Novel Coaxial Cable Sensors for Large Strain Measurement in SHM

Transcription

1 Civil Structural Health Monitoring Workshop (CSHM-4) - Poster 20 Novel Coaxial Cable Sensors for Large Strain Measurement in SHM Zhi ZHOU *, Peng LI *, Yuan LI *, Peng ZHAO *, Hai XIAO **, Jinping OU * * School of Civil Engineering, Dalian University of Technology, Dalian, , China ** Electrical & Computer Engineering, Missouri Univ of Sci & Tech, Rolla, MO, USA Abstract: Monitoring of structure integrity is technically challenging because these engineered structures are inherently large in dimension and geometrically complex. The general requirements on the monitoring technology include high resolution, large dynamic range, low cost, excellent reliability, and remote operation at a long working distance. However, current sensing technologies still have difficulty to meet these requirements. Therefore, there is a continuing need for developing new sensor technologies to address the challenges and ensure the safe operation of the nation s critical infrastructures. Inspired by the concept of one-dimensional photonic crystal and fiber Bragg grating signal mechanism, a novel coaxial cable Bragg grating (CCBG) is proposed. This paper firstly investigated the working mechanism and the Bragg condition of CCBG by transmission line theory and coupled mode theory.then, through advanced modeling and simulation the large strain sensor was designed and fabrication for SHM. And a maximum range around 70000µ (7%) and good linearity were demonstrated by the sensing experiments. Finally, a kind of high-precision demodulation techniques based on a positive feedback analogue oscillator system was realized, which can obtain high signal to noise ratio, narrow bandwidth signal, making the resolution of CCBG of 11.4 µε. The results showed that: CCBG has the characteristics of a wide range, high-resolution to meet the needs of the harsh environment for SHM. Introduction The development of large strain sensors has recently attracted worldwide attentions [1]. To this endeavor, the main challenge remains in achieving a large dynamic range while maintaining high resolution. Conventional strain sensors represented by electro-resistive strain gauges have the satisfactory resolution but a limited dynamic range of less than 1.5%. For strains higher than 2%, extensometers, linear variable differential transformers [2], and grating based mark tracking technique are commonly used [3]. They can typically measure a strain of up to 5% with low resolution of 0.45%. A common issue associated with these large strain sensors resides in the difficulty for sensor embedment into the structure due to the large size of the transducer. Other issues include electrical wiring/connection, poor stability and large temperature cross-sensitivity. In the past two decades, fiber optic sensors Licence:

2 have found many successful applications in SHM due to their unique advantages such as compactness, high resolution, immunity to electromagnetic interference, remote operation and multiplexing capability [4]. In general, fiber sensors have relatively small dynamic range due to the limited deformability of silica glass. Various strain transfer mechanisms have been investigated to extend the dynamic range of the sensor devices. For example through a specially-designed sensor package, a high strain resolution of 10 μ within a large dynamic range (12,000 μ) has been demonstrated using an extrinsic Fabry-Perot interferometer (EFPI) [5]. However, when embedded into the structure, the signal transmission line (i.e., the optical fiber) can easily break when it is subjected to a large strain (about 10 m or 1%) and/or a shear force, causing serious challenges for sensor installation and operation [6]. As such, fiber optic sensors have restricted applications in heavy duty or large strain measurement. Considering the large strain capability and robustness to ambient environment, we report a novel coaxial cable Bragg grating (CCBG) structure for large strain sensing to enhance the measurement sensitivity. Inspired by the traditional FBG, we have developed the CCBG governed by the same electromagnetic (EM) theory. The modeling of CCBG has been fully understood and established. In this paper, transmission line theory and coupled mode theory based analytical model is used to explore reflection spectrum, and together with the software HFSS the deterministic structural/material parameters that affect the sensor Q-factor is analyzed to designed and fabricate the large strain sensor. A series of axial strain measurements of the CCBGs have been tested. Experimental results show the CCBG sensor performs well in terms of sensitivity and linearity. To obtain high signal to noise ratio, narrow bandwidth signal, a kind of high-precision demodulation techniques based on a positive feedback analogue oscillator system was realized. 1. Principle of Coaxial Cable Bragg Grating 1.1 Transmission Line Theory Firstly, According to transmission line theory [7], one perturbs the EM waves in the otherwise continuous coaxial transmission line, resulting in a localized characteristic impedance change and thus a partial reflection from the impedance discontinuity. Assuming all the discontinuities are the same, the overall reflection can be obtained based on the well-established transmission line theory: e 1 (1 ) e reflection spectrum 1 (1 ) e j2 2 j2 N 2 j2 (1) Where N is the number of discontinuities in the cable; β is the propagation constant of the EM wave travelling inside the cable; Λ is the period of the gratings; and, Г is the reflection coefficient of each individual discontinuity. However, it is not suitable for the device design because the reflection coefficient is unknown.

