**3. Methods**

In this section, will be presented specific devices that have been used for experimental vibration measurements, therefore standard seismic station, fiber-optic interferometric system and pneumatic system.

#### *3.1. Seismic Equipment BRS32*

The BRS32 seismic station is one of the most widely used seismic stations in Central Europe; it is used for the purposes of seismic monitoring in engineering practice. BRS32 is, therefore, a universal seismic station, used for measurements both with battery power in field conditions for short-term measurements and for long-term seismic monitoring with connection to the electrical network and the possibility of remote data transmission. The compact station contains a three-component seismic velocity geophone. USB interface is used for all settings. The frequency range of the internal geophone (depending on the type of installed geophone) is between 0.5 Hz and 80 Hz at the dynamics of up to 120 dB. Sampling frequency is 250 Hz. The device, after switching on is automatically connected to the Global Positioning System (GPS) signal. The measurement coordinates are saved and the time is synchronized. The battery lasts more than 48 hours. BRS32 is very compact with simple control. Use of this device is in all application in the field of natural and induced seismicity. Internal geophones can be selected during the production. Two types are the most used: Dutch SM6-3D with frequency range 4.5 to 100 Hz and German LE3D Lennartz with frequency range 1 to 80 Hz [32]. Geophone SM6-3D has been installed in the device used. The seismic station BRS32 is serially manufactured in the Czech Republic by Arenal s.r.o., it is calibrated according to the relevant standards, and certified.

#### *3.2. Fiber-Optic Interferometric System Being Developed for Seismic Monitoring*

Fiber-optic sensors can be divided into several basic categories, wherein one of them includes phase-modulated sensors. Phase-modulated sensors compare the phase of the radiation source (light) in a measurement fiber to a reference fiber in a device called an interferometer. In other words, the relative phase change between two light waves is measured. Phase-modulated sensors are one of the most sensitive principles known, with large dynamic range suitable for various applications.

The phase delay of light due to passing through the optical fiber section *φ* is given by relation (1), where *n*0 is the refractive index of the fiber core, *l* represents the fiber length and *λ* the wavelength of the radiation source used. A change in the fiber length *l* or the refractive index of the core of the measuring fiber *n*0 causes a phase change that can be described as follows (2).

$$
\phi = k n\_0 l = \frac{2\pi n\_0 l}{\lambda} \tag{1}
$$

$$
\phi + \Delta\phi = \frac{2\pi}{\lambda} (n\_0 l + n\_0 \Delta l + l \Delta n\_0) \tag{2}
$$

The external conditions can affect the characteristics of light waves within the optical fiber one of them being the phase delay. The optical fiber is sensitive to the mechanical stress (the expansion or compression) acting in the fiber axis which is based on the theory of elasticity. The mechanical stress results in the changes of the refractive indices of the

fiber core and cladding, the fiber length and the fiber core diameter [33]. Interferometer translates these mechanical changes into optical intensity changes measurable by regular optical power detectors. The interferometric sensor output can be described by (3), where *C* is the mean value of the optical intensity, *A* is the amplitude of the variation of the optical intensity, and Δ*φ*(*t*) is the phase difference between the interferometer arms.

$$I(t) = \mathbb{C} + A \cos(\Delta \phi(t))\tag{3}$$

Since several known fiber-optic connections lead to wave interference, it was necessary to choose the most suitable one for solving the issue of vibration measurement. Eventually, the connection of the Michelson interferometer, which uses two short sections of fibers terminated by a reflective element, such as a mirror, became the most suitable one. This type of interferometer is not very sensitive to changes in the wavelength of the radiation source, assuming a balanced fiber length of the interferometer arms, is compact because it requires only short sections of optical fibers in the sensor, has as large dynamic range as the Mach–Zehnder interferometer, and is fairly sensitive to low-frequency vibrations and acoustic signals [33].

The basic connection of the fiber-optic Michelson interferometer (MI) is determined by fiber optical symmetrical 2 × 2 coupler which has two input and two output ports. An optical radiation source is connected at the input port and is supplemented by an isolator, to suppress the back reflections. The short fiber sections at the outputs form the measurement and reference arms of the interferometer. The fibers are terminated with mirrors and the output signal is transmitted by the same coupling element to the photodetector via the second input port, see Figure 1.

