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Accurate identification of tension in multiwire strands is a key issue to ensure structural safety and durability of prestressed concrete structures, cable-stayed bridges, and hoist elevators. This paper proposes a method to identify strand tensions based on scale energy entropy spectra of ultrasonic guided waves (UGWs). A numerical method was first developed to simulate UGW propagation in a seven-wire strand, employing the wavelet transform to extract UGW time-frequency energy distributions for different loadings. Mode separation and frequency band loss of

As the crucial component bearing tensile loads, steel strands can efficiently improve concrete crack resistance and are commonly employed for prestressed concrete structures, cable-stayed bridges, hoist elevators, and so forth. However, tensile force is difficult to maintain at design levels within strands over time, because of stretching, material characteristics, and various practical circumstances. Tension increases or decreases can lead to decreased bearing capacity and potentially cause major safety incidents [

Many studies have investigated steel strand tension, mainly based on optical fiber, magnetoelasticity, magnetic flux leakage (MFL), and ray path methods. Lan et al. [

Ultrasonic guided wave (UGW) is a structural nondestructive detection method widely studied in recent years, because UGWs are formed by multiple reflections at the waveguide boundary. Therefore, UGW propagation characteristics are strongly affected by boundary conditions and local media defects, compared with body waves used for traditional ultrasonic testing, and can effectively provide waveguide defect characteristics and mechanical boundary variation. Thus, UGW based methods have been widely used for defects detection, for example, in bolts [

However, UGW propagation in strands is somewhat more complex than bolts, pipes, or plates. Kwun et al. [

Strands are assembled in spiral and straight wires, and UGWs have a complex energy transfer between the wires due to mutual coupling; hence strand waveguide must be treated significantly different from spiral and straight wires. The main factor affecting the coupling state between wires is the contact stress caused by axial tensile force in the strands. Therefore, UGW propagation in strands includes tension effects, but it is extremely difficult to find a feature to characterize tension magnitude from complex UGW signals, although this would be greatly desired for engineering applications. Rizzo and Lanza di Scalea [

Most previous studies have focused on identifying high tension strands and have poor recognition accuracy for low tension strands. Thus, although they are suitable for prestress loss evaluation where the strand still has large pulling force, the whole process of tension variation cannot be constantly monitored. Propagation effects have also been almost entirely ignored. Nevertheless, many studies have shown that UGWs propagated in strands carry significant tension information, but further studies are required to identify suitable tension identification method(s) for the wide range of practical conditions.

The current study selected seven-wire steel strands, commonly used in engineering structures, as the research object, and used UGW scale energy entropy spectra to identify steel strand tensions. Section

Let the UGW signal be

Applying Fourier transform, (

Since

The Morlet wavelet is a complex exponential function under a Gaussian envelope, which has advantages of small time-frequency window area, strong localization in the time-frequency domain, and good symmetry. Therefore, the complex Morlet wavelet was adopted as the mother wavelet for CWT.

The amplitude spectrum of a signal is assumed to be a discrete random variable

The UGW time-frequency energy matrix shown in (

Any element in TFR can be regarded as a set of random variables, and the Shannon entropy of every element can be calculated from (

The UGW complexity at different decomposition levels in the time domain can be effectively described by

Since there is mutual contact between adjacent wires, a complex energy transfer relationship is generated by UGW propagation. At different loading levels, contact state discrepancies alter UGW transfer characteristics, providing further sensitivity to the time-frequency domain energy distribution, and entropy is altered accordingly. Therefore, we adopted

Propagation of UGWs in a seven-wire strand was numerically simulated by the ABAQUS/explicit time-transient solver with strand length

Strand geometric and material parameters adopted for numerical analysis.

Geometric parameter | Material parameter | ||
---|---|---|---|

Center wire diameter, | 5.08 | Young’s modulus, | 196 |

Peripheral wire diameter, | 5.08 | Poisson’s ratio, | 0.29 |

Strand diameter, | 15.2 | Density, ^{3}) | 7850 |

Peripheral pitch, | 230 | Yield load, | 203 |

Peripheral twist angle, | 7.9 | Ultimate tensile stress, UTS (MPa) | 1860 |

Finite element model (FEM) mesh size is usually imposed by the minimum UGW wavelength. Accurate calculation of the volatility effect requires every wavelength to have at least 8 calculation nodes [

Mesh size was reduced near contact regions to better simulate contact between adjacent wires. Therefore, the element size in the axial direction was chosen as RES = 1 mm (slightly above 0.92 mm), and the minimum element size in the contact regions was RES = 0.1 mm. The final FEM mesh comprised 1,745,623 linear hexahedral 8 node elements. Figure

Finite element model for the seven-wire strand.

Excitation load and the boundary condition

Finite element mesh

The time integral step is another significant factor in controlling precision. A structure’s dynamic response can be considered a combination of each vibration mode, and the minimum time integral step should be sufficient to solve the highest order vibration mode. Thus, the time integral step is typically required to be less than 1/20 of the minimum period in the finite element solution for transient dynamics problems. Automatic time integral step was applied due to the strand complexity.

Normal and tangential contacts between wires were simulated using hard contact and friction, respectively. The friction coefficient was defined as 0.6. To simulate anchorages, all displacements were constrained at one end, and all displacements aside from axial direction displacements were constrained at the other end to apply tension and excitation. The constraint regions were the edge of the wire end face.

