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اگه انگلیسی می خوای :
Electric time-domain reflectometry distributed flow sensor
Aurimas Dominauskasa, , , Dirk Heidera, d and John W. Gillespie, Jr.a, b, c
aCenter for Composite Materials, University of Delaware, Newark, DE 19716, USA
bDepartment of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, USA
cDepartment of Material Science and Engineering, University of Delaware, Newark, DE 19716, USA
dDepartment of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
Received 14 September 2005; revised 6 January 2006; accepted 9 January 2006. Available online 25 September 2006.
Abstract
Liquid composite molding (LCM) has become an important processing technique to manufacture high-performance composite parts. The sensing of the process parameters, such as resin fill of the porous material, are key to improve repeatability, maximize quality and minimize cost. This paper describes a distributed flow sensor, which considerably decreases tooling integration costs and improves spatial resolution by allowing sensing of hundreds of sensing elements with a single input/output port. The transmission line sensor is virtually divided into a large number of small discrete transmission lines treated as a long array of sensing elements. Piecewise sensing is achieved by electric time-domain reflectometry and inversion of a non-uniform transmission line model. The paper describes the distributed sensing approach, experimentally validates distributed sensing in a LCM setup, and analyzes critical sensor parameters.
Keywords: D. Process monitoring; E. Resin flow; E. Resin transfer molding; E. Tooling
Article Outline
1. Introduction
2. Distributed sensing concept
3. Non-uniform transmission line modeling
4. Inverse modeling of dielectric distributions
5. Experimental validation
6. Sensor parameter analyses
7. Conclusions
Acknowledgements
References
1. Introduction
Knowledge of the distributed resin flow behavior in porous fiber systems is fundamental in many composite manufacturing processes. Such information allows design and control of the process to obtain desired quality and reduces overall cost of the composite part. For example, in liquid composite molding (LCM) [1], uncorrected flow disturbances may lead to dry spots in the fiber system (preform) and potentially scrap of an expensive part. To achieve the desired flow patterns, infusion processes are optimized [2] prior to the infusion through flow simulation and/or small scale prototype development. In addition to off-line optimization, often on-line control actions must be taken to address flow disturbances due to low repeatability of flow behavior in complex fiber systems [3]. In these instances, a sensor system is needed that can monitor the arrival of the resin at desired locations during the filling process.
A number of flow sensors and sensor systems for composite applications are already developed, however they are still incapable of addressing all distributed sensing requirements. SMART-Weave, AC/DC linear, and optical sensors are used for flow sensing. Short descriptions with references of these sensors are provided in [4]. Among these sensors, the SMART-Weave sensor is the only system that could be used for low-cost 2D or 3D flow sensing; however its application is limited due to ingress/egress issues (i.e., a large number of embedded wires are needed) and relatively low spatial resolution. A 1D transmission line flow sensor, which uses two parallel wire miniature cables, was developed and validated in a LCM setup [4] and [5]. The sensor, which is based on electric time-domain reflectometry (ETDR), provides 3 mm accuracy for a single resin flow front detection on the sensor over 1 m range and can be used in thick section preforms. Other transmission line integrations into the reinforcement have been studied including simple copper wires with a metal tool as a ground plane to reduce the wire count [6] and carbon fibers [7] for potential use as conductors of the sensors to provide no mechanical property degradation due the sensor ingress.
The ETDR technique sends a picosecond rise-time voltage step wave in a transmission line and measures voltage reflections resulting from impedance discontinuities as a function of wave propagation time. In flow measurements, impedance discontinuities are created by the infiltrating resins. The previous ETDR sensor setups [4] and [5] use a simple threshold algorithm to obtain resin position of single or multiple resin flow fronts on the sensor line. The accuracy and sensitivity of these systems to detect multiple resin flow fronts are limited due to the dispersive nature of the resin, transmission line losses, and multiple reflections. For typical vinyl-ester and epoxy resins and sensor lengths of up to 1 m, the threshold algorithm can provide ±30 mm distributed sensing accuracy when multiple flow fronts exist. The newly developed approach described in this paper significantly improves the detection capability to ±7 mm sensing accuracy. It also enables a better understanding of the degradation of spatial resolution as a function of sensor and resin characteristics while allowing accurate inversion of the dielectric distribution rather than providing resin arrival information only.