**Figure 1.** A basic connection of the Michelson interferometer.

To determine the value of <sup>Δ</sup>*φ*(*t*), a demodulation technique is essential to perform the measurements. The operational passivity of the so-called homodyne demodulation [34] is advantageous in the sensor construction as it uses a 3 × 3 coupler instead of 2 × 2 and therefore having phase-shifted signal outputs, which can be described by the following Equations (4)–(6), where *δi* is 3 × 3 coupler phase asymmetry.

$$u\_1 = C\_1 + A\_1 \cos\left(\Delta\phi(t) - \frac{2\pi}{3} - \delta\_1(t)\right) \tag{4}$$

$$
u\_2 = \mathbb{C}\_2 + A\_2 \cos(\Delta \phi(t))\tag{5}$$

$$
\Delta u\_3 = \mathcal{C}\_3 + A\_3 \cos \left( \Delta \phi(t) + \frac{2\pi}{3} + \delta\_2(t) \right) \tag{6}
$$

In the first step, the DC offset *Ci* and modulation amplitude *Ai* are equalized for all channels, *Ci* is set to 0 and *Ai* is set to 1. Subsequently, following Formula (7) can be applied [35]. The demodulation can be performed digitally with harmonic arctangent function.

$$
\tan \Delta \phi(t) = \frac{\sqrt{3}(\mu\_2 - \mu\_3)}{\mu\_2 + \mu\_3 - 2\mu\_1} \tag{7}
$$

The unwrapped phase difference can be continuously measured in real time with basically no limit to its measuring range. The accuracy and amplitude limit of phase difference is given by the photodetector bandwidth and sampling rate. For the particular application, single MHz photodetector and 100 kS/s sampling rate is well above the expected measured vibration frequency and amplitude range. The entire connection of the actual measuring system with the interferometer is shown in Figure 2.

**Figure 2.** Connection of the sensor system with the fiber-optic interferometer.

The radiation source is a narrow-spectrum laser diode operating at a wavelength of 1550 nm with an output power of 3 mW. An optical three-port circulator separating the forward and reverse directions is connected to the laser output. This circulator can be located just behind the diode, behind the connecting optical cable, or be a part of the sensor, but is typically located just behind the radiation source, thereby saving one fiber in the cable connecting the optoelectronics and the sensor itself. The sensor then consists only of a 3 × 3 coupling element with even ratio and a measuring and reference fiber terminated with fiber mirrors, e.g., Newport F-FRM. Three output signals are fed to InGaAs photodetectors, the electrical output of which is connected to a measuring card (A/D converter). The ADC used is the 9222 module in the cDAQ-9181 chassis made by National Instruments. The signals are further processed by software (passive demodulation, filtering, spectral analysis).

The sensor design incorporates a waterproof aluminum box measuring 253 × 159 × 72 mm. A three-meter single-mode fiber in primary protection was affixed to the bottom of the box using epoxy resin (hard material with a high Young's modulus of elasticity, for good vibration transmission). Shorter fiber lengths provide lower sensitivity, while longer lengths limit the lower cut-off frequency of the sensor due to the still present slow drift of the sensors. The drift comes from several imperfections, such as finite polarization extinction ratio of passive optical components and fibers, radiation source wavelength stability but mainly due to the small temporal variation of temperature. The length of three meters is the compromise value for both. A vertical vibration then uniformly applies mechanical stress perpendicular to the fiber axis. A reference arm of the same length and a fiber coupler were then loosely placed in the acoustic insulating foam to minimize the transmission of vertical vibrations to the other arm [36]; in addition, this arm was made in a higher degree of protection with a 3 mm jacket further reducing the amount of vibration affecting the fiber length and core refractive index. Optical connectors for connecting

the optical cable or fibers were built into the front panel. An example of the complete connection of the Fiber-optic interferometric system is shown in Figure 3.

**Figure 3.** Example of connection of the fiber-optic interferometer and the sensor system.

#### *3.3. Pneumatic System Being Developed for Seismic Monitoring*

The device works as a converter of mechanical vibrations propagated by the surrounding material to a change in the sound pressure, which is sensed by a pressure sensor. The device consists of a flexible polyvinyl chloride (PVC) tube, which is in direct contact with a pad through which the desired signal is propagated. The tube is sealed on both sides, specifically with a microphone on one side and a seal on the other one. The surface of the tube acts as a membrane that is dilated by seismic/mechanical waves, thus changing the volume of the tube. A system sealed in this manner has, at a constant temperature, a direct relationship between the volume and the pressure of the gas enclosed within the tube, so this system works as a converter of physical quantities (Figure 4).