The simulation process consisted of three stages.

Tension is applied to the end where axial displacement is permitted. To prevent interference signal generation, the applied tension amplitude curve should be as smooth as possible and over suitable time frame. We selected the time frame as 300

Loading time-history curve.

We employed a triangular pulse as the excitation load with excitation time = 3

Excitation load.

Simulating UGW propagation in the strand required 697

The UGW time-frequency energy matrices were obtained by wavelet transform to axial acceleration signals at the center node of end face in the center wire, with decomposition scale = 128. Figure

UGW time-frequency energy distribution.

Without tension

70% ultimate tensile stress (UTS)

Peripheral steel wire without tension (Figure

When the strand tension was equivalent to 70% of the ultimate tensile stress (UTS), the restraining effect of the outer wire on the center wire was significantly strengthened, causing

Section

Scale energy entropy spectrum (

Figure

The signal differences can be generally described by the eigenvector differences for these signals, using the eigenvector established at a tensile force as the reference. The deviation level between a tension which is waiting to be detected and a tension corresponding to the reference is vividly characterized by the differences of eigenvectors. Therefore, we defined the distance

Figure

Proposed identification index and tension.

Propagation distance has a significant influence on UGW characteristics. Therefore, we investigated

Effects of propagation distance on the proposed identification index (

Figures

Propagation of UGWs in strands has multiple propagation paths due to mutual coupling of wires in strands. In the previous sections, UGW excitation and receiving points were located on the same wire, that is, the uncoupled propagation path. Propagation path effects can be estimated by ensuring that the excitation and receiving points are located on different wires.

Figure

Proposed identification index for coupled propagation path.

Although

Attenuation is the basic UGW characteristic. UGWs have a wider wave packet when propagating longer distances, which can cause lower amplitude, and material damping can also reduce UGW energy. Calculation limitations meant only undamped short distance UGW propagation was considered for the FEM. However, test distances are usually significantly larger for actual engineering tests; hence UGW signals will have lower energy and narrower frequency band. Therefore, a long seven-wire strand was used for ultrasonic guided wave propagation experiments to investigate longer distance propagation influence on tension identification.

Large reaction walls and through-core hydraulic jacks were employed for the seven-wire strand loading experiment, as shown in Figure

Long propagation experiment layout and pictures.

The PCI-2 acoustic emission system produced by American PAC was selected to conduct the UGW long propagation experiment. The system frequency range was 0–4000 kHz, sensors were WD broadband piezoelectric transducers with testing frequency range 100–1000 kHz, and sampling rate was 2000 kHz. It is difficult to generate sufficient energy using the normal FEM triangular pulses due to material damping over the long strands. Therefore, to ensure high signal-to-noise ratio for the measured signals, a series of 100–700 kHz single cycle sinusoidal pulses with 2 kHz step frequency were selected as the excitation source:

The excitation sensor was arranged on one end of the center wire and receiving sensors were arranged on the center and helical wires, respectively. Each load is held for 2 min after loading; then the same excitation pulse was generated to excite UGWs in the strands. The measured waveforms were used for judging strand tensions.

Figure

UGW time-frequency energy distribution.

No tension

70% UTS

Although a wide band is excited (100–1000 kHz), measured UGW energy is concentrated near 270 kHz, because UGW high frequency components are severely attenuated over the long propagation. For the zero tension case, UGW arrival time for the maximum energy is reasonably consistent with the theoretical time-frequency curve, and only

Figure

Proposed identification index and tension relationships for different long propagation pathways.

Uncoupled propagation path

Coupled propagation path

Sensitivity for the uncoupled propagation path is 1.221, 60.19%, and 20.30% larger than that for the coupled propagation path and FEM results with short propagation path, respectively. This supports the FEM based conclusions that identification index has higher sensitivity for the uncoupled propagation path, and sensitivity is enhanced with increasing propagation distance.

Contacts between wires in the long propagation path experiment are somewhat different from the ideal state assumed for FEM analysis. The experimental UGWs only carry contact information between the central and outer wire for coupled propagation paths. Therefore, the local coupling state of the contact area has a large influence on the measured UGW, and hence coupled pathway sensitivity = 0.762 and 6.91% is lower than FEM results.

For both FEM and experimental results,

These outcomes confirm that that the proposed method could be used to identify tension in longer strands and would be suitable for practical engineering tests.

This study proposed a tension identification method for seven-wire strands. Numerical simulation and experimental measurements were employed to study tension effects on UGW propagation. A tension identification index based on UGW scale energy entropy spectra

UGW time-frequency energy distribution shows significant differences for different loading levels, exhibiting

The variety of tension in strands has significant influence on

The proposed identification index becomes more sensitive to tension as UGW propagation distance increases. However, this enhancement decreases with further propagation distance increase.

The proposed identification index can accurately identify strand tension for coupled and uncoupled paths, although the propagation path influences sensitivity to tension due to the different contact information carrying UGWs in the two cases. The effect of propagation path on sensitivity becomes more significant as propagation distance increases. Coupled path sensitivity (

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was supported by the National Natural Science Foundation of China (Grants 51478347 and 51408090) and the Chongqing Research Program of Basic Research and Frontier Technology (Grant cstc2015jcyjB0014).