Identification Of Damping Ratios Research Articles

Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

Structural Damping Ratio Identification through Iterative Frequency Domain Decomposition

The frequency domain decomposition method (FDD) is a commonly used method to identify structural modal parameters and analyze the structural dynamic performance. Although FDD has a high identification accuracy in natural frequencies and mode shapes, damping ratios cannot be identified accurately. The logarithmic decay method to identify the damping ratio in FDD needs the transformation from a narrow frequency band to the time domain, which leads to the loss of the corresponding mode outside the narrow band and add other modes in the narrow band. In this paper, an iterative frequency domain decomposition method (iFDD) is proposed to identify the structural damping ratio in frequency domain. Firstly, the natural frequencies and mode shapes are obtained by the FDD method, and the damping ratios during this identification process are assumed to be unknowns. Then, the natural frequencies, mode shapes, and unknowns are substituted into the output power spectrum formula to construct nonlinear equations. The damping ratios are obtained by solving the equations using iterative optimization methods. Finally, a numerical example and benchmark model are employed to validate the effectiveness of the proposed method. The results showed that the proposed iFDD method can identify the damping ratio precisely in the frequency domain, which is better than the traditional FDD performance.

Identification Algorithm and Improvement of Modal Damping Ratios for Armature Assembly in a Hydraulic Servo-Valve with Magnetic Fluid

The high-frequency vibration and resonance of armature assembly in the hydraulic servo valve are the main reasons for instability and failure. Magnetic fluid (MF) operating in the squeeze mode can be taken as an effective damper for resonance suppression in the servo valve. Due to excitation difficulty and the low signal-to-noise ratio of high-frequency vibration signals, the capability of MF to modify multiple-order modal damping ratios in a multi-degree-of-freedom system is still unclear. To reveal the mechanism of magnetic fluid for improving modal damping ratios, an algorithm for modal damping ratio identification is proposed. The modal damping ratios of the armature assembly with and without magnetic fluid are identified based on the tested resonance free decay responses. Four resonance frequencies of armature assembly are observed, and the corresponding damping ratios are identified. The equivalent modal damping ratios due to squeeze flow of MF are obtained. The results show that the proposed algorithm can identify damping ratios with an accuracy of up to 98.79%. The damping ratios are improved by double or more due to the magnetic fluid, and the maximum resonance amplitudes are significantly reduced by 65.2% (from 916.5 μm to 318.6 μm).

Damping ratio identification using attenuation responses extracted by time series semantic segmentation

Damping ratio is an essential dynamic characteristic of bridge structures, and its properties have still not been well understood due to the difficulties in accurate calculation with structural health monitoring (SHM) data. It is widely accepted that the exponential attenuation (EA) method using free attenuation responses is a reliable way to calculate damping ratio. To identify the damping ratio from SHM data with EA method, a time series semantic segmentation method is proposed in this paper to extract free attenuation segments from the massive data of monitored acceleration responses. A labeled semantic dataset is firstly constructed based on the long-term monitoring data of the Z24 bridge which is a continuous bridge widely used as a benchmark model for SHM, and the labeling standard is introduced to illustrate the preference of selecting desirable attenuation segments. Then an adapted U-net model is developed and trained with the constructed dataset, and key hyper-parameters including the configuration of convolutional kernel and decision boundary are investigated and determined to meet the requirement of processing time series data of acceleration responses. A large number of attenuation segments have then been extracted by the well-trained model, based on which the damping ratio of the 1st vibration mode in 10 months is obtained with the EA method. The identified damping ratios are found reliable as compared with those identified by the stochastic subspace identification method, thus enabling further investigation of the properties of damping ratio. Finally, the influence of the temperature variation is explored, revealing an obvious correlation relationship between the temperature and the damping ratio. The results of this study not only provide a novel method to calculate damping ratio with SHM data but also could deepen the understanding of damping ratio properties and serve as a reference for more reasonable utilization of the damping ratio in structural dynamic analysis or condition assessment.

