Analytical Mode Decomposition Research Articles

Monitoring-based identification of nonlinear aerodynamic damping in multi-mode vortex-induced vibrations of a stay cable

New issues of wind-induced cable vibration, i.e., multi-mode vibrations, increasingly occur in long-span bridges, which are closely associated with underlying damping features. In this study, an analytical method is proposed to identify nonlinear aerodynamic damping in multi-mode wind-induced cable vibrations in fields, involving the assessment of total and mechanical damping. The method is available to extract a series of mono-component resonances/decays from the measured signals based on the analytical mode decomposition (AMD) and random decrement technique (RDT), and then to determine the damping parameters using the Hilbert transform (HT) combined with the smoothing spline or linear least-square fitting. Furthermore, this method is applied to address the vortex-induced vibrations (VIV) of an ultra-long stay cable on the Sutong Bridge. Firstly, the vibrations are reported in terms of a typical event and one-year statistics. Subsequently, the damping parameters are identified to illustrate the in-situ aeroelasticity. The results show that the cable exhibits high-frequency vibrations primarily in the 41st to 43rd modes, and the aerodynamic damping exhibits significant amplitude-dependent nonlinearity. Finally, the damping identifications are employed to reveal the onset mechanism for the vibrations, and a Scruton number (Sc) criterion, i.e., Sc > 5.4, is suggested for mitigating the vibrations.

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

Structural damping estimation from live monitoring of a tall modular building

AbstractThe damping ratio is a key indicator of an individual structure's susceptibility to dynamic loads, including the level of discomfort experienced by the occupants of a tall building subjected to wind loading. While computational models, laboratory studies and empirical data can provide estimates of structural damping, the most reliable way to evaluate true damping ratio values is through modal identification using data from field tests on full‐scale finished structures. As an innovative form of construction, high‐rise modular buildings have not been the subject of previous vibration monitoring investigations, implying an absence of essential structural dynamics information. This paper assesses the reliability of four modal identification methods for estimating the damping ratio of a structure using ambient acceleration response data recorded from the world's tallest modular structure, the Ten Degrees building in Croydon, South London. The methods considered are two implementations of 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‐RDT). Each method is applied to response data collected during 10 significant wind loading events to evaluate the inherent modal properties of the structure, with the computed damping ratio values compared between methods and events. By reporting the first measured damping ratios for a tall modular structure, the paper makes an important contribution to knowledge about the vibration properties of an emerging form of construction.

Hilbert–Huang Transform Incorporating Analytical Mode Decomposition and Its Application in Fractured-Vuggy Carbonate Reservoir Prediction

High-precision time-frequency (TF) analysis (TFA) can accurately detect anomalies in oil and gas reservoirs. However, conventional TFA methods cannot effectively identify fractured-vuggy carbonate reservoirs, which are deep and strongly heterogeneous. In this paper, a TFA method based on analytical mode decomposition (AMD) and the Hilbert-Huang transform (HHT) is proposed. Specifically, seismic signals are decomposed by empirical mode decomposition (EMD) and then by AMD. Finally, the TF distribution of the seismic signals is obtained after Hilbert spectrum analysis (HSA). Synthetic seismic data demonstrate that the AMD-HHT method can effectively eliminate mode mixing and provide higher time and frequency resolutions and energy focus than conventional TFA methods. In addition, model and field seismic data also verify that the AMD-HHT method can effectively detect hydrocarbon-related energy anomalies hidden in broadband seismic data.

An unsupervised learning algorithm for computer vision-based blind modal parameters identification of output-only structures from video measurements

Operational modal analysis (OMA) is required to maintain large-scale and necessary civil infrastructures. The non-contact method of OMA using digital image correlation and point tracking algorithms requires a speckle pattern placed on the structure. Alternatively, advanced computer vision methods like optical flow and phase-based video motion magnification (PBVMM) techniques are used to measure modal parameters. Despite the importance of PBVMM, the users should know the range of frequencies in which the natural structure frequency lies. A methodology based on an unsupervised machine learning technique is developed to extract the modal parameters blindly from its recorded digital video. The proposed methodology uses complex steerable pyramids and an unsupervised machine learning technique, also known as principal component analysis, and analytical mode decomposition with a random decrement technique to blindly extract the modal parameters of a structure. This study validated the proposed methodology using a multi-degree of freedom (DOF) numerical model. The results are compared with theoretical and estimated values and are in good agreement. Furthermore, it is implemented on a laboratory benchmark SDOF, MDOF, and real-time videos of the London Millennium and Tacoma Narrows bridges for blindly extracting the modal frequencies and damping ratios.

