A Passive Wireless Crack Sensor Based on Patch Antenna with Overlapping Sub-Patch

Monolithic patch antennas for deformation measurements are designed to be stressed. To avoid the issues of incomplete strain transfer ratio and insufficient bonding strength of stressed antennas, this paper presents a passive wireless crack sensor based on an unstressed patch antenna. The rectangular radiation patch of the proposed sensor is partially covered by a radiation sub-patch, and the overlapped length between them will induce the resonate frequency shift representing the crack width. First, the cavity model theory is adopted to show how the resonant frequencies of the crack sensor are related to the overlapped length between the patch antenna and the sub-patch. This phenomenon is further verified by numerical simulation using the Ansoft high-frequency structure simulator (HFSS), and results show a sensitivity of 120.24 MHz/mm on average within an effective measuring range of 1.5 mm. One prototype of proposed sensor was fabricated. The experiments validated that the resonant frequency shifts are linearly proportional to the applied crack width, and the resolution is suitable for crack width measuring.


Introduction
Nowadays, bridges, civil architectures, and mechanical engineering systems continue to provide service despite aging and associated damage accumulation [1]. Failure of these structures can become a serious threat, causing both life and property loss [2]. Furthermore, to a great extent this type of structural failure can be due to the formation and expansion of cracks [3]. Hence, crack monitoring of aged and damaged structures is progressively becoming more important.
Crack monitoring sensors are categorized as wired or wireless types. Cables for wired crack sensors supply energy power and transmit data. For its individual functionality, a crack's existence and growth can be directly monitored by crack sensors, such as the optical fiber grating sensor [4,5], capacitance-based sensor [6], conductive area sensor [7], resistance based sensor [8], infrared sensor [9], and optical sensor [10,11]. These cable-powered sensors usually show reliable accuracy and high stability. However, the installation and application of wired crack sensors is both time-and labor-consuming due to the cable deployment and periodical manual inspection. Wireless crack sensors can significantly reduce instrumentation time and system cost [12,13]. However, wireless This paper is organized as follows. Section 2 introduces the concept of a concrete crack sensor based on a patch antenna with a covered radiation patch and illustrates the sensing mechanism using the cavity model theory. This section introduces the innovative concept of one prototype of the crack sensor. In Section 3, the appropriate dimension parameters are determined for the sensing system. Section 4 describes the fabrication of sensors and the instrumentation setup of experiments. The resonant frequency of the chipless crack sensor is analyzed wirelessly by a wide band antenna over the sensor. Conclusions are then drawn, and future research potential is discussed.

Crack Sensor Using a Combined Radiation Patch
Monolithic patch antennas as strain or crack sensing units are designed to be stretched. The alternative way is to make the sensing unit unstressed by combining two radiation patches, whose total electric length depends on the overlapped length of two components.
According to the cavity model theory, a patch antenna composed of a radiation patch and a ground plane can be treated as a resonant cavity, and the resonant frequencies of the cavity are related to the dimension of the radiation patch [33]. Based on this principle, a patch-antenna-based crack sensor is proposed, as illustrated in Figure 1. This crack sensor consists of a partially-covered patch antenna and an overlapping sub-patch with the same width as the patch antenna. The overlapping sub-patch is placed over the underlying rectangular radiation patch, and the electric current induced by interrogation waves can flow within the combined radiation patch. For practical use, the patch antenna is placed on one side of the crack, while the sub-patch is connected with the other side of the crack. Once the crack is expanded, the relative position between the patch antenna and the movable sub-patch will change and lead to an increased electric length of the combined radiation patch, which produces the crack sensor's shift in resonant frequencies.