Damping parameter estimation using topological signal processing

Energy is dissipated in engineering systems through a variety of different, typically complex, damping mechanisms. While there are several common damping models with physical interpretations, it is often necessary to examine noisy, experimental data in order to identify and fit the damping parameters. One class of methods fits the damping parameters based on the decay envelope of the signal’s peaks based on some assumed damping mechanism. While there exist results in the literature, especially for viscous damping, to guide the selection of the spacing between the peaks for the optimum damping ratio identification, these methods often overlook the difficult and classic problem of identifying the signal’s “true” peaks in the presence of noise. Therefore, in this work we utilize tools from Topological Data Analysis (TDA) to address the problem of robust and automatic power-law damping identification from decay or free-response function. The decay function can be obtained from initial excitation, or using random decrement method thus making our approach a viable tool for operational modal analysis. We present our approach using one-dimensional examples, and describe extensions to multiple degree of freedom systems. Our damping identification framework uses the persistent homology of zero dimensional (0D) sub-level sets, one of the main tools of TDA, to separate the true topological features of the signal (i.e. the peaks and valleys) from measurement noise. Using persistent homology we are able to automatically represent the damped response in a noise-robust, two-dimensional summary of the peak–valley pairs called the persistence diagram. The persistence diagram is then analyzed using two methods: (1) a theoretical analysis of the significant persistence pairs and (2) function fitting to the persistence space. We present theoretical results that establish the class of general power-law damping terms where our approach applies, and develop specific tools to identify damping parameters for viscous, coulomb, and quadratic damping. We show that our approach is computationally fast, operates on the raw signal itself without requiring any pre-processing, and reduces the number of decisions needed by the user to perform the needed calculations. The results are validated using a combination of numerical and experimental data.

Experimental study of corroded RC beams: dissipation and equivalent viscous damping ratio identification

Corrosion of steel reinforcement is one of the most common durability issues for reinforced concrete (RC) structures, especially when located in marine areas. The study of the mechanical consequences of this pathology is of great importance to assess their performance. Experimental campaigns have been carried out on corroded structures. So far, assessing quasi-static behavior or predicting the dynamic response of structures have been based exclusively on quasi-static loadings. In particular, the dissipated energy and the damping capacity, which are important features to study when assessing the seismic performance of corroded RC members, are evaluated based on quasi-static loadings. The objective of this study is to characterize these two significant engineering demand parameters (EDP) using both quasi-static and dynamic tests. To reach this goal, an experimental campaign is conducted on large-scale RC beams. The corroded and non-corroded RC beams are subjected to a four-point bending loading and to dynamic loading keeping the same loadings and boundary conditions. The dynamic loading is applied on the specimen by means of the AZALEE shaking table. In this paper, a brief description of the experimental campaign is made. Then, results showing the influence of the corrosion rate on the dissipation capacity of RC structures are exposed. Especially, the consistency between quasi-static and dynamic results is assessed and discussed.

Bridge Damping Extraction Method from Vehicle–Bridge Interaction System Using Double-Beam Model

When vehicles interact with a bridge, a vehicle–bridge interaction (VBI) system is created. The frequency and modal shape of VBI systems have been widely studied, but the damping of VBI systems has not been adequately investigated. In recent years, several incidents of abnormal bridge vibration due to changes in bridge damping have occurred and aroused widespread concern in society. Damping is an important evaluation index of structural dynamic performance. Knowing the damping ratio of a VBI system is useful for analyzing the damping changes while a bridge is in service. This paper presents a method to extract bridge damping values from a VBI system, which can serve as a guide for bridge damping evaluation. First, a double-beam theoretical model was used to simplify the VBI system for cases involving uniform traffic flow. The damping ratio equation for the simplified VBI system was obtained using the extended dynamic stiffness method (EDSM). A double-beam finite element model and a VBI finite element model were established. The damping ratios of the two models were separately calculated and then compared with the simplified VBI model results. The results verified the accuracy of the simplified method. This paper then explains that bridge damping values can be extracted by estimating the equivalent traffic flow parameters and using the damping formula for the simplified VBI system. The bridge damping ratios extracted using this method in an engineering case ranged from 0.75% to 0.78%, which is smaller than the range that was directly identified using monitoring data (0.83–1.19%). The results show that the method can effectively extract bridge damping ratios and improve damping ratio identification.

