Abstract

In this study, a novel data focusing technique is proposed and examined to image FRP-confined concrete using wideband microwaves as a non-destructive evaluation (NDE) technique. The data-focusing scheme is developed based on the concept of synthetic aperture radar (SAR) and is an alternative to the lens focusing technique. By implementing the proposed scheme, images are reconstructed using the wavenumber-frequency migration inverse algorithm and the 2-Dimensional Fast Fourier Transform (2D-FFT) procedure, which employs scattered signals generated from our Finite Difference - Time Domain (FD-TD) simulations. Advantages and feasibility of this data-focusing scheme are studied through the use of wave-scattering simulation and image reconstruction numerical models.

1. Introduction

Fiber-Reinforced Plastic (FRP) composite jacketing systems have rapidly emerged as a high performance alternative to conventional techniques for construction, strengthening, and repair of reinforced concrete columns and piers. Studies, however, indicate that concrete cores can crack and/or crumble to a severe extent without showing substantial jacket damage on the outside. Further, damages of concrete in the vicinity of the FRP-concrete interface, bond delamination within the jacket and in overlap joints could collectively lead to catastrophic failures when the defects aggregate to a certain magnitude [Au 2001]. Destructive evaluation methods such as sample extraction and jacket removal would pose a danger of structural collapse, and therefore there is a need for an effective non-destructive evaluation (NDE) technique for assessing and quantifying interior damages. As such, a NDE technique that makes use of wideband microwaves has been proposed as an attempt to detect and image interior conditions of FRP-confined concrete structures, in view of its inherent benefits such as non-contact sensing capability, fast couplant-free measurement, high-resolution images, highly portable devices, and safe and weather independent operations [Buyukozturk and Rhim 1995].

The technique, called the Automatic Progressive Stepping - Converging Wave (APS-CW), is developed based on the concept of Synthetic Aperture Radar (SAR) or Inverse Synthetic Aperture Radar (ISAR) to focus data by means of data processing of the received signals measured along a prescribed trajectory, as shown in Figure 1. This approach is different from the techniques that make use of wave focusing through dielectric lens [Feng et al 2002] to produce focused waves at discrete measurement points. Both techniques, nevertheless, aim at producing strong and relatively low-noise signals. The proposed data focusing technique is suitable for detecting damages in large-scale structures and is inherently efficient and flexible for large area scanning of most structural configurations. With the use of a mono-static antenna setup, hardware cost will be reduced and versatility of measuring over various surface geometries be provided.

2. APS-CW Technique

2.1 Data-Focusing Scheme

Fig 1: Automatic Progressive Stepping - Converging Wave (APS-CW) Setup.

Data focusing is performed by processing the coherent scattered signals obtained at multiple locations around the FRP-confined structure by means of a data-focusing function. At each location, a horn antenna transmits wideband radar waves with a beam pattern covering partial areas of interest (Figure 1). With a prescribed step size (or number of antenna locations, N), the antenna moves circumferentially in a progressive manner. The method is herein referred to as Automatic Progressive Stepping - Converging Wave (APS-CW) technique. Both mono-static (one antenna transmits and receives signals using a duplex switch) and bi-static (one antenna transmits while another receives signals) setups are feasible. Figure 1 illustrates the APS-CW technique with a mono-static measurement setup.

By processing the scattered signals u(r_n,q_n,t) measured in the time domain at multiple locations, the measured microwaves are converged or focused. The image profile F(r,q) in 2-dimension is then reconstructed by (1) multiplying the measured signal U(r_n,q_n,w_m) in the frequency domain by the focusing function C(r_n,q_n,w_m,c) and (2) summing up over all apertures and frequencies as in the following operation:

(1)

where r and q are the coordinates in the polar coordinate system, c the wave speed in the medium of interest, N and M are the total number of measurement points (or apertures) and frequencies involved, respectively, C(r_n,q_n,w_m,c) is the focusing function and is defined as [Deshchenko 2000]:

(2)

Practically, the above operation can be more efficiently conducted by means of a 2-D FFT algorithm, which employs the same data-focusing concept, as discussed below. The proposed APS-CW technique can use incident waves of either a long pulse chirped waveform or a short pulse sinusoidal waveform. For the long waveform such as the step-frequency continuous wave, the frequencies are modulated linearly in time. To obtain high-resolution images, the relative bandwidth (bandwidth divided by central frequency) of the transmitted pulses can be set to be greater than 25%. Use of the step-frequency continuous waveform will enhance significantly the image quality [Weedon et al 2000]. Range distance in the specimens can be coded based on time-frequency mapping. Yet, physically generating long pulse chirped waves will usually inflate the cost due to required use of special circuitry. For the short pulse such as the Gaussian impulse wave, waveform generation will be easier. In the present paper, we focus only on the use of short pulse and the associated results.

