• Structural Engineering and Mechanics
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• 제68권4호
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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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• 제10권4호
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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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• 제56권6호
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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.

• 한국산업융합학회 논문집
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• 제25권5호
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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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• 제7권5호
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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.

• 한국산학기술학회논문지
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• 제22권4호
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• pp.295-311
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• 2021

본 연구에서는 사장교 케이블에 대한 장력계측장치의 현장적용성에 대한 실험을 수행하였다. 사장교 케이블의 장력을 추정하기 위해서 진동법을 이용하였으며 대상교량에 대해서 케이블의 가진을 통해서 모드특성을 분석하였고 케이블의 장력을 추정하기 위한 계측장치로는 GTDL360, NI Module, 9 Axes Motion Sensor등을 적용하였고 5개의 대상교량에 대해서 상기 계측장치들을 이용하여 케이블의 모드특성을 분석하여 케이블장력측정실험의 적정성을 평가하고 케이블의 장력을 추정하였다. 또한 5개의 대상교량에 대해서 수치해석을 실시하여 케이블의 고유진동수 및 케이블장력을 해석하였다. 현장 계측결과에 의한 케이블의 추정장력과 수치해석에 의한 케이블의 추정장력을 비교하여 현장계측방법의 적정성을 판단하였으며 분석결과 현장 계측에 의한 케이블의 계측장력과 해석에 의한 추정장력은 오차범위내에 있어서 상기 계측장치들을 현장에 적용하여도 무방할 것으로 판단된다. 현장실증교량의 가속도 기반의 케이블 추정장력과 수치해석에 의한 해석장력과의 값을 비교분석한 결과 값이 허용범위 내로 가속도 기반의 케이블 추정장력값은 적정한 것으로 판단된다. 또한, 현장적용성 분석결과 센서의 설치위치 및 기상조건의 제한 등 계측장치의 한계점이 존재하므로 추후 케이블 스마트 장력계측시스템에 관한 지속적인 후속연구가 필요할 것으로 판단된다.

• 한국소음진동공학회논문집
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• 제15권3호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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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.

• 한국산학기술학회논문지
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• 제21권3호
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• pp.414-419
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• 2020

본 연구에서는 사장교의 케이블 가속도계로부터 확보한 방대한 계측데이터의 활용을 확대하고자 인공지능 기반의 케이블 장력 추정 모델을 개발하였다. 케이블 장력 추정 모델은 진동법에 따른 장력 추정 과정에서 고유진동수를 판정할 수 있는 알고리즘을 핵심으로 하며 학습데이터 구성에 적합하고 판정 결과에 대한 성능이 확보될 수 있도록 입력층, 은닉층, 출력층으로 구성되는 인공신경망(Artificial Neural Network)을 적용하였다. 인공신경망의 학습데이터는 케이블 가속도 계측데이터를 진동수로 변환 후 구성하였으며 고유진동수를 중심으로 일정한 패턴을 갖는 특성을 활용하여 기계학습을 진행하였다. 학습데이터 구성 시 다수 패턴의 고유진동수를 대표할 수 있도록 다양한 크기의 진폭을 갖는 진동수를 사용하고 일정 수준으로 진동수를 누적하여 사용할 경우 고유진동수에 대한 판정 성능이 개선됨을 확인하였다. 장력 추정 모델의 성능을 판단하기 위해 계측분석 기술자에 의해 추정한 장력의 관리기준과 비교하였다. 케이블 가속도계로부터 확보한 139개의 진동수를 입력값으로 사용하여 검증을 수행한 결과 실제 정답과 유사하게 고유진동수를 판정하였고 고유진동수에 의해 케이블의 장력을 추정한 결과는 96.4%의 수준으로 관리기준에 부합하는 결과를 보여주고 있다.