Estimation and Analysis of Cable Tension Based on Frequency Method

Cable tension force is one of the most important structural parameters to monitor in cable-stayed bridges. For example, cable tension needs to be monitored during construction and maintenance to ensure the bridge is not overloaded. To economically monitor tension forces, this study proposes the use of an automated wireless tension force estimation system (WFTES) developed solely for cable force estimation. The design of the WFTES system can be divided into two parts: low-cost hardware and automated software. The low-cost hardware consists of an integrated platform containing a wireless sensing unit constructed from commercial off-the-shelf components, a low-cost commercial MEMS accelerometer, and a signal conditioning board for signal amplification and filtering. With respect to the automated software, a vibration-based algorithm using estimated modal parameters and information on the cable sag and bending stiffness is embedded into the wireless sensing unit. Since modal parameters are inputs to the algorithm, additional algorithms are necessary to extract modal features from measured cable accelerations. To validate the proposed WFTES, a scaled-down cable model was constructed in the laboratory using steel rope wire. The wire was exposed to broad-band excitations while the WFTES recorded the cable response and embedded algorithms interrogated the measured acceleration to estimate tension force. The results reveal the embedded algorithms properly identify the lower natural frequencies of the cable and make accurate estimates of cable tension. This paper concludes with a summary of the salient research findings and suggestions for future work.

In the maintenance of cable structures, such as cable-stayed bridges, cable safety is assessed based on the cable tension. In Japan, the cable tension is generally estimated from the cable’s natural frequencies using the higher-order vibration method. In recent years, dampers have been installed onto cables to suppress aerodynamic vibrations. Because the damper changes the cable’s natural frequencies, the damper is removed to measure the natural frequencies and estimate the cable tension without a damper, and the damper is then reinstalled. To avoid damper removal and reinstallation, the authors previously proposed Method 2F for estimating the tension of a cable with a damper from the natural frequencies without removing the damper. Because the tension estimation error of the higher-order vibration method for a cable without a damper has been reported as 5%, the authors set the target tension estimation error within 5%. However, the tension estimation error of Method 2F exceeded 5% in the experimental verification. Furthermore, although Method 2F estimates the tension and bending stiffness of the cable and the damper parameters simultaneously from the natural frequencies, the accuracy of the bending stiffness and damper parameters is unsatisfactory. In this paper, the new Method 2FM is proposed to estimate the tension and bending stiffness of the cable and damper parameters using the natural frequencies and two-point mode shapes. With the addition of mode shapes, Method 2FM attempts to improve the accuracy of estimating the tension and other parameters. The validity of Method 2FM was confirmed by numerical simulations and experiments. The numerical verification confirmed that Method 2FM is superior to Method 2F in estimating the cable tension and damper parameters. The experimental verification confirmed that the tension estimation accuracy of Method 2FM is higher than that of Method 2F, and the estimation error is lower than 5%. However, the damper parameters estimated by Method 2FM are different to the design values. The reason for this is the modeling error of the damper, as found by conducting an element test on the damper.

The cable plays a more and more important role in civil engineering recently. As an effective construction member, cable is used in many long-span spatial structures. The cable tension measurement is required in the construction control, assessment and long-term monitoring of cable-supported structures. The academic wireless sensing prototype co-developed at Stanford University and the University of Michigan is characterized by a powerful computational core and low power consumption characteristics. Two embedded engineering algorithm, namely the fast Fourier transform algorithm and the peak-picking algorithm, are implemented in the wireless sensing and to identify the frequencies of cables. Moreover, as a conventional method for cable tension measurement, the Fourier Transform can only be used in the static cable tension force test, but not dynamic cable tension test. It represents the intrinsic dynamic properties of cables. In this paper, wavelet transform tool that has the time-frequency analysis ability is used to analyze the signal, and obtain the cable tension dynamic change along with the time.

The measurement accuracy of the cable tensions in the hanger rods of concrete filled steel tube arch bridges is important for the correct evaluation of bridges condition. Based on Jinpan Bridge-a half through concrete filled steel tube arch bridge with 80 m span in Tiantai, it was put forward the vibration frequency method for testing and evaluate suspender tensions with the help of analysis vibration characters of the suspender. The precision of cable force calculation formula was verified after comparing the practical tension with the designed tension obtained from tension jack method. Then, according to the test results and values predicted by the presented cable force calculation formula, the cable tensions were adjusted. Cable tension test results in the finished bridge show that this method is feasible.

