Biaxial FBG Vibration Sensor With a Single Edge Filter and Matching Demodulation

This work developed, simulated, and characterized a high sensitivity vibration sensor for low-frequency applications. The fiber Bragg grating (FBG) overlapping method was used to demodulate the wavelength shift of the sensing gratings, but only one FBG for each axis was utilized (unlike two FBGs in the common approach), along with another one acting as a filter for both axes and temperature compensator; this enhanced method could measure acceleration in two axes simultaneously, although only the X-axis had constant sensibility in the entire operating range. The difficulty in achieving constant sensitivity in both axes lies in the need to match three Bragg gratings, resulting in a set of gratings with similar Bragg wavelengths. The new results showed constant sensitivity in both accelerometer axes (0.735 and 0.684 <inline-formula> <tex-math notation="LaTeX">$\text{V}\cdot \text{m}^{-1}\cdot \text{s}$ </tex-math></inline-formula>2 for the X- and Y-axis, respectively). The usable frequency and acceleration amplitude ranges were from 0.5 to 20 Hz and from <inline-formula> <tex-math notation="LaTeX">$14\times10$ </tex-math></inline-formula>−3 to 9 m/s2, respectively, which both meet the requirements for detecting seismic-induced movements. Furthermore, the present results demonstrate that we can utilize a smaller number of gratings in accelerometer development compared to the common approach.


I. INTRODUCTION
Buildings may be greatly affected by seismic movements, whose effect on them must thus be monitored. The response and health of buildings can be effectively assessed by measuring the spectral acceleration of their movement induced by ground motion [1], [2]. Optical sensors, compared to electronic ones, offer advantages such as electromagnetic interference immunity and high sensitivity that make them suitable for installation in all types of building, regardless of the electromagnetic noise level.
Several types of fiber Bragg grating (FBG)-based accelerometers have been developed in one, two, or three axes. For example, a uniaxial device includes a microstructure for measuring vibration and temperature simultaneously, The associate editor coordinating the review of this manuscript and approving it for publication was Md. Selim Habib . within a 0.5-10 Hz range, and it uses filters and photodetectors to demodulate the FBG Bragg wavelength [3]. A twodimensional (2D) vibration sensor [4] has been endowed with adjustable sensitivity to make it equal in both axes within a detection range of 0-180 Hz; however, no measurements under 20 Hz have been reported, and an interrogator was used to demodulate the FBG Bragg wavelength. A biaxial accelerometer using only 2 FBGs arranged on one axis and relying on axial and transverse forces has also been developed [5]. It has a resonant frequency of 34.42 Hz and needs an interrogator to demodulate its wavelength shift. Reference [6] presented a biaxial vibration sensor based on a multiaxis flexure hinge, with a measurement range of  Hz and the same sensitivity in the two axes. However, for the application at which our work aims, this frequency range is not sufficiently low and requires the use of an interrogator.
Besides the accelerometers listed above, the development of this kind of sensor has been focused mainly on uniaxial models [7]. Nonetheless, since vibration is a multidimensional vector signal, we developed a 2D sensor. As described above and reported in other studies [8], [9], [10], [11], [12], when researchers develop a new model, they use two FBGs for each axis when the edge filter demodulation method is utilized or a smaller number of FBGs but coupled with an interrogator. An interrogator with good precision and scanning speed has a high cost that is affordable for distributed sensing but not for applications in independent sensors. In our previous work [13], we proposed a biaxial vibration sensor that uses only one FBG for each axis and does not need an interrogator, but we could not attain constant sensitivity in both axes in its measurement range.
In addition to the experimental work, this work also includes sensor simulation and in-depth theoretical analysis of the physical structure. Additionally, we changed the characteristics of its sensing FBGs, specifically the central Bragg wavelength, to better approximate the optimal operation point where the FBG response to deformation is linear. With this modification, we achieved a better sensing performance with almost constant sensitivity in both axes within the target range, which is intended for measuring the building's response to seismic ground motions; our previous work was unable to achieve this performance.
The proposed application for this sensor in seismically active areas is critical, and it is unique because each monitoring structure, such as buildings, tunnels, or bridges, has specific frequency and amplitude measurement requirements. This sensor is an additional option for measurement vibration applications.
First, the working principle and theoretical model of the accelerometer is discussed in this study. Then, a finite element analysis (FEA) simulation of the sensor's natural frequency, conducted to verify the theoretical results, is reported. Finally, the experimental results for the sensitivity, frequency response, and natural frequency of the sensor are presented.

II. WORKING PRINCIPLE A. FBG
An FBG is essentially a temperature and strain sensor. Its Bragg wavelength (λ B ) is determined by the effective refractive index of the fiber core (n eff ) and the grating period ( ) as follows: A change in temperature and axial strain will cause a wavelength shift ( λ B ) in the FBG: where α is the thermal expansion coefficient of FBG, η is the thermo-optic coefficient of FBG, T is the temperature variation, ρ e is the fiber optic photoelastic coefficient, and ε is the axial strain.  When an appropriate interface is designed, other physical quantities can be measured with respect to the temperature or strain change in the FBG. The vibration applied to the whole accelerometer results in a strain change in the FBGs.
The accelerometer proposed has a reference FBG that acts as an edge filter in the optical demodulation scheme, which is not affected by the acceleration. Moreover, this FBG allows us to cancel the temperature effects in the output signal of the sensor, simplifying (2) as follows: B. STRUCTURE AND THEORETICAL MODEL Fig. 1 displays the structure of the proposed sensor, which consists of a flexible cylindrical beam, an inertial mass (m), one FBG for each sensing axis, and fixed parts with respect to the sensor movement. The fibers are fixed to optical fiber clamps by pressure. VOLUME 10, 2022 To analyze this biaxial sensor, we consider it as two independent one-dimensional systems (Fig. 2). According to Newton's laws of motion, a one-dimensional system is equivalent to a second-order vibration system. k s is the bending stiffness of the flexible beam, and the FBG is represented as a spring with a tension stiffness coefficient of k f .
From the mechanics of materials, k f can be expressed as where E f and A f are the Young's modulus and cross-section area of the optical fiber, respectively, and L f is the length of the fiber between the fixed points.
The k s values can be obtained as where E s and L s are the Young's modulus and length of the flexible beam, respectively, and I s is its second moment of inertia, which is equal in all directions and given by I s = (π/4)r 4 , where r is its radius. When the excitation frequency is much lower than the natural angular frequency (ω 0 ), the sensitivity (S) and first resonant frequency (f 0 ) for the one-dimensional system are expressed as follows [9]: and Equations (6) and (7) are used to calculate the S and f 0 for each axis of the accelerometer. Fig. 3 illustrates the interrogation scheme of the sensor, which can be divided into an upper and a lower branch corresponding to the X-and Y-axis, respectively. This optical scheme allows us to demodulate the Bragg wavelength by overlapping each sensing FBG with the same reference FBG (FBG REF ). Unlike the two FBGs commonly used for each axis, which would result in four FBGs for a biaxial accelerometer, we use only three FBGs without losing the ability to compensate for the induced Bragg wavelength shift caused by temperature changes. FBG REF is subject to acceleration but is attached at both ends with fixed fiber clamps; thus, it is only affected by temperature changes. A detailed explanation of the principle of this method is provided in [14], [15] and for this specific approach in [13].

III. FEA SIMULATION
For the sensor simulation, the free software FreeCAD was used to model the structure, build the assembly, and perform the frequency analysis. Then, the simulation results were visualized with Paraview. The simulation included the  flexible beam where the inertial mass component is on, the X-and Y-axis optical fibers, and the inertial mass.
The inertial mass was made of polylactic acid. The flexible beam was made of polyamide 6/6, which is a long-lasting material [16]. All the other parts (i.e., sensor base, fixed poles, and optical fiber clamps) were made of aluminum, except for the clamp fixing one end of each fiber and the inertial mass (see Fig. 1).
The accelerometer parameters used in the FEA for the frequency analysis are summarized in Table 1. Fig. 4 displays the finite element mesh of the sensor, which was obtained using second-order tetrahedral elements for better accuracy in the curved shapes, with fixed constraints applied to the base. The element sizes were divided into regions with smaller elements in curved shapes, especially for the optical fibers, to achieve better accuracy, whereas bigger element sizes were organized in plane shapes to optimize the computational resources. The maximum element size was 0.1, 2, 4, and 15 mm for, respectively, the optical fibers, the flexible beam, the optical fiber clamps, and the base and  fixed poles. As a result, the first-order natural frequency was 171.6 Hz on the X-axis and 172.6 Hz on the Y-axis; the normalized displacements are illustrated in Fig. 5 and Fig. 6. In both cases, the point with maximum displacement was at the center of the optical fiber. Fig. 7. shows the vibration test system. A superluminescent diode (SLD) (SLD1005S, Thorlabs) with a 50 nm bandwidth, a near-Gaussian spectral profile, and low ripple, together with a current and temperature controller (LDC3744B, ILX Lightwave) provided light with 1 mW of constant power at 1550-nm central wavelength. The light passed through the reference FBG, as shown in Fig. 3, and reached the optical sensor. The proposed biaxial FBG vibration sensor and an encapsulated arrange of three uniaxial capacitive accelerometers (MMA2260D and MMA1260D) arranged orthogonally were fixed in a vibration table. The vibration table is driven by a universal motor, with a set of pulleys providing a vibration range of 0.1-50 Hz in an almost sinusoidal waveform.  The arrangement of capacitive accelerometers was used as a reference to know the input excitation acceleration to the optic sensor. Then, the output light carrying information on the vibration as its intensity changes reached a photodetector (PD-A-25, oeMarket) with a bandwidth of 2.5 GHz and a responsivity of 0.9 A/W at 1550 nm; the amplification stage included a transimpedance circuit for the photodetector and signal conditioning to visualize the information as a voltage through an oscilloscope.

IV. EXPERIMENTAL SETUP
Three FBGs with acrylate coating on the SMF-28e fibers and similar Bragg wavelengths (oeMarket.com) were used in this work. The length, reflectivity, and bandwidth of each FBG were 5 mm, >95%, and 0.2 nm, respectively. The initial central wavelengths at 21.0 • C of the reference FBG, X-axis FBG, and Y-axis FBG were 1549.449, 1549.470, and 1549.439 nm, respectively; they were measured by an optical spectrum analyzer (Fiberer-OSA-M-(1525-1565), Fiberer) with an operating wavelength range of 1525-1565 nm, 2-pm wavelength resolution, an operating optic power range of −75 to +5 dBm, and wavelength repeatability of ±5 pm. When the FBGs were mounted, a prestress was applied to them and their central wavelengths were left as close as possible. After the FBGs were fixed, the final wavelengths were 1549.637 and 1549.640 pm for the X-and Y-axis, respectively. Finally, the Bragg wavelength of the reference FBG was tuned using a translation stage to leave it in the central operation point [13].

A. NATURAL FREQUENCY
The natural frequency of the sensor is an important parameter that affects its sensitivity and working frequency range. An impulse signal contains all frequencies; hence, an input impulse signal was applied to the vibration table to determine the natural frequency of our accelerometer. The impulse response observed in the oscilloscope was recorded, obtaining its frequency spectrum. The time domain response and corresponding frequency spectrum for the accelerometer X-and Y-axis are shown in Fig. 8 and Fig. 9, respectively. The X and Y axes have been chosen in a horizontal plane because buildings preferentially move in a horizontal XY plane in a seismic event. The X and Y axes are orthogonally arranged.
The experimental resonant frequency of the accelerometer was about 174 Hz and 182 Hz for the X-and Y-axis, respectively. We calculated the theoretical natural frequency of the accelerometer by substituting, in (7), L f with L x and L y (i.e., for the X-and Y-axis), whose values were 184.7 and 184.5 Hz, respectively.   Table 2 shows the theoretical, simulated, and experimental natural frequencies of our accelerometer for the X-and Y-axis, with relatively small discrepancies, indicating that all results are valid. These small differences may be due to errors in some parameters, such as the stiffness coefficients of the optical fiber and flexible beam as well as the inertial mass density.
Since the frequency range of interest in the current study is 0.5-20 Hz, the natural frequency of our sensor on both axes is more than twice the maximum frequency of interest and, thus, could provide a reasonably uniform sensitivity curve in the lower-frequency region.

B. FREQUENCY RESPONSE AND SENSITIVITY
The biaxial FBG-based sensor was characterized through an amplitude-frequency scanning experiment in the 0.5-50 Hz range, whereas the input acceleration amplitude varied from 0.02 to 8.5 m/s 2 .
The output amplitudes of the capacitive and optical sensors were recorded and processed on a computer to determine their sensitivity with respect to the experimental frequency range.
The theoretical sensitivity of the optical accelerometer was derived from (6) using ρ e = 0.22 and λ B = 1.55 µm, giving 16 × 10 −12 s 2 . This is a reasonable sensitivity value since we used a reference FBG as an edge filter matched with the sensing FBGs, all the FBGs had a bandwidth of 0.2 nm, and hence the Bragg wavelength change where it is proportional to the photodetector input power was 150 pm [13]. Therefore,  our sensor could measure in an acceleration amplitude range that was 9 m/s 2 wide.
Instead of the Bragg wavelength changes of the sensing FBGs, we measured the sensor output voltage (V out ), which is proportional to such changes, and the acceleration input (a g ). Fig. 10 plots the sensitivity of the optical sensor against the frequency and also shows an amplification of the frequency range of interest (0.5-20 Hz), where the sensitivity was almost constant with an average value of 0.735 and 0.684 V·m −1 · s 2 for the X-and Y-axis, respectively.

C. LINEARITY OF THE BIAXIAL FBG SENSOR
We analyzed the linear response of the accelerometer. Sensor amplitude output is shown in the Fig. 11 as a function of the applied acceleration at different excitation signals (2, 5, and 10 Hz), along with the fitter curves. These experimental results indicate that our FBG accelerometer has good linearity with an R 2 value between 0.985 and 0.991, R 2 is the coefficient of determination. The specific sensitivity at 2, 5, and 10 Hz was, respectively, 0.728, 0.675, and 0.677 V·m −1 ·s 2 for the X-axis and 0.661, 0.644, and 0.666 V·m −1 ·s 2 for the Y-axis. Fig. 12 compares the output signals of the capacitive and optical sensors of an arbitrary input vibration of 1.6 Hz; the fast Fourier transform was applied to the recorded signal. The detected frequency was the same in the two accelerometers, demonstrating the good response of the optical sensor. The output waveform was also the same. The amplitude of the output signals, instead, differed due to the different sensitivity coefficients of the accelerometers. Fig. 13 shows the noise and its equivalent spectral density between 0 and 500 Hz. The proposed sensor exhibited low noise dominated by the 60 Hz power line: about 1 × 10 −3 m·s −2 ·Hz −1/2 on the X-axis and 1.6 × 10 −3 m·s −2 ·Hz −1/2 on the Y-axis. The root-mean-square value of the noise was 5.0 and 4.1 mV for the X-and Y-axis, respectively. Given the accelerometer mean sensitivity and a signal-to-noise ratio of 2, the minimum detectable acceleration was 14 × 10 −3 m/s 2 for the X-axis and 12 × 10 −3 m/s 2 for the Y-axis.

F. DYNAMIC RANGE
The dynamic range (DR) is an important parameter that reflects the ratio between the strongest and weakest detection signals. In the case of our accelerometer, it expresses the relationship between maximum (a max ) and minimum acceleration (a min ): For the FBG accelerometer, a max was limited to 9 m/s 2 by the linear range of the wavelength shift of the sensing FBGs in the overlapping interrogation scheme, whereas a min was limited by the noise. According to (8), DR was 56 and 57 dB for the X-and Y-axis, respectively, in the target range of frequency.

VI. CONCLUSION
We presented a vibration sensor that uses an enhanced FBG overlapping interrogation method, which allows us to utilize a smaller number of FBGs compared with the traditional FBG overlapping method. We also described its working principle and reported simulation and experimental results, which agreed with each other. This sensor has almost constant sensitivity, with a mean value of 0.735 and 0.684 V·m −1 ·s 2 in the X-and Y-axis, respectively, in the 0.5-20 Hz range. The frequency range of this accelerometer makes it suitable for seismic applications and in places with electromagnetic noise to measure, for instance, the response of a building to ground motion. Its minimum acceleration detection is about 14 × 10 −3 m/s 2 , which corresponds to a weak shaking felt only by a few persons at rest, especially on the upper floors of buildings.
Since the proposed sensor has a high degree of sensitivity, it can be used in other applications, such as inertial navigation systems. This sensor can be used to measure vibration in rotating electrical machines in their current configuration by adjusting parameters such as inertial mass and the material of the flexible beam, i.e., the modulus of elasticity of the material.
Furthermore, this sensor does not need an interrogator for individual measurement points. The use of sensing FBGs with similar central wavelength (a difference below 21 pm before prestress, which was even reduced to 3 pm after prestress) allows their tuning. The central wavelengths of the sensing FBGs in the proposed interrogation scheme must be as close as possible to achieve the best performance in both axes.