2.2 Image Reconstruction Algorithm
By implementing the APS-CW data-focusing concept, images are reconstructed using the Rayleigh-Sommerfeld holography or the wavenumber-frequency migration (k-w) [Cafforio et al 1991] inverse algorithm, which is based on the scalar wave equation or the Helmholtz equation. The use of scalar wave equation has assumed that there is no depolarization when the wave propagates through the medium and this assumption is valid for our problem at hand [Gunes 1998]. The inverse algorithm involves the back propagation of scattered fields F_S(x, z = 0,t) along the orbit, say at z = 0, (or a planar surface in 3-dimension) towards the scatterer at incremental depths to obtain an image for z < 0. For multi-frequency experiments, i.e. w¹constant, the back propagation procedure, which is linear, can be repeated for each temporal frequency (or wavelength) and the scattered fields superimposed. The final image is then obtained by taking the inverse Fourier transform of the superimposed fields at each depth [Gunes 1998]. In a physical radar experiment, measured data can either be in time domain or frequency domain depending upon the equipment being used.

Assuming that the field at the measurement orbit is recorded in time domain, the algorithm can be explicitly implemented as follows [Cafforio et al 1991; Gunes 1998]:

1. Take the 2-Dimensional temporal and spatial fast Fourier transform (2D-FFT) of scattered field F_S(x, z = 0, t) recorded along the measurement orbit with respect to time t and space x to obtain (x, z = 0, w).
2. Back-propagate the transformed field (x, z = 0, w)to the corresponding position for each w using

(3)

to obtain the field distribution at z = -d_i, where is the backward propagator (or focusing function) given in the following form:

(4)

where c is the wave speed in the medium.

3. Take the inverse Fourier transform of (k_x, _z=-d_i)with respect to k_x to find the field distribution F_S(x,z=-d_i) at the new position.
4. Repeat 2 and 3 at incremental depths to form a 2-dimensional image of the scatterer.

With the APS-CW measurement technique, we adopt this backward propagation algorithm to retrieve the object function to form high-resolution images. The fast computing time of the 2D-FFT algorithm will make real time imaging possible. It is well known that the use of iterative transform-based algorithms such as the Born iterative method [Chew 1995] can provide higher resolution images of cracks and crumbles, which is a candidate method to be considered in the next phase project recently proposed by the authors. In that project, the subspace decomposition technique [Gunatilaka and Baertlein 2000] will also be applied to improve image resolution. In particular, this technique is effective in improving image quality of FRP-FRP interface and FRP-concrete interface, which are of major concerns as discussed earlier.

Image reconstruction performed in this study employs scattered signals generated from FD-TD simulations (forward modeling) to reconstruct images accordingly. Actual radar measurement data, when available, should be used in place of the simulation results.

2.3 Advantages of APS-CW Data-Focusing
The APS-CW technique has multiple advantages and is particularly effective to use with electromagnetic (EM) waves for damage detection. Fundamentally, APS-CW is the representation of numerous static focused wave measurements at different discrete locations within the subject of interest. At each of these discrete points, the respective condition can be detected and quantified. Compared to the lens focusing technique [Feng et al 2002], data focusing provides easier measurement setup and wider incident wave coverage. Lens focusing usually suffers from tedious measurements, as a pre-defined grid needs to be set up and numerous points measured. Without knowing the size and location of undercover damages beforehand, it may be difficult to locate and quantify damages. Furthermore, due to its inherent measurement efficiency, APS-CW can literally be applied to all geometric and dielectric media. From an operation perspective, the method is easy to work with. The operator needs only to setup the equipment at several locations around the subject and key in the appropriate parameters into the radar device to generate images in real time.

