Identification Of Natural Frequencies Research Articles

Probabilistic damage identification for bridges using multiple damage-sensitive features and FE model update

A specific damage-sensitive feature (DSF) is usually sensitive to damage in a certain area, and the specific location of damage in a specific area can be detected by selecting appropriate DSFs. However, damaged components are seldom known before inspections. This makes it difficult to find an appropriate DSF, and damage identification is sometimes challenging. This paper aims to propose a natural frequency and displacement ratio-based probabilistic damage identification method for bridges using the finite element (FE) model update to solve this issue. The displacement ratio measured at two positions on the bridge is proposed as a new DSF. It is a useful DSF because it is independent of external loads. By integrating displacement ratios and natural frequencies, that is, multiple DSFs, as a decision-level data fusion approach, this paper identifies damaged components without choosing an appropriate DSF beforehand. In addition, probability density functions (PDFs) of structural parameters are estimated from PDFs of derived DSFs through the FE model update to consider errors and uncertainties in measurements. An in-house model bridge experiment is carried out to investigate the feasibility. The results demonstrated that the two kinds of damages in a bearing and girder reproduced in the experiment were successfully identified without false positives even when these damages simultaneously occurred.

Identification of natural frequencies of machine tools during milling: comparison of the experimental modal analysis and the operational modal analysis

AbstractModal parameters (natural frequencies, mode shapes and modal damping) help to understand the dynamic behaviour of complex systems like machine tools. There are several approaches for finding the modal parameters. The Experimental Modal Analysis (EMA) has proven to be effective at standstill of a machine tool. The excitation, realized with impulse hammer or shaker, and excited responses at several locations are measured. Alternatively, the Operational Modal Analysis (OMA) can be deployed for finding the modal parameters during operation. Here, responses to excitation resulting from operation are only measured. The modal parameters are mathematically identified from the measured signals in both cases but with different methods. This paper discusses, to what extent both approaches (EMA and OMA) can lead to plausible identification of natural frequencies of a machine tool during milling. Concerning the EMA, attention is paid to capturing the excitation. Process forces can be assumed to be the most significant excitation. However, there are other excitation sources beside the process forces (e.g. drives, hydraulic and pneumatic aggregates), which are considered by this assumption to be a part of disturbances with consequence for the identification of the modal parameters. Regarding the OMA, attention is paid to the fact that the excitation is assumed to be broadband like the white noise. Unfortunately, this assumption does not match the characteristics of a real excitation. This paper contains the identification of natural frequencies of a machine tool during milling within both approaches. The achieved results are compared and discussed.

Natural frequency identification model based on BP neural network for Camellia oleifera fruit harvesting

Vibratory harvesting is an important means of mechanically harvesting tree fruit. The optimal excitation parameters are usually experimentally determined under complex conditions with different environments and machine configurations. Optimisation methods include tree modelling and dynamic analysis but experimental validation can take much time due to the complexity of tree structure and properties. A simple and appropriate identification model that could identify the natural frequencies of trees might simplify the process and promote the technology. A natural frequency identification model is proposed based on back propagation (BP) neural network to identifying the natural frequency of the tree based on its structure. Taking Camellia oleifera tree with its upright canopy as an example, the excitation parameters that can achieve better harvesting of fruit was determined here by orthogonal test. A dynamic model was established, and the tree structure variables were derived as the input layer of the model. The dataset of tree dynamics was established by finite element analysis and the effective natural frequency region was set as the model output layer. A natural frequency identification model was established based on TensorFlow, where the input and output parameters are fitted using a BP neural network. Application of the model was carried out after substantial training and testing. In the range of natural frequencies 6-7Hz, the mean square error between the natural frequency identification value and the measured value was only 0.0408, which verified the reliability of the model.

Understanding the force motion trade off of rigid and hinged floating platforms for marine renewables.