Synchro-Squeezed Adaptive Wavelet Transform-Based Optimized Multiple Analytical Mode Decomposition: Parameter Identification of Cable-Stayed Bridge under Earthquake Input

Deriving critical parametric information from recorded signals for system identification is critical in structural health monitoring and damage detection, while the time-varying nature of most signals often requires significant processing efforts due to structural nonlinearity. In this study, synchro-squeezed adaptive wavelet transform-based optimized multiple analytical mode decomposition (SSAWT-oMAMD) is proposed. The SSAWT algorithm acts as the preprocessing algorithm for clear signal component separation, high temporal and frequency resolution, and accurate time–frequency representation. Optimized MAMD is then utilized for signal denoising, decomposition, and identification, with the help of AWT for bisecting frequency determination. The SSAWT-oMAMD is first verified by the analytical model of two Duffing systems, where clear separation of the two signals is presented and identification of complex time-varying stiffness is achieved with errors less than 2.9%. The algorithm is then applied to system identification of a cable-stayed bridge model subjected to earthquake loading. Based on both numerical and experimental results, the proposed method is effective in identifying the structural state and viscous damping coefficient.

Flexibility matrix identification using the moving vehicle induced responses for beam type bridge

Bridge flexibility matrix is widely used in damage detection and condition assessment. As the mass-normalized mode shapes with high spatial resolution are required in formulating the flexibility matrix, the difficult tasks of measuring excitation and arranging a large number of sensors are normally involved. This paper proposes a flexibility matrix identification method by using the moving vehicle induced responses for beam type bridges. Firstly, the proportional relationship between the modal flexibility matrix and the matrix formulated by the bridge influence lines (ILs) of several points is derived theoretically. Then the quasi-static component response of the moving vehicle induced responses is extracted through the analytical mode decomposition (AMD), and the IL of the measurement point is obtained via polynomial fitting accordingly. Finally the flexibility matrix is formulated based on the measured ILs and the derived proportional relationship, and employed to estimate the static displacement of the bridge. Numerical and experimental examples are conducted to verify the accuracy and feasibility of the proposed method. The results indicate that it can identify the bridge flexibility matrix and estimate the static displacement with high accuracy and efficiency at the cost of few sensors. Besides, the proposed method is insensitive to vehicle parameters (velocity, spring stiffness, wheelbase, and weight), road surface roughness and measurement noise.

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.

A novel ANN-RDT approach for damage detection of a composite panel employing contact and non-contact measuring data

A non-destructive method is proposed in this study for damage detection of a composite panel using random decrement (RD) signature technique and artificial neural network (ANN) algorithm. For this purpose, a 10-layer rectangular composite panel is built and the experimental test is carried out employing contact and non-contact sensing equipment to capture the vibration characteristics of the system. The experimental scenarios are defined using both intact and damaged models in two pinned and fixed supporting condition. The free damping response of the structure is extracted by RD method and employed for training the ANN neurons. The proposed ANN-RDT method is compared with the multimode random decrement technique (MRDT) and analytical mode decomposition- random decrement technique (AMD-RDT) method in damage detection process considering two error indexes. It is shown that the present method performs better than the MRDT and AMD-RDT. According to the results, the proposed approach is shown to be effective for diagnosing the presence of damage in both specified supporting systems. The trained algorithm performed more successful in the scenarios with pinned conditions with a damage closer to the supports. As indicated, the efficiency of the method is highly sensitive to location of the damage and sensors along with the type of the support. The experimental non-contact data is also shown to be significantly beneficial to utilize a simpler linear equation and also to gain the system dynamic characteristics.

