Modal Identification Method Research Articles

A hybrid time-frequency method for robust drive-by modal identification of bridges

Indirect bridge health monitoring (iBHM) has gained significant attention in recent years as an alternative to direct bridge monitoring techniques. iBHM leverages the use of a vehicle traveling over a bridge as a sensing device as well as an actuator. The resulting data acquired from the vehicle contains dynamic information about the bridge, vehicle suspension, engine noise, ambient traffic noise, road roughness, etc. Due to the presence of sensor-vehicle-bridge interactions in vehicle measurement, a powerful decoupling framework of system identification is required to extract useful information about the bridge and delineate the effect of vehicle and driving frequencies. This paper proposes a hybrid time-frequency method capable of decoupling vehicle-bridge interactions of vehicle measurement and performing a robust bridge modal identification under various operational challenges. In the proposed research, wavelet packet transformation (WPT) is first used to decompose the vehicle measurement into various WPT coefficients. Then, the modal frequencies of the bridge are extracted from the resulting WPT coefficients using Synchro-Extracting Transform (SET) and are separated from the vehicle and driving frequencies. The proposed method is validated using numerical and laboratory studies as well as a full-scale study comprising of a 220 m long box-girder bridge. The results provide strong evidence that the proposed hybrid time-frequency method can serve as a promising iBHM method.

Observation and characterization of the high order modes in a six-mode fiber using an OFDR method.

High order modes in a six-mode fiber are separately observed and characterized using an Optical Frequency Domain Reflectometry (OFDR) method. Due to the difference in group refractive index between fundamental mode and the high order modes, Fresnel reflection peaks for each mode can be separated in beat frequency domain with their corresponding time delay. In the experiment, the fundamental mode and high order modes are excited in turn and observed at a 6.6 m six-mode fiber end, which agree with their beat frequency difference in theoretical simulation. The demonstration provides a flexible and feasible method for mode identification and characterization of all kinds of fibers.

A Robust Technique for Polymer Damping Identification Using Experimental Transmissibility Data.

This paper presents a robust method to estimate polymers’ damping, based on modal identification methods on frequency functions. The proposed method presents great advantages compared to other traditional methods such as the HPB method for polymeric materials where high damping or noise levels can limit their use. Specifically, this new method is applied on an experimental transmissibility function measured in a composite cantilever beam and the complex modulus is determined as a function of frequency. From this, a regenerated function is obtained based on the Euler–Bernoulli beam theory, and it is compared with experimental data. It can be concluded that the best way to apply the curve-fitting method for further testing of polymeric materials is when it is used with the whole frequency range by means of the MDOF method considering the residuals. In addition, this has the added advantage that the number of experimental tests to be carried out is much lower compared to using the SDOF method.

Experimental and numerical investigations on the influence of center-hung scoreboard on dynamic characteristics of suspend-dome structure

The LED display, i.e., the center-hung scoreboard, nowadays has become an indispensable display device in large stadiums, and some of which with weight is more than 30t. To investigate the influence of center-hung scoreboard load on the dynamic characteristics of the suspend-dome structure, a 1:20 dynamically scaled model of the Lanzhou Olympic Sports Complex was designed, considering different lifting-lowering heights of the center-hung scoreboard by changing the sling length. Shaking table dynamic characteristics experiment was conducted by using the white noise excitation method for the suspend-dome structure with the sling lengths of 200 mm, 400 mm, and 600 mm individually. The change rule of dynamic characteristic parameters such as natural frequencies and damping ratios was concluded by the Hilbert-Huang Transformation method for modal identification and the transfer function method for checking. With the increase of sling length, the natural frequencies of the center-hung scoreboard become smaller, and the damping ratios become more extensive. Compared with the results of the scaled model without a center-hung scoreboard, the high-order natural frequencies and damping ratios of the overall structure with the center-hung scoreboard are significantly increased, and the coupling effect between the center-hung scoreboard and the structure should not be ignored in the dynamic analysis. The test values were compared with the simulation results of Abaqus as well. It is shown that the test values of the scaled model are essentially consistent with the simulation results, which indicates that the test points are reasonably arranged, the test method is correct, and the finite element modeling method is accurate. The effects of sling stiffness and sling length on the dynamic characteristics of the suspend-dome structure were studied by Abaqus software. The results show that the sling stiffness hardly affect the dynamic characteristics of the overall model. When the sling length is less than 300 mm, the lifting-lowering of the center-hung scoreboard influences the distribution of the natural frequency and the vibration mode of the overall structure. In this range, the lifting-lowering of the center-hung scoreboard should be focused on actual engineering.