The distributed ETDR sensing is implemented by inverting a non-uniform transmission line model via reflection history based algorithms. The model predicts the time-domain reflection response of the waves propagating along a multi-section transmission line sensor embedded in a non-uniform dielectric medium. The technique captures the changes in voltage reflection and propagation speed as a function of the dielectric distribution. A dielectric distribution is being computed via optimization of the model’s dielectric inputs to fit experimental waveforms. This study validates the distributed sensing capability in an LCM setup and analyzes the critical sensor parameters. Results with the new sensor indicate a considerable improvement over distributed sensing compared to standard ETDR flow sensing.
2. Distributed sensing concept
ETDR flow sensing in porous medium detects the increase of the dielectric constant during infiltration of the preform. As illustrated in Fig. 1, the bulk dielectric constant Kf of the filled medium increases compared to the unfilled medium Ku, because the dielectric constant of the resin Kr is higher than the air pockets Ka in the porous medium. Sensing can be accomplished by any partially unshielded transmission line, where the electromagnetic field extends beyond the geometrical boundaries of the transmission line and interacts with the surrounding medium. As a result, the presence of resin influences the propagation behavior of EM waves which can be used to detect the arrival of resin.
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Fig. 1. Concept of flow sensing in porous medium via transmission line sensor where labels 1, 2, 3, and 4 show conductor, insulator, electric field (conceptual) and magnetic field (conceptual), respectively.
Fig. 2 illustrates the distributed transmission line sensor model, the actual ETDR time-domain response, and reconstruction of the distance-domain dielectric distribution from time-domain measurements. Multiple impedance discontinuities are formed at each interface of the two different dielectrics (K1 and K2). As a result, multiple reflection transmission waves are emanated and superimposed on the step response V− of the line. The waveform contains distributed impedance information, shown as a set of multiple peaks and valleys of the signal in the time-domain. Appropriate signal treatment is needed to obtain the distributed dielectric (impedance Zq) profile in the distance-domain. The impedance distribution, and thus dielectric distribution (Fig. 2c), has been calculated by inverting a non-uniform transmission line model. The model is iteratively executed to fit the measured signal (Fig. 2b). The model addresses all multiple reflections and transmissions occurring in the non-uniform waveguide in order to obtain good fit and accurate reconstruction of distributed parameters.
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Fig. 2. Distributed flow sensing concept (a) sensor model (l, q, and S is section length, junction number, and scattering coefficient, respectively), (b) response signal, and (c) distance-domain data.
3. Non-uniform transmission line modeling
The distributed flow sensor is modeled as a non-uniform transmission line consisting of n number of small uniform line sections, which are characterized by the length lq, dielectric permittivity εq, impedance Zq, propagation constant γq, and other parameters found in [8] and [9]. The junctions of these sections are modeled using a 2-port scattering coefficients called S-parameters [8]. S-parameter representation for junction q is shown in Fig. 3, where incident V+q and reflected waves V−q are related by
(1)
Here, is the input reflection coefficient, load reflection coefficient, and are reflection coefficients, and and are transmission coefficients. Since the junctions of the multi-section line are assumed lossless, the following conditions apply to Eq. (1):
(2)
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Fig. 3. 2-Port junction model representation for junction q in terms of S-parameters.
Multiplier e-2γqlq allows a shift of q + 1 junction and transformation of that section q into an impedance load . By rearranging Eq. (1), the recursive formula for can be obtained:
(3)
In this equation, all S-parameters, except , are treated as local reflection and transmission coefficients of the section q. Recursive modeling starts with the section n − 1 (Fig. 2) and calculates all consecutive scattering coefficients towards the input of the line. Parameter is assumed to be unitary due to an open ended configuration of the sensor line. When is obtained, V− is calculated according to Eq. (1).