Detection of CRTS II slab track arching based on dynamic responses of the car body

Slab arching is one of the most common damages of the slab track system in Chinese high-speed railway, which causes the instability of the track structure, changes the wheel-rail dynamic characteristics, and even affects the safety. Therefore, to prevent the occurrence of the above problems, the first important step is to detect the slab arching in advance. There have been some detection methods for slab arching, but it is difficult to detect the arching under different degrees, especially for the arching in the early stage. Aiming at the current situation, this paper proposed an arching detection method based on the dynamic responses of the car body. Integrated the analytical mode decomposition and continuous wavelet transform, the arching-induced characteristics in the car body vertical acceleration data, calculated by the vehicle-track finite element model, were found. After that, the measured data from different inspection areas were used for arching detection based on the discovered characteristics. The results showed that the amplitude of the component of the wavelength from 4 m to 6 m of the car body vertical acceleration could be used for slab arching detection. The method has good adaptability to different arching degrees. In practice, the proposed method can be used to detect slab arching, thus guide scientific maintenance.

Application of transient transport analysis method for modulation experiment

A transient TRansport Analysis method for Modulation (t-TRAM) has been developed. This method consists of two methods. One is an instantaneous modulation analysis method using the Hilbert transform (HT) with the analytical mode decomposition (AMD). In the modulation experiments, plasma transport can be changed periodically by modulated external input. Profiles of the modulation amplitude and phase change in time due to the change in the plasma transport. The HT with AMD method can evaluate an instantaneous analytic signal in the presence of changes in the modulation amplitude and phase in time. The other is a transport analysis method to evaluate the diffusion coefficient and the convection velocity from the analytic signal. The t-TRAM has enabled us to evaluate a momentum diffusion coefficient and momentum convection velocity in the presence of a momentum source. The t-TRAM is applied to momentum modulation experiments in JT-60U. The evaluation reveals that a normalized momentum flux has a linear dependence on a normalized momentum gradient during a half cycle of the modulation.

Damping characteristics of single-layer aluminum alloy reticulated spatial structures based on improved modal parameter identification method

An improved identification method is proposed for the modal parameter identification of multi-modal vibration attenuation signals based on the analytical mode decomposition and the particle swarm optimization. Through examples of analog signals, it is proved that the proposed method can identify modal parameters under a strong colored noise environment. Field tests were carried out on four in-service aluminum alloy reticulated structures to obtain the acceleration response of the structures. The improved identification method proposed in this paper is used to identify the modal parameters of each acceleration response curve, based on which the damping characteristics of the aluminum alloy reticulated structures are analyzed. The results show that the damping characteristics of such structures obey a three-stage change rule, with the increase of the acceleration amplitude. In addition, a practical calculation method of the damping ratios of aluminum alloy reticulated structures is proposed on the basis of the experimental results.

Enhanced vibration decomposition method based on multisynchrosqueezing transform and analytical mode decomposition

This paper proposes an enhanced vibration decomposition approach based on analytical mode decomposition (AMD) and multisynchrosqueezing transform (MSST). Although AMD-based low-pass filter has been applied for signal decomposition with time-varying cutoff frequencies, these cutoff frequencies are usually manually selected from the wavelet scalogram of the target signal. This process therefore significantly reduces the computational efficiency and could affect the accuracy of using AMD-based low-pass filter for non-stationary signal analysis. To overcome this problem, in this study, MSST with a time-varying cutoff frequency detection algorithm is used to automatically define the time-varying bisecting frequencies for the AMD analysis. Once the time-varying cutoff frequencies are identified, AMD can be used to adaptively decompose the non-stationary signal into individual components. To investigate the effectiveness of the proposed approach, termed as MSST–AMD, for vibration signal decomposition and its application, numerical studies on a non-stationary signal with overlapped frequency components are conducted. To further apply the proposed approach for structural vibration response analysis, a three-story shear-type structure with varying stiffness subjected to earthquake excitations is simulated in this study for instantaneous modal parameter identification. In experimental verifications, the proposed MSST–AMD approach combined with a damage index is further extended to evaluate the damage severity of a structure under earthquake excitations. The results in both numerical simulations and experimental validations demonstrate that the proposed approach is reliable and accurate for non-stationary signal analysis and vibration decomposition, which can be further used for instantaneous modal parameter identification and structural damage detection.

