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A novel fiber-optic interferometric sensor is presented for vibrations measurements and analysis. In this approach, it is shown applied to the vibrations of electrical structures within power transformers. A main feature of the sensor is that an unambiguous optical phase measurement is performed using the direct detection of the interferometer output, without external modulation, for a more compact and stable implementation. High resolution of the interferometric measurement is obtained with this technique (<1 nm). The optical-fiber transducer is also specifically designed for magnifying the localized vibrations in order to modulate deeply the interferometric signal. Other advantages of the implementation for measurements within transformers are also highlighted.
©2006 Optical Society of America
1. Introduction
There is a great interest on monitoring the working parameters and the quality of power machines, generators and transformers that are critical in a power delivery network [1,2]. Several magnitudes are being measured with commercial sensors, but they are off-line measurements with the power switched off and the sensors are externally located. In the case of the vibrations of internal structures, the harsh environment limits the use of most sensors, but the fiber optic technology provides promising solutions in the design and installation of the sensors and the measurement systems.
Optical fibers have been used in non-contact vibrometers for simply guiding the light to a target [3]. Mechanical vibrations can be also measured with optical fiber sensors based on spring-mass accelerometers, [4–7] and/or cantilevers [8,9] but some of them have limitations on the sensitivity and most of them have reduced bandwidth. In order to measure the vibrations of transformers, high resolution and wide dynamic range must be provided at the same time.
The proposed measurement system is based on a laser interferometric scheme for detecting the dynamic strain induced by the mechanical vibrations onto a fiber-optic sensing head. Among different fiber-optic transducers of the strain, such as in-fiber Bragg gratings and in-fiber Fabry-Perot cavities, the optical fiber is intrinsically the most sensitive, if its path length is interrogated with a laser interferometer. In the case of dynamic strain, as in vibrations measurements, this approach is effective if the optical set-up and the solutions of long bare optical fiber keep the linearity in the mechanical transduction on the optical fiber.
Regarding the in-field installation, robustness, low-cost, simplicity and scalability are pursued, as well, for the sensing head, the optical interferometer and the optical phase processing. Most demodulation schemes are based on external modulators for heterodyning or for an active compensation by locking the phase in quadrature [10], but these implementations are difficult and costly: complex set-ups that are difficult of being controlled, the signal processing is at last dependent on the signal amplitude and the actuators exhibits drift and limited operating range and bandwidth. We have developed a new fiber-optic interferometric sensor and a more robust optical phase measurement system using the direct detection of the interferometer output. The optical-fiber transducer is specifically designed for magnifying the localized vibrations in order to modulate linearly the interferometric signal with a result of higher resolution in the sub-nm range.
2. Sensor system
The measurement system consists on the fiber-optic sensing head, the reading laser interferometer and the optical phase processing. The sensing head detects the vibrations as the optical phase change Δϕ transferred to the fiber gage of length L through the dynamic strain (ΔL/L), by the expression:
The magnification factor M is the number of parallel fiber segments exposed to identical vibration that increase the sensitivity of the probe. Other terms are the mean refractive index n, the wavelength λ, a strain-optic factor of the fiber ξ, and the efficiency factor η of the transducer. An example of installation is presented in Fig. 1, with the fiber completely bonded to the monitored structure that stretches the sensing segments with an efficiency of η. Using typical values (n=1.456, ξ=0.71 [10], η=0.65 experimentally evaluated [11]), the optical phase change of 0,65·M·2p rad corresponds to ΔL=λ of 633 nm. Therefore, the resolution within the range of a wavelength is 0.65·M times better using the same optical phase measurement.
The high-sensitivity probe [11] is a fiber wrapped to perform a localized sensor of large sensing length (Fig. 1), which is installed in contact with the monitored structure (the surface of a magnetic core or between the borders of two windings blocks). It is designed for increasing the transducer sensitivity obtained with a single segment [12] by disposing several segments of the same fiber in parallel. We have studied this last by using several probes of different magnification M bonded on the core surface of a low-power transformer, obtaining a good linear dependence of the sensitivity with this factor M, demonstrated with M=1, 5, 10, 15, 20 and 30.
Fig. 1. High-sensitivity intrinsic probe of optical fiber. (a) Probe completely bonded for monitoring dynamic strain. (b) Front view of the coil for M segments; (c) Bottom view of the sensor with M segments.
The optoelectronic set-up is based on a multi-channel Mach-Zehnder interferometer with fiber-optic arms as it is shown in Fig. 2. One arm is a reference coil and each other are sensing arms that are compared with this. The paths of the sensing fibers are common for addressing to the monitored region with reduced disturbance. The signal of the interference output with direct detection (2) is proportional to the cosine of the optical phase, the mean output onto the detector I0 and the visibility V.
