Vibration Analysis using Extrinsic Fabry-Perot Interferometric Sensors and Neural Networks

Transcription

1 1 Vibration Analysis using Extrinsic Fabry-Perot Interferometric Sensors and Neural Networks ROHIT DUA STEVE E. WATKINS A.C.I.L Applied Optics Laboratory Dept. of Electrical and Computer Dept. of Electrical and Computer Eng, University of Missouri-Rolla, Eng. University of Missouri-Rolla, Rolla, MO-65409, USA Rolla, MO-65409, USA DONALD C. WUNSCH A.C.I.L Dept. of Electrical and Computer Eng. University of Missouri-Rolla Rolla, MO-65409, USA ABSTRACT An Extrinsic Fabry-Perot interferometric (EFPI) sensor attached to a vibrating structure will see a sinusoidal strain. Harmonic analysis on this strain yields well defined harmonics. Strain level measurement, on a periodically-actuatedinstrumented structure, can provide information about the health of that structure. This approach can form a smart health monitoring system for composite structures. A simple demodulation system employing artificial neural networks (ANN) was used to extract harmonics and predict the maximum strain level on a smart composite beam. This paper deals with the computer simulation of the sinusoidal strain and implementation of the demodulation system. The system employs two back-propagation neural networks. The first network extracts the harmonics from the strain profile and the second predicts the strain levels through harmonic analysis extracted. INTRODUCTION The choice of particular sensor types for a given sensing application depends upon the parameter being measured and the physical properties of the sensor. The parameter being measured can be strain, temperature, pressure, or force on the structure. Fiber optic sensors have gained importance in recent years and have been used in a variety of structural applications including strain sensing and damage detection [1]-[3]. These sensors integrated with composite structures have been an active area of research in recent years [4]-[7]. However some sensors exhibit non-linear output, which poses a requirement on processing capabilities and a processor must accomplish these tasks quickly and efficiently to make the smart structure an on-line system. Artificial neural networks have attracted increasing attention, in recent years due to their capabilities including pattern recognition, classification and function approximation. For large monitoring systems having numerous built-in sensors (and actuators), real time operation requires high computing speeds. Artificial neural networks have parallel computing architectures, and when implemented in hardware, can quickly process multiple inputs [8]. Neural networks can learn to process data one way, and when conditions change, the processing can adopt to new conditions. They have been extensively used for health monitoring, which involves damage assessment, fatigue monitoring, delamination

2 detection, etc. For instance, the ability to predict failure and to provide real-time structural monitoring for advanced fiber-reinforced polymer composites can be realized with neural network based smart sensing system [7], [9]. Strain sensing techniques are shown to be capable of characterizing and assessing impact induced damage and warning of impending weakness in structural integrity of a composite structure [9]. Analysis of periodically actuated composite structures yields modal frequencies, which are related to the structural integrity. For composite structures, these modal frequencies vary with delamination and other damage. Extrinsic Fabry-Perot Interferometric (EFPI) sensors have been shown to have more sensitivity and better signal-to-noise ratio in obtaining these modal frequencies. These frequency components have been shown to relate to information pertaining to the health monitoring of composite beams [9]. Shifts in natural frequencies have been used to identify damage generated by various mechanical loadings and vibration of the composite structure [10]. Neural networks have been used to locate and classify damage using these modal frequencies [9]. A Fourier series neural network (FSNN) has been employed in obtaining modal frequencies from the fiber optic sensor output [11]. This paper proposes an alternative, customized and faster neural network implementation to obtain harmonic amplitudes from the strain output of the sensor and predicting the strain level acting on the structure. The next section provides an introduction to EFPI sensors in addition to explaining in detail the sinusoidal strain output. Theoretical generation of the required data for training and testing the required networks is discussed in the third section. Implementation of two neural networks, one for extracting harmonics from strain output and second to predict the strain level from the extracted harmonic amplitudes, is described in the fourth section. The fifth section presents the results obtained from the test data. The final section gives the conclusions and further work to be carried out. FIBER OPTIC SENSORS Common fiber optic sensors are based on interferometric and attenuation effects. Apart from being immune to electromagnetic interference, non-conductive to electrical sources, capable of wide temperature operation, and safe in inflammable or explosive environment, fiber optic sensors can be embedded into composite structures, have high bandwidth, may be multiplexed, and are capable of serving not only as sensors but also mediums to relay their information [1]-[3]. Interferometric sensors are more sensitive and are localized in sensing compared to attenuation systems, but they suffer from nonlinearity requiring extra processing [11]. Fabry-Perot sensors have added advantages over other interferometric types. They have no reference arm requriement as in Michelson or Mach-Zehnder sensor and are single ended[3]. This research uses the extrinsic Fabry-Perot interferometric (EFPI) sensor, figure (1), to sense the strain levels. EFPI sensors have short gauge length and consequently are used for point strain measurement. The optical output is the reflected signal formed by the interference of multiple reflections from the glass-air interfaces of the cavity. The output of the sensor is proportional to the optical output of the EFPI from small perturbations, but extends into the nonlinear regions for larger strains. Various types of demodulation methods exist to extract strain information from these waveforms [1]- [13]. An important case in strain measurement sensors occurs for sinusoidal strain. The periodic sensor output is modulated by this sinusoidal strain. This situation may occur in resonance or vibration experiments due to the sinusoidal excitation from an actuator.

