• Structural Engineering and Mechanics
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• v.68 no.4
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• pp.399-408
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• 2018

Cable supported structures have been widely used in civil engineering. Cable tension estimation has great importance in cable supported structures' analysis, ranging from design to construction and from inspection to maintenance. Even though the Bernoulli-Euler beam element is commonly used in the traditional finite element method for calculation of frequency and cable tension estimation, many elements must be meshed to achieve accurate results, leading to expensive computation. To improve the accuracy and efficiency, a dynamic finite element method for estimation of cable tension is proposed. In this method, following the dynamic stiffness matrix method, frequency-dependent shape functions are adopted to derive the stiffness and mass matrices of an exact beam element that can be used for natural frequency calculation and cable tension estimation. An iterative algorithm is used for the exact beam element to determine both the exact natural frequencies and the cable tension. Illustrative examples show that, compared with the cable tension estimation method using the conventional beam element, the proposed method has a distinct advantage regarding the accuracy and the computational time.

• Structural Monitoring and Maintenance
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• v.10 no.4
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• pp.361-379
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• 2023

In cable structure maintenance, particularly for cable-stayed bridges, cable safety assessment relies on estimating cable tension. Conventionally, in Japan, cable tension is estimated from the natural frequencies of the cable using the higher-order vibration method. In recent years, dampers have been installed on cables to reduce cable vibrations. Because the higher-order vibration method is a method for damper-free cables, the damper must be removed to measure the natural frequencies of a cable without a damper. However, cables on some cable-stayed bridges have two dampers: one on the girder side and another on the tower side. Notably, removing and reinstalling the damper on the tower side are considerably more time- and labor-intensive. This paper introduces a tension estimation method for cables with two dampers, using natural frequencies. The proposed method was validated through numerical simulation and experiment. In the numerical tests, without measurement error in the natural frequencies, the maximum estimation error among 100 models was 3.3%. With measurement error of 2%, the average estimation error was within 5%, with a maximum error of 9%. The proposed method has high accuracy because the higher-order vibration method for a damper-free cable still has an estimation error of 5%. The experimental verification emphasizes the importance of accurate damper modeling, highlighting potential discrepancies between existing damper design formula and actual damper behavior. By revising the damper formula, the proposed method achieved accurate cable tension estimation, with a maximum estimation error of approximately 10%.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.939-957
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• 2015

In this paper, a new approach based on the continuum model is proposed to estimate the main cable tension force of suspension bridges from measured natural frequencies. This approach considered the vertical vibration of a main cable hinged at both towers and supported by an elastic girder and hangers along its entire length. The equation reflected the relationship between vibration frequency and horizontal tension force of a main cable was derived. To avoid to generate the additional cable tension force by sag-extensibility, the analytical solution of characteristic equation for anti-symmetrical vibration mode of the main cable was calculated. Then, the estimation of main cable tension force was carried out by anti-symmetric characteristic frequency vector. The errors of estimation due to characteristic frequency deviations were investigated through numerical analysis of the main cable of Taizhou Bridge. A field experiment was conducted to verify the proposed approach. Through measuring and analyzing the responses of a main cable of Taizhou Bridge under ambient excitation, the horizontal tension force of the main cable was identified from the first three odd frequencies. It is shown that the estimated results agree well with the designed values. The proposed approach can be used to conduct the long-term health monitoring of suspension bridges.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.5
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• pp.773-782
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• 2022

Estimation of cable tension through proper measurements is one of the essential tasks in evaluating the safety of cable structures. In this paper, a study on cable tension estimation using the built-in accelerometer and camera in a smartphone was conducted. For the experimental study, visual displacement measurement using a smartphone camera and acceleration measurement using a built-in accelerometer were performed in the cable-stayed bridge model. The estimated natural frequencies and transformed tensions from these measurements were compared with the theoretical values and results from the normal visual displacement method. Through comparison, it can be seen that the error between the method using the smartphone and the normal visual displacement is sufficiently small to be acceptable. It has also been shown that those errors are much smaller than the difference between the values calculated by the theoretical model. These results show that the deviation according to the type of measurement method is not large and it is rather important to use an appropriate mathematical model. In conclusion, in the case of cable tension estimation, it can be said that the visual displacement measurement and acceleration using a smartphone can be a sufficiently applicable method, just like the normal visual displacement method. It is also noteworthy that the smartphone accelerometer has a larger magnitude error and has more limitations such as high-frequency sampling instability compared to the visual displacement method, but shows almost the same performance as the visual displacement method in this cable tension estimation.

