Neural Networks Improving Robustness on Fiber Bragg Gratings Interrogation Systems under Optical Power Variations Celso L. N. Veiga1, Leonardo S. Encinas1, Antonio C. Zimmermann1 Metrology and Automation Laboratory of Federal University of Santa Catarina - LABMETRO, Postal Box 5053, Florianopolis, SC, BRAZIL, 88040 970. ABSTRACT The herein article presents a signal processing methodology based on the process knowledge learned by Artificial Neural Networks – ANN aiming to compensate the undesirable power variations of the light in a Fiber Bragg Grating – FBG demodulation system. Conventional ratiometric signal conditioning requires the acquisition of the intensity light signal related to the power light source, minimizing only linear variations of the light imposed to the interrogation system. The proposed method brings better benefits, particularly when the measuring range of the system shall be extended, because of the redundant information generated by the addition of more fixed filters, improving the generalization capacity of the ANN. A temperature interrogation system is also presented and arranged on a typical and useful demodulation architecture, which adopts three filters to extend the measuring range. Preliminary results from a temperature experiment showed the ANN ability to make the FBG demodulation system robust to light variations, including some non-linear characteristic. Keywords: Fiber Bragg Gratings, Optic Fiber Sensors, FBG Interrogation, FBG demodulation, Artificial Neural Networks.
1. INTRODUCTION Light power variations are an undesirable factor in measuring systems based on Fiber Bragg Grating – FBG amplitude demodulation. Variable losses in the fiber circuit, mainly in the fiber sensor, a mechanically free arm of this optical circuit, and/or the broadband light source are considered the responsible for this light variation. To solve this problem, some strategies were developed as seen in [1] and [2], among them, the ratiometric measurement is the most common technique. A new paradigm to solve that problem applying an Artificial Neural Networks – ANN is presented. Signal processing by ANN is very interesting and can perform results very quickly. Once trained, the computational cost is small, consisting only in a matrix addition and multiplication operations, [3]. The proposed solution is particularly useful when allied with the extended measuring range, by the use of two or more FBG to demodulate the sensor signal [4]. On the other hand, it can simplify the optical circuit and overcome eventual nonlinearities. This paper presents the model and an experimental evaluation of the proposed method.
2. FBG OPTICAL CIRCUIT The optical circuit of the Figure 1 is a typical fixed filter FBG demodulation system [5] and [6]. Temperature (T) or strain (ε) quantities affect the sensor signal (S) and three fixed filters (FA, FB and FC) promote convolution and demodulation of the sensor signal. Three photo detectors (PD1, PD2 and PD3) convert signals from the optical convolution [4] to a measurable electrical signal, proportionally to the light intensity that reaches each photo detector. For comparison purposes, a forth photo detector (PDR) is adopted to implement the conventional ratiometric measurement approach. The current sensed in the photo detectors comes from the convolution between the FBG sensor power spectrum and the 1 Celso L. N. Veiga, (professor),
[email protected], Leonardo S. Encinas,
[email protected], (master student) and Antonio C. Zimmermann,
[email protected], (scientist researcher), at Metrology and Automatization Laboratory of the Federal University of Santa Catarina, Florianopolis, SC, Brazil, Phone: +55 48 3239 2033; Fax: +55 48 3239 2039.
19th International Conference on Optical Fibre Sensors, edited by David Sampson, Stephen Collins, Kyunghwan Oh, Ryozo Yamauchi, Proc. of SPIE Vol. 7004, 700462, (2008) 0277-786X/08/$18 doi: 10.1117/12.786945
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FBG filters power spectra. So, the maximum output signal occurs when both spectra match. This current signal is converted into an electrical voltage signal by a transimpedance amplifier and then acquired by an Analog to Digital Converter - ADC. Hence, the output voltage signal is expressed using the Equation 1 below: ∞
V(λS ) = ∫ αS Fi (λ , λFi ) S S (λ , λS )dλ ,
(1)
−∞
where, SFi (λ ,λFi) are the signal spectra for the filters (FA, FB and FC), SS(λ, λS) is the signal spectrum for the sensor (S), and α is a constant, which represents conversion factors present in the electronic circuit. PD1 Quantity
T,
ε
Coupler
S
Broadband Light Source
FA
PD2
FBG Sensor
FB Coupler
PD3
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Temperature Reference Filters
PDR Signals
Fig. 1. Optical circuit used to demodulate the temperature and/or strain quantities.