3 Discontinuity segment Transmission line (TL) segment 1.2 Coupled Mode Theory Fig 1. Structure Form of CCBG According to coupled mode theory [8], Similar to the well-studied case of fiber Bragg gratings, the periodic perturbations [9] in CCBG eventually act as weak reflection mirrors. All the frequencies will be weakly reflected back but only a particular frequency (in phase) could be added up constructively. As a result, a narrowband spectrum will be reflected back, and the center wavelength is known as a Bragg wavelength λ : =2n B Where n is the refractive index of the grating and is the grating period. The orthogonal modes do not exchange energy and the modes are coupled due to the dielectric perturbation. Particularly, in CCBG, the TEM mode is the dominant propagation mode, so the coupling only happens between forward and backward TEM (2) waves. It is assumed that A s and B s are the amplitude of the backward and forward waves. They are functions of frequency f and position z in the wave travelling direction. The following coupled wave equations depict the forward wave and backward wave coupling as d A z K B z i z s ab s s dz exp 2 d B z K A z i z s ba s s dz exp 2 (3) (4) where s s is the propagation constant of the TEM waves in the coaxial cable, and l.the term s K ab is known as the coupling coefficient 0 2 = i s Kab r Es dxdy 4 (5) Where is angular frequency; is the dielectric deformation in the coaxial cable; r s 2 E is the modal electric field for the TEM waves. Equations (1) and (2) indicate that the amplitude of the forward (backward) wave changes as a function of the dielectric deformation, the modal field distribution, and the amplitudes of the forward and backward waves. Then, the reflection spectrum of the CCBG can be obtained by solving the

4 differential equations (3) and (4) using a finite difference method. The reflectivity can be written as Kab sinh Kab L R (6) sinh Kab L Kab cosh Kab L Fig 2. Reflection Spectra versus Normalized Wavelength for Bragg Reflection in Uniform Gratings with Different Coupling Coefficient Since the mathematical expressions had been got, a CCBG sensor can be studied to investigate the effects of various geometrical parameters on its performance. 2. Modeling and simulation for CCBG It is necessary to model and simulate CCBG to optimize the important parameter. In this paper, software HFSS and finite element method are used to reach the goal. As shown in the rest paper,where the discontinuities are shown as holes and deformation as examples, the entire cable will be divided into many pieces,especially where the holes or deformation exist. 2.1 Simulation for Hole-drilling CCBG According to modeling and simulation of CCBG emerged by different aperture sizes, the CCBG's signal can be obtained by the hole drilling method. An optimization can be made for the drilling model of CCBG as well as the optimum drilling diameter. A determination of CCBG's model parameters was made by the performance of the computer and the signal strength of CCBG: the period of CCBG is 2 cm, the number of impedance discontinuity of CCBG is 10. The aperture(r) of CCBG model were 0.2mm, 0.4mm, 0.8mm, 1.0mm, 1.5mm, 2mm, 2.5mm separately, and the other parameters are all the same.

5 Medium Change of Hole-drilling Fig 3. CCBG Modeling for Hole-drilling Method Reflection(dB) R=0.2 R=0.4 R=0.8 R=1.0 R=1.5 R=2 R= Frequency(GHz) Fig 4. CCBG Signal Spectrum Performance for Hole-drilling Diameter Q 5.0 Quality factor R Fig 5. Quality Factor of CCBG Changes with Hole-drilling Diameter The diameter increasing, larger reflection makes the signal more detectable. However, the Q-factor decreases as a function of the drilled-hole diameter as shown in Figure. When the Q-factor decreases, the sensitivity of the sensor reduces (more difficult to detect a small frequency change). Hence, the size of the drilled holes shall be optimized to achieve the best possible performance, which is 1.5mm. 2.2 Simulation for Controlled-deformation CCBG Just like the previous the treatment, L will be given different values: 0.2mm, 0.4mm 0.6mm, 0.8mm, 1.0mm, and similar results appeared as in Fig 7. and Fig 8.