Monitoring dynamic characteristics of 600 m+ Shanghai Tower during two consecutive typhoons

Though the dynamic performance of high-rise buildings under wind has been widely investigated, there have been relatively limited studies focusing on the wind effects on 600 m+ super high-rise buildings based on real measured data during typhoons. This paper presents the field measurement results of structural dynamic characteristics and wind-induced responses of the Shanghai Tower with a height of 632 m during two successive typhoons, from August 12 to 18, 2018. Additionally, based on the analytical mode decomposition method, a modified discrete-time Fourier transformation method combined with moving window technology in time domain is developed to analyze the time-varying characteristics of natural frequencies. The relationship between the mean wind speed and acceleration amplitudes is investigated as well. A numerical experiment is carried out to verify the effectiveness of the random decrement technique, by using which the time-varying average damping ratios of the first mode associated with the Shanghai Tower are identified. In addition, the damping ratios do not exhibit an increasing trend with the increase of vibration amplitudes without the contribution of the tuned mass damper. It recommends that the critical damping ratios under high vibration amplitude are 2.5%–3.0% when the damper is active and 0.5%–1.0% when the damper is inactive. The analytical results can provide useful information for the dynamic characteristics as well as the wind-resistant design for 600 m+ super high-rise buildings.

Feature extraction by enhanced analytical mode decomposition based on order statistics filter

The methods of mode decomposition based on the amplitude of spectrum are widely used in the fault diagnosis of bearings and gears in rotating machinery such as centrifuges, slurry pumps, fans, etc. Analytical mode decomposition with excellent filtering could set the bisecting frequency to distinguish useful modes. However, the vibration signal of equipment in actual operation is complex. This paper is devoted to the research of a novel spectral segmentation mode decomposition method. The proposed enhanced analytical mode decomposition takes advantage of the trend of spectrum fluctuations. In order to obtain the most critical bisecting frequency, the trend spectrum estimation method was proposed based on order statistics filter. The filtering effect of enhanced analytical mode decomposition was verified by the simulated signal. The experimental results show that the proposed method is efficient and the bearing inner and outer ring faults in the rotating machine can be successfully extracted.

Bridge Damage Detection Using Quasi-Static Component of Moving Vehicle-Induced Dynamic Response

The critical signal component extracted from the bridge response caused by a moving vehicle is normally used to construct damage index for damage detection. The dynamic response of bridges subjected to moving vehicle includes several components, among which the quasi-static component reflects the inherent characteristics of the bridge. In view of this, this paper presents a bridge damage detection method based on quasi-static component of the moving vehicle-induced dynamic response. First, damage-induced changes of the natural-frequency component, moving-frequency component and quasi-static component responses are investigated via a simply-supported beam bridge. The quasi-static component response is proved to be less sensitive to the moving velocity of the load and more suitable for damage detection. Subsequently, a quasi-static component response extraction method is proposed based on analytical mode decomposition (AMD) and moving average filter (MAF). The extracted quasi-static component response is further employed to localize and quantify damages. Finally, numerical simulations are conducted to examine the feasibility, accuracy and advantages of the proposed damage detection method. The results indicated that the proposed method performs well in different damage scenarios and is insensitive to the moving velocity of the load and road roughness.

Application of adaptive wavelet transform based multiple analytical mode decomposition for damage progression identification of Cable-Stayed bridge via shake table test

Extracting useful information (damage existence, location, identification, and quantification) from measured signals for damage identification is critical in structural health monitoring, while time-varying nature of most signals often require huge efforts. In this paper, adaptive wavelet analysis AWT is first introduced as a preprocessing approach of clearer, smoother and more accurate time–frequency representation. Optimized analytical mode decomposition (AMD) is then utilized for signal component extraction, with the help of AWT for bisecting frequency determination. Examples of time-varying signals of sinusoidal function and Duffing systems are used to illustrate the advantages of the algorithm, which proves to be successful in signal decomposition. Multiple AMD (MAMD) with the optimized algorithm is then utilized together with AWT for signal decomposition and system identification of the shake table test of a 1/20-scale cable-stayed bridge model. The extracted stiffness and damping coefficients retain a preliminary indication of the damage progression during the earthquake input.