The researching, designing, calculating, and controlling cable-driven parallel robots (CDPRs) are being promoted in recent years. The researches focus on optimizing the design of CDPRs configuration, computing workspace, calculating cable tension distribution, designing the mechanical structure, and developing controller. However, due to the complexity of the structure and unidirectional characteristic of cable, many computational methods have been applied to solve the above problems. To facilitate the performance of theoretical studies on important issues in the design and control of the CDPRs, a summary of computational methods is needed for important issues related to the functionality and accuracy of CDPRs such as defining the workspace, distributing the cable tensions, and calculating the sagging of the cable. This paper summarizes published studies on CDPRs and focuses on classifying and analyzing methods used to calculate important issues in the process of calculating and designing CDPRs. The efficiency of these calculation methods is also analyzed and evaluated based on the mathematical theories of kinematics and dynamics of CDPRs. The content of this study is an effective reference for studies on important problems in the process of designing and implementing CDPRs, helping researchers shorten the time to review related topics.

In 2022, researchers at Pacific Northwest National Laboratory (PNNL) used the Accelerated and Real-Time Environmental Nodal Assessment (ARENA) cable and motor test bed to characterize spread spectrum time domain reflectometry (SSTDR) and compare the responses of an SSTDR instrument to those of a frequency domain reflectometry (FDR) instrument. Results showed both techniques could detect and locate cable anomalies such as phase-to-phase low resistance and shorts, thermal insulation damage, mechanical insulation damage, and the presence or absence of water in some conditions. The SSTDR tests used a commercial instrument provided by LiveWire Innovations Inc. This commercial instrument performed tests at 6, 12, 24, and 48 MHz bandwidth. The results of these tests were compared to FDR tests where bandwidths could be extended up to 1.3 GHz, although the best responses for cable tests were from 100 to 500 MHz. Lower bandwidth signals can propagate better along the cable while higher bandwidths have higher resolution for impedance change reflections allowing more precise indication of location and separation of anomalies. The 2022 research found that FDR responses were clearer than SSTDR and speculated that a higher bandwidth SSTDR could more successfully detect and locate cable anomalies. One advantage of the SSTDR system investigated was that it was designed for energized online use up to 1,000 volts, which may be a significant advantage for nuclear power plant use. The LiveWire SSTDR instrument is an established product in the rail and aircraft industry and updating the SSTDR hardware parameters is difficult to justify without more conclusive testing. Therefore, a software adjustable laboratory SSTDR instrument was developed by PNNL and was used to test extended bandwidth SSTDR cable tests. Within the ARENA test bed, 42 cable conditions were tested with the PNNL SSTDR, FDR, and the LiveWire SSTDR—each operating at four different bandwidths. Observations and conclusions regarding the relative performance of the three instruments over different bandwidths are note below. Responses of the PNNL SSTDR (at 50 MHz) and the LiveWire SSTDR (at 48 MHz) were similar. The PNNL SSTDR higher frequency bandwidths behaved as expected showing sharper peaks and higher noise. This validated the PNNL SSTDR as a reasonable implementation of the SSTDR technology. Lower bandwidth SSTDR responses (particularly 6 and 12 MHz) may have increased value for use within longer cables but were not particularly effective at identifying anomalous cable behavior in the 100 ft cables tested here. The higher bandwidths of the PNNL SSTDR (50, 100, 200, and 400 MHz) did not provide substantially clearer cable reflectometry responses, but having the higher frequency responses available did add to the cable test evaluation. Strong responses to shorts and low impedance faults between phases were particularly evident in the higher bandwidth PNNL SSTDR and the FDR data. Measurements were repeatable, with similar responses obtained from a thermally aged cable for tests taken a month apart. Signal noise was affected in the unshielded cable by the local in-tray cable arrangement including proximity to metal edges and rungs of the cable tray. Foam isolation of the cable from the tray metal reduced in both FDR and SSTDR responses. Cable condition monitoring in nuclear power plants will likely benefit from both more informative off-line testing methods and from the development of on-line methods for continuous monitoring of cables in use. The LWRS-funded ARENA test bed was a valuable resource for this development and direct comparison of nuclear electrical cable condition monitoring technologies. Test results are targeted to guide industry advancement of testing and monitoring tools for cable aging management.