The initial optical phase ϕ 0 represents the quasi-static initial conditions that changes as a low frequency drift and Δϕ(t) is the optical phase shift with time in response to the vibrations. In order to separate them the interference signal is forced to be multi-period in response to the vibrations (Δϕ>2π rad pk-pk). This is achieved by the design of this fiber-optic transducer. The required sensitivity is adjusted by the number of segments M of the same fiber that are disposed in parallel (Fig. 1). Thus the sensing area remains localized with a moderated L base length and M times the fiber outer diameter of width.
A multi-period interference signal is presented in Fig. 3 for the vibration detected by a probe (L=30mm, M=30) installed in a low-power (770VA) transformer. The core vibration is sensed through the dynamic strain experienced by the magnetic sheets and transferred to the fiber-optic probe. The strain is forced dynamically by the magnetostriction in response to the magnetization of the core, which is directly related to the applied voltage [12]. As a result, the core vibrations (100 Hz) follow a quadratic function with the applied voltage (50 Hz). The voltage input is also a reference of the synchronism with the vibrations. Each zero-cross, peak and valley of the voltage reference the dynamic strain changes its slope, which is a change of the multi-period displacement of the interference output. This synchronism between the interference output and the voltage reference is highlighted with the dotted circles in Fig. 3 that mark these instants of time. It is used for obtaining the optical-phase measurement.
Fig. 3. Synchronism between the forced multi-period interferometric output and the voltage input to the transformer that is used as a reference signal for the optical phase measurement.
3. Calibration of vibrations
The experimental set-up for the calibration tests is shown in Fig. 4a. A piezo-electric actuator (PZT) was used as the vibrating surface. The PZT was excited using a signal generator and an amplifier. A single frequency and low-voltage (up to 19V peak) was applied in order to get a very linear response of the actuator to the excitation tone. In order to calibrate the vibration generated by the actuator, a non-contact vibrometer was aligned on one extreme of the actuator as a target. A mirror anchored to the vibrating surface was used for this purpose, which is the reflector of the measuring arm of a bulk Michelson interferometer. In addition, the results obtained with the fiber optic interferometric sensor were compared with the output of a commercial accelerometer (4371, Bruel&Kjaer) conditioned with a specific purpose amplifier (2692A 0I4, Bruel&Kjaer). A fiber-optic probe 25mm of length and 10 turns (×10) was used in all calibration tests.
The excitation applied to the actuator, the accelerometer output, the vibration detected by the Michelson Vibrometer and the results with the fiber-optic interferometric sensor were recorded with the oscilloscope and processed with a PC. Good agreement was found between the Michelson calibrator and the fiber-optic instrument in the characteristic frequencies for the application (100 Hz or harmonics of 100 Hz), as shown in Fig. 4. The voltage at the output of a transimpedance amplifier connected to the photo-detector was recorded for the fiber-optic interferometer. This signal, as in Fig. 3, was processed for obtaining the optical phase read-out, which is the vibration signal in terms of the target displacement. After the calibration with the Michelson vibrometer the output of the fiber-optic instrument is the displacement with the time. These results in terms of velocity are compared with those of the accelerometer in Fig. 4 for 100 Hz, 200 Hz, and 400 Hz. It can be noticed that the deviation of the accelerometer read-out is more evident at lower frequencies (Fig. 4b), where our instrument maintains a response in good agreement with the reference vibrometer (about 250 nm peak-peak).
Fig. 4. Calibration of vibrations at different frequencies: (a) Experimental set-up; Results with the fiber-optic interferometer and the accelerometer: (b) 100Hz, (c) 200Hz, (d) 400 Hz. The linearity of the sensor system was evaluated in terms of the induced harmonics when a single frequency input is used (Fig. 5). The power for each frequency different to the excitation was compared with the power at the excited frequency in relative means. They are shown in Fig. 5, where the traces of the calibrations at 100 Hz, 200 Hz and 400 Hz are overstrike (data from Fig. 4 was used). The maximum relative power in a band-width of 10 kHz corresponds to a harmonic of 100 Hz that was proven one order of magnitude better that with the accelerometer for all frequencies [11].
Fig. 5. Harmonic decomposition of the output of two sensors with pure tone inputs. Overstrike traces of responses to 100 Hz, 200 Hz and 400 Hz in relative units to the amplitude of the output at the main frequency: (a) Fiber-optic interferometer (b) Accelerometer.
Operating range of a single channel fiber-optic vibration sensor was determined in the limits of the actuator band-width. Assuming a time resolution limit of at least 10 samples each semi-period of the acquired interference signal, the range is up to 36.75 µm for the resonant frequency of the actuator (1.7 kHz) with a sampling rate of 10 MSps. This range can be improved with a higher sampling rate, but larger storage capacity is needed. In this case, the data record for a vibration cycle is about 6000 samples. The digital processing at higher frequencies – higher vibration amplitude is limited by the maximum sampling rate of the acquisition board. In the present implementation, this parameter and the time resolution are adapted to the monitored vibration frequency.