3. Feasibility of the APS-CW Technique

To demonstrate the feasibility of the APS-CW methodology, we have considered two problems using numerical simulation. The first problem involves the FD-TD simulation of wave scattering and measurement using the proposed data-focusing scheme. Results are illustrated by plotting the scattered waves in the space-time domain. The second problem involves image reconstruction using scattered waves generated from the FD-TD simulation. The 2D-FFT algorithm is being implemented. As the study is at its exploratory stage, rectangular hybrid-material panels are used in our simulations for feasibility assessment, instead of the more realistic yet more complex FRP-confined reinforced concrete columns. The major difference between using rectangular and cylindrical simulation models hinges upon the use of a different focusing function. This deviation, nevertheless, does not impinge our ability to judge the feasibility of the APS-CW scheme, as the underlying data focusing mechanism remains unchanged. In addition, the use of physical panel specimens would facilitate the introduction and measurement of various defects during the manufacturing process for correlation and verification of our numerical simulations. The two problems are described in more detail below.

3.1 Wave Scattering Simulation

Two model panels have been analyzed in time-domain using FD-TD simulation, as shown in Figures 2(a) and (b). These are reinforced concrete (RC) panel reinforced with FRP plate systems with and without a defect (or air void). The two hybrid panels are subjected to a downward plane incident wave of Gaussian impulse with a maximum frequency of 5GHz. A 161 x 1201 FD-TD grid with a grid size (Dx and Dz) of 0.00254m is used to discretize the total computational domain of 0.4m x 3.0m. Figures 2(a) and (b) show only the domain near the rebar vicinity in which the wave motions are of interest. Scattered microwaves are measured along a line above the top surface of the models. Time-domain signals are collected in the same fashion as in our proposed APS-CW technique and the images in Figures 2(c) and (d) show distinct differences between the two cases. The defect (or air void) in the FRP-concrete interface region has been detected. On the other hand, the FRP layers are not showing very well in the time-domain images due mainly to the maximum frequency we used for detecting the void. It is, therefore, shown that 5GHz is not high enough to detect the thin-layer FRP system, although it is capable of showing the defect. This emphasizes the significance of using incident waves with a wide range of frequencies to detect various contents with different penetration power, as discussed in earlier sections. Nevertheless, it has been verified from the time-domain analysis that the proposed APS-CW technique is a viable solution that can detect even small defects in a hybrid system consisting of various dielectric properties.

Fig 2: (a) FRP-reinforced RC panel without defect; (b) FRP-reinforced RC with defect; (c) time-domain signals simulated for case (a) model; (d) time-domain signals simulated for case (b) model.

3.2 Image Reconstruction
To evaluate the imaging algorithm described by Equations (3) and (4), in which the APS-CW concept is incorporated, a numerical model of reinforced concrete panel (Figure 3(a)) is studied using signals generated from data focusing (Figure 3(b)). In this example, the incident wave, measurement scheme, and the FD-TD model being used are identical to those in the wave scattering simulation studies of Section 3.1.

Fig 3: (a) Concrete panel with a rebar; (b) Time-domain signal simulated by the FD-TD model; (c) Image reconstructed by the proposed algorithm; (d) Image reconstructed by the proposed algorithm with the help of the ensemble averaging technique.

It has been observed that the rebar image is reconstructed with some success in terms of its location and size. By using the ensemble averaging technique [Deshchenko 2000], the strong reflection from the top surface has been successfully removed, as shown in Figures 3(c) and (d). It also reveals that this technique results in a higher signal-to-noise ratio of the focused image and it helps improve the contrast between the subject and the background. Yet, much needs to be done to improve the image quality by further developing the proposed algorithm. Figure 3(d) reveals that the shape of the subject being imaged is not quite close to the real situation. Noise level is still considered too high. For imaging multiple objects embedded in the medium, added complexity may arise. To tackle these problems, we plan to apply the subspace technique of Gunatilaka and Baertlein [2000] and other associated techniques in the near future.

4. Conclusion

In this study, the Automatic Progressive Stepping - Converging Wave (APS-CW) data focusing scheme with the use of microwaves has been demonstrated as a possible method for use in NDE of FRP-confined concrete. To result in high-resolution images, an efficient wavenumber-frequency migration technique has been employed. Since the work is still at its exploratory stage, signals created from FD-TD analyses have been used instead of those from physical measurements, as the data inputs of our image reconstruction computation. By means of two numerical models, the APS-CW scheme has been shown to be advantageous in terms of damage detection effectiveness, measurement efficiency, and implementation practicality. It has also been shown that the data-focusing concept is a feasible technique, which requires further refinements to improve image resolution and conformation. To address these issues, we propose to implement, in our future studies, the subspace technique of Gunatilaka and Baertlein [2000] to improve image resolution near the interface and outer surface of the hybrid material system. It might also be necessary to refine the temporal characteristics of the incident waves in accordance to the target size and geometry of the defects.

5. References

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