The cable sagging problem of cable-driven parallel robots (CDPRs) is very complicated, because several models for calculating cable sag based on the well-known catenary equation have been studied, but time and computational efficiency are a problem to be solved. There is still no simple mathematical model to calculate cable sag by considering all relevant conditions due to the complexity and nonlinearity of the cable sagging model, which involves many dominant variables and their influence on the position accuracy of CDPRs. In this study, we proposed an ANFIS (adaptive neuro-fuzzy inference system) architecture to estimate cable sag for large-sized CDPRs. The ANFIS model can be used to solve nonlinear functions and detect nonlinear factors online in the control system; this characteristic is consistent with the nonlinear model of cable sag. The trained data for ANFIS models were taken from calculation results by Trust-Region-Dogleg algorithm based on two cable tension calculation algorithms as Dual Simplex Algorithm and Force Distribution in Closed Form. Cable sagging data obtained from ANFIS and Trust-Region-Dogleg algorithm are compared and evaluated by statistical factors of evaluations consisting of root-mean-square error, correlation coefficients, and scatter index. The analytical results show that the ANFIS gave computed results with small errors and can be applied to predict cable sagging for any CDPR configuration, with the advantage of fast calculation time and high precision. The results of these models are also applied on a CDPR that contains two redundant actuators.

As power networks move toward increased digitalization and the smart grid is becoming more of a reality, power networks are hosting elements of smart grids to meet the growing demands and requirements of advanced digital networks. One of the components of a smart grid is the use of measuring sensors. Low-power instrument transformers are one part of these advanced systems and are increasingly being used within distribution networks. As these sensors are being widely installed, network operators must ensure that the addition of such sensors will not affect the normal operation of the network. This paper discusses the potential impact of using voltage sensors in power networks to perform VLF (very low frequency) cable testing, which is a common practice in distribution networks and is used during commissioning tests and to support maintenance and condition monitoring of underground cables. This paper also investigates and compares the impact of different sensor technologies on the performance of cable VLF diagnostic testing.

Optimized scale factors for calculating vibrational harmonic and fundamental frequencies and zero-point energies have been determined for 145 electronic model chemistries, including 119 based on approximate functionals depending on occupied orbitals, 19 based on single-level wave function theory, three based on the neglect-of-diatomic-differential-overlap, two based on doubly hybrid density functional theory, and two based on multicoefficient correlation methods. Forty of the scale factors are obtained from large databases, which are also used to derive two universal scale factor ratios that can be used to interconvert between scale factors optimized for various properties, enabling the derivation of three key scale factors at the effort of optimizing only one of them. A reduced scale factor optimization model is formulated in order to further reduce the cost of optimizing scale factors, and the reduced model is illustrated by using it to obtain 105 additional scale factors. Using root-mean-square errors from the values in the large databases, we find that scaling reduces errors in zero-point energies by a factor of 2.3 and errors in fundamental vibrational frequencies by a factor of 3.0, but it reduces errors in harmonic vibrational frequencies by only a factor of 1.3. It is shown that, upon scaling, the balanced multicoefficient correlation method based on coupled cluster theory with single and double excitations (BMC-CCSD) can lead to very accurate predictions of vibrational frequencies. With a polarized, minimally augmented basis set, the density functionals with zero-point energy scale factors closest to unity are MPWLYP1M (1.009), τHCTHhyb (0.989), BB95 (1.012), BLYP (1.013), BP86 (1.014), B3LYP (0.986), MPW3LYP (0.986), and VSXC (0.986).

Remote actuation solutions such as cable-conduit transmissions are beneficial in wearable robotics to reduce dynamic loading on distal joints. However, these systems often introduce high reflected impedance or require rigid sensors for force control that hinder their integration in wearables. Low impedance and ease of integration could be both obtained by combining distributed cable strain sensing with dynamic modeling to estimate output force and position. In this article, we present a new computational model to analyze the dynamics of cable-conduit systems. The model features bidirectional propagation of motion within the transmission, which allows for simulation of human-interacting systems, where either or both the human and the robot can be force or position sources. Moreover, we present a new method for rapidly solving for the system of equations based on iterative linearization of the system of nonlinear equations. The model and the solution method are validated in a physical prototype through experiments involving physical interaction with a human subject. Finally, we develop methods for model-based estimation of cable tension given measurements from multiple noisy strain sensors embedded in the transmission, and quantify the accuracy achievable via different methods as a function of the number and location of sensors. Results demonstrate that the model accurately predicts behavior observed in the prototype. Moreover, the newly developed iterative linearization solution method allows a 100-fold increase of computation speed compared to a standard solver. Finally, we demonstrate that cable tension can be estimated with increasing accuracy when increasing the number of sensors, but accuracy decreases if the output portion of the transmission is not instrumented.