4. Experimental results within a power transformer
Several fiber optic probes were installed within a medium-power transformer (25kVA) for monitoring the vibrations of its core (Fig. 6). The complete process of installation and the exhaustive enumeration of the probes are beyond the scope of this paper. However their purposes are described below: probes #1 and #2 are for axial vibrations and probes #3 and #4 are for transversal vibrations at different points of the core. Probe #6 is a reference coil with similar characteristics as of probes #1 and #2, but it is not fixed to the core. The transformer was excited without electric load and the input voltage (50 Hz, 220V nominal) was used for obtaining the reference signal of synchronism used in the optical phase processing.
The results of the vibrations detected by probe #3 are presented in Fig. 7. This sensor monitors the transversal vibration of the core-block due to the dynamic deformation of the borders and the relative displacement between the sheets. The interference output and the waveform of the voltage input are shown in Fig. 7. Two additional signals are presented, the clock signal extracted for timing the demodulation and the obtained optical phase. The clock signal is synchronous with the zero-crosses, with the peaks and with the valleys of the voltage reference (as in Fig. 3).
The transitions of the clock signal as showed in Fig. 7 delimitate the start and end points of each half-period of vibrations. The multi-period interference output has a displacement of about 3.5 periods between the transitions of the synchronization signal. These instants of time are separated by 5 ms that is the duration of half a period of the vibrations. The up and down displacements alternate completing a vibration cycle each 10 ms for this excitation of 100 Hz. Note that the interference output starts with different value at the instants of time after a period of the clock signal. This change of the initial optical phase can cause a signal fading of the measured vibrations in an interferometer with direct detection. Even thought they have very different dynamic behavior, they only can be filtered after obtaining the optical phase read-out. In this case its impact in the demodulation is overcome by the synchronous approach and it is removed afterwards from the optical phase measurement.
Fig. 7. Optical phase measurement of the multi-period interferometric output with a reference signal of synchronism.
5. Optical phase demodulation and measurement
Digital optical phase processing permits the achievement of very good metrological performance of the developed system. The interference signals and the reference signal are acquired to a PC that carries out a post-processing for obtaining the optical phase within a period fe at each instant of time and the cumulated optical phase with time (Fig. 7).
A direct relation between the optical phase in the range of ±π rad and the amplitude of the interferometric output is obtained with this technique. Therefore, the optical phase resolution is limited at last by the quantization error of the A/D and the non-linear demodulation (cos-1). With a linear A/D conversion of 8 bits (255 levels) adjusted to the range, a resolution of ~1.5×10-2 rad is achieved (~3.6×10-3 of the wavelength) by disregarding the last 5 quantization levels next to the maximum and minimum of the cosine function. If the sampling frequency is selected provided that the time resolution matches this last (~200 samples each semi-period of interference), a resolution of ~0.1 nm with M=40 (3.6×10-3×633/40 nm).
For the processing of fe the detected interference signal is normalized (3) within each half a period between adjacent extremes. The normalization process provides a correspondence of the maxima with value 2, the minima with value 0, and the intermediate values to 1, which corresponds to the normalized mean output signal I0 onto the detector.
The vibrations signal is finally obtained using a calibration factor that mainly determines the efficiency of the transducer η in (1) [11]. In Fig. 7, the amplitude of vibrations is about 83 nm and the resolution is better than 0.5 nm, provided that the sampling rate is 50×103 Samples/s (~35 samples each semi-period of interference). In this case, the results differ from the predicted (better than 0.1 nm) because of the limited time resolution (35 samples, instead of 200), but the final resolution is good enough because of the magnification M=40.
6. Conclusion
In conclusion, the good performance is allowed by the following characteristics of the implemented sensor. The transducer of longer sensing fiber increases the sensitivity and provides a dynamic displacement of several periods of the interference signal in response to the vibrations. In addition, the response to the vibrations is improved compared with the parameters of influence, mainly the temperature drift and environmental vibrations. The sensing head remains compact and is able of being installed in contact with the surface at the core or the windings within transformers and detects the dynamic strain or the displacement of the monitored internal structures. The resulting multi-period output in direct detection is robustly post-processed and additional high resolution is provided by using a cos-1 function over a quantization of 255 levels.
Some advantages of the implementation for measurements within transformers are the ability of being installed in contact with the monitored structure and the discrimination between different sources of vibrations (core and windings). In addition, there are many potential applications for which this instrumentation system is quiet adequate: Since it is based on synchronous multi-period signals forced by improving the sensitivity of the sensor head, this technique is useful with other synchronous instrumentation applications, such as vibrations in electric machines and excited systems, or for nondestructive testing of structures in which the dynamic mechanical excitation is available for the synchronization during the tests.
The sensor resolution can be improved by the optical phase measurement within the p rad range. About this last, with a linear A/D conversion of 12 bits (4095 levels), a resolution of ~3.8×10-3 rad (~0.9×10-3 of the wavelength) is achieved with the proposed algorithm, which represents better than 0.1 nm with this sensor system.
Acknowledgments
This work was supported in part by the Spanish electrical company Union Fenosa S.A. under Project FUTURE and partially funded by the Spanish-Comunidad de Madrid through the GR/MAT/0508/2004 project.
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