3 3 Incident Light Optical Fiber Reflected Signal Cavity Capillary Tube FIGURE 1: EFPI Sensor The transmittance (ratio of the output irradiance to the input irradiance) equation for an EFPI sensor is given by [14] Ir F sin ( δ / ) [4R /(1 R) ] sin ( δ / ) 1 sin ( δ / ) Ii + F 1+ [4R /(1 R) ] sin ( δ / ) (1) where F gives the cavity Finesse and δ depends on the optical path length difference between the cavity reflections. The finesse of the fiber is set by the interface reflectance, R, of the in the cavity ends. The parameter δ depends on the cavity length d as 4π d n δ λ cavity 4π ( d + d) n λ where n cavity is the refractive index of the cavity (air in this case) and λ is the wavelength of the light travelling in the fiber. A sinusoidal strain level acting on the sensor can be related to the change in cavity length by d ε εmax sin(πft+ φ) (3) L Combining equation () and (3) and inserting them in equation (1), the final equation for the output irradiance of the sensor is given by 4πn ( + ε sin(π + φ) Ca din L m ft F sin I λ r (4) Ii 4πn ( d + L ε sin(πft+ φ) Ca in m 1+ F sin λ in cavity () FIGURE : Actuation Signal and Sensor Output The output varies as a function of maximum strain change, ε max, and actuation frequency, f. The other parameters including finesse, cavity length, gauge length,

4 4 wavelength of operation and refractive index in the cavity are fixed quantities, and will depend on the type of sensor and its operational conditions. Figure () depicts a typical sensor output under sinusoidal strain condition with an actuation frequency of 1000 Hz and strain level of 105 µε. The highly nonlinear output is a weighted sum of sinusoidal components at the actuation frequency and its harmonics [11]. DEMODULATION SYSTEM A two-stage artificial neural network (ANN) demodulator is proposed that maps the sensor output to the strain level by analyzing its harmonic components was used. The first stage accepts the sensor profile and provides the amplitudes of the first ten harmonics. The second stage predicts the strain amplitude from the extracted harmonics. Data Generation The sensor profiles where generated using equation (4) with the following typical experimental values [9]. L8mm, R0.9, n cavity 1, λ1300 nm, d in 101 µm ε max The change in strain,, was varied from 10 µε to 00 µε and the frequency of actuation ranged from 1 Hz to 1000 Hz. First 10 harmonic amplitudes were extracted from the sensor profiles using simple FFT analysis. It can be seen from figure (4), that the sensor output and the harmonic amplitudes vary with the variation of the strain level. Figure (5) depicts the variation of harmonic amplitude levels for four strain levels. FIGURE 4: Sensor Output & Harmonic Amplitudes For 100 µε Variation of Harmonic Amplitudes with Strain change Amplitude ue 5 ue 55 ue 105 ue ue FIGURE 5: Varitaion of Harmonic Amplitudes with Strain Neural Network Implementation & Training[8] Two neural networks were used to implement the demodulation system. A 1001,5,30,10 ANN was used for training and simulating the first stage of the system.