The advantages of this demodulation system are the relatively high frequency response allied to low cost and simplicity in the hardware and software implementation. The weakness of this method relies on the amplitude demodulation nature of the optical circuit, which is sensible to light variations. The optical circuit in Figure 1 has more attractiveness when wider measuring ranges are demanded, what can be obtained using n concatenated demodulation filters [6]. Adopting two or more demodulation filters, three in this proposed arrangement, it is possible to get extra information of the undesirable power light changes, improving the signal processing performance and achieving the optimal compensation.
3. PROPOSED SIGNAL PROCESSING 3.1 Ratiometric Measuremants Classic ratiometric measurements2 try to minimize the influence of the light source variations during the temperature or strain estimation process. The computation behind ratiometric methodology for FBG interrogation systems can be seen in [1]. In this case, the ratiometric model assumes total positive correlation between the light source power and the light intensity sensed by the photo detector after the signal has passed through the FBG filter. This assumption, in some applications, may not be true, due to the presence of nonlinearities, such as the reduction of light power when the optical fiber is bended on below the curvature radius allowed by the fiber manufacturer. In order to compensate those variations, an extra reference light photo detector PDR shall be applied (like in Figure 1). This limitation gives opportunity to explore other signal processing methodologies that are robust to the light source variations. 3.2 Neural Networks Signal Processing Researches on Artificial Neural Networks applied to signal processing in FBG interrogation systems are being recently adopted to extend the measuring range [4], to increase the resolution and to detect signals from different FBG sensors arranged in a sensor network [7]. Then, taking advantage of the main characteristic of ANN, its generalization capacity, it is proposed a signal processing input/output (I/O) map, to compensate the light source variation without measuring the reference power light related signal. This map is presented in Figure 2. The minimization of the light source influences is achieved during the ANN learning process, where the signals (PD1, PD2 e PD3,) in different levels of light source intensity, and the desired temperatures (T) are submitted to the ANN, that recursively computes the neurons weights and biases until the required training error or training time are reached. Once this exhaustive process is concluded, the ANN is ready to estimate the temperature with good overall accuracy from any 2
Ratiometric measurements: Sensor signal divided by the related light source signal, resulting in a normalized signal
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new dataset (PD1, PD2 and PD3,) even if the light source intensity changes between levels that were not present during the training process. PD1 (V) o
T( C)
PD2 (V) PD3 (V)
ANN
Fig. 2. Proposed I/O map for the ANN signal processing robust to light source variations.
3.3 Architecture and Training Setup The signal processing task is done by a neural network model based on a commonly architecture used with the backpropagation algorithm, the multilayer feedforward network [3]. This kind of network can be used as general function fitter, approximating any function with a finite number of discontinuities. The quality of this approximation depends on the number of hidden layers and neurons which are chosen from an empirical process and same training accuracy level can be achieved with different neuron configurations. So, in order to minimize this effort, a methodology to optimize the number of neurons and layers in feedforward neural networks through subsequent training with different neural network arrangements is presented in [3]. A neural network MATLAB toolbox was applied to optimize and to train the ANN reaching the insensibility to light fluctuations, with the following parameters: (i) 3 neurons in the input layer with tangent-sigmoid activation function; (ii) 5 neurons in the hidden layer with tangent-sigmoid activation function; (iii) 1 neuron in the output layer with the linear activation function; (iv) Scaled Conjugate Gradient backpropagation learning algorithm; (v) maximum training epochs of 50000 and (vi) minimum training error reached of 0.1°C.