Modal measurement and identification of hexagonal air cushions

Air cushions have been widely utilised as roofs and facades for large-span buildings owing to their advantages such as ultra-light weight and aesthetic appearance. The dynamic performance of air cushions, which is a typical fluid-solid interaction problem, is complex, because the top layer, bottom layer, and inner air are highly coupled. However, there is a paucity of effective dynamic experimental studies to test the modal characteristics of entire air cushions. Therefore, in this study, a modal measurement and identification method was developed to simultaneously calculate the dynamic properties of both the top and bottom layers of air cushions. A laser displacement sensor array was employed to record the time-history displacement data at the observation points, and the combined application of the fast Fourier transform (FFT) and stochastic subspace identification (SSI) methods was used for modal identification. A hexagonal air cushion was adopted for testing, and the first eight frequencies and modes were successfully identified. The test results indicated that the first mode shape was significantly different from that of a single-layer foil. The one-wave vibration mode shape appeared after the multi-wave mode shapes, which was a unique phenomenon for air cushions. The frequencies and mode shapes of the top and bottom layers were almost identical. The mode deformation of the two layers can be in the same direction or opposite directions, and the frequencies corresponding to the mode shapes of layers vibrating in the same direction were higher than those of layers vibrating in opposite directions.

Output-only complete mode shape identification of bridges using a limited number of sensors

Mode shape is an important structural property that needs be identified in structural condition monitoring and analysis. The conventional modal identification methods usually can only provide sparse and low-spatial resolution mode shape measurements because of the limited number of sensors, which could seriously affect the effectiveness and accuracy of the mode shape-based structural damage detection methods. In this paper, a new output-only method is proposed for identifying the complete mode shapes for beam-like bridge structures under a moving load using a limited number of sensors based on proper orthogonal decomposition (POD). Firstly, the physical interpretation of the POD of the responses of a beam-like bridge under a moving load is derived. It is proved that each component of the POD consists of a mode shape of the bridge and a dynamic component with the frequency corresponding to this mode. The contribution ratio of the component in the POD gives an excellent estimation of the modal contribution ratio (CR) in terms of the vibration energy. The mode shape can be identified by filtering out the dynamic information in each component of the POD. The identified mode shapes have a high spatial resolution that they can be regarded as the complete mode shapes of the bridge. To demonstrate the proposed method, a beam bridge with different boundary conditions is numerically modelled and a simply supported beam bridge model is tested in the lab. Both the numerical and experimental results demonstrate that this method can successfully identify the complete mode shapes with high resolution and modal contribution ratios with a limited number of sensors. This method breaks through the challenge on the requirement of a large number of sensors in vibration tests for full mode shape identifications in traditional methods.

A tracking method of equivalent constraint boundary for offshore monopile wind turbines from measured accelerations

For offshore wind turbines, the foundation constraint boundary is important for safe operation yet difficult to determine due to the invalidity of the fixed point assumption and influences from soil variability, liquidation, scour, etc. In this paper, a tracking method of equivalent constraint boundary is proposed on the basis of a limited numbers of measured responses, which are entirely different from the results by fixed constraints. The most theoretical achievement of the proposed method is that the time series of so-called first-order displacements can be accurately retrieved from the measured accelerations, leading to the significant difference from the first-order mode shape of conventional modal identification methods. The obvious advantage of the proposed method is that the change in the equivalent constraint boundary can be easily tracked just from the assembled accelerometers, which means that the difficulty and uncertainty of considering soil and water can be avoided. To verify the performance of the proposed method, two numerical examples and a beam experiment are conducted, and measured sea test data from a monopile wind turbine is processed. In detail, the first example is a cantilever beam with a theoretical fixed constraint position, and the results show that the fixed boundary position of the cantilever beam can be accurately estimated with a maximum relative error of 5.3% when six sensors and a fifth-order polynomial are used. The second example is a physical experiment of a cantilever beam and the change of constraint is considered by removing segments one by one. The experimental results show that the predicted constraint position is consistent with the cut length, with a maximum error of 0.009 m at 1.9 m. Furthermore, a 4 MW offshore monopile wind turbine evaluated by commercial software Ansys considering pile–soil interaction is analyzed, and the changes of the predicted equivalent constraint position are in good agreement with the preset values. Finally, the proposed method is applied to the field test data of a 6 MW monopile wind turbine, and a stable estimation of the equivalent constraint position can be obtained. The good accuracy of the proposed method demonstrates its capability in monitoring structural health for offshore wind turbines.