**Figure 4.** Diagram of the pneumatic system.

This system is resistant to ambient acoustic interference. According to the previous experiment in which the signal inside and outside the tube was sensed, the measurement showed that the attenuation of the signal measured with a wobble frequency of up to

2.5 kHz was 20 to 40 dB [37]. Furthermore, it was found that despite the self-supporting PVC pipes, there were changes in the measured signal due to sudden changes in the ambient pressure, e.g., when opening the doors or windows. In the case of industrial use, it would be necessary to bury this sensor, cover it with sand or place it in a box with a constant pressure to prevent the influence of changes in the ambient pressure on the measured signal. These error signals appear to be short-term extremes, but in the case of evaluating seismic activity at critical points, they could be evaluated as a hazardous condition.

Previous experiments have also confirmed that this system measures more easily mechanical vibration propagated through materials with acoustic impedance similar to the tube material rather than through ambient air. In the case of using a material with similar acoustic impedance, this results in minimal reflection of the passing wave and the highest signal gain.

Due to its low construction costs, the measuring system is suitable for outdoor use or for incorporation into the building structure. The sensitive part of the measuring system, a soft tube with the advantage of a PVC material, is resistant to electromagnetic influences, mechanical and chemical damage, so it can be used even in places where standard sensors could be harmed or affected. An example of the complete connection of the pneumatic system is shown in Figure 5.

**Figure 5.** Example of connection of the pneumatic system.

## **4. Experimental Setup**

The experiment was conducted in the heavy laboratories of the Faculty of Civil Engineering, VSB-Technical University of Ostrava, on a massive, poured concrete floor in the basement of the building. Two BRS32 seismic stations, two experimentally developed interferometers for vibration measurement, five pneumatic sensors and one tri-axial accelerometer were used throughout the experiment (not all results from all devices from this comparative measurement are presented in this paper). For further processing, for the purposes of this publication, data from only one BRS32 seismic station, one interferometric sensor and one pneumatic sensor (marked in red) were used. The distance of the sensors from the source of the calibrated stroke was 0.5 m (Figure 6a), or 1.0 m (Figure 6b), or 1.5 m (Figure 6c). The diagram of the entire calibration experiment is shown in Figure 7.

**Figure 6.** Comparative experiment (the alternative types of the sensors being developed presented in this paper are marked in red): (**a**) a distance of 0.5 m from the calibrated stroke; (**b**) a distance of 1.0 m from the calibrated stroke; (**c**) a distance of 1.5 m from the calibrated stroke.

**Figure 7.** Diagram of the entire comparative experiment.

The source of the calibrated stroke consisted of a drop weight weighing 10 kg and falling from a height of 0.7 m on a circular impact plate with a diameter of 0.3 m and a weight of 5 kg. The induced impulse of force of the weight is 7.1 kN and the duration of the impulse is 45 ms.

In each stage of the measurement, at a distance of 0.5 m to 1.5 m, 100 strokes were performed. A time delay of at least 5 s was allowed between each stroke. After each stroke, the recordings from the experimental sensors were stored and marked with the appropriate time according to GPS for the purpose of unambiguous identification. The BRS32 seismic station was started in a continuous recording mode, which is synchronized with GPS.

#### **5. Results of Experiments**

In the following section, the results from experimental measurements in the time domain, which were obtained both from the BRS32 seismic station and from both sensory devices being developed, will be presented and described in detail.

Figure 8 shows a time recording of the calibrated stroke at a distance of 1 m from the BRS32 seismic station. The horizontal axis represents GPS time, while the vertical axis represents amplitude of the oscillation velocity [mm.s−1]. A calibrated stroke was recorded at time "T". After a rapid and sharp increase to the maximum, there was very quick attenuation. This is a typical manifestation of such an isolated dynamic phenomenon in the time domain. In general, seismic station BRS32 records in three perpendicular directions (vertical, horizontal radial and horizontal transversal). The comparative experiment was simplified with dynamic impulse in vertical direction, in the near zone also we can expect the main dynamic response in vertical direction, thus only the vertical component was compared with experimentally developed devices.