In this work, we compare the motion and structural response of a rigid and hinged floating structure subject to regular waves. We do this to understand better whether what is the best option for floating marine renewable installations. The hinged structure has two hinges and three pontoons, whilst the rigid structure is made by replacing the hinges with rigid steel bars. We instrument the pontoons with motion detection spheres and with strain gauges to measure vertical point loads. We find that the motion response of the platforms is similar between hinged and rigid at low and high frequencies. However, at intermediate frequency waves, single and triple sagging occur for rigid and hinged structures, respectively. We find significant load alleviation for the hinged structure in the range of frequencies where sagging behaviour occurs. These insights reveal that hinged design can contribute to long term survivability by reducing loads in the structure, whilst identification of motion patterns and natural frequencies are necessary to select operating modes for marine renewable generators mounted on the platforms.

Damping Identification From Subsea Logger Axial Riser Response Data

Summary For decades, it has been known that, as drilling riser deployment depths increase, the potential for excessive hookload response will also increase. Using data collected from a drilling riser deployed to a record-setting water depth, nearly 12,000 ft, this paper provides insight that significantly reduces uncertainty about the severity of this resonant response. The typical drilling riser and blowout preventer (BOP) stack, disconnected from the wellhead, has its first axial resonant period at approximately 1 second for every 2,000 ft of deployed length, thus 5 seconds for 10,000 ft, 6 seconds for 12,000 ft, and so on. Therefore, vessel heave response can incite a significant, adverse axial resonant condition in very deep water. Damping reduces resonant response. Historically, the true amount of damping has been uncertain, and damping has been applied in the form of hydrodynamic drag. This typically produces a predicted response with total damping that is well under 1% of critical. This can lead to the prediction of a large dynamic hookload that can produce significant restrictions on riser configuration (running weight) and seastate for BOP stack deployment as well as storm hang-off of the riser and lower marine riser package (LMRP). A recent drilling riser deployment to the record-setting water depth of 11,903 ft produced a unique opportunity to collect high-quality data that reduces damping uncertainty. This paper describes damping ratio and natural frequency identification for the first few axial riser modes for this deployment. The data were collected during deployment and retrieval using subsea vibration data loggers (SVDLs) installed on the BOP stack, drillship, and riser. These measurements reveal damping that is between 2% and 3% of critical. This result can be used to provide more accurate predictions of dynamic hookload response.

A multimodal natural frequency identification method of long-span bridges using GNSS

Multimodal natural frequency is a crucial factor in determining the structural stability of bridges. Global navigation satellite system (GNSS) has become an increasingly important tool for monitoring the structural health of long-span bridges. This paper proposes a method for accurately determining multimodal natural frequencies in these structures using GNSS monitoring data. The proposed method involves decomposing GNSS displacement data into several signals that correspond to each mode using auto-regressive power spectrum decomposition, extraction of Intrinsic Mode Functions (IMFs) using empirical mode decomposition (EMD), identification of multimodal natural frequencies from the extracted IMFs using random decrement technique and Hilbert transform. The proposed method was validated through a simulation test and was applied to the Yingwuzhou Yangtze River Bridge. Results showed that this method was able to accurately identify the first six modal frequencies with a relative error of less than 8.09% compared to the theoretical values obtained through a finite-element model. This method outperforms other methods such as peak-picking, Complete Ensemble EMD with Adaptive Noise, and empirical wavelet transform, which can only identify the first three modes or fewer. Finally, four fieldwork experiments with different GNSS data show that the maximum range of relative errors of each identification is 3.65%, which fully demonstrates the effectiveness and universality of this method.