To increase simulation and reconstruction accuracy, we have incorporated finite resistance (DC) losses of the cable conductors, “skin” effect (AC) losses, and dispersive behavior of dielectric medium. For AC losses, we adopted the model [9], derived on the bases of conduction-current fields and magnetic fields. To obtain relative dielectric permittivity, we have employed the Cole–Cole model [10], which uses four parameters: low frequency constant ε0, high-frequency constant ε∞, relaxation frequency fr, and relaxation peak spread constant α. In addition, the effective dielectric properties of the dielectrics in the surrounding field of the sensor are being used because the electric field (Fig. 1) interacts with different dielectric mediums (PVC, air, resin, fibers etc.).
4. Inverse modeling of dielectric distributions
The inversion technique is based on the optimization of electrical waveguides or reconstruction of distributed characteristic impedance in electrical engineering [11] and [12]. In this approach, the time-domain signal is divided into a series of small and equal time intervals that have to be optimized successively utilizing non-uniform transmission line models. However, this technique is limited to transmission lines with uniform and non-dispersive dielectric properties usually used for electronic circuits. In this work, the procedure has been modified to allow distributed measurements of resin flow. Variation of section location in time-domain has been introduced to be able to invert non-uniform dielectric medium.
The time-domain response of two sensor lines with the same dielectric distribution is assumed to be invariant up to corresponding time interval of section q even if the dielectric distributions are varying after sectionq. This allows sequential and unique (independent) determination of the dielectric value at each section q starting from the first section until the q = n − 1 section (refer Fig. 2). For a full exhaustive search, n − 1 by a (with a being the number of possible dielectric variations) cycles have to be executed in the model rather than an−1 to allow for the best fit of experimental and optimized waveforms. After all sections have been optimized, sensor array S[0, … , n − 1] is created to indicate the dielectric distribution.
Fig. 4 illustrates the technique, where a 10-section transmission line model with 50 mm long sections is used to simulate a 500 mm long sensor. Nine dielectric functions (Table 1) are being considered. The waveform (thick line in Fig. 4b) is being reflected by the non-uniform dielectric profile (Fig. 4a) and the signal raises and falls based on the local impedance increases or decreases, respectively. The inversion process of sections 1, 5, and 9 is illustrated in Fig. 4a. At iteration cycle 1, nine dielectric cases for sensor section 1 are being modeled. The best dielectric match for this particular transmission section is determined to be material index a = 0 from Table 1. Another example is provided for cycle 5, where the procedure computes a = 8 to be the best match compared to the sensor feedback. The process is continued until the last section is reached and the dielectric distribution has been computed. During the optimization process, positions of a particular section q are obtained for each dielectric optimization cycle.
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Fig. 4. Illustration of distributed sensing technique, with dielectric distribution profile (a) and sensor response to this profile (b) with optimization of sections 1, 5, and 9 as an example.
Table 1.
Cole–Cole parameters and apparent dielectric constant K used for the optimization of dielectric properties in Fig. 4 Index a ε0 ε∞ K
0 3.0 2.4 2.4
1 4.5 2.6 2.8
2 6.0 2.8 3.2
3 7.5 3.0 3.6
4 9.0 3.2 4.0
5 10.5 3.4 4.4
6 12.0 3.6 4.8
7 13.5 3.8 5.2
8 15.0 4.0 5.6
Parameters fr and α were kept constant at 2 MHz and 0.5, respectively.
The optimization uses a point (or few point) least square difference of the actual waveform and varying one (thin line in Fig. 4b). In order to correctly reconstruct dielectric distribution, position Pq (Fig. 4) of the optimizing section has to be adequately predicted in time-domain. Accurate prediction of section boundaries in time-domain is complicated due to wave dispersion. However, approximate prediction of the middle point of the section position Pq is sufficient for inversion procedure. As shown in Fig. 4, the position Pq for the fifth section is estimated as the offset (in this case four points) to the right from the cross-section of the dotted curve and the threshold. The dotted curve is a maximal least square difference (response range) of actual waveform and varying one with the end portion being cut for clarity purpose. The threshold is set at level to be higher than system noise and lower then lowest response. For the successful prediction of Pq, it is important to maintain high enough sampling rates for the point number per section to be about 10. Point number per section Ns can be approximately estimated by using the following formula:
(4)
Here, Fs, l, K, and c are sampling frequency, section length, apparent dielectric constant (Table 1), and velocity of light, respectively. Then, the offset number is approximately equal to the half of Ns.
