Design and Experimental Validation of an Optimized FSS Sensor for Wireless Communications

A Frequency Selective Surface (FSS) is a passive, periodic structure composed of identical conductive elements arranged in a single unit or a two-dimensional infinite grid. The smallest identical element of any FSS array may comprise one or more elements, known as a unit cell. These unit cells are periodically arranged in a one- or two-dimensional array to form the entire FSS structure. Generally, the unit cell consists of either a conductive patch-type element or an aperture-type element on a dielectric substrate. The incident plane wave is either reflected or transmitted around its resonant frequency. A periodic array can be excited in two distinct ways: either by an incident plane wave (in a passive array) or by connecting a separate voltage source with identical amplitude and phase to each element of the array (in an active array).

Structural Health Monitoring (SHM) has become an essential component in ensuring the longevity and safety of civil infrastructure. Various sensor technologies, such as fiber optics, piezoelectric sensors, and strain gauges, have been employed to monitor the structural integrity of buildings, bridges, and other critical structures. However, these methods often suffer from high cost, complex integration, and maintenance challenges. FSS-based sensors present a passive, wireless alternative that enhances SHM applications by providing a non-intrusive means of detecting structural anomalies through electromagnetic response analysis.

FSS sensors can be embedded within structures to continuously monitor material deformations, load-induced stresses, and crack formations. Their ability to function as frequency-tuned electromagnetic resonators makes them highly effective in identifying even minor structural changes. Unlike conventional sensors, FSS does not require a power supply for sensing operations, making it a cost-effective solution for long-term SHM. Additionally, their ability to operate in TE and TM polarization modes enhances sensitivity and detection accuracy across a range of environmental conditions.

The deployment of FSS sensors in SHM is justified by their unique ability to detect structural cracks and deformations passively. The resonance frequency of an FSS shifts when physical changes, such as cracks, alter the local dielectric environment. This shift can be analyzed to determine the presence, location, and severity of damage. Traditional sensors require direct contact or embedded wiring systems, whereas FSS-based sensors can be seamlessly integrated into composite materials or applied as surface-mounted structures.

Given the increasing demand for reliable and long-term monitoring solutions, it becomes essential to examine how FSS-based sensing compares with existing SHM approaches. While the work established the functional principles and advantages of FSS sensors, a broader comparison with other established techniques is needed to highlight the specific motivations for adopting FSS in structural monitoring. Such a comparative perspective also clarifies the unique gaps that conventional sensors fail to address, thereby underscoring the relevance of choosing FSS as the sensing framework in this work.

Conventional sensors require direct physical contact or an embedded circuit board, whereas FSS-based sensors can be embedded in composite materials or surface-mounted.

• Fiber Optic Sensors: High sensitivity but costly and challenging to integrate over large surfaces.
• Piezoelectric Sensors: Provide accurate localized measurements but require an external power source and suffer from signal degradation over time.
• Strain Gauges: Simple in design but limited in terms of scalability and environmental resistance.

FSS sensors, on the other hand, offer broadband functionality, polarization stability, and non-contact operation, making them ideal for large-scale monitoring without significant retrofitting costs. They are particularly effective in environments where traditional sensor deployment is difficult, such as high-temperature zones or structures with complex geometries.

The performance of an FSS sensor for SHM is heavily influenced by its geometric configuration and electromagnetic properties. The optimization of FSS parameters—including unit cell dimensions, substrate material selection, and spacing between elements—is crucial for maximizing sensitivity and stability. A multi-objective optimization approach ensures that key performance metrics, such as angular stability, frequency selectivity, and robustness to environmental variations, are simultaneously enhanced.

To achieve this, a multi-objective evolutionary algorithm based on decomposition (MOEA/D-M) is employed to refine FSS designs. This method enhances the trade-offs between competing objectives, such as bandwidth expansion and polarization insensitivity. By leveraging AI-driven optimization techniques, the FSS sensor design can be iteratively improved to achieve higher accuracy in crack detection and better resilience against environmental perturbations.

Additionally, the integration of machine learning models can further improve the detection capabilities of FSS-based SHM systems. By analyzing historical resonance shift data, predictive models can be trained to classify various types of structural anomalies, thereby enabling early-warning systems for infrastructure monitoring.