Development and Verification of Wireless Vibration Sensors

Structural vibration testing is an effective guarantee for the Structural Health Monitoring (SHM) of large-scale civil engineering. Traditional vibration testing has drawbacks such as difficulties in wiring and picking up low-frequency signals, low communication speed, and susceptibility to testing site conditions. In order to improve the universality of wireless vibration sensors, this article develops a wireless vibration sensor, introduces the module composition and basic principles of the sensor, and conducts standard vibration table performance comparison tests between wired acceleration sensors and wireless vibration sensors, verifying the accuracy of wireless vibration sensors. In order to further explore the feasibility of wireless vibration sensor applications, the wired acceleration sensor and wireless vibration sensor were used to analyze the structural dynamic characteristics of the four-layer steel frame structure model in the laboratory, and the comparison was made based on ABAQUS finite element simulation. Finally, the field vibration test was carried out outdoors. The results show that the natural frequency identification results of the wireless vibration sensor and the wired acceleration sensor for the four-story steel frame structure through fast Fourier transform, short-time Fourier transform, and wavelet transform are basically the same, the half-power bandwidth method and logarithmic decrement rate method are used to identify the damping, and wavelet transform is used to identify the vibration mode with minimal error and high accuracy. It shows that the wireless vibration sensor is feasible in practical engineering, has stable and reliable transmission capacity, and can provide certain reference values for earthquake monitoring, building Structural Health Monitoring, etc.

Identification of natural oscillation frequencies of constructions from low-amplitude seismic signals (on the example of the Sayano-Shushenskaya HPP dam according to the monitoring data of 2001-2021)

Based on the spectral analysis of low-amplitude seismic signals records (continuous monitoring data for 2001-2021) from one of the stations of the seismological network located at a distance of 4.4 km from the Sayano-Shushenskaya HPP, a method for determining the daily values of natural oscillation frequencies of constructions has been developed (the frequencies of the first seven modes are identified with an error no more than 0.01 Hz). The results of processing and analysis of unique data indicate a continuous and non–slowing increase in the values of the natural oscillation frequencies of the dam in the range of 0.02-0.05 Hz during the observation period. This is explained either by silting up the bottom of the reservoir in the area adjacent to the dam, or by adapting the dam and its base with subsequent increase in mechanical rigidity of the construction. At the same time, the intervals are analyzed at which the influence of seasonal environmental influences on the construction is insignificant (summer-autumn period, the water level in the reservoir is close to the maximum). The developed method of identification of natural oscillation frequencies of constructions from low-amplitude seismic signals is intended to monitor their technical condition, in order to prevent the risks of destruction of dams, industrial structures, infrastructure facilities and civil buildings with a high degree of reliability and is economically profitable in comparison with known solutions.

Automatic modal identification of bridges based on free vibration response and variational mode decomposition technique

Free vibration tests are often performed for the dynamic characterization of structural systems and components. In the field of road bridges monitoring, such tests require minimal equipment (i.e., a sparse network of few sensors, even a single one) in order to gather – quickly and at low cost – some essential information about the dynamic behavior of the structure. The experimental free-vibration response is thus processed for estimating structural modal features which, in turn, can be useful to corroborate or update available numerical models as well as to evaluate current bridge conditions. Within this framework, an efficient computational strategy is here developed for the modal identification of bridges based on their free vibration response. The procedure combines the variational mode decomposition technique with the area ratio-based damping identification method, which ensures enhanced robustness to noise-related effects in field-test signals. A novel procedure is implemented to make the whole identification process fully automatic, in such a way that it does not depend on specific structural features (e.g., to identify even closely-spaced modes) or subjective user’s settings. After a preliminary validation with a synthetic multi-modal signal, the proposed procedure is applied to two real case-studies. The first case-study deals with the identification of natural frequencies, modal damping ratios and mode shapes of prestressed concrete girder bridge decks. Particularly, experimental natural frequencies and mode shapes are compared with numerical predictions obtained from a finite element model of the bridge. The dynamic characterization of the cables of a cable-stayed bridge is considered in the second case-study. Herein, experimental natural frequencies of all the stay-cables are initially analyzed for estimating their stress levels, which have been critically analyzed to detect the existence of relaxation losses. Moreover, modal damping ratios of all the stay-cables are identified and compared to estimates obtained by alternative ambient-vibration-based techniques.