Theoretical Calculation for Proposed Crack Sensor
For a normal rectangular patch antenna [33] as shown in Figure 2a, assuming the electrical length is L e and the electrical width is W e , the resonant frequencies can be calculated as [33]: (a) (b) 9: Because the longitudinal elongation only affects the length of the radiation patch, the fundamental resonant frequency in longitudinal direction can be calculated as where f 10 is the fundamental resonant frequency in the longitudinal direction. The electric length can be calculated from the geometric dimensions of the radiation patch and the fringe extensions as where L is the length of the radiation patch and ∆L is the line extension. When the substrate height h is much smaller than the dimensions of the radiation patch, the line extension ∆L can be neglected [33]. Therefore, Equation (3) can be reduced to Analogously, applying Equation (4) to the proposed crack sensor with combined radiation patches as shown in Figure 2b, the fundamental resonant frequency can be calculated as: where f 10c is the fundamental resonant frequency in the longitudinal direction for the proposed crack sensor, L r is the length of the radiation patch, L s is the length of the sub-patch, and L o is the overlapped length between the radiation patch and the covering sub-patch. When a crack opens wider, the overlapped length would decrease, which changes the resonant frequency as: where ∆L o is the difference of the overlapped length after the crack opens and is equal to the crack width d. We can then rewrite Equation (6) as: As the crack width d is trivial compared with the dimensions of the crack sensor, the increment in denominator can be ignored and Equation (8) can be rewritten as: where L c is the combined length of the crack sensor, which can be calculated as: The shift of the fundamental resonant frequency in longitudinal direction can be then determined by Equation (11): where ∆ f 10c is the shift of the fundamental resonant frequency in the longitudinal direction; that is, the fundamental resonant frequency in the longitudinal direction changes linearly with the increasing overlapped length.

Design of Crack Sensors
According to the theoretical calculation in Section 2.1, the sub-patch should contact fully with the radiation patch, which depends on the flatness of the surface between the sub-patch and the radiation patch. To achieve this, a prototype with a dielectric board over the sub-patch was fabricated to stiffen the patch, and the dimensions of the sensor are shown in Figure 2b. Other solutions could also be practical, such as enlarging the height of the sub-patch or finding a material of the sub-patch with higher stiffness. This paper's featured patch antenna is demonstrated as working at around 2.4 GHz in the laboratory's available testing environment. The relationship between the fundamental resonant frequency in longitudinal direction and the dimension of the crack sensors is described in Equation (4), and the length of the combined radiation patch L c is calculated by Equation (10).
The width of the patch antenna is defined as follows to ensure the radiation efficiencies [33]: where f is the working resonant frequency of the patch antenna. Based on Equations (10) and (11), the setting domain for the crack sensor is determined as shown in Table 1. To ensure the working performance of the sensors, an Ansoft high frequency structure simulator (HFSS) was used to simulate the crack sensors with different sizes, to be described in Section 3.

Modeling and Simulation
The radiation properties of the crack sensor are simulated using the Ansoft HFSS. Figure 3 shows the HFSS model, which consists of a patch antenna and a sub-patch. The sub-patch is made up of a copper sheet and a coated dielectric board. The material of the dielectric board is Rogers RT/®duroid 5880. Copper is the chosen material of the radiation patch. The crack sensor is arranged inside a perfectly matched layer (PML) air box with a radius of about a quarter wavelength to ensure computational accuracy of the far field radiation. The whole system is fed by a plane wave above the patch antenna. Because the electric field should be perfectly perpendicular to the surface, a perfect E was selected as the boundary condition of the ground plane.  After calculating the fundamental resonant frequency within the setting range in Table 1 by HFSS, one set of the crack sensors with a better performance is proposed. The parameters are shown in Table 2. Then, the simulation of the crack sensor with the moving sub-patch is carried out. In the initial state, the overlapped length between the radiation patch and sub-patch is 0 mm. With the movement of the sub-patch, the overlapped area expanded continuously until it reached 6 mm. The induced current distribution pattern on the combined radiation patch for the fundamental mode is shown in Figure 4. The current flows from the radiation patch to the movable sub-patch. After calculating the fundamental resonant frequency within the setting range in Table 1 by HFSS, one set of the crack sensors with a better performance is proposed. The parameters are shown in Table 2. Then, the simulation of the crack sensor with the moving sub-patch is carried out. In the initial state, the overlapped length between the radiation patch and sub-patch is 0 mm. With the movement of the sub-patch, the overlapped area expanded continuously until it reached 6 mm. The induced current distribution pattern on the combined radiation patch for the fundamental mode is shown in Figure 4. The current flows from the radiation patch to the movable sub-patch.
One step of the movement is set at 0.05 mm. The monostatic radar cross section (RCS) around the fundamental resonant frequency in the longitudinal direction is acquired for each moving step, as shown in Figure 5. The fundamental resonant frequency of the displacement sensor is then extracted from each of the radar cross section (RCS) curves. The scatter diagram of the fundamental resonant frequency and overlapped length (which represents the crack width) is plotted in Figure 6.
Then, the simulation of the crack sensor with the moving sub-patch is carried out. In the initial state, the overlapped length between the radiation patch and sub-patch is 0 mm. With the movement of the sub-patch, the overlapped area expanded continuously until it reached 6 mm. The induced current distribution pattern on the combined radiation patch for the fundamental mode is shown in Figure 4. The current flows from the radiation patch to the movable sub-patch.    In general, a nearly linear relationship between the overlapped length and resonant frequency is observed in Figure 6, as described by Equation (10). The correlation coefficient of the fitted line is 0.9788, which shows the resonant frequency to nearly shift linearly with the increasing of overlapped length. The slope of the fitted line representing the sensitivity coefficient of the crack sensor is 0.07 GHz/mm. At the radiation boundary, the interrogating method and environmental situation in simulation are different than that found in the actual occasion. Experiments were designed and the procedures are defined in Section 4 to verify the performance of the proposed sensor.  I n general, a nearly linear relationship between the overlapped length and resonant frequency is observed in Figure 6, as described by Equation (10). The correlation coefficient of the fitted line is 0.9788, which shows the resonant frequency to nearly shift linearly with the increasing of overlapped length. The slope of the fitted line representing the sensitivity coefficient of the crack sensor is 0.07 GHz/mm. At the radiation boundary, the interrogating method and environmental situation in simulation are different than that found in the actual occasion. Experiments were designed and the procedures are defined in Section 4 to verify the performance of the proposed sensor.