Fig. 5 shows an example in which the threshold and inverse model based distributed measurement methods are compared for an epoxy resin distribution prediction in a glass-fiber matrix. Here, sections of a 1-m transmission line are wetted out at different intervals in the following sequence: between (1) 100 mm and 320 mm, (2) 350 mm and 500 mm, (3) 600 mm and 820 mm, and (4) 850 mm and 1000 mm (see Fig. 5a). The responding TDR signal for the all dry and wet as well as for the partially wetted out preforms is displayed in Fig. 5b. For data reduction, the line was modeled with 150 virtual sensing sections with a length of 6.7 mm.
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Fig. 5. Simulated comparison of threshold and model based distributed sensing. Epoxy resin distribution in glass-fiber medium (a) has been used to simulate ETDR waveforms (b). Here, grey areas denote unfilled dry regions.
The threshold measurements subtract the measured signal from the signal obtained prior to infusion and is shown as a “Difference” signal with an additional offset level of 100 mV for illustration purposes only. The threshold is optimized to provide best overall readings for all dry/wet discontinuities. However, the threshold method is inaccurate in predicting multiple discontinuities. One of the main sources of the error is the dispersive nature of the resin providing an increase of rise and fall times of the time-domain signal clearly seen (as an example) at about the 10 ns mark when the wet fill location is over predicted by 23 mm at 600 mm dry/wet boundary. Another source of the error is the varying voltage drop or rise as a function of length of dry/wet discontinuities making prediction of dry regions, smaller than 30 mm (such as one from 820 to 850 mm), complicated. Other factors, such as multiple reflections negatively affect the accuracy of the threshold algorithm.
In contrast, model based approach takes into consideration pulse distortions due to frequency dependant permittivity (dispersion) and losses, accounts for multiple reflection process, and correctly interprets signal variation due to dielectric discontinuities. As a result, signal interpretation in the model based approach is more accurate then in the threshold based approach which, indeed, is based on a simple loss-less, non-dispersive, and one directional wave propagation. For example, as shown in Fig. 4, model based sensing accuracy is within the range of individual section length (6.7 mm) enabling prediction of dry spots such one in the interval from 820 to 850 mm. Overall, the threshold algorithm can be used for flow prediction of few flow fronts on the sensor whereas the model based system can be used for accurate prediction of complex infusion scenarios.
5. Experimental validation
A controlled impedance miniature two-wire cable has been used for distributed flow sensing validation experiments. These cables are commercially available at low cost and in a wide variety of geometries. However, to minimize impedance variations and undesired reflections along the line, the tolerance of the conductor separation distance should be low. The sensor used consists of two parallel copper wires embedded in a PVC insulator, which provides partial screening of electric field. The diameter of the wires is approximately 250 μm, separation distance is 600 ± 50 μm, and PVC wall thickness is 200 μm.
To allow distributed flow sensing, the effective dielectric properties of the sensor embedded in the unfilled (dry) and filled (wet) porous medium have to be known. A single long section transmission line was used to calculate the four Cole–Cole parameters from the experimentally obtained ETDR waveforms. The inverse modeling, which is based on least square difference between the measured and simulated waveforms, allows determination of the characteristic impedance (conductor separation distance) and dielectric parameters at the same time. After calculation of the effective separation distance for dry (590 μm) and wet (570 μm) preforms, an average distance (580 μm) was used for all further calculations. The calculated value of 580 μm is within the tolerances provided by the manufacturer. Fig. 6 shows the measured and optimized waveforms together with the input/incident signal, measured as a reflection from the connecting coaxial cable without the sensor connected. This input signal is used in the modeling as the excitation signal of the sensor.
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Fig. 6. Input and response waveforms of 3863 mm long ETDR sensor. The response waveforms were obtained in unfilled (dry) and filled (wet) preform arrangements.