Investigation of microtremors observed at historic masonry townhouse buildings after Nepal earthquake

The Gorkha earthquake in 2015 was a recent large-scale earthquake that caused severe damage to many historic masonry buildings in the Kathmandu Valley, Nepal. The authors conducted a visual inspection survey of seismically damaged buildings after the earthquake in the historic town district of Bhaktapur in the Kathmandu Valley. The first part of this paper reports the distribution of the historic masonry buildings for each damage level in the surveyed area. A concentrating zone of severely-damaged buildings was explicitly found in the damage-level distribution map. Almost half of all the surveyed buildings were severely damaged during the earthquake, and most of these were historic masonry townhouse buildings. In the second part, the ambient vibration characteristics of the conventional historic masonry buildings in Bhaktapur are investigated. Typical dwelling houses in a historic town district in Nepal, which generally formed terraced houses built around a courtyard, were targeted for the measurement. Thus, the influence of adjacent buildings, which makes it difficult to identify the predominant natural frequencies from building vibration measurements, was also observed. Microtremor measurements using two accelerometers were conducted at 11 historic masonry buildings to investigate the discrimination degree for identifying the predominant natural frequency of conventional townhouse buildings. The estimated primary natural frequencies of these buildings were compared with the results of the screening model analysis. The advantages of using the proposed screening model analysis to improve the uncertainty of the first natural frequency identification by the microtremor measurement are discussed. Additional measurements of the microtremors at 4 of the 11 measured buildings were conducted using a different location combination of the two acceleration sensors. The sensors were placed between two different floors, and the transfer functions of each floor were investigated to observe the predominant vibration components on the floors in the entire building. Moreover, the coherence values observing the in-plane correlation of the floor responses were also analyzed for the dataset measured at two points separated on the same floor. Finally, an effective method for measuring the microtremors is discussed to improve the assessment of the vibration characteristics of conventional historic masonry buildings in Nepal.

Numerical investigation on natural vibration characteristics of ship propulsion shafting under uncertainty based on nonparametric approach

In order to investigate the natural vibration characteristics of ship propulsion shafting under uncertainties, the random matrixes of mass, damping, and stiffness are constructed based on a nonparametric approach. The effect of uncertainties on the natural vibration characteristics of ship propulsion shafting is discussed by the distribution characteristics of natural frequency. Meanwhile, the natural frequency identification experiment of ship propulsion shafting was used to illustrate the effectiveness of the nonparametric modelling method. The results show that different levels of uncertainties in stiffness, mass and damping matrixes could be obtained by controlling the divergence parameter. The natural frequency could fluctuate significantly under uncertainties. Furthermore, the uncertainties of stiffness and mass have significant impact on the natural frequency. However, the uncertainty in damping has little influence on it. Therefore, it is essential to consider the uncertainties in the analysis of natural vibration characteristics of the ship propulsion shafting.

Investigation of time-varying natural frequencies of high-rise buildings under harsh excitations using a high-resolution combined scheme

High-rise buildings subjected to harsh excitations like typhoons or earthquakes usually present nonlinear features and exhibit time-varying behavior of structural modal properties. Under such circumstances, variation in structural natural frequencies can serve as a critical indicator for structural condition assessment. However, limited by noises contained in measurement records and time-frequency resolution of signal analysis, most instantaneous frequency identification methods are difficult to provide accurate estimation of time-varying natural frequencies of high-rise buildings. To address this issue, a combined scheme based on the variational mode decomposition method and adaptive superlets transform (VMD-ASLT) for time-varying natural frequency identification is presented in this paper. Through numerical simulation studies and field measurements of dynamic responses of a 508 m high skyscraper, the noise robustness and accuracy of the combined scheme for time-varying structural natural frequency estimation are validated. Moreover, the combined scheme is further utilized to investigate the time-varying features of natural frequencies of the skyscraper under typhoon and earthquake excitations. This paper aims to provide an effective tool for time-varying structural natural frequency estimation and further reveal the variation of the dynamical behavior of high-rise buildings under harsh excitations.