**Figure 8.** Time recording of the calibrated stroke at a distance of 1 m from the BRS32 seismic station.

Figure 9 shows a time recording of one calibrated stroke at a distance of 1 m from the interferometric sensor being developed. The horizontal axis represents time, while the vertical axis represents phase response [Deg]. A calibrated stroke was recorded at time "T". After a rapid and sharp increase to the maximum, there was very quick attenuation and at time T + 0.045 s a second impulse of a very similar nature was recorded, only with a lower maximum. The first maximum is a manifestation of the impact of the drop weight on the circular impact plate, the second maximum is a manifestation of the plate in contact with the concrete base. The time difference between the two maxima corresponds exactly to the impact time of the drop weight, which is 45 ms. This is a phenomenon that can be observed when placing the place on a relatively very rigid layer (e.g., a concrete floor). If the plate is placed on a less solid surface (e.g., soil) then the second maximum is significantly smaller.

**Figure 9.** Time recording of a calibrated stroke at a distance of 1 m from the interferometric sensor being developed.

Figure 10 shows a time recording of one calibrated stroke at a distance of 1 m from the pneumatic sensor being developed. The horizontal axis represents time, while the vertical axis represents pressure [Pa]. A calibrated stroke was recorded at time "T". After a rapid and sharp increase to the maximum, there was attenuation, but before the pulse was completely attenuated, so, at time T + 0.045 s, a second impulse of a very similar nature was recorded again, and again only with a lower maximum. The first maximum is, as with the interferometric sensor, a manifestation of the impact of the falling weight on the circular impact plate; only this manifestation was not so quickly attenuated, which is related to the construction of the pneumatic sensor; and the second maximum is again a manifestation of the plate in contact with the base. As with the previous recording, the time difference is 45 ms.

**Figure 10.** Time recording of one calibrated stroke at a distance of 1 m from the pneumatic sensor being developed.

Time recordings from all 300 strokes at distances of 0.5 m, 1.0 m and 1.5 m were always of the same nature for the BRS32 seismic station as well as for both sensory devices being developed, both in terms of the length of each phenomenon and in terms of the size of the maxima. As the distance from the calibrated stroke increased, only the maxima measured decreased.

#### **6. Basic Recalculation of Measured Values between Fiber-optic Interferometric Sensor and Pneumatic Sensor, Respectively and Seismic Station**

To the finding of the mathematical relationship between the values of optical measurement system and the oscillation velocity measurements, an analysis of the subsets of the measured data for each distance and each dynamic stroke was first performed. From each of the two corresponding partial recordings of the oscillation velocity and the phase response for a certain distance and a certain stroke, we obtain a pair of values, which correspond to the absolute maxima of these two recordings mentioned. Maxima are not exactly at the same time. This does not allow neither an environment of experiment, nor a completely different design of sensors working on other physical principles and with a different sampling frequency. By merging the results of the primarily processed subsets, we then receive a global set of results—maximum values obtained by optical measurement (independent variable in the regression analysis) and corresponding maximum absolute values of oscillation velocity (dependent variable in the regression function). Using the least squares method, the regression function with the highest coefficient of determination *R*2, was determined. In this case, a linear regression function was the best:

> *v*

$$
\hat{a} = a + b\mathfrak{x} \tag{8}
$$

*v*—amplitude of the oscillation velocity,

*x*—maximum phase response obtained from optical measurements,

*a*, *b*—constants.

In the case of the finding of the mathematical relationship between the results of pneumatic measurements and the measurement of oscillation velocity, an analogous approach was applied to determine the optimal shape of the regression function with the highest determination coefficient *R*2. The exponential regression curve is the best:

$$w = a \times \exp(bx) \tag{9}$$

*v*—amplitude of the oscillation velocity,

*x*—maximum value of pneumatic measurements,

*a*, *b*—constants.

The results of both mathematical relationships for the optical interferometer and the seismic station, and the pneumatic sensor and the seismic station are presented in Figures 11 and 12, respectively. Both dependences show a very high correlation coefficient *R*2. Table 3 then summarizes the main results from the entire experiment, i.e., the correlation relations for both sensory devices being developed, the relevant correlation coefficients and the deviations from the measured values of the amplitude of the oscillation velocity obtained from the seismic station.

**Figure 11.** Mathematical relationship for the optical interferometer.

**Figure 12.** Mathematical relationship for the pneumatic sensor.


**Table 3.** Summary results of data mathematical processing of the comparative measurement of the optical interferometer system and the pneumatic system.