4. EXPERIMENTAL EVALUATION An experimental setup was performed in order to evaluate the ANN ability for estimating the sensor temperature without the light power information (PDR). The prototype under test has the configuration according Figure 1, and consisting on the following components: (i) a broadband SLED light source centered at 1550 nm; (ii) one FBG sensor and three FBG filters with central wavelength spaced by 1 nm; (iii) three photo detectors and three signal amplifiers; (iv) data acquisition system and (v) a work station to process and analyze the acquired data. Additionally, the experiment was conducted in a controlled temperature oven with a thermocouple sensor adopted as temperature reference for the entire evaluation. Different temperature levels were generated in this controlled environment, where the FBG sensor and the thermocouple were inserted. At each temperature level, the reference temperature T and the output voltage from the signal amplifiers were acquired. The test was carried out in a range from 25 to 200°C, in non regular intervals of 10 to 20°C. The data collection was performed in two steps: (i) data for the ANN training, where PD1, PD2, PD3 and PDR were acquired as function of reference temperature, as can be seen in Figure 3a (although PDR is not actually used). Each data set was obtained with a different light power, approximately +5% and -5% from a central value, only in crescent temperature cycle; (ii) data for the ANN verification, which was collected as above, but with an intermediate light power. In a closer focus, the FBG filter temperatures were also acquired, with another thermocouple, and its small variations were compensated on the thermocouple reference temperature. The ANN was trained with the first data set PD1, PD2, PD3, reaching a residual error of ± 0.1°C. The second data set PD1, PD2 and PD3 were used to evaluate the ANN efficiency and the resulting errors are shown in Figure 3b. The results confirm the competence of the ANN model to discriminate different levels of light power, being capable to interpolate intermediate conditions and becoming the system immune to this kind of perturbation. Note that this happens even if only two of the three signals are significant to the solution (PD1 or PD3 are quite small along the tested temperature range). There is a mean error of approximately 0.4°C, which can be justified by a thermal delay between the FBG sensor and the reference thermocouple probe, once the data acquisitions were conducted dynamically without preoccupation with the thermal equalization of the sensors.
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1.2
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Fig. 3. (a) Data set used for the ANN training (except PDR). (b) Temperature errors using the ANN verification data set. The ANN can be applied also for the ratiometric signal processing, instead of the single signal division. This possibility was tested and confirmed with the present real data. Although more complex, the ANN solution can be a good choice in presence of nonlinearities in such systems.
5. CONCLUSIONS The proposed method proved to be suitable for solving the multiple FBG filters signal. Its application can simplify the electro optical circuit, by omitting the measurement of the light power related signal, and some nonlinearities can be compensated. Despite of its implementation and training effort, the ANN has shown promising capabilities for this type of FBG interrogation.
ACKNOWLEDGMENTS We would like to thanks the FINEP and CNPq that provided funding for the Optical Temperature Measurement System for Power Transformers project, which generated this research work.
REFERENCES 1 2 3 4
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A. Othonos, Fiber Bragg gratings: Fundamentals and applications in telecommunications and sensing. Artech House, Norwood, 1999. K. Raman, Fiber Bragg Grating, San Diego, Academic Press, 1999. S. Haykin, Neural Networks: A Comprehensive Foundation. Prentice Hall, New York, 1998. L. S. Encinas, A. C. Zimmermann, C. L. N. Veiga, T. A. Weege, “Unambiguous Signal Demodulation Extending the Measuring Range of Fiber Bragg Gratings Sensors using Artificial Neural Networks - a Temperature Case,” Third European Workshop on Optical Fibre Sensors, EWOFS 2007, Napoli. L.C.S Nunes, L.C.G Valente, A.M.B Braga, Analysis of a demodulation system for Fiber Bragg Grating sensor using two fixed filters. Elsevier, Optics and Lasers in Engineering, vol.42, pages 529-542, 2004. L. S. Encinas, A. C. Zimmermann and C. L. N. Veiga, “Fiber Bragg Grating Signal Processing Using Artificial Neural Networks, an Extended Measuring Range Analysis”, 2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference - IMOC2007, ISBN: 1-4244-0661-7, Salvador. E. Udd, Fiber Optic Smart Structures. John Wiley & Sons Inc., New York, 1995.
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