Synthetical Modal Parameters Identification Method of Damped Oscillation Signals in Power System

It is vital to improve the stability of the power system by accurately identifying the modal parameters of damped low-frequency oscillations (DLFO) and controlling the oscillation in time. A new method based on empirical mode decomposition (EMD), stochastic subspace identification (SSI), and Prony algorithms, called synthetical modal parameters identification (SMPI) method, is developed by efficiently matching the modal parameters of DLFO which are acquired from the SSI and Prony algorithm. In this approach, EMD is used for denoising the raw oscillation signals thereby enhancing the noise resistance, and then using the SSI and Prony algorithms to identify the precise modal parameters assisted by parameter matching. It is demonstrated that the proposed SMPI method holds great accuracy in identifying full modal parameters including natural frequencies, damping ratios, amplitudes, and phase angles with simulated signals with known modal parameters and real-time signals from some power system case studies. The strategy of SMPI has effectively overcome the weakness of a single approach, and the identification results are promising to heighten the stabilization of power systems. Besides, SMPI shows the potential to troubleshoot in different fields, such as construction, aeronautics, and marine, for its satisfactory robustness and generalization ability.

Unified method for fully automated modal identification and tracking with consideration of sensor deployment

Automated modal identification and tracking provides the key technique for modal parameters based structural condition evaluation. However, the existing automated modal identification and tracking methods have limitations for situation with very few sensors deployed and require manual intervention. This paper proposes a unified fully automated modal identification and tracking method that can be used for structures with many or very few sensors deployed, for closely spaced modes with severe spatial aliasing and for structures with high flexibility or rigidity. A new index, which is called Modified Modal Observability Correlation, is proposed to estimate the similarity of two modes. New spurious mode elimination method and fully automated mode separation and tracking methods are proposed to realize the automated modal identification and tracking. The feasibility and novelty of the proposed method are validated using in-field monitoring data from a long span suspension bridge with high flexibility and a short span bridge with high rigidity and closely spaced modes. Automated modal identification and tracking for situations with many and very few sensors deployed for the two bridges are conducted, and extreme situation of closely spaced modes with spatial aliasing in mode shape is also considered to prove the novelty of the proposed method. Comparisons with existing mainstream methods are also conducted. The results show that the proposed method yields the right identification and tracking results in all situations, showing novelty in automated modal identification and tracking for structures with closely spaced modes having severe spatial aliasing when only very few sensors are deployed.

Failure mechanism and design method of reticulated shells considering joint damage accumulation effect under earthquake load

Prefabricated joints have been widely used in steel structures because of their high construction efficiency, high quality and environmental protection. However, during the seismic design of the single-layer reticulated shells structure (SLRSS) connected by prefabricated joints, the prefabricated joints were generally simplified as hinged joints, and the engineering applications of the SLRSS with prefabricated joints was greatly limited. In this study, the numerical simulation and theoretical analyses were used to investigate the seismic performance of the semi-rigidly jointed SLRSS under the earthquake load. Based on ABAQUS, a finite element model (FEM) of the semi-rigid SLRSS was established, considering the joint damage accumulation, material damage accumulation, three-dimensional seismic action and initial defects. Four typical structure failure modes were obtained: member strength failure, joint strength failure, mixed strength failure, and dynamic instability. The effect of two joint parameters including joint stiffness and joint bearing capacity on the failure modes of the structure was obtained. Meanwhile, the corresponding failure mode identification method and control method were proposed, and the effectiveness of the proposed methods were verified by comparing the results of the numerical simulation results.

Numerical and Experimental Study on Mode Identification Error Characteristics of Fan Noise

The influence of different test methods on the accuracy of mode identification is not clear, and it is necessary to explore the error transfer characteristics in mode decomposition of fan noise. Numerical and experimental research studies are carried out on the advantages and disadvantages of radial rake and axial microphone array and error transmission characteristics in mode decomposition. In the numerical study, the error transmission characteristics of different arrays are investigated by adding random disturbances to the artificial sound field, so as to evaluate the applicability and limitations of the two typical arrays in mode identification based on the error analysis theory. The mode recognition error of the single-stage axial flow fan is investigated experimentally using the designed radial rakes and axial arrays. The results show that although the radial rake can directly measure the radial distribution of the modal amplitude, it has a large error in the mode identification at low frequencies. Compared with the radial rake, axial array will take more priority in practical applications. The accuracy of the axial microphone array in mode recognition strongly depends on the axial spacing of the array measuring sensors. The small deviations in the mode identification when applying the two typical arrays are caused by the different signal-to-noise ratio of the sound pressure signals acquired by the two arrays and their discriminative sensitivities to the duct airflow. Based on the obtained modal identification error characteristics, an effective mode identification method can be proposed to help fan noise reduction design.

Modal Identification Technologies for High-Rise Buildings Under Non-Stationary Excitations

For high-rise buildings subjected to typhoon or earthquake actions, the excitations are likely non-stationary, which inevitably violates the stationary assumption that is generally adopted by conventional modal identification methods. Under such a condition, conventional modal identification methods may not be applicable, and their performances need to be evaluated. To this end, the performances of seven widely used modal identification algorithms for structural modal estimation under non-stationary excitations are evaluated via a numerical simulation study. Then, three methods with good performance are selected to evaluate their applicability and accuracy for field measurements involving non-stationary excitations. From the comparative study, a time–frequency domain method with the best performance among these seven methods is employed to investigate the structural dynamic properties of a 509-m-tall skyscraper under typhoon and earthquake excitations. Based on the reliable modal estimates, the relationships between the modal properties with response amplitude and environmental temperature are presented and discussed. This paper aims to identify the effective methods for accurate estimation of structural modal parameters based on non-stationary structural responses and investigate the structural dynamic properties of high-rise buildings under typhoon and earthquake excitations.

Modal properties identification of damped bridge using improved vehicle scanning method

This paper is concerned with an improved Vehicle Scanning Method (VSM) for modal properties identification of bridges with allowances for damping and road roughness. Owing to the bridge damping, signals are small and degrade over time and may be corrupted by the road roughness. In order to enhance VSM in reading these weak signals, an appropriately tuned elliptic filter is employed instead of the conventional bandpass filter, such as the Butterworth filter. The VSM is improved further by adopting the recently developed Moving Internal Node Element (MINE) method that can furnish more accurate predictions of the higher natural frequencies of the bridge. Illustrative example problems involving undamped and damped bridges with or without road roughness are presented to show the superiority of the improved VSM over conventional VSM that uses a standard bandpass filter and finite element method for analysis. It will be shown herein that the improved VSM can identify the higher mode shapes even with a bridge damping ratio of 3% and standard road roughness, whereas the existing VSM could not do so.

Experimental modal analysis using velocity feedback excitation

In this study, we proposed a new multi-point excitation method with velocity feedback (FB) excitation to capture the resonance peak clearly as well as a modal identification method. The specific procedure for identifying the modal damping ratio that we proposed is as follows: the modal damping ratio that reduces the damping is designed as the control gain; the reduced modal damping ratio is identified from the frequency response function (FRF) measured by velocity FB excitation using the control gain; and the damping by the control gain is added to identify the original mode damping ratio of the target structure. After summarizing the theory of the proposed methods, we explained their validity by presenting numerical analysis. A two-degree-of-freedom system with high damping characteristics was used, and when absolute and relative velocity FB excitation were applied, the damping of the vibration system was reduced and the FRF was captured. Then, following the procedure of the proposed method, we were able to identify the original modal damping ratio of the target system under consideration. The proposed method is expected to accurately identify the modal characteristics of vibration modes whose resonance peaks do not clearly appear.

Research on Anti-Noise Ability of Offshore Platform Health Monitoring System Based on Strain Mode Structural Damage Identification

Strain modal structural damage identification is widely used in offshore platform health monitoring. However, due to the limitation of structural testing technology, the complex marine environment around the offshore platform structure is superimposed, such as wind, wave, tidal current and other dynamic environments. In the actual test, many factors interfere with modal identification and damage detection, which brings a certain amount of errors to the identification of modal parameters of offshore platform structure, Thus, the accuracy of loss identification of offshore platform structure is affected. In this paper, the health monitoring system of offshore platform based on strain mode structural damage identification is studied by analyzing the damage identification effect of strain mode structure under different degrees of environmental noise superimposed by single member damage and multi member damage. The research results show that strain mode damage identification can not only accurately locate members, which has better anti-noise ability, but the anti-noise ability under multi member loss is also lower than that under single damage condition. For single member damage, it has better damage identification effect within 10% noise level, and for multi member damage, it just has better damage identification effect within 8% noise level. The research results of this paper find out the base number of damage identification ability of jacket platform structure based on modal parameters, which is a great significance for using strain modal damage identification method in offshore platform structure health monitoring.

