# Dynamic Responses Measured by Optical Fiber Sensor for Structural Health Monitoring
## 3 Strain-Induced Light Intensity Variation  
It is well known that the resonant wavelength of LPFG can be affected by the temperature. To compensate the temperature, [PERSON] et al. [42] proposed a model that mounted a bent LPFG on a beam with a suitable thermal expansion coefficient. The effect of temperature on the resonance wavelength of LPFG can be significantly reduced. An alternate method to compensate the temperature effect on the LPFG was reported by [PERSON] and [PERSON] [27]. The temperature sensitivity of LPFG can be eliminated by balancing the thermo-optic coefficients of the fiber core and cladding. In this work, LPFG is connected with FBG in series. FBG is attached onto the structure subjected to mechanical loading. LPFG is free standing and kept in the environment with constant temperature to avoid the influence of the temperature on the resonant wavelength of LPFG. The shift of Bragg wavelength induced by the strain in the FBG sensor is converted to the change of the light intensity through an LPFG filter. The light intensity is measured by a photodetector and recorded in the voltage signal. To calibrate the relationship between the strain and the light intensity, experimental tests of a cantilever beam subjected to a loading at its free end were conducted. In the middle of the cantilever beam, an FBG sensor and a strain gauge were adhered to the top and bottom surfaces, respectively. The reflected Bragg wavelength (\(\lambda_{B}=1533.118\) nm) of the FBG sensor used in this study without applied strain is shown in Figure 4. The center wavelength of the FBG is located in the right half of LPFG band filter (as shown in Figure 2). Thus, the light intensity is increases linearly with the increase in strain. A schematic diagram of FBG-LPFG spectra is illustrated in Figure 5. The cantilever beam is made of copper with Young's modulus and density of 120 GPa and 8740 Kg/m\({}^{3}\), respectively. The length,  
Figure 3: Schematic diagram of the integrated optical fiber sensing system.  
width and thickness of the beam are 0.285 m, 0.02 m and 0.001 m, respectively. The cantilever beam is loaded at its free end with various displacements ranging from 5 mm to 30 mm. The strain (measured by strain gauge) and light intensity (measured by photodetector) are recorded and plotted in Figure 6. Three tests were conducted to demonstrate the reproducibility. The results show a linear relationship between the strain \(\varepsilon\) and light intensity variation \(\Delta V\) as follows.  
\[\varepsilon=380.01\frac{V-V_{0}}{V_{0}}=380.01\frac{\Delta V}{V_{0}}\qquad R^ {2}=0.997 \tag{5}\]  
where light intensity variation \(\Delta V\) is normalized by \(V_{0}\), the light intensity is reflected from the FBG sensor without applied strain.  
A good linear correlation between the strain and light intensity variation with standard deviation of 2.7% demonstrates that the proposed optical fiber sensing system can be used to detect the strain by measuring the light intensity through a photodetector. The proposed FBG sensing system consists of  
Figure 4: Wavelength of FBG sensor.  
Figure 5: Schematic diagram of FBG-LPFG spectra.  
FBG, LPFG and photodetector. The sensitivity and resolution of the sensing system are dependent on the characteristic of these sensing units. In this work, the sensitivities of FBG and LPFG are 1.2 pm/\(\mu\varepsilon\) and 3.25 dBm/nm, respectively, while the responsivity of photodetector (EOT 3010, Electro-Optic Technology, Inc., Traverse City, MI, USA) is 1.1 A/W at 1550 nm. Experimental tests showed that the sensitivity of the proposed sensing system is 5 \(\mu\varepsilon\), which is close to the results (3 \(\mu\varepsilon\)) reported by [PERSON] and [PERSON] [24] using the demodulation technique based on a wavelength division coupler. The optical fiber sensing system is fast response, easy to implement, and capable of monitoring the transient and vibration responses of a structure.