5 5 There are 5 and 30 neurons in the first and second hidden layer, respectively, and 10 neurons in the output layer. Transfer functions of all the three layers is 'TANSIG'. Sampled sinusoidal strain profile (1001 samples), normalized and scaled between 1 and 1 formed the input to the network. The network was trained to the first ten harmonic amplitudes of the strain profile, necessitating 10 neurons in the output layer. A 10:10:1 ANN was used for training and simulating the second stage of the system. There are 10 neurons and 1 neuron in the hidden and output layer respectively. Transfer functions of both the layers is 'TANSIG'. The first ten harmonic amplitudes, normalized and scaled between 1 and 1, were used as inputs to the network. The network was trained to output the strain level. A total of 1950 vectors were generated, of which, 1755 were used for training and 195 for testing the network. Standard backpropagation with different training algorithms was used for both the neural networks. Owing to the large input vector size (1001 elements), Levenberg Marquardt and Newtons algorithm could not be used to train the first stage. The network was trained using conjugate gradient method (using the scalar from Polak & Ribiere), suitable for large vector size, for 3000 epochs to reach the desired mean square error. The second stage, having an input vector size of only 10 elements, was trained using Levenberg Marquardt algorithm. The network converged to the desired mean square error in 50 epochs Test Results Figure (7) shows some typical results from the first stage. The circles represent the simulated outputs and the 'stars' represent the known outputs for a test sensor profile. It can be seen that the network can extract the amplitude of the harmonics with a high degree of accuracy. A minute error occurs in extracting the lower frequency components of sensor profiles with low strain values. FIGURE 7: Typical Results From First Stage FIGURE 8: Typical Results For Second Stage Figure (8) shows some typical results from the second stage. It is observed that the network outputs have small errors at low strain values. For higher strain values, it demonstrates high accuracy. Since the simulated outputs of the first stage were used as

6 6 test inputs to the second stage, the error can be contributed to the first network's minute error in extracting lower frequency components. CONCLUSION AND FURTHER WORK A two-stage demodulation system employing neural networks was implemented for an EFPI sensor under sinusoidal strain to extract harmonic amplitudes and predict the strain acting on it. Data generated from the sensor output equation and FFT analysis was used to successfully train and test the demodulation system. This work represents a theoretical implementation. The network has to be fine-tuned to adapt noisy patterns of experimental data. Further work will include experimentally obtaining sensor profiles and harmonic amplitudes by periodically actuating a fiber optic based smart composite beam. NOMENCLATURE I r : Output irradiance I i : Input irradiance F: Cavity finesse of the sensor R: Interface reflectance δ: Cavity parameter d: Cavity length L: Gage length n cavity : Refractive index of the cavity ε: Strain level acting on the sensor REFERENCES [1] M. R. Sayeh, R. Viswanathan, and S.K. Dhali, "Neural Networks for Smart Structures with Fiber Optic Sensors", Proceedings of OE/Midwest: 1990, Proc. SPIE. 1396, (1990). [] K. F. Hale, "An Optical-fiber Fatigue Crack-detection and Monitoring System", Smart Materials and Structures,, (199). [3] Eric Udd, Fiber Optic Sensors, 1 st ed. (John Wiley & Sons, Inc, New York, NY, 1991), , , [4] K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, and R.O. Claus, "Quadrature Phase-Shifted, Extrinsic Fabry-Perot Optical Fiber Sensors", Optics Letters 16(4), (1991) [5] K. Liu and R. M. Measures, " Signal Processing Techniques for Interferometric Fiber-Optic Strain Sensor", Journal of Intelligent Material Systems and Structure, 3, (199) [6] T. Valis, D Hogg, and R. M. Measures,"Fiber-Optic Fabry-Perot Strain Rosettes", Smart Materials and Structures, 1, 7-3 (199). [7] F. Akhavan, S. E. Watkins and K. Chandrashekhara, "Measurement and Analysis of Impact- Induced Strain using Extrinsic Fabry-Perot Optic Sensors", Smart Materials and Structures, 7(6), , (1998) [8] M.T. Hagan, H.B. Demuth, and M. Beale, Neural Network Design (PWS Publishing Company, Boston), 1996 [9] S.E. Watkins, G. W. Sanders, F. Akhavan, and K. Chandrashekhara, "Modal Analysis using Fiber Optic Sensors and Neural Networks for Prediction of Composite Beam Delamination," Smart Materials and Structures, 11(4), , (00). [10] P.M. Mujumdar and S. Suryanarayan, "Flexual Vibrations of Beams with Delamintaions," Journal of Sound and Vibration, 15, (1988) [11] A. Abdi, "Neural Network Demodulation for Frequency Response Measurement of a Fiber Optic-Based Smart Beam", M. S. Thesis, University of Missouri-Rolla, T767, 1999 [1] D. Hogg, D. Janzen, T. valis, and R.M. Measures, "Development of a Fiber Fabry-Perot Strain Gauge", Smart Structures and Skins, 1991, Proc. SPIE, 1588, (1991) [13] F. Schiffer, N. Furstenau, and W. Schmidt," Fiber Optic Interferometirc Strain Sensing on Composites using an Active Homodyne Sawtooth Fringe Counting Technique", Smart Structures and Skins, 1995, Proc. SPIE. 509, 0-9 (1995) [14] M. Born and E. Wolf, Principles of Optics; Electromagnetic Theory of Propagation, Interference, and Diffraction of light, 6 th ed. (Pergamon Press, Terrytown, NY, 1980)