Fig. 7 shows the real and imaginary dielectric constant curves measured with this technique. The following Cole–Cole parameters have been calculated for dry: ε0 = 3.15, ε∞ = 2.48, fr = 1.35 MHz, α = 0.47; and wet: ε0 = 4.40, ε∞ = 2.92, fr = 1.86 MHz, α = 0.58. Significant difference between the dry (glass-fibers and air) and wet (glass-fibers and vinyl-ester resin) real dielectric constants provide the basis for the sensor to predict unfilled and filled regions of the preform. The imaginary dielectric parameter represents the loss factor responsible for signal attenuation. However, such attenuation levels are not high and permit distributed sensing over several meters.
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Fig. 7. Dielectric properties for dry (glass random-mat) and wet (vinyl-ester resin) preform arrangements.
For the flow experiments, the sensor is connected to a low loss coaxial cable by soldering each sensor’s conductor to the appropriate cable’s conductor and casting soldering connections in a small clear epoxy droplet to assure stable and robust connectivity. The coaxial cable is connected to a digitizing oscilloscope HP54750A which contains a pulse generator, capable of producing voltage step of about 40 ps rise time and 200 mV magnitude, and sampling head assuring less that 1% inaccuracy of time scale measurement in the range from 1 ns to 1 μs. Data acquisition and the instrument control is performed by the software, written in LabVIEW™ (National Instrument), through a GPIB-PC interface. Three separate programs were developed in LabVIEW for modeling, distributed sensing, and data analyses. The sensor (3863 ± 3 mm long) was placed on the mold surface and fixed with 2 mm wide strips of Kapton® tape in a “zigzag” arrangement as shown in Fig. 8. Such arrangement allowed an examination of the sensor for 2D distributed sensing by creating multiple dielectric/resin discontinuities during a simple resin infusion scenario. The sensor was virtually divided into 150 sensing sections (25.75 mm) and the coordinates were graphically measured from the picture. Specially designed software used these coordinates to create a multi-section sensor indicator on the infusion picture highlighting the elements on which resin has been detected.
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Fig. 8. Distributed sensor arrangement on the mold surface (left) and multi-section sensor indicator in infusion setup (right). Labels 1 and 2 denote sensor start point and end point, respectively, where labels 3 and 4 denote dry and wet preforms, respectively.
The modeled baseline is set as close as possible to the measured (baseline) signal of the dry preform. Such superposition is achieved by an optimization of the characteristic impedance for each discrete section while keeping the dielectric properties of the dry reinforcement. The characteristic impedance can be affected by the tolerances of the wire, differences of the dielectric properties from the baseline, inaccuracy of the model, and inaccuracy of the measuring system.
Fig. 9 shows actual resin location and distributed sensor data at different time intervals, where light grey colored sensor sections indicate impregnation (wet) status, while dark grey colored sections indicate resin absence (dry) status. The data are processed on a 1.3 GHz PC off-line due to extensive computation time (90 s) required to reconstruct all 150 sensor sections. Computation time can be reduced by selecting less sensing sections or increasing computational power. A maximum of five false sensor (3.3% total error) readings after 550 s is observed. False readings may be due to bending of the cable changing some of the cable geometry, local fiber volume fraction variations resulting in dielectric differences of the dry/wet behavior and overall inaccuracy of the acquisition system. Nevertheless, two dimensional flow front curve prediction with a single sensor in the area of 500 × 500 mm is about 5%.
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Fig. 9. Distributed sensor data and actual resin distribution at particular infusion time intervals.
Fig. 10 shows some of the waveforms used to reconstruct the distributed sensing data of Fig. 9. In general, a good fit is achieved between the measured and optimized (model) signals. A better match is observed at shorter times and when a smaller sensor area is being wetted out (Fig. 10a). However, when the sensor coverage of the resin increases (Fig. 10b), the attenuation of the signal increases with the propagation time more rapidly resulting in a low response range (refer Fig. 4b, dotted curves) and causing two erroneous measurements at the 25 and 35 ns marks (refer Fig. 9, 418 s). Better fit of the waveforms can be achieved by inverting more then two dielectric profiles ranging between dry and wet status to allow for small variations of the effective dry/wet dielectrics.