The natural frequencies of the resting human brain: An MEG-based atlas

Brain oscillations are considered to play a pivotal role in neural communication. However, detailed information regarding the typical oscillatory patterns of individual brain regions is surprisingly scarce. In this study we applied a multivariate data-driven approach to create an atlas of the natural frequencies of the resting human brain on a voxel-by-voxel basis. We analysed resting-state magnetoencephalography (MEG) data from 128 healthy adult volunteers obtained from the Open MEG Archive (OMEGA). Spectral power was computed in source space in 500 ms steps for 82 frequency bins logarithmically spaced from 1.7 to 99.5 Hz. We then applied k-means clustering to detect characteristic spectral profiles and to eventually identify the natural frequency of each voxel. Our results provided empirical confirmation of the canonical frequency bands and revealed a region-specific organisation of intrinsic oscillatory activity, following both a medial-to-lateral and a posterior-to-anterior gradient of increasing frequency. In particular, medial fronto-temporal regions were characterised by slow rhythms (delta/theta). Posterior regions presented natural frequencies in the alpha band, although with differentiated generators in the precuneus and in sensory-specific cortices (i.e., visual and auditory). Somatomotor regions were distinguished by the mu rhythm, while the lateral prefrontal cortex was characterised by oscillations in the high beta range (>20 Hz). Importantly, the brain map of natural frequencies was highly replicable in two independent subsamples of individuals. To the best of our knowledge, this is the most comprehensive atlas of ongoing oscillatory activity performed to date. Critically, the identification of natural frequencies is a fundamental step towards a better understanding of the functional architecture of the human brain.

Fully automated natural frequency identification based on deep-learning-enhanced computer vision and power spectral density transmissibility

As image acquisition devices have outstanding potential for gathering vibration information, computer vision has received a lot of interest in structural health monitoring (SHM). In this work, a fully automated peak picking methodology based on computer vision in tandem with deep learning is proposed to realize vibration measurements and identify natural frequencies from the plot of the power spectral density transmissibility (PSDT). A deep-learning-enhanced image processing technology was used to extract the vibration signals with automatic active pixel selection, while a convolutional neural network was used to further process the vibration measurements so that the frequencies could be identified from PSDT-based functions. The proposed method was verified by three case studies, including the dynamic testing of two laboratory models and the field testing of the stay cable. The findings showed that the proposed deep-learning-enhanced approach has a high potential for use in SHM by automatically performing vibration measurement and frequency extraction.

Frequency identification based on power spectral density transmissibility under unknown colored noise excitation

In this paper, a new natural frequency identification method is proposed for the modal parameter identification under an unknown colored noise excitation. The presented method can effectively eliminate the influence of incentive frequency on the identification of the natural frequencies when there are several colored noise excitations applied to the structure. However, it would be cumbersome or even difficulty to determine the natural frequencies when there is only one unknown colored noise excitation applied to the structure. In this paper, a new frequency indicating function using the second singular value of the transmissibility matrices is proposed for the first time to determine the natural frequencies of the structure under only one unknown colored noise excitation. The reason for using the second singular value in theoretically is also a novelty of this paper. The proposed method is verified using a six-degree-of-freedom system and a laboratory plane frame. The results show that the proposed method can effectively eliminate the resonant peak that does not belong to the structural model and is robust to noise.

Encapsulation Based Method for Natural Frequency Identification of Deployable Solar Arrays with Multiple Plates

The ground modal test is an important approach to the natural frequency of solar arrays to support the attitude control of spacecraft. However, for the batch production of small satellites, the accuracy and efficiency of traditional ground modal testing methods are limited. This shortcoming restricts the development of satellite constellations. Based on the encapsulation method widely used in the computer field, this paper proposed a natural frequency identification method of deployable solar arrays with multiple plates. This method is of high accuracy and efficiency that meets the demand of attitude control and makes sense to accelerate the batch production of small satellites. First, a suspended modal test system with gravity compensation function is designed. Second, the mathematical model of the test system is established. Abstracting parts of the parameters of the test object into an encapsulated entity, the mathematical model is simplified by equivalent variables. Thus, the direct mapping relationship between the ground test result and the true natural frequency is proposed. Finally, to verify the identification accuracy, finite element analysis (FEA) and the ground modal test of a two-folder solar array simulant are carried out. The results show that the relative error of the first-order natural frequency after correction and the theoretical value is less than 3%. Meanwhile, the identification accuracy of the ground modal test is improved by more than 50%. This method improves the availability of ground test results and reduces the calculation amount, so that it is convenient for engineering applications.