Discrete analytical mode decomposition with automatic bisecting frequency selection for structural dynamic response analysis and modal identification

Analytical mode decomposition (AMD) is one of dynamic response decomposition methods. However, the discretization of the dynamic responses and the selection of the bisecting frequency may cause the failure of the decomposition. In this study, the discrete analytical mode decomposition (DAMD) is investigated. In addition, an automatic bisecting frequency selection algorithm based on the auto-regressive power spectrum is proposed to effectively extract modal responses from the measured dynamic response. The efficiency of the proposed method is verified by a simulated dynamic signal with amplitude decays. Moreover, a 36-story frame structure with closely spaced modes subjected to a Gaussian white noise is simulated as a numerical example, and the dynamic responses of the frame structure are obtained based on the numerical simulation. The individual modal responses of the frame structure considering noise effect are effectively extracted by using the proposed method. Finally, the dynamic responses of a steel-concrete composite girder bridge are measured in the field under operational conditions. It is demonstrated that the measured dynamic responses are effectively decomposed into the modal responses. Based on the extracted modal responses, the modal parameters including natural frequencies, damping ratios and modal shapes of the 36-story frame structure and the tested bridge are further successfully identified accordingly.

Simplified and fast method without considering filter for voltage flicker detection

Voltage fluctuations caused output variation in the distributed energy system (such as solar, photovoltaic, and wind) produce flickers. The extraction of voltage flicker envelope parameters and accurate calculation of voltage flicker values are important for voltage flicker detection. Traditional digital filters need to be calculated according to the sampling frequency before they can be designed so that the flicker meter can only sample at a fixed frequency. To overcome the shortcomings of digital filters, a new method for measuring flickers is presented in this study. The proposed method uses analytical mode decomposition (AMD) based on spectral correction and a novel constructed mutual convolution window. The voltage flicker envelope can be extracted using an AMD method, which can replace the filter used in traditional methods, it can be analysed to obtain the corrected spectrum, which is based on an improved fast Fourier transform. The proposed method simplifies the voltage flicker detection process and exhibits high detection accuracy, which with lower detection relative error and stronger anti-interference ability. The simulation analysis and experimental results show that this approach can effectively overcome problems associated with voltage flicker measurements, such as single modulation wave frequency change and multi-frequency modulation wave fluctuation.

Time–Frequency Signal Processing for Integrity Assessment and Damage Localization of Concrete Piles

This paper presents a new integrity assessment and damage localization method for piles based on one-dimensional wave propagation theory by integrating the analytical mode decomposition (AMD), recursive Hilbert transform (RHT) and complex continuous wavelet transform (CCWT) into a single assessment tool. The AMD is first used as a band pass filter to extract the mono-component over a frequency band of interest from the response of a pile head, aimed at attenuating the interference from various noisy signals. Then, the mono-component signal is demodulated into a purely frequency-modulated signal by means of RHT, which greatly reduces the interferences from the amplitude-modulated function. Finally, the CCWT is utilized to process the frequency-modulated signal and to calculate phase angles; the latter are subsequently mapped into the time–frequency domain to localize pile damage. The methodology is verified by a numerical example, in which a concrete pile is modeled by the finite element method considering the soil-pile interaction, and by an experimental case study on an actual pile. The results from the numerical and experimental examples demonstrate that the proposed method improves the efficiency of damage identification when compared with other three methods ([Formula: see text], [Formula: see text] and CCWT). In addition, the proposed method enables the localization of damage in full-scale piles situated in soil with an acceptable engineering accuracy by mutual validation with other pile integrity assessment methods, e.g. the ultrasonic emission method.