In the real world, the main cables of suspension bridges are commonly inspected by conducting a periodic visual inspection of the exterior cover of the cable. Although there is a need to conduct a nondestructive evaluation (NDE) of the damage of the main cable, a suitable NDE technique has not yet been developed due to the large diameter and low accessibility of the cable. This study investigates a magnetic sensing cross-sectional loss quantification method that can detect internal and external damage to the main cables. This main cable NDE method applies an extremely low-frequency alternating current (ELF-AC) magnetization method and search coil sensor-based total flux measurement. A total flux sensor head consists of a magnetization yoke and a search coil sensor. To magnetize the main cable, a magnetic field was generated by applying a triangular ELF-AC voltage to the electromagnet yoke. The sensing part measures the magnetic flux that passes through the search coil, and the B-H loop was then obtained using the relationship between the ELF-AC voltage that has been input and the total flux that was measured. Also, the cross-sectional loss can be quantified using a variation of magnetic features from the B-H loop. To verify the feasibility of using the proposed NDE technique, a series of experiments were performed using a main cable specimen with a gradual increase in the cross-sectional loss. Finally, the relationship between the cross-sectional loss and extracted magnetic feature was determined and used to quantify the cross-sectional loss via the proposed method.
In suspension bridges, steel cables are the core supporting materials that suspend most of the load of the structure. However, cross-sectional damage can occur in steel cables due to external causes, including corrosion and fracture. And it can lead to stress concentration as a direct cause of structural failure due the rapid expansion of the damage. Therefore, a suitable nondestructive evaluation (NDE) method is needed to inspect the initial stages of damage in a steel cable so that accidents can be prevented. However, it is difficult to diagnose cables since the damage in cable can be invisible and inaccessible.
To overcome these limitations, this research proposes a noncontact NDE technique incorporating magnetic sensing technology to exploit the ferromagnetic characteristics of steel cables. Magnetic sensors have been extensively used to monitor the safety of structures due to their great reproducibility and reliability [
Typically, the magnetic flux leakage (MFL) method is an optimal technique for use with continuum structures that have a constant shape in their cross-section, such as railroads and pipelines, and it has been utilized to inspect steel wire ropes for elevators and cranes and for other applications [
However, the hidden damage within large-diameter cables has not been detected since the MFL technique can only detect a local defect near the surface. Therefore, the MFL method is not a suitable NDE method to inspect the main cables of suspension bridges with a very large diameter. In addition, research and development to replace conventional visual inspection methods have not been actively conducted due to the large size of the main cables.
To overcome such limitations, a new method was proposed to inspect the whole cross-section, including the internal and external section. The proposed technique incorporates an extremely low-frequency alternating current (ELF-AC) magnetization method with total flux measurement using a search coil sensor to obtain magnetic hysteresis loops (B-H loop) according to each condition of the main cable [
When the material is positioned within a strong external magnetic field, ferromagnetic materials can be magnetized because the magnetic domains within the material are aligned [
When the solenoid coil is used for the magnetization process, the electric current flows through the carrying conductor in coil; a strong concentrated magnetic field is then generated at the center of the solenoid coil. The strength of the magnetic field in the coil increases as the applied current increases with additional turns of the coil [
However, the magnetization method using a solenoid coil makes it difficult to apply for the continuum specimen in the real field due to its closed-loop shape.
Therefore, a yoke-type electromagnet is utilized in this study to replace the solenoid and improve the applicability in the field. Typically, an electromagnet yoke consists of a solid steel bar core and a solenoid that is winded around the core, as shown in Figure
Yoke-type electromagnet for magnetization.
When an electric current flows through a solenoid around the steel bar, a magnetic flux is exhibited at the steel bar core of the magnetization yoke. When the magnetic flux passes through the magnetization yoke, both ends of the yoke become the north pole and the south pole, respectively. As shown in Figure
This magnetic field can be used to indirectly induce a magnetic field in a material so that the specimen can be magnetized for inspection.
In this study, the ELF-AC voltage is applied to magnetize the entire specimen of the main cable using an electromagnetic yoke. The magnetic field produced via ELF-AC can generally penetrate the entire cross-section of the ferromagnetic materials. ELF-AC is very effective when inspecting the entire cross-section of a large specimen because ELF-AC generates an efficient magnetic field that penetrates deeper into the material.
The principle of the search coil sensing method is based on Faraday’s law of induction [
According to Faraday’s law and Lenz’s law, the electromotive force generated in a linked search coil by the time variation of the induction is calculated using
The magnetic flux density
The electromotive force
According to equation (
Therefore, the cross-sectional loss can be quantified by measuring the total flux using the search coil sensor and fluxmeter.
The B-H loop (magnetic hysteresis loop) represents the relationship between the magnetizing force (magnetic field) (
B-H loop (magnetic hysteresis loop) [
The B-H loop is obtained by measuring the total flux of a ferromagnetic material while the magnetizing force changes as a cycle. The B-H loop of the whole cycle obtained from a sufficient bipolar magnetic field to make a fully magnetized condition is referred to as a major B-H loop. Utilizing the major B-H loop is the most effective method to conduct the magnetic inspection since the major loop indicates the various magnetic properties of the specimen [
To quantify the cross-sectional loss, the magnetic properties that change according to the cross-sectional loss were extracted. Among the various magnetic properties from the B-H loop, the slope of the B-H loop was extracted and is referred to as the permeability. Permeability is a property of the ferromagnetic material which describes the degree of magnetization of a material in response to a magnetic field. In general, the permeability is used to estimate the tension force of a cable by measuring the voltage from the search coil sensor under the assumption that the constant cross-sectional area is in accordance with equation (
Figure
Design of the total flux sensor head.