The main contributions of this work may be summarized as follows:

• Design and Optimization of an FSS-Based SHM Sensor: The development of a novel FSS sensor tailored for SHM, integrating an optimized unit cell geometry for enhanced sensitivity to structural anomalies.
• Integration of Multi-Objective Optimization: Implementation of the MOEA/D-M optimization algorithm to refine key design parameters, achieving improved angular stability, resonance frequency selectivity, and polarization independence.
• Simulation and Experimental Validation: Validation of the proposed FSS sensor through extensive simulations using CST Studio, followed by experimental testing in an anechoic chamber using horn antennas and a vector network analyzer (VNA).
• Electromagnetic Response-Based Crack Detection: Demonstration of the sensor’s ability to detect structural cracks via shifts in resonance frequency, enabling passive, non-invasive monitoring of material deformations and stress distributions.
• Comparative Analysis of FSS Geometries: Comprehensive assessment of different FSS unit cell geometries, evaluating their performance in terms of bandwidth, polarization stability, and environmental adaptability.
• Integration with Active Structural Control Systems: Discussion on how FSS-based SHM sensors can be integrated into wireless sensor networks (WSNs), AI-driven predictive maintenance systems, and smart structural materials for real-time monitoring.
• Advancement in Passive Wireless Sensor Technology: Development of an ultra-low-power, maintenance-free sensor that provides reliable long-term SHM capabilities without requiring an external power supply.

3.1 Design

The design parameters of FSS are resonant frequency, bandwidth, and the configuration of the transmission and reflection curves. These properties collectively depend on a number of variables, including the shape and dimensions of the element, the distance between the elements, the dielectric material in the area, the angle of incidence, and the various polarizations of incoming waves. An FSS element's shape has a significant impact on its bandwidth [21]. The new designed FSS features a single rectangular loop design with square patch integrated at its corners. The frequency response is recorded and the operational frequency is found to be near 6.25 GHz for FSS element on substrate. The substrate is made of FR-4 and is of dimension 13.5 × 13.5 mm and thickness 0.8 mm. The square loop is of length 8 mm. The square patch integrated is of length 3.5 mm and thickness of the conducting element is 0.035 mm shown in Figure 1. The unit cell geometry, including the introduction of square patches at the corners, was carefully chosen through iterative design and simulation to optimize the performance of the FSS. The square patches at the corners provide specific benefits, such as enhancing the angular stability of the FSS and improving its polarization independence. These features ensure better performance across a wider range of incident angles and polarization modes. Additionally, the corner patches contribute to tuning the resonance frequency and achieving the desired frequency-selective behavior, as they influence the overall capacitance and inductance of the unit cell.

1.jpg

Figure 1. Proposed FSS design

A square loop with a side length of 8 mm, integrated with 3.5 mm square patches at each corner, forms the core resonant structure of the proposed design. The optimized combination of geometric and material parameters ensures consistent resonance performance across the 4–8 GHz frequency band, making the configuration suitable for identifying and monitoring cracks in civil infrastructures.

After conducting several design refinements and electromagnetic simulations using CST Studio Suite, the configuration incorporating corner square patches was finalized. This design enhances the FSS performance by promoting symmetrical current flow and strong capacitive coupling between adjacent unit cells. The addition of corner patches also contributes to improved angular stability and polarization independence, thereby maintaining consistent frequency responses under varying incidence angles and polarization states.

For the simulation environment, periodic boundary conditions were applied along the X and Y directions to emulate an infinite array of unit cells, while open (add space) boundaries were implemented along the Z-axis to represent free-space propagation. A plane wave excitation was used to evaluate the sensor’s behavior under both TE and TM polarization modes, with incidence angles ranging from 0° to 60°. These simulation parameters effectively capture the electromagnetic response of the proposed FSS design, ensuring reliable and accurate prediction of its performance under different structural and environmental scenarios.

The sensor showed response at 6.07 GHz within the window of 2–10 GHz. This will be used as reference to compare the response of the FSS sensor with the sample integrated with crack. Both the TE and TM mode showed the same response as shown in Figure 2.

2-1.jpg

2-2.jpg

Figure 2. Transmission characteristics in TE and TM mode

3.2 Simulation of cracks

In order to test the sensor for detection of crack, multiple cracks were simulated using CST Studio as shown in Figure 3. The cracks were made up of concrete material of dielectric 5.28. The crack brings change in the dielectric with presence of air gap thus varying the frequency response. The FSS was tested for cracks designed with multiple dimensions.