In practical bridge engineering, cable tension reflects the safety performance of the entire bridge structure. Vibration frequency-based cable tension measurement methods have been proven to be practical and effective. In recent years, research on non-contact measurement of cable vibration frequencies has increased significantly. However, non-contact measurements are susceptible to environmental interference, and the stability of signal acquisition equipment can markedly affect the results, leading to impure spectrum and making it difficult to identify the fundamental frequency (FF) used for cable force calculation. To address this problem, an automatic Fundamental Frequency identification in Spectrum (FF-FAS) algorithm is proposed. First, to obtain potential vibration FF from the spectrum, a feature peak screening algorithm is introduced to automatically identify peak points and assign weights based on the smoothness of the peaks and their equivalent width. Subsequently, to accurately identify the FF from the peaks, a new FF determination mechanism is designed, which automatically extracts the frequency sequence based on string vibration theory and selects the FF by synthesizing the contribution of each peak. The FF-FAS algorithm addresses the limitations of traditional FF identification methods, which rely on peak detection and are highly susceptible to noise. This algorithm has been evaluated through both experiments on a cable-stayed cable in a public square and field tests on operational bridges, demonstrating significant improvements in FF identification compared to existing methods.

Snap load dynamics in non-metallic armored umbilical cables under heave excitation

In this work the first- and second-order shear and normal deformation as well as the third-order shear deformation theories are applied to delaminated sandwich shells having constant radii of curvatures. The normal deformation of the first- and second-order models was captured by quadratic functions in the core, while it was ignored in the facesheets. The third-order model was created using cubic displacement functions in the terms of through-thickness coordinate in the core, the facesheets were still captured by second-order shear deformable shell theory. The governing equations were deduced through the virtual work principle, eventually three possible scenarios were considered: core-core, face-core and face-face delamination, respectively. To prove the applicability of the developed shell models several examples were solved including the former three scenarios combined with elliptic and hyperbolic doubly-curved sandwich shell geometries with different facesheet/core material pairs. The traditional simply-supported boundary conditions were assumed involving the Lévy-type formulation. Moreover, the state space method was applied to solve the examples. The mechanical fields calculated were compared to results obtained through spatial finite element models. The J-integral was also determined and separated into mode-II and mode-III components making it possible to perform the comparison to energy release rates computed by the virtual crack closure method. The results indicate that the proposed models capture the mechanical fields with high accuracy in the vicinity of points lying along the delamination front. The J-integrals are also very well predicted by the proposed shell models.

Relevance. The article discusses the design solutions of a new pile structure, which is a monolithic reinforced concrete cone-shaped pile, enclosed in a crushed stone shell and resting on a spherical crushed stone broadening. In the course of a numerical study, carried out using the finite element method, the influence of the geometric parameters of the crushed stone formations of the pile foundation, such as the wall thickness of the crushed stone shell and the radius of the crushed stone broadening, on its bearing capacity was revealed. The aim of the study is to perform a comparative numerical analysis of the stressstrain state of a pile structure with different design solutions, operating as part of a soil massif. Materials and methods. Numerical static analysis of the structure of a monolithic reinforced concrete pile foundation operating in a soil massif was carried out using a spatial finite element model in the CAE-class software package. The article presents the results of a numerical analysis of the stress-strain state of a rammed monolithic reinforced concrete cone-shaped pile with different wall thicknesses of the crushed stone shell and different diameters of the lower spherical crushed stone broadening. The analysis showed that changes in the specified geometric parameters of the pile foundation have a significant impact on its bearing capacity under external forces. The rational choice of these parameters allows you to economically use the concrete mixture and reinforcing rods intended for the manufacture of monolithic reinforced concrete rammed piles, which, in turn, leads to a decrease in financial costs for the manufacture of the pile foundation and the entire building as a whole. The next research is supposed to carry out a comparative analysis of the numerical results with experimental data obtained in laboratory and field conditions.

The accuracy of main cable construction in suspension bridges is directly influenced by the sag of the strands during the erection process. Thus, effective methods for controlling strand sag are crucial. However, the current control standards and methods are primarily based on practical engineering experience, lacking quantitative analysis and a sufficient basis. This paper aims to address this gap by summarizing four commonly used strand sag control methods and proposing a quantitative analysis model that considers the influence of random factors. The model quantifies the impact of these methods on the main cable shape and strand tension after cable tightening. To illustrate the practical application, a suspension bridge is utilized as a case study. The results of the study illustrate a linear relationship between the main cable sag and inter-strand distance, with each control method exhibiting a varying linear change rate. Moreover, the discrepancy in strand distance contributes to uneven strand tension after cable tightening. Random errors contribute to the dispersion of the main cable sag and strand tension, which are further exacerbated by cumulative errors between layers of general strands. Based on the study’s results, this paper provides valuable references for the erection and control of the main cable in suspension bridges.