Simulation Study of Electromagnetic Standing Wave Method for Pre-stress Detection of Steel Strands

With the widespread application of pre-stressed technology, effective pre-stress monitoring has become a key research area in the field of health monitoring, such as bridges. This paper conducts a simulation-based validation study based on the electromagnetic standing wave pre-stress measurement method. Through the analysis of the implementation process and principles of the electromagnetic standing wave measurement method, frequency domain simulations are performed in HFSS software, and then the frequency domain results are imported into ADS for time domain simulations, ultimately verifying the feasibility of the electromagnetic standing wave pre-stress measurement method. Experimental results indicate that the electromagnetic standing wave method can achieve non-destructive and effective monitoring of in-service pre-stressed steel strands.


Introduction
The introduction of prestressing technology not only increases the load-carrying capacity of bridges but also extends their service life, making it widely applied in the field of bridge engineering.With the passage of time and the increase in load levels, the structural performance of existing bridges gradually deteriorates [1].Prestressing loss can cause a significant decrease in load capacity, making prestress detection one of the important indicators to assess the health condition of prestressed bridges [2].In prestressed bridges, the measurement of effective prestress in steel strands is the primary objective.Many scholars have conducted extensive research on the measurement methods of effective prestress in steel strands, mainly divided into local damage detection and non-destructive detection based on the extent of the method's impact on the structure [3].Among them, local damage detection methods mainly involve cutting a portion of the steel strands and conducting stress release, reverse loading, and transverse increment measurements in the cut section [4].
The accuracy of local damage detection is higher, but it can cause damage to stress structures.Therefore, the current research focus is on simple and effective non-destructive testing methods.Non-destructive testing mainly involves research in areas such as material properties, acoustics, and electromagnetics.According to the applicable environment, non-destructive testing can be divided into measurements for structures under construction and structures in service.Methods applicable to structures under construction include smart steel strands, adhesive sensors, and electromagnetic methods that require embedded coils.For example, Yang et al. proposed a smart steel strand with embedded DOFS and CCFPI as sensors [5].In addition to the combination of sensors, the distribution of sensors also has an impact.For instance, Zhu et al. studied a helical arrangement of distributed optical fiber sensors [6].Smart steel strands are a new type of steel strand that is incompatible with traditional steel strands.In the production process of traditional steel strands, many scholars have used different distribution methods of various sensors, such as strain gauges, electromagnetic sensors, and surface eddy current sensors, to adhere them to steel strands or corrugated pipes.Effective prestressing can be monitored through the reserved sensor interfaces [7].
However, adhesive sensors have some issues: they are easily damaged during the process of adhesive application or subsequent use, and the sensors are typically placed internally within the structure, which poses certain difficulties for existing structures.To address this problem, Zhang et al. (8) employed the method of embedding electromagnetic coils to monitor cable tension using elastic magnetic induction (EMI) and self-induction phenomena.The method of embedding coils typically does not require internal operations on the structure; monitoring can be accomplished by accessing only the damaged portion.Additionally, scholars such as Xiu, Karjalainen, and Li have studied the relationship between electromagnetic fields and prestress from the perspectives of inverse magnetostrictive effect, magnetic domain wall jumping during magnetization, electromagnetic oscillation, and magnetoelastic effect.They have proposed corresponding effective methods for measuring prestress levels .
Non-destructive and effective prestressing monitoring of in-service structures can be achieved through vibration and acoustic emission methods.Previous experiments have shown that changes in prestress can affect vibration frequencies [9].Breccolotti developed a numerical procedure to evaluate the dynamic performance of continuous prestressed concrete bridges, considering multiple environmental influencing factors [10].Li, Shi, and others evaluated the stress monitoring capability of Lamb waves using numerical simulation based on the analysis of intrinsic frequencies [11].In addition to the above methods, the acoustic emission (AE) method based on the acoustic-elastic effect is widely applied in the field of effective prestress measurement.Hou and colleagues studied the propagation mechanism and attenuation law of acoustic emission waves in prestressed steel strands through numerical simulations and experimental verification [12].Tonelli, Elfergani, and other scholars have used the acoustic emission method (AE) for bridge health monitoring, which mainly reflects parameters such as amplitude, energy, frequency, and duration in the level of effective stress using the acoustic-elastic theory .Furthermore, Nucera and Scalea discussed the nonlinear characteristics of ultrasonic guided waves [13].The frequency of the acoustic emission method is relatively low and is susceptible to interference from low-frequency environmental noise, making it not suitable for large structures.
Implementing prestress monitoring based on electromagnetic standing waves is a novel nondestructive measurement method with a relatively simple operating principle.This method primarily considers the fact that prestressed steel strands are ferromagnetic materials and exhibit characteristics of conductivity and magnetostrictive effects.Changes in the stress of the steel strands directly affect parameters such as magnetic permeability and magnetic flux.To verify the feasibility of this method, simulations of electromagnetic standing wave phenomena are needed.Currently, simulating electromagnetic standing waves using existing mechanical simulation software is relatively challenging.Additionally, this method achieves prestress monitoring by observing changes in the wavelength of electromagnetic standing waves.Observing the wavelength requires implementation in the time domain.Currently, software such as ADS and CST provides good support for time domain simulations.In addition to time domain simulations, the S-parameters obtained in the frequency domain are also crucial.Therefore, it is necessary to utilize HFSS to obtain simulation results in the frequency domain and import those results into time domain simulation software to achieve joint time-frequency domain simulations.

Electromagnetic Standing Wave Simulation
Using frequency domain simulation software to obtain the S parameters in the frequency domain, the S11 and S21 parameters in the S parameters are analyzed.By inputting the frequency domain S parameters into the time domain simulation software to observe the time domain output results, a complete joint simulation process is established, and modeling simulation of the real seven-strand steel wire is conducted.

electromagnetic standing wave measurement method
Based on the propagation characteristics of electromagnetic waves, when electromagnetic waves pass through interfaces between different media, reflection and refraction phenomena occur due to impedance mismatch.The interference between the reflected and incident waves forms standing waves, where the nodes remain fixed while the antinodes oscillate up and down.The stress on the steel wire causes changes in coefficients such as permeability, resulting in a change in wavelength, translation of the standing wave, and variation in terminal amplitude, as shown in figure 1  In the measurement of standing wave method, we derive the relationship between terminal voltage, wavelength, magnetic permeability, and stress (as shown in equation ( 1)) to ultimately obtain the relationship between terminal voltage and prestress (equation ( 2)).To simplify the simulation approach, we employ a simulation method to achieve force variations.During the derivation process, we find that the electromagnetic standing wave prestress measurement method relies on magnetic permeability as an intermediate variable.By changing the magnetic permeability in the simulation software, we can simulate the processes of applying and unloading forces, significantly reducing the computational time of the simulation.Considering that this research primarily aims to validate the feasibility of the method, it is sufficient to simulate force variations only in terms of magnetic permeability. (1) (2)

Simulation process
First, conduct frequency domain simulation using the HFSS software.In the electromagnetic standing wave measurement method, multiple strands of steel wire are treated as a unified structure for theoretical derivation and validation.Therefore, an equivalent and simplified model of the steel wire is established in HFSS.By combining the theoretical transmission of electromagnetic waves in a single conductor and the actual environment of the seven-strand steel wire (typically coated with a layer of corrosion protection), an equivalent model of the steel wire with a diameter of 15.2 mm and a length of 1500 mm is created.This model is placed inside an air cavity as shown in figure 2. The simulated model of the actual steel wire is depicted in figure 3. Through frequency domain simulation, the S-parameters can be obtained, along with the corresponding impedance Smith chart.Subsequently, the S-parameter file obtained from the frequency domain simulation is exported as an S2P file.This file is then used in ADS software for time domain simulation, and impedance matching is performed on both ends of the port to ensure smooth input of electromagnetic waves to the steel wire.In order to demonstrate the rigor of this method, modeling and analysis of the seven-strand steel wire are conducted in HFSS, and the results at different time points in the frequency domain are observed.

Simulation results
After establishing an equivalent model for simulation, we will compare the simulated phenomena and results with theory to verify the feasibility of using the standing wave method for measurement from multiple perspectives.

S-parameter results
By scanning the frequency from 0 to 1GHz and obtaining the S-parameters, we can determine that dot1, dot2, dot3, and others (only three points are marked in the text) at similar frequencies can all achieve the transmission of electromagnetic waves in figure 4.

Field Distribution Results
A frequency of 0.2 GHz was chosen as the simulation observation frequency.Slices were added to the cross-section of the steel strand to observe the distribution of the field.The results in figure 5 show that there is no electric field distribution inside the cross-section of the steel strand, indicating that in this model, the electromagnetic waves propagate along the surface of the steel strand By adjusting the relative permeability of the steel wire in the HFSS simulation, we derived the wavelengths (Lambda) corresponding to different relative permeabilities and listed them in table 1.When the relative permeability changes, the wavelength also changes accordingly.Simulate using HFSS software and export S-parameters.Then, simulate the exported S-parameters in the time domain simulator in ADS.When the impedance is matched at both ends, the electromagnetic signal can propagate in the model in the form of a plane wave, as shown in Fig 7 (top) (where P1 represents the input voltage and P2 represents the terminal voltage).However, when the output end is set to a high impedance state, we can observe that the electromagnetic signal reflects under the condition of impedance mismatch at both ends and forms a standing wave superimposed with the incident wave.Figure 7 (bottom) shows that the voltage of the signal at port P2 is approximately twice the voltage at the input end P1.

Conclusion
The main objective of this study is to verify the feasibility of using the electromagnetic standing wave method for prestress measurement.Through electromagnetic simulation software, simulations are conducted from the frequency domain to the time domain to further demonstrate the effectiveness of the electromagnetic standing wave method.Prestress technology enhances the load-bearing capacity of structures, but there has been a lack of stress monitoring tools in the past.Therefore, an efficient and simple non-destructive method for prestress measurement is crucial for monitoring the health of prestressed structures.The electromagnetic standing wave method, which utilizes ferromagnetic materials as stress bars, provides a simple approach for stress measurement.Through simulations in the frequency and time domains, we can more accurately perform preliminary design for different materials, provide a reliable parameter range for the electromagnetic standing wave method prestress measurement device, and demonstrate its feasibility in structures with large spans such as bridges, thereby reducing construction costs.

Figure 1 .
Figure 1.Peak voltage situation at the wavelength variation L point

Figure 2 .Figure 3 .
Figure 2. Simulated equivalent model of a steel wire rope (thin wire rope, outer environment is air)

Figure 5 .Figure 6 .
Figure 5. Distribution of electromagnetic wave transmission field on the steel wire rope

Figure 7 .
Figure 7. Time-domain Downward Wave Results (Top) and Standing Wave Results (Bottom) in Wavelength

Table 1 .
The Relationship between Wavelength Lambda and Permeability