3-1.png

External crack

3-2.jpg

Vertical Internal (Crack 1)

3-3.jpg

Horizontal Internal (Crack 2)

3-4.jpg

Centered Irregular (Crack 3)

3-5.jpg

Lateral Irregular (Crack 4)

3-6.png

Branched (Crack 5)

d6b64544-e13d-412f-8b41-0fb4e6894fe2.png

The transmission characteristics in TE and TM modes with various types of cracks are shown in Figure 4 and Figure 5. Comparing the frequency response of all the simulated cracks reveals that the sensor exhibits significant variation in the operating frequency range depending on the dimension and position of the crack. The frequency response variation for cracks occurs due to shift in frequency, location and size of cracks and sensor response patterns. The shift that the sensor shows notable fluctuations in the operating frequency range are measured. For the simulated cracks the variation is within the window of 4–7 GHz. The cracks are analysed in both TE as well as in TM mode. The tangential component of the electric field must be continuous across the boundary. This ensures that the fields on opposite sides of the boundary are periodic. The tangential component of the magnetic field must be continuous across the boundary. This ensures that the magnetic field phase changes by a constant amount across the boundary.

4.png

Figure 4. Transmission characteristics in TE mode (with crack)

5.png

Figure 5. Transmission characteristics in TM mode (with crack)

The designed FSS is polarization insensitive since it responds to both polarization modes (TE and TM) in a nearly identical way. The FSS unit cell is developed for the measurement findings that are obtained. The results of the simulation and measurement coincide well.

The relationship between fracture characteristics and resonant frequency shifts can be better understood by methodically altering crack parameters like as position, depth, and form. A quantitative evaluation of the sensor's sensitivity and capability for precise fracture identification will be made possible by this analysis. Furthermore, experimental validation is essential for verifying the simulation results and proving the sensor's usefulness. The performance of the sensor can be assessed in real-world settings by creating test specimens with controlled fracture shapes and measuring vibration. Strong proof of the sensor's dependability and potential for practical application will be provided by this combined simulation and experimentation method.

3.3 Optimization algorithm for FSS design

A multi-objective optimization problem (MOP) involves finding a vector of decision variables within a specific domain that meets all constraints and optimizes a set of multiple objective functions. These objective functions often consist of subgoals that may conflict with each other. When one subobjective improves, the performance of one or more subobjectives may suffer. That is to say, in order to maximize the optimization of each subobjective, cooperation and compromise amongst them are necessary rather than trying to obtain the ideal values for multiple subobjectives. MOPs are common in real-world scenarios and are often explored in scientific research and practical applications. To address the limitations of existing algorithms, we propose MOEA/D with adaptive exploration and exploitation (MOEA/D-AEE). This algorithm improves global search and adaptive capabilities by using dynamic search and joint development, enhancing sparse distribution and search effectiveness. The approach integrates a joint exploitation coefficient between parent solutions, which helps generate better offspring by adaptively adjusting the relationships between parents and offspring during optimization. Additionally, it utilizes uniformly distributed random integers to explore the solution space more thoroughly, balancing exploration and exploitation. The method actively selects a parent from the original population when two chosen parents are similar, while gradually employing an exploitation strategy to pick a parent from neighbouring solutions when the two selected parents are significantly different. This combination enhances the overall optimization process.

Numerous academics have attempted to use evolutionary algorithms to solve these kinds of issues. Setting weights is the initial step towards turning the two-dimensional problem into a single-objective problem. Nevertheless, the population's distribution is unequal and the basic weighting approach is unable to accurately represent the true state of affairs due to the objective function's increased dimensions. The traditional nondominated genetic sorting algorithm II (NSGA-II) was then proposed by researchers who carried out additional research on the application of multi-objective evolutionary algorithms (MOEAs).