Experiment
For the fabricated sensors, copper was selected as the material for the radiation patches. Rogers RT/duroid 5880 was selected as the middle substrate of the rectangular patch antenna and the substrate of sub-patch. The patch antenna was produced in laboratory and the fundamental resonant frequency of the crack sensor was interrogated wirelessly by a wide-band antenna.

Antenna Production in Laboratory
The antenna used in this study's experiments was produced in the authors' laboratory. A sandwich of a selected length and width having a dielectric substrate and two copper sheets coated on the both side of the dielectric substrate was used for antenna making. First of all, a heat toner transfer paper was cut to match the same width and length as the radiation patch. The paper's surface was then covered with toner by laser printer. The paper was then added as a sandwiched layer of the radiation patch. Another sheet of paper with the same dimensions as that of the ground plane was disposed and then attached to the other copper sheet of the sandwich. A thermal transfer printer was used to transfer the toner from the paper to the copper sheet of the sandwich. The sandwich was put into the thermal transfer printer ten times to concern the toner thar was attached to the copper sheets. The heat toner transfer paper was then casted off. Finally, the sandwich coated with tonner was placed into a kind of corrosive liquid. The uncoated area in the sandwich was corroded, and the sandwich after corrosion served as the patch antenna used in this experiment. The sub-patch was produced in the same way.
The flow chart seen in Figure 7 shows the equipment used to produce the patch antenna, as shown in Figure 8. In addition, the manufactured crack sensor is shown in Figure 9. The parameters of the sensor are the same as in the simulation section.
placed into a kind of corrosive liquid. The uncoated area in the sandwich was corroded, and the sandwich after corrosion served as the patch antenna used in this experiment. The sub-patch was produced in the same way.
The flow chart seen in Figure 7 shows the equipment used to produce the patch antenna, as shown in Figure 8. In addition, the manufactured crack sensor is shown in Figure 9. The parameters of the sensor are the same as in the simulation section.

Instrumentation Setup
The testing device for crack sensing is established and shown in Figure 10. A micrometer shown in Figure 10c consists of a fixed table, a fine-tuning table and a screw type micrometer rod. The minimum step advance of the screw micrometer rod is 0.01 mm. The fine-tuning table can be pushed by the screw micrometer rod to move relative to the fixed table and then simulate an expanding crack.  (a) (b) 9: Figure 9. The manufactured crack sensor.