Specification of the total flux measurement system [
Search coil diameter | 320 mm |
Yoke size | |
Average magnetic path | 290 mm |
Coil winding | N1: 800 turns, N2: 30 turns |
Max current | ±14 A |
Total flux range | |
Input voltage range | ±4 V |
Examination time | <60 sec |
Magnetizing depth | Entire cross-sectional area |
Control program | LabVIEW-based UI |
An electromagnetic yoke consisting of a steel bobbin and a winded solenoid coil is applied to magnetize the large diameter cable specimen. In addition, the total flux signals were measured using a search coil sensor, and the search coil sensor was configured as an openable belt type using a flexible coil and a PCB board for convenient in situ installation. The fabricated total flux sensor head is displayed in Figure
Fabricated total flux sensor head: (a) magnetization yoke; (b) belt-type search coil sensor.
The magnetization yoke size is
The internal diameter of the flexible search coil sensor for sensing the total magnetic flux is 320 mm, and the winding number is 30 turns. The test time for a cycle of the measurement is 60 seconds.
In this system, the ELF-AC voltage is applied to magnetize the entire inside and outside of the specimen. A bipolar power supply generated an ELF-AC voltage, and it is supplied to the primary coil at the electromagnetic yoke to magnetize the main cable specimen.
The cycle of a triangular ELF-AC voltage is supplied to obtain a cycle of the B-H loop in this study. Its amplitude range is ±4 V, and it is supplied to the magnetization yoke for 60 seconds [
Input voltage shape for magnetization [
After the magnetizing process, a search coil sensor measures the magnetic flux density from the entire cross-section of the magnetized cable specimen, and the obtained magnetic flux density values are integrated using a fluxmeter to calculate the total magnetic flux.
Since an excessive measurement system is required to obtain a major B-H loop through saturation magnetization of the main cable that has a large size diameter, the voltage range of initial magnetization, shown as the red line in Figure
Among the characteristics of the B-H loop according to the condition of the cable specimen, the permeability that means the slope of the B-H loop is used to be an index to quantify the variation in the cross-sectional condition.
Figures
Measured raw signals and raw B-H loop: (a) raw signal; (b) raw B-H loop.
To avoid errors due to drift, a series of denoising processes were performed since the raw signal contains the drift and an offset error. Although this signal processing can induce some distortion in the original B-H loop characteristics, the focus of this study was the index extraction which changes with the cross-section change. Therefore, the following consistent compensation was performed to form the closed B-H loop. This procedure is helpful in providing reference points for index extraction that reflects the B-H loop such as the slope of the B-H loop.
To compensate for the drift error, the total error was divided into a number of sampling points, and the value was added in direct proportion to the sampling point, as shown in Figure
Denoised signal and B-H loop: (a) denoised signals; (b) denoised B-H loop.
A series of experimental studies were performed to examine the capabilities of the cross-sectional loss quantification using the variation of the B-H loop.
A main cable specimen of 200 mm in diameter and 800 mm in length was fabricated for the experimental study, as shown in Figure
Main cable specimen.
Figure
Experimental setup for total flux measurement.
The test procedure to quantify the cross-sectional loss was the same as that shown in Table
Test procedure and steps for the cross-sectional loss.
A minor B-H loop from the main cable specimen is obtained at each step of the cross-sectional loss by a cycle of the total flux acquisition and denoised process. The obtained B-H loops using the average value of each case are displayed in Figure
Variation in the B-H loop according to the cross-sectional loss.
As shown in Figure
Enlarged plot of the dead end of the B-H loops.
The variation in the B-H loop implies a variation in various magnetic characteristics according to the specimen’s condition, such as permeability, conductivity, and retentivity. Therefore, feature extraction of the magnetic characteristic from the B-H loop is needed to quantify the cross-sectional loss. In this study, the slope of the B-H loop, which means the permeability, was extracted from the B-H loops for each step.
The slope derived from the B-H loop is plotted in Figure
Relation between the extracted feature and the cross-sectional loss.
To improve the accuracy of the damage detection, the cross-sectional loss level between each step was reduced to 1.67%. Figures
Enlarged plot of the dead end of the B-H loops of the 1.67% reduction case.
Relation between the extracted feature and cross-sectional loss of the 1.67% reduction case.
As shown in Figures
In addition, the change in the relation curve in Figure
These results indicate that the proposed cable inspection method using the total flux sensor can quantitatively diagnose the cross-sectional loss of the large-diameter cable.
A main cable NDE method is proposed incorporating ELF-AC magnetization using an electromagnet yoke with a total flux measurement via a search coil to diagnose the cross-sectional loss of the main cable in suspension bridges. A magnetic sensor head for the total flux measurement was fabricated incorporating an electromagnet yoke and a search coil sensor to obtain a B-H loop from the main cable. A series of experimental studies were performed using the fabricated total flux sensor head and the main cable specimen that can remove part of the wire. For each cross-sectional loss level, a B-H loop according to the cross-sectional loss is obtained by using the relationship between the input ELF-AC voltage signal and the measured total flux signal. The slope of the B-H loop, which reflects the permeability, was extracted at each obtained B-H loop to quantify the variation in the B-H loop. This experimental result shows that the slope of the B-H loop decreases gradually according to the stepwise cross-sectional loss and also shows that a constant relationship exists between the variation of the B-H loop and the cross-sectional loss of the main cable specimen. The total flux sensing-based main cable NDE technique can be utilized to diagnose cross-sectional loss without the need for complex destructive testing by obtaining only the B-H loop using a total flux measurement system. This total flux-based main cable NDE technique can be an effective inspection tool to ensure the safety of cable-stayed structures through further research and through the convergence of robots and IT technology.
The raw data of the total flux signal used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there is no conflict of interest regarding the publication of this paper.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017-R1A6A3A04011933 and NRF-2017-R1A2B3007607).