A fast damping ratio identification method for rotating machinery based on the singular value of a directional power spectra density function matrix

It is of great importance to accurately evaluate the stability margin of a turbomachine both in shop tests and in operation. The damping ratio of the first forward whirl mode is the key indicator of rotordynamic stability. In this paper, a fast operational modal analysis (OMA) technique based on the singular value of the directional power spectra density function (dPSDF) matrix was developed to estimate the damping ratios of the first forward and backward whirl modes. Numerical simulations and experiments were carried out to verify the accuracy of this method on a high-speed test rig. Moreover, the dPSDF-based method was compared to two conventional OMA methods - data-driven and covariance-driven stochastic subspace identification (SSI) methods - resulting in more stable and accurate estimates for the damping ratio along with a much faster identification time (less than 0.5 s). This study provides an accurate and fast method for performing stability shop tests for turbo machines and stability online monitoring.

Numerical and experimental verifications on damping identification with model updating and vibration monitoring data

Identification of damping characteristics is of significant importance for dynamic response analysis and condition assessment of structural systems. Damping is associated with the behavior of the energy dissipation mechanism. Identification of damping ratios based on the sensitivity of dynamic responses and the model updating technique is investigated with numerical and experimental investigations. The effectiveness and performance of using the sensitivity-based model updating method and vibration monitoring data for damping ratios identification are investigated. Numerical studies on a three-dimensional truss bridge model are conducted to verify the effectiveness of the proposed approach. Measurement noise effect and the initial finite element modelling errors are considered. The results demonstrate that the damping ratio identification with the proposed approach is not sensitive to the noise effect but could be affected significantly by the modelling errors. Experimental studies on a steel planar frame structure are conducted. The robustness and performance of the proposed damping identification approach are investigated with real measured vibration data. The results demonstrate that the proposed approach has a decent and reliable performance to identify the damping ratios.

Predominant period and equivalent viscous damping ratio identification for a full‐scale building shake table test

SummaryThe predominant period and corresponding equivalent viscous damping ratio, also known in various loading codes as effective period and effective damping coefficient, are two important parameters employed in the seismic design of base‐isolated and conventional building structures. Accurate determination of these two parameters can reduce the uncertainty in the computation of lateral displacement demands and interstory drifts for a given seismic design spectrum. This paper estimates these two parameters from data sets recorded from a full‐scale five‐story reinforced concrete building subjected to seismic base excitations of various intensities in base‐isolated and fixed‐base configurations on the outdoor shake table at the University of California, San Diego. The scope of this paper includes all test motions in which the yielding of the reinforcement has not occurred and the response can still be considered ‘elastic’. The data sets are used with three system identification methods to determine the predominant period of response for each of the test configurations. One of the methods also determines the equivalent viscous damping ratio corresponding to the predominant period. It was found that the predominant period of the fixed‐base building lengthened from 0.52 to 1.30 s. This corresponded to a significant reduction in effective system stiffness to about 16% of the original stiffness. The paper then establishes a correlation between predominant period and peak ground velocity. Finally, the predominant periods and equivalent viscous damping ratios recommended by the ASCE 7‐10 loading standard are compared with those determined from the test building. Copyright © 2017 John Wiley & Sons, Ltd.