Calibration of the numerical model of a track section over a railway bridge based on dynamic tests

Progressive updating strategies are commonly used for the calibration of numerical models such as those of a track-bridge system. These strategies involve, first, updating the track model based on dedicated dynamic tests, and second, the calibration of the bridge model based on ambient vibration tests considering the updated track parameters. This subsequent procedure is suggested as some track parameters are, in relation to the modal responses of the bridge, generally not sufficiently sensitive for a successful parameter estimation. This work describes the calibration of a specific finite element (FE) model of a track section over a bowstring-arch railway bridge. The model includes the rails, rail pads, sleepers, the ballast layer and the interfaces with the bridge and neighbouring track sections. A track receptance test allowed for the identification of natural frequencies and mode shapes of the track by applying two different techniques, an output-only and an input-output. Several modes of vibration related to the movement of the sleepers on the ballast were identified using the SSI-DATA method, at frequencies between 83.8 Hz and 142.2 Hz. The calibration of the track FE model was performed using an iterative methodology by means of a genetic algorithm, which proves efficiency and robustness in estimating several track numerical parameters, besides a significant upgrade in relation to the numerical model before calibration.

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor.

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 rad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

Natural Frequencies Identification by FEM Applied to a 2-DOF Planar Robot and Its Validation Using MUSIC Algorithm.

In this paper, the natural frequencies (NFs) identification by finite element method (FEM) is applied to a two degrees-of-freedom (2-DOF) planar robot, and its validation through a novel experimental methodology, the Multiple Signal Classification (MUSIC) algorithm, is presented. The experimental platforms are two different 2-DOF planar robots with different materials for the links and different types of actuators. The FEM is carried out using ANSYS™ software for the experiments, with vibration signal analysis by MUSIC algorithm. The advantages of the MUSIC algorithm against the commonly used fast Fourier transform (FFT) method are also presented for a synthetic signal contaminated by three different noise levels. The analytical and experimental results show that the proposed methodology identifies the NFs of a high-resolution robot even when they are very closed and when the signal is embedded in high-level noise. Furthermore, the results show that the proposed methodology can obtain a high-frequency resolution with a short sample data set. Identifying the NFs of robots is useful for avoiding such frequencies in the path planning and in the selection of controller gains that establish the bandwidth.

Implementation of video motion magnification technique for non-contact operational modal analysis of light poles

Damages on lights and utility poles mounted on the elevated highway or railway bridges were observed in the past several large earthquakes. The damages could have serious consequences to public safety, travelling vehicles or trains, and nearby properties. A previous study shows that the damages were caused by buckling and yielding of the pole due to excessive response amplification during large earthquake. Such amplification occurs when the bridge's natural frequency is close to the light pole's fundamental frequency. An investigation of the seismic performance of existing light pole mounted on elevated highway bridges is needed to avoid the response amplification. This includes the identification of the light pole's natural frequency and damping ratio. Vibration testing of the light pole using conventional contact sensors individually would require enormous effort and is time-consuming. Moreover, such vibration testing on a highway bridge deck would require traffic disruption to provide access. Video camera-based non-contact vision sensing is seen as a promising alternative to the conventional contact sensors for this purpose. The objective of this paper is to explore the use of non-contact vision sensing for operational modal analysis of light pole on highway viaduct. The phase-based video motion magnification method is implemented to obtain the light pole response in an ambient condition. Using this method, small and invisible displacement is magnified for a certain range of frequency of interest. Based on the magnified video frames, structural displacement is extracted using the image processing technique. The natural frequency and damping ratio of the light pole are estimated using the random decrement technique. The method is verified in a laboratory-scale experiment and implemented to practical field measurements of a light pole on a highway viaduct in Kanagawa, Japan. The results are compared with measurement by Laser Doppler Vibrometer. Both experiments suggest that the method could effectively obtain the natural frequency and damping ratio of the structures under the ambient condition where vibration amplitudes are very small and invisible with reasonable accuracy.