• Smart Structures and Systems
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• v.7 no.5
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• pp.379-392
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• 2011

This paper presents a multi-functional system, consisting of a magnetorheological (MR) damper and an electromagnetic induction (EMI) device, and its applications in stay cables. The proposed system is capable of offering multiple functions: (1) mitigating excessive vibrations of cables, (2) estimating cable tension, and (3) harvesting energy for wireless sensors used health monitoring of cable-stayed bridges. In the proposed system, the EMI device, consisting of permanent magnets and a solenoid coil, can converts vibration energy into electrical energy (i.e., induced emf); hence, it acts as an energy harvesting system. Moreover, the cable tension can be estimated by using the emf signals obtained from the EMI device. In addition, the MR damper, whose damping property is controlled by the harvested energy from the EMI device, can effectively reduce excessive cable vibrations. In this study, the multi-functionality of the proposed system is experimentally evaluated by conducting a shaking table test as well as a full-scale stay cable in a laboratory setting. In the shaking table experiment, the energy harvesting capability of the EMI device for wireless sensor nodes is investigated. The performance on the cable tension estimation and the vibration mitigation are evaluated using the full-scale cable test setup. The test results show that the proposed system can sufficiently generate and store the electricity for operating a wireless sensor node twice per day, significantly alleviate vibration of a stay cable (by providing about 20% larger damping compared to the passive optimal case), and estimate the cable tension accurately within a 2.5% error.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.295-311
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• 2021

In this study, an experiment was carried out on the field applicability of tension measuring devices of the cables in cable-stayed bridges. The vibration method was used to estimate the tension of cables of cable-stayed bridge, and the mode characteristics of the cable were analyzed using a cable tension measuring device. GTDL360, NI Module, and 9 Axes Motion Sensorwere applied to estimate the cable tension of five target bridges. Numerical analysis of the five target bridges was conducted to analyze the natural frequency of the cable and cable tension. The estimated tension of the cable based on field measurements and estimated tension of cable by numerical analysis were compared with the estimated tension of the cable based on field measurements. The analysis showed that the measured tension of the cable based on field measurements was within the margin of error. Therefore, it is safe to apply these measuring devices to the site. As a result of comparing and analyzing the values of the acceleration-based cable estimation tension and numerical analysis of the field demonstration bridge, the acceleration-based cable estimation of tension is deemed appropriate within the allowable range. On-site applicability analysis revealed limitations of the measuring devices, such as the installation location of sensors and weather conditions, so continuous follow-up research on smart cable tension measuring systems is expected.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.3 s.96
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• pp.346-353
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• 2005

In this paper, the tension of assembly stay cable connected with massive anchorage block was calculated through back analysis of in-situ frequencies measured from a stadium structure. Direct approach to back analysis is adopted using the univariate method among the direct search methods as an optimization technique. The univariate method can search the optimal tension without regard to the initial ones and has a rapid convergence rate. To verify the reliability of back analysis, Tension formulas proposed by Zui et al. and Shimada were used. Tensions estimated by three methods are compared with the design tension, and are in a reasonable agreement with an error of more or less than 15%. Therefore, it is shown that back analysis applied in this paper is appropriate for estimation of cable tension force.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.435-440
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• 2004

In this paper, the tension of assembly stay cable connected with massive anchorage block was calculated through back analysis of in-situ frequencies measured from a stadium structure. Direct approach to back analysis is adopted using the univariate method among the direct search methods as an optimization technique. The univariate method can search the optimal tension without regard to the initial ones and has a rapid convergence rate. To verify the reliability of back analysis, Tension formulas proposed by Zui et al. and Shimada were used. Tensions estimated by three methods are compared with the design tension, and are in a reasonable agreement with an error of more or less than 15%. Therefore, it is shown that back analysis applied in this paper is appropriate for estimation of cable tension force.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.121-126
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• 2002

In a recent construction industry, cable supported structures such as a cable-stayed bridge or space stadium have been increasingly constructed. Generally the stay cables as a critical member should be adjusted to be satisfied with the design tension forces. In this purpose, a vibration method has been applied to estimate the tension forces exerted to the existing stay cables. In this study, cable vibration tests were carried out to estimate the cable tension forces comparing with theoretical and practical formulas. From the measured frequencies obtained from free vibration and impulsive tests, the accuracy of 1he estimated tension forces is confirmed according to use only the first single mode or higher multiple modes.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.3
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• pp.414-419
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• 2020

An artificial intelligence-based cable tension estimation model was developed to expand the utilization of data obtained from cable accelerometers of cable-stayed bridges. The model was based on an algorithm for selecting the natural frequency in the tension estimation process based on the vibration method and an applied artificial neural network (ANN). The training data of the ANN was composed after converting the cable acceleration data into the frequency, and machine learning was carried out using the characteristics with a pattern on the natural frequency. When developing the training data, the frequencies with various amplitudes can be used to represent the frequencies of multiple shapes to improve the selection performance for natural frequencies. The performance of the model was estimated by comparing it with the control criteria of the tension estimated by an expert. As a result of the verification using 139 frequencies obtained from the cable accelerometer as the input, the natural frequency was determined to be similar to the real criteria and the estimated tension of the cable by the natural frequency was 96.4% of the criteria.