Modal damping ratio analysis of dynamical system with non-stationary responses

During the long term monitoring of the structure, the damping ratio reflects the characteristics of the structure from perspective of energy loss, and its changes can reflect the structural damages to some extent. But in the structural modal analysis based on the prototype measurement, the damping ratio identification results are difficult to identify, especially for the non-stationary structural responses, besides, ICA loses accuracy in the presence of higher-level damping. In allusion to these problems, a modal identification method based on the stationary filter-time frequency independent component analysis (filter-TFICA) is proposed. First a stationary filter using moving average is used to eliminate the non-stationary components. Then the modal identification of mooring system is incorporated into the blind source separation formulation where TFICA is introduced. The validity of the proposed method is confirmed through the identification of a multi degree of freedom numerical simulation system under non-stationary random excitations. Further, the prototype measurement data of the floating production, storage and offloading (FPSO) single point mooring system are analyzed. Compared with the traditional method, the differences of identified damping ratios at the same frequency range by the proposed method are smaller. The distribution of identified modal frequencies is more scattered and the mutually coupled modes are decoupled well. Each of the calculated motion tracks corresponding to the mode shapes presents single form of motion more prominently.

Virtual testing for modal and damping ratio identification of submerged structures using the PolyMAX algorithm with two-way fluid–structure Interactions

Based on the powerful Computational Structural Dynamics method coupled to a Computational Fluid Dynamics approach, the PolyMAX algorithm is used along with the simulation of two-way fluid–structure interactions, as a new virtual testing method for estimating the structural modal parameters and damping ratios of a vibrating structure in either air or some other fluid. The viscosity and motion of fluid are accounted for, as are the shape of the flow passage and a variety of boundary conditions. The method is shown to be able to simulate the vibration of a structure within a real operating environment in which the structure experiences a specified excitation load while the vibration responses of the structure are obtained through a two-way FSI model. Based on the PolyMAX method for estimating the modal parameters, these vibration responses are processed and analyzed. Finally, the dynamic parameters (i.e., the natural frequencies and the damping ratios) of the vibrating structure are identified. For validation, the natural frequencies and damping ratios of two simple submerged cantilever plates were simulated both in air and water and the simulated results were found to agree closely with experimental data.

Damping ratio identification using a continuous wavelet transform to vortex-induced motion of a Truss Spar

The paper presents an application of the continuous wavelet transform (CWT), a time-frequency method based on Gabor wavelet function and widely used in many engineering fields, in ocean engineering for the first time. The advantage of the CWT over commonly used methods like time-domain and frequency-domain methods is its ability to decompose signals simultaneously both in time and frequency. The essential information is the wavelet ridge where the modal parameters like the damping ratio and frequency can be extracted. This paper developed an algorithm to extract the wavelet ridge from the wavelet transform. The method is validated by a numerical example which is similar to the experimental data. Finally the method is applied to estimate the damping ratio and frequency of a Truss Spar in vortex-induced motion. The results indicate that the CWT method performs remarkably well.

Synchrosqueezed wavelet transform for frequency and damping identification from noisy signals

Identification of vibration parameters from the analysis of the dynamic response of a structure plays a key role in current health monitoring systems. This study evaluates the capabilities of the recently developed Synchrosqueezed Wavelet Transform (SWT) to extract instant frequencies and damping values from the simulated noise-contaminated response of a structure. Two approaches to estimate the modal damping ratio from the results of the SWT are presented. The results obtained are compared to other signal processing methods based on Continuous Wavelet (CWT) and Hilbert-Huang (HHT) transforms. It was found that the time-frequency representation obtained via SWT is sharped than the obtained using just the CWT and it allows a more robust extraction of the individual modal responses than using the HHT. However, the identification of damping ratios is more stable when the CWT coefficients are employed.

An Identification Method for Damping Ratio of <i>In Situ</i> Building

Damping evaluation is of great importance in predicting the dynamic response of systems. To get the accurate damping ratios of a system, many identification methods have been proposed and developed. But only few of them achieved accurate results for in-situ buildings due to the fact that the responses are significantly influenced by noise. This paper proposes a new method to accurately identify the damping ratios of in-situ buildings. The method is based on ambient excitