Acc

ele

ratio

n, g

MEMS PCB

(a)

230 232 234 236 238 240 242 244 246 2480

0.2

0.4

0.6

0.8

1

1.2

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB(b)

230 232 234 236 238 240 242 244 246 248 2500

0.5

1

1.5

2

Frequency, Hz

FR

F A

mp

litu

de

MEMS/PCB Accelerometer

230 232 234 236 238 240 242 244 246 248 250104

106

108

110

Frequency, Hz

FR

F P

has

e, d

eg.


(a)

230 232 234 236 238 240 242 244 246 248 2500.5

1

1.5

2

2.5

Frequency, Hz

FR

F A

mp

litu

de


230 232 234 236 238 240 242 244 246 248 2500

20

40

60

Frequency, Hz

FR

F P

has

e, d

eg.


(b)

-8-

Fig. 12 Comparison of the amplitude spectra of the Test accelerometer (line with star) and the Reference accelerometer (line with plus) for the sinusoidal signal at 377 Hz, (a) before correction, (b) after correction

Fig. 13 FRF plots the MEMS with respect to the Reference Accelerometer for the sinusoidal signal at 377Hz (indicated by circle), (a) before correction, (b) after correction.

CONCLUSIONS

The amplitude and phase of two typical Test accelerometers (MEMS accelerometers) response showed significant deviation when compared with a conventional reference accelerometer. Hence, a method for correcting both amplitude and phase response of any accelerometer in frequency domain has been presented. The method is based on the generation of a characteristic function (CF) using well known reference accelerometer in Lab test and then this CF has been used in correcting the signals in frequency domain. The method has been qualified through number of tests. The promising results indicate that the suggested approach can be used for the practical applications if the reliability of the measured signals from an accelerometer is suspected.

350 355 360 365 370 375 380 385 390 395 4000

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB

(a)

350 355 360 365 370 375 380 385 390 395 400

0

0.2

0.4

0.6

0.8

1

1.2

Frequency, Hz

Acc

eler

atio

n, g

MEMS PCB

(b)

360 365 370 375 380 385 3900

0.2

0.4

0.6

0.8

Frequency, Hz

FR

F A

mp

litu

de


360 365 370 375 380 385 390-200

-100

0

100

200

Frequency, Hz

FR

F P

has

e, d

eg.


(a)

360 365 370 375 380 385 3900

2

4

6

8

Frequency, Hz

FR

F A

mp

litu

de


360 365 370 375 380 385 390-200

-100

0

100

200

Frequency, Hz

FR

F P

has

e, d

eg.


(b)

-9-

REFERENCES

Albarbar A, Badri A., Sinha Jyoti K, Starr A. Performance evaluation of MEMS accelerometers. Measurement, 42; 5; 2009, p. 790-795.

Badri A.E., Sinha JK. Correcting Amplitude and Phase Measurement of Accelerometer in Frequency Domain. Proceeding of The Fifth International Conference on Condition Monitoring & Machinery Failure Prevention Technologies (2008) 94-100.

Pandiyan J., Umapathy M., Balachandar S., Arumugam M. Design of Industrial Vibration Transmitter Using MEMS Accelerometer. Journal of Physics: Conference Series, 34; 2006 p.442–447.

Ratcliffe C., Heider D., Crane R., Krauthauser C., Yoon M.K., Gillespie Jr. J.W. Investigation into the use of low cost MEMS accelerometers for vibration based damage detection. Composite Structures, 82; 2008 p. 61–70.

Sinha JK. Vibration based Diagnosis Techniques used in Nuclear Power Plants: An Overview of Experiences. Nuclear Engineering and Design 238; 9; 2008, p. 2439-2452.

vibe

Documents