6 Fig 6. CCBG Modeling for Controlled-deformation Method Reflection(dB) Frequency(GHz) Fig 7. CCBG Signal Spectrum Performance for Controlled-deformation Length Q 9 Quality factor L(mm) Fig 8. Quality Factor and Amplitude of CCBG Changes with Controlled-deformation Length The figure shows that Q-factor continuous declines when the Controlled-deformation length increases, because the CCBG made by controlled-deformation method have stronger reflecting power,so the length can be chosen less than 1mm. 2.3 Window Function CCBG Model To effectively reduce the side lobe, one method is that discontinuity can be made non uniform. Taking drilling hole method as an example, holes can be drilled to different size

7 which are in accordance with Guass time-domain wave ( R R cos2x ), or 2 1 2n Hamming time-domain wave ( R(n)=exp - 3 ). 2 N-1 Fig 9. Uneven Drilled Hole normal gauss hamming Reflection(dB) Frequency(GHz) Fig 10. Result of Window Function CCBG model The above simulation data show that the CCBG window structure design can effectively reduce the bandwidth of the CCBG signal and suppress of the side lobe of the peak signal, and can play the role of the smooth waveform. CCBG of the Hamming window function structure and Gauss window function structure both can generate higher signal to noise ratio, narrower bandwidth and higher Q-factor signal. 3. Fabrication of CCBG Based on the study of working mechanism of CCBG and advanced simulation, discontinuity can be realized by two methods: hole-drilling method (Fig 11.) and the controlled-deformation method (Fig 12.). The first one is simpler, and Hole-drilling on a coaxial cable may degrade the mechanical strength of the cable. On the other hand, the hole-based CCBG sensor might open the opportunity for filling the holes with other types of materials for the purpose of temperature compensation. In addition, the device might be useful for measurement of other parameters such as corrosion and chemical concentration. Therefore, it deserves a detailed investigation. In our proof-of-concept work, we used a drill-bit to drill holes on a coaxial cable for the creation of periodic discontinuities. The strong resonant peaks and the negligible signal loss clearly prove the effectiveness of this method. However in our

8 preliminary studies, the drilling process was performed manually. The depth, size, shape, surface quality and orientation of these holes were hard to manage. The spatial separation of these holes was also not precisely controlled. The other is better for the structural integrity and can withstand a greater strain, which disrupts the EM wave propagating inside the cable to generate a reflection. Fig. illustrates a controlled deformation in the form of waist reduction and the associated fabrication processes to be investigated in this project. It is expected that the protected discontinuity structure will not degrade the mechanical strength of the cable. Such a waist reduction can be made by compressing a metal sleeve onto the coaxial cable using a crimping tool (e.g., the coaxial cable hexagonal crimper shown in Fig 5.). Metal sleeves and crimping tools are commercially available in a series of standard sizes. If specific shape, size, and width of the deformation are required, the metal sleeve and the crimping tool can also be custom-made or home-fabricated. Using the modeling and simulation tools established in Subtask 1.1, we will derive the quantitative relationship between the grating behavior and the amount of deformation. In addition, we will experimentally investigate the grating performance and test the mechanical strength of the device. Fig 11. Hole-drilling Method Fig 12. Controlled-deformation Method 4. Experimental Work 4.1 Maxima strain test of the CCBG The advantage of using the coaxial cable as a strain senor is the large strain and stress capability compared to the silicon fiber. In order to test the maxima strain capability, a large load step was applied until the cable was break. Hence, we chose a 1000µ increasing step and tested several CCBGs. From way before, a pre-stressing force was applied before testing. We found that the inner conductor of the random discontinuities was broken in each experiment. In the plotted lines, the cross-correlation method still seems better than the peak search method. The maxima strain was around 70000µ (7%) by averaging several tests data. The strain-frequency shift relationship was almost linear, which indicated this CCBG device could be a good large strain sensor in terms of linearity and repeatability.

9 50 Frequence shift(mhz) Equation y = a Adj. R-S Value Standard C Interc C Slope Residual Independent Variable Residual strain Fig 13. Limit-strain for Hole-Drilling CCBG Made of RG-400 CCBG large strain sensor has been proposed and investigated. The fabrication method has been developed and optimized in terms of high Q factor. Different kinds of cables and fabrication parameters were tried. It has been demonstrated to have a large dynamic range up to 70000µ (7%) and a detection limit of 100µ. The experimental results perform well in terms of sensitivity and linearity. The unique large strain capability and robustness to survive harsh conditions maybe fit for large strain monitoring in SHM. 4.2 Temperature Sensing Experiment A variety of substances can serve as the insulation of the coaxial cable insulation, so CCBG made of different cables have dramatically different temperature sensitivity. Hence, CCBGs can be used as a temperature sensor by tracking the shift in resonant frequency as a function of temperature, or only sensitive to the strain. Fig 14. Temperature-sensitive of Two CCBGs Made of Different Cables CCBGs with different temperature sensitivities can be used for simultaneous measurement of strain and temperature.

