Proceedings of the IMAC-XXVIII February 1 4, 1, Jacksonville, Florida USA 1 Society for Experimental Mechanics Inc. Calibration and Processing of Geophone Signals for Structural Vibration Measurements Rune Brincker, Professor Bob Bolton, Associate professor Anders Brandt, Associate Professor Department of Industrial and Civil Engineering, University of Southern Denmark, Niels Bohrs Allé 1, DK-53 Odense M, Denmark NOMENCLATURE x(t) base displacement y(t) coil displacement M moving mass k suspension stiffness c suspension damping ratio f frequency ω cyclic frequency damping ratio ς H transfer function V voltage G transduction constant ABSTRACT Geophones are highly sensitive motion transducers that have been used by seismologists and geophysicists for decades. The conventional geophone's ratio of cost to performance, including noise, linearity and dynamic range is unmatched by advanced modern accelerometers. However, the problem of this sensor is that it measures velocity, and that the linear frequency range is limited to frequencies above the natural frequency, typically at 4-1 Hz. In this paper an instrument is presented based on geophone technology. The sensor is aimed at low vibration level measurements on large civil structures, thus the problem of correcting the bad frequency response becomes essential. The instrument is based on a digitally wired system principle where time synchronization is obtained by GPS, and a good frequency response is secured by calibration and subsequent correction using inverse filtering techniques. 1. INTRODUCTION This sensor type has several advantages. Because of the simple construction, the sensor element is robust and cheap. The sensor is simple to apply in long cable or wireless systems because the passive sensor element does not require power supply. Further, if the sensor is well engineered, it has an excellent linearity
and a large frequency range. Since normally not only a single coil is used, but two coils in differential coupling, and since the sensor does not include any active elements to introduce potential additional noise, the sensor has an extremely low noise floor. Mainly because of the bad frequency response, the sensor has not been used much in modal applications like Operational Modal Analysis (OMA). However, using a measurement system that samples the signal at the source, transmits the signal trough a digital transmission line, and correcting the signal digitally after sampling, the geophone sensor element is a good alternative to more complicated sensors like sensors based on a force balance principle. In this paper a digital system is introduced that allows the user to perform OMA of very large structures, since two independent systems can be used, each synchronized through GPS, allowing the user to perform OMA using one system for reference measurements and moving the other system around to acquire data for different data sets.. SENSOR ELEMENT The problem of the geophone sensor is that the linear frequency range is limited to frequencies above the natural frequency, typically at 4-1 Hz. Also, some would add that it might also be a problem that it measures velocity. However, that can also be seen as an advantage, since if one might need to obtain displacement by integration, the velocity signal needs to be integrated only once. Further, for OMA it does make any difference if the measured signal is velocity or acceleration, thus, in this paper, the main problem is considered to be the non-linear frequency response. The geophone sensor consists of a coil suspended around a permanent magnet, see figure 1. Describing the suspended coil as a one DOF system and using the Faraday law, the frequency response function between velocity of the base and the relative velocity between coil and magnet can be found to, Brincker et al [1] (1) H ω = ω + jω ως ω See figure 1. The natural frequency ω and the damping ratio ς of the suspended system is given by k ( ) ω = ς = M c km It is useful to note that the following results for the phase ϕ can be obtained at the natural frequency ω = πf, Brincker et al [1] (3) dϕ 1 ϕ = π / = df ςf These relations can be used for identification of the natural frequency and damping of the sensor element. The actual geophone sensor element has the following mean properties, G = 8.8Vs / m, f = 4. 5 Hz, ς =.56
y(t), coil displacement x(t), base Figure 1. Left: Definition of base and coil displacements, Right: Theoretical transfer function for the geophone sensor element. The main advantage of the geophone sensor element is its simple and robust sensor configuration and the long term experience with the sensor from many geophysical applications. However, also the noise properties are outstanding. For the actual sensor the inherent noise floor is specified by the vendor to U noise =.1 nm / s Hz corresponding to an electrical signal of V noise = 3 nv / Hz. With proper sealing and electromagnetic shielding, this noise floor can be assumed to be the noise floor of the applied sensor. 3. MEASUREMENT SYSTEM The measurement system is purely digital and consists of a client/computer, a sensor base, and a measurement chain of sensor nodes, see figure. The sensor base serves as a hub for all communication to and from the sensor nodes along with GPS handling and time stamping of data and communication of measurement and status information to the client. The base station uses primarily GPS time for time synchronization; however it is also equipped with an internal clock, which ensures that all sensors connected to the base remains synchronized even in the absence of a GPS signal. A typical measurement setup is shown in figure. The time synchronization error is smaller than.5 ms. The digital technology of the A/D converter is similar to the one described in Brincker et al []. The sensors have been produced by CAP ApS, Denmark, and further information can be found in the data sheet, [4]. 4. CALIBRATION Sensor elements can be easily calibrated if a 3D shaking table is available, in this case, the movement of the shaking table can be measured by a laser, and the frequency response function can be estimated as described in Brincker et al [1]. The main problem in this procedure is to estimate the time delay that might be present in the applied laser, to deal with the inherent non-linearities in many industrial lasers, and finally, to ensure enough movement of shaking table in the low frequency region in order to obtain a good estimate of the FRF in this region.
Figure. One measurement system with base and GPS, and one measurement chain that can contain up to 3 nodes, each housing 3 geophone sensor elements in a 3D configuration and local A/D converters. f, ς can easily be found either by simple When an FRF is estimated, the sensor element properties, G, means like using Eq. (3) or by fitting a parametric model to the FRF for instance by using the MATLAB Signal Processing toolbox, [5]. An alternative to calibrating each sensor element separately using a laser to measure the exact movements of the sensor base like described in Brincker et al [1], is to calibrate on the site putting all sensors close to each other and using a reference accelerometer. 5. SIGNAL CORRECTION The measured data u = y x are divided into data segments and taken from the discrete time domain to the discrete frequency domain by the Fast Fourier Transform (FFT). In the frequency domain the measured signals are corrected using the inverse transfer function given by Eq. (1) ( 4) X = U / H and the corresponding time signals are then obtained by an inverse FFT transform and added by a similar procedure as described in Brincker et al [3]. After such correction and assuming that the noise floor is constant and limited to the inherent noise, the dynamic range of the sensor element can be found to be as shown in figure 3, Brincker et al [1].
Figure 3. Dynamic range estimated for the considered geophone sensor element after digital correction. 6. CONCLUSIONS A system has been developed that is capable of being used for OMA on large structures. The system supports high accuracy synchronization using several measurement stations far apart from each other, it supports high sensor counts, and takes full advantage of the high sensitivity and low noise floor of the geophone sensor element. 7. REFERENCES [1] Brincker, R., Lagö, T., Andersen, P., Ventura, C.: Improving the Classical Geophone Sensor Element by Digital Correction. In Proc. of the International Modal Analysis Conference. 5, Orlando, FL, USA, Jan 31 - Feb 3, 5. [] Brincker, R, Larsen, J.A, Ventura, C.: A General Purpose Digital System for Field Vibration Testing. In Proc. of the International Modal Analysis Conference. Orlando, FL, USA, Feb. 19-, 7. [3] Brincker, R. Brandt, A., Bolton, R.: FFT Integration of Time Series using an Overlap-Add Technique. In Proc. of the International Modal Analysis Conference. 1, Jacksonville, FL, USA, Feb 1-4, 1. [4] Data sheets: CAP Geophone Sensor Node, and CAP Sensor Base, CAP ApS, info@cap.dk [5] MATLAB Signal Processing Toolbox, Mathworks Inc., www.mathworks.com