Instrumentation Setup
The testing device for crack sensing is established and shown in Figure 10. A micrometer shown in Figure 10c consists of a fixed table, a fine-tuning table and a screw type micrometer rod. The minimum step advance of the screw micrometer rod is 0.01 mm. The fine-tuning table can be pushed by the screw micrometer rod to move relative to the fixed table and then simulate an expanding crack. Two pieces of foam were attached to the fixed table and the fine-tuning table to isolate the crack sensor from the tables. This helped to minimize the electromagnetic interference caused by the crack simulator. The rectangular patch antenna was attached to the foam over the fixed table by glue, and the sub-patch was attached to the fine-tuning table. When the screw rod is rotated, a crack forms and then expands, which leads to the increase of the overlapped length, thereby changing the resonant frequency of the sensor. To simplify the testing device, the installed method for the experimental sensor is different from the way described at Section 2, and the moving direction between the sub-patch and the patch antenna is opposite compared with the moving direction described at Section 2. A wide-band antenna is used to give a plane wave feeding to the sensor and, thus, to receive the backscattering of the patch antenna. To reduce the background reflection, the wide-band antenna was set about 2 cm or closer above the crack sensor. A vector network analyzer (VNA) analyzed the signal of the wide band antenna received from the crack sensor. The sweeping range of the VNA was chosen to range from 2 GHz to 3 GHz, and the working band of the wide-band antenna's range is from 1 GHz to 2.8 GHz to match the crack sensor and the VNA. The experiment was carried out with the overlapped length changing from 1.5 mm to 3 mm; thus, the linearity suffered when the overlapped length was below 1.5 mm. By receiving and transmitting the backscattering signal, the resonant frequency can be wirelessly analyzed.
The experiment was carried out as follows: First, the sub-patch was set over the patch antenna with the overlap length at 1.5 mm. Then the micrometer moved with each incremental step set at 0.1 mm, thereby forming an expanded crack between two pieces of foam. The signal from the backscattering was then monitored by a VNA to get the radar cross section (RCS) curve of the sensor for each step. By extracting the resonant frequency at the local minimum of each curve, the shift of the resonant frequency was obtained and is described in Section 4.3.

Results and Discussion
Based on the experimental results, Figure 11 shows the radar cross section curve. Figure 12 shows the relationship between the fundamental resonant frequency and overlap length in the calculated theory of Equation (10). Table 3 compares the results of sensitivity in GHz, the measuring range in GHz, and correlation coefficient of the fitted line as they pertain to theory calculation, numerical simulation and the experiment. The correlation coefficient of the fitted line of each group are all over 0.9. The sensitivity in theory calculation is close to the numerical simulation results, but the sensitivity measurement in the experiment is more than double that of the theoretical and numerical results. The sensitivity difference could be due to the air gap between the sub-patch and the patch antenna. Moreover, the measuring range of each method varied slightly. This discrepancy is probably due to the following reasons: 12: Figure 11. The monostatic radar cross section (RCS) in the experiment.

Resonant frequency (GHz)
Overlapped length(mm) Figure 12. The relationship between resonant frequency and overlapped length in theory calculation, numerical simulation, and in the experiment.
(1). The impact of the substrate of the sub-patch was ignored in theoretical calculation. However, the impact of the substrate was taken into consideration in both the numerical simulation and the experiment.
(2). The patch antenna produced in the laboratory became defective when a little toner remained on the surface of the radiation patch, as shown in Figure 9.
(3). The monostatic RCS is measured in near field, so the value of the monostatic RCS during the frequency sweep would be affected by the interrogating distance, which would decrease the treatability and accuracy of the measuring results.
(4). The use of a micrometer can produce electromagnetic interference, which was not a consideration in either the theoretical calculation or numerical simulation.

Conclusions
This paper introduces a novel crack sensor based on a patch antenna with an overlapping sub-patch. Using the theory of cavity model, the authors revealed a linear relationship between the fundamental resonant frequency in both the longitudinal direction and the overlapped length of the crack sensor. One prototype was modeled and fabricated for numerical simulation and experiments. The resonant frequency of the crack sensor was wirelessly interrogated by a wide band antenna, and the results showed a sensitivity of 120.24 MHz/mm on average within an effective measuring range of 1.5 mm.