10 5. Demodulation Techniques The positive feedback system for CCBG is developed based on the idea of laser oscillator. The electronic-controllable gain-adjustable amplifier works with the band-adjustable band-pass filter to provide a narrow band amplification of the RF signal. The positive feedback is realized by employing a directional coupler and the coupling is from Port 1 to Port 3. The CCBG sensor terminated by a 50Ω matched load is connected to Port 1 of the directional coupler. Besides a positive feedback, the Barkhausen conditions (i.e. loop gain must be unity and loop phase shift must be 0 ) have to be satisfied in order to start with oscillation [10]. Due to the Bragg grating reflections, the RF signal spectrum at Port 1 is very low (i.e. about -30dB) in broadband except at the resonances. The center frequency and the bandwidth of the adjustable filter can be electronically controlled so as to make narrow-band amplification around a resonance frequency. The condition of unity loop gain can be satisfied at this particular frequency by adjusting the gain of the adjustable amplifier. Then tune the loop phase to be zero at this frequency by changing the length of the coaxial cables. As long as these two conditions are satisfied, signal at this particular frequency begins oscillating, while signal at the other frequencies does not oscillate because the Barkhausen conditions are not satisfied. Consequently, a sharp resonance at this frequency is expected to see on the signal spectrum, if measuring at the isolated end of the directional coupler. Fig 15. A positive feedback system for CCBG sensor Aside from an improvement of Q factor, the positive feedback oscillator system also helps reduce the cost of CCBG sensing and measurement. Hence, by employing the positive feedback system, the instrument cost can be saved significantly and therefore the overall cost of monitoring can be reduced considering the electronic components in the feedback oscillator circuit are much cheaper than instruments. The overall system budget could be further reduced by replacing the spectrum analyzer by a commercial frequency counter.

11 0-20 Output Signal [dbm] Frequency [GHz] Fig 16. Signal spectrum observed at Port 4 by a spectrum analyzer To test the minimum strain that this positive feedback system can detect, another set of strain test with 20 µm axial distance increment at each step. Similarly, 9 equal steps are conducted resulting in a total displacement of 180 µm. Again, considering the entire length of cable under strain is 174 cm, the strain variation per step is 11.4 µ Measurement data Closed form prediction Resonance Frequncy [MHz] Displacement [um] Fig 17. Resonance frequency as a function of strain with as step of 20 µm An even smaller strain step test (i.e. 15 µm) was conducted but the resonance frequency of the output signal spectrum did no longer change monotonically with strain variation. Therefore, the minimum detectable strain using the CCBG sensor with the positive feedback system is 20 µm or 11.4 µ. It improves the device sensitivity/accuracy about 10 times [3] in terms of these strain tests. 6 Conclusions In this paper, a novel CCBG large strain sensor has been proposed and investigated. The principle of CCBG was introduced and the software HFSS was used to for CCBG modeling and simulation. The fabrication method has been developed and optimized in terms of high Q factor. Different kinds of cables and fabrication parameters were tried. It has been demonstrated to have a large dynamic range up to 70000µ (7%) and a detection limit of 100µ. A cross correlation method was applied for data processing and sensitivity enhancement. The experimental results perform well in terms of sensitivity and linearity.

12 The unique large strain capability and robustness to survive harsh conditions maybe fit for large strain monitoring in SHM. What s more, a positive feedback oscillator analogue system was developed in this paper, and experiments showed that the Q factor of the signal can be improved by 3500 times using this feedback system. Further strain tests demonstrate that the minimum detectable strain is 11.4 µ, which is almost 10 times smaller than a direct VNA measurement of the reflection. References [1] J. M. KO and Y. Q. Ni "Technology developments in structural health monitoring of large-scale bridges," Engineering Structures 27, [2] E. Schedin and A. Melander, "The evaluation of large strains from industrial sheet metal stampings with a square grid," Journal of Applied Metalworking 4, [3] I. Aoki and T. Takahashi "Material flow analysis on shearing process by applying Fourier phase correlation method - Analysis of piercing and fine-blanking," Journal of Materials Processing Technology 134, [4] M. D. Todd, J. M. Nichols, S. T. Trickey, M. Seaver, C. J. Nichols, and L. N. Virgin "Bragg grating based fibre optic sensors in structural health monitoring," Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, [5] H. Ying and et al "An extrinsic Fabry Perot interferometer-based large strain sensor with high resolution," Measurement Science and Technology 21, [6] P. Biswas, S. Bandyopadhyay, K. Kesavan, S. Parivallal, B. A. Sundaram, K. Ravisankar, and K.Dasgupta "Investigation on packages of fiber Bragg grating for use as embeddable strain sensor in concrete structure," Sensors and Actuators, A: Physical 157, [7] D. M. Pozar Microwave Engineering (John Wiley & Sons, Hoboken, NJ), p. 52. [8] H. Kogelnik Theory of optical waveguides, in Guided-Wave Optoelectronics,T. Tamir, Ed. New York: Springer-Verlag. [9] H.T. Erdogan "Fiber grating spectra" Journal of Lightwave technology, vol.15, pp [10] A. Sedra and K. Smith Microelectronic circuits 6th edition, Oxford University Press, New York