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Fig. 10. Comparison of measured and optimized waveforms used for distributed data reconstruction of Fig. 9: (a) 205 s and (b) 418 s.
6. Sensor parameter analyses
Measurement uncertainty analysis shows that the length of the sections and the dielectric medium on the sensor are important to the accuracy of the distributed measurements. Fig. 11 plots the predicted absolute voltage difference (sensor model response range) between the dry/wet states for each section on fully dry and wet sensor lines. The maximum difference is obtained at the beginning of the sensor and reduces along the sensor length due to losses in the line and dispersion. The response range reduces more rapidly for wet sensor due to increased material losses compared to the dry sensor setup. To accurately invert the dry/wet state, the absolute voltage difference has to be twice larger than the noise level (2Δ) between the measured and modeled signals. It can be seen that the noise level is not increasing as a function of sensor length (no accumulation of errors) and are mostly below 2 mV. Nevertheless, after 1.6 m and 3.3 m for the wet and dry state, respectively, the response range fall below the noise level reducing the accuracy of the sensor system for longer range sensing.
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Fig. 11. Sensor response (dry and wet) attenuation as a function of linear sensing range with the double difference between actual and measuring signals (noise – 2Δ).
The reduction in sensing over longer distances can be overcome if the section length is adjusted as a function of position (signal attenuation) on the sensor. The response range can be increased by increasing the length of the section. Fig. 12 analyzes this relationship for the sensor used in the study as a function of sensing section location. The section length has been increasingly adjusted for each section so that the response voltage is at 3 mV level, providing accurate sensing for all sensor sections. Fig. 12a plots the corresponding ETDR signal for an all dry preform with one optimized wet section, while Fig. 12b illustrates the optimization of dry section on an all wet preform. Basically, such optimization assures the same and high certainty of dry/wet status sensing for all elements, however linear measurement resolution drops as function of sensing distance. As can be seen from Fig. 12, the decrease of the resolution is caused by increasing diffusion of discontinuity boundaries (due to losses and dispersion) as a function of sensing distance.
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Fig. 12. Theoretical optimization of the length of the sensing section of 10 transmission lines, where the section was inserted at different distances ranging from 1 m up to 10 m. Wet (a) and dry (b) preform cases are modeled.
Fig. 13 shows the corresponding section length plot as a function of dry/wet state and location on the sensor plotted for a 10 m long sensor. The length of sensing section can be small (below 50 mm) for sensors up to 2 m long resulting in minimum 40 sensing sections of the same length or about 100 sections of increasing lengths starting with 5 mm and ending with 50 mm length. The sensor detection spatial resolution reduces to approximately 0.4 m at 10 m distance, however, by using the adjustable sections, high resolution sensing can be maintained at shorter sensing distances while allowing a large quantity of virtual sensors (i.e., 200 sensors) to be monitored over long range in one ETDR setup.
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Fig. 13. Sensing section length (linear resolution) as a function of sensor length (linear sensing range) for wet (a) and dry (b) preform cases.
7. Conclusions
In this paper a novel ETDR data reduction scheme has been proposed allowing accurate flow measurements in any LCM processes where multiple resin flow fronts exist. An ETDR model has been implemented and is being used during inverse modeling to calculate the dielectric distribution on the sensor. The dielectric distribution provides the resin location on the sensor. The system has been validated experimentally on a 3.8 m sensor line with 150 virtual sensors. The sensor accuracy is a function of dielectric material being used and position on the sensor. A sensitivity analysis shows that the system can be extended to very long sensors with the application of variable sensor element lengths. Overall, the sensor provides a new tool for accurate distributed flow measurements in LCM processes.
Acknowledgement
The authors gratefully acknowledge the support of the Office of Naval Research through support of the Advanced Intelligent Materials and Processing Center.
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Composites Part A: Applied Science and Manufacturing
Volume 38, Issue 1 , January 2007, Pages 138-146
2 of 287
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