Experimental and computational evaluation of modal identification techniques for structural damping estimation

The damping ratio is a key indicator of a structures susceptability to human discomfort due to dynamic loads. Computational models, wind tunnel studies and empirical data can provide estimates of the damping ratio of a structure. However, the only true way to investigate the damping ratio of a structure is through modal identification using data from field tests carried out on the full-scale finished structure. This paper investigates the efficacy of three modal identification methods for estimating the damping ratio of the first two modes of a structure from ambient data. The three methods considered are the Bayesian Fast Fourier Transform (BFFT), the Random Decrement Technique (RDT), and a hybrid of the RDT which first decomposes the ambient data into sub signals using Analytical Mode Decomposition (AMD) and is referred to as the AMD-RDT. Each method is applied to two case studies in order to investigate the accuracy of their damping estimates. The first case study is experimental and involves the excitation of a scaled model structure using a shake table; the second case study considers a computational model of a tall building under simulated wind loads. It was found that the AMD-RDT was the superior method for damping estimation, particularly for the estimation of damping ratio in the second mode, even when the modes were closely spaced. The length of time series data used and the noise within the data was seen to affect the accuracy of the three methods studied.

Vibration Mode Identification Method for Structures Using Image Correlation and Compressed Sensing

All objects have deformed shapes (vibration modes) that tend to vibrate, and measuring these modes is extremely useful in structural design and failure diagnosis. Traditionally, expensive measurement equipment and many vibration sensors were commonly used to measure vibration modes, but a method that measures displacement from images (Digital Image Correlation) has made it possible to identify vibration modes with a single camera. However, the identification of high-frequency vibration modes requires a high-speed camera, which increases the cost and reduces the resolution. In this study, a low-cost and highly accurate method for identifying vibration modes and frequencies (RSES: Randomized Single Exposure Sampling) was developed by applying compressed sensing to images taken with a strobe flash and a low-speed camera. This method successfully identified vibration modes and frequencies of structures vibrating at frequencies more than 300 times the shooting speed.

Modal Parameter Identification of Structures Using Reconstructed Displacements and Stochastic Subspace Identification

A method of modal parameter identification of structures using reconstructed displacements was proposed in the present research. The proposed method was developed based on the stochastic subspace identification (SSI) approach and used reconstructed displacements of measured accelerations as inputs. These reconstructed displacements suppressed the high-frequency component of measured acceleration data. Therefore, in comparison to the acceleration-based modal analysis, the operational modal analysis obtained more reliable and stable identification parameters from displacements regardless of the model order. However, due to the difficulty of displacement measurement, different types of noise interferences occurred when an acceleration sensor was used, causing a trend term drift error in the integral displacement. A moving average low-frequency attenuation frequency-domain integral was used to reconstruct displacements, and the moving time window was used in combination with the SSI method to identify the structural modal parameters. First, measured accelerations were used to estimate displacements. Due to the interference of noise and the influence of initial conditions, the integral displacement inevitably had a drift term. The moving average method was then used in combination with a filter to effectively eliminate the random fluctuation interference in measurement data and reduce the influence of random errors. Real displacement results of a structure were obtained through multiple smoothing, filtering, and integration. Finally, using reconstructed displacements as inputs, the improved SSI method was employed to identify the modal parameters of the structure.

Autoregressive spectrum-guided variational mode decomposition for time-varying modal identification under nonstationary conditions

Modal identification is an important research subject in structural health monitoring. It is a mature subject for modal identification of time-invariant and stationary conditions. Because time-varying properties are valuable for damage detection and time-varying system identification, and because the environmental loads do not always satisfy the assumption of stationarity, it is necessary to develop accurate identification methods for time-varying structures, structures under nonstationary excitations, or the coupling of the two conditions. The variational mode decomposition (VMD) method, which adaptively decomposes the signal into narrow-band intrinsic modes, shows the potential for time-varying and nonstationary conditions. However, parameter selection greatly affects the accuracy of mode decomposition. In this study, a new modal identification method based on an autoregressive spectrum-guided variational mode decomposition method is proposed for the application of time-varying and nonstationary conditions. First, the determination of the initial center frequencies for VMD is proposed using an autoregressive spectrum-guided method to greatly improve the accuracy. Second, a method to select the optimal balancing factor is developed to improve the decomposition accuracy by controlling the proper bandwidth. Subsequently, an instantaneous frequency identification method is presented by detecting the ridge of the time–frequency distribution. Finally, studies of numerical and actual structures demonstrate the capacity of the proposed method for practical applications of time-varying cases and nonstationary conditions.

Performance assessment of modal parameters identification methods for timber structures evaluation: numerical modeling and case study

Performance assessment of modal parameters identification methods for timber structures evaluation: numerical modeling and case study