A type of optimization problems known as MOPs are those that have several competing objectives. The purpose of MOP is to acquire a set of optimal solutions that best balance its numerous objectives, as opposed to one optimal solution, as with a single-objective optimization problem (SOP). All possible solutions in the feasible issue area that are independent of other solutions are contained in such an optimal-set Pareto front. The weighted sum method, the Chebyshev method, and the boundary crossing method are common decomposition techniques in this approach. The following is the formula for the most widely used Chebyshev decomposition method:

$z^*=\min \left(f_1, f_2, \ldots, f_M\right)$          (1)

6.jpg

Figure 6. Flowchart of optimization procedure

An improved hybrid optimization method, referred to as MOEA/D-M, is introduced as a sophisticated automated design approach specifically for developing compact FSS antennas. This technique combines the advantages of both particle swarm optimization (PSO) and binary particle swarm optimization (BPSO), integrating them into the structure of MOEA/D. By utilizing group operators in a parallel configuration, the approach improves the search efficiency and precision, offering a more robust solution for optimizing multiple conflicting objectives simultaneously in the antenna design process. This results in a more effective and automated approach to achieving compact and high-performance FSS antennas. During the algorithm's execution, every particle has several neighboring particles, and they are all divided into a few groups. Access to potential or beneficial information is available to members of both groups and communities. Then, within predetermined bounds, MIMO antenna with anticipated performance can be targeted and intelligently generated. In certain MIMO antenna design scenarios, this can serve as an alternative approach. The effectiveness of the design strategy is demonstrated through both single-band and dual-band compact high-isolation FSS antenna designs for SHM applications, which share a common reference model. The proposed method has the potential to significantly enhance the design flexibility of FSS. The figure illustrates the step-by-step optimization process. Figure 6 shows the flowchart of optimization procedure. The detailed procedure of MOEA/D-M is outlined as follows.

While S₁₁ is analyzed to understand reflection characteristics, S₂₁ provides insight into how effectively the FSS transmits signals. The optimization algorithm may emphasize minimizing the S₁₁ parameter to enhance reflection capabilities, it is essential to also consider transmission properties (S₂₁) when discussing overall performance. Both parameters provide a comprehensive view of how the FSS operates within its intended application, particularly in SHM contexts. This dual focus allows for a robust evaluation of both filtering and transmission efficiencies critical for effective sensor design and implementation.

Step 1: Initialization

Construct N weight vectors λ₁,λ₂,….λ_N

Generate initial population through random sampling

Find N_best and G_best

where N_best and G_best are the best solution for fitness function and objective value

Initialize z*=(z₁*,z₂*,….z_m*)^T

where z is objective function or a decision variable within the optimization framework

Set external population=0

Step 2: Reproduction and update

(1) Update weight vector

(2) Revaluate x_i and update F_i for each particle i, where, x_i is individual decision variable or a vector of variables that define a potential solution in the optimization landscape, where, f_i is a fitness value

(3) Update N_best and G_best

Step 3: Return

The design of FSS is restricted to a predefined to 13.5 mm × 13.5 mm. The evaluation function is given by:

$f=\frac{1}{h} \sum_{i=1}^h \min \left(s_{11},-10\right)$          (2)

where, h is the number of sampling points in the operation band and f is the average value of S₁₁.

Furthermore, multi-objective functions are defined as follows:

$f_1=\frac{1}{h} \sum_{i=1}^h \min \left(s_{11},-10\right)$         (3)

$f_2=\frac{1}{h} \sum_{i=1}^h \min \left(s_{11},-15\right)$         (4)

The performance evaluation of the optimized FSS design with the literature is presented in Table 2. The suggested FSS's unit cell size is optimized through the use of the MOEA/D-M algorithm, ensuring a 60° angular stability.

Table 2. Performance evaluation of optimized FSS design

Achieving the best possible balance between convergence precision and computing economy was the main focus of the algorithm's parameter setting. In order to maintain feasible computing effort and guarantee sufficient coverage of the design space, a population size of 10,000 was chosen. In order to attain steady convergence for both goals—reducing reflection loss and improving angular stability—the optimization procedure was carried out for 1,500 generations.

The crossover and mutation probabilities were chosen at 0.9 and 0.1, respectively, to preserve diversity within the evolving population and avoid early stagnation. Using uniformly distributed weight vectors, the multi-objective optimization challenge was broken down into several scalar subproblems, each of which was able to reflect a distinct trade-off between the objectives. In order to improve the algorithm's capacity to converge effectively toward the Pareto-optimal front and guarantee a fairly distributed collection of optimal design solutions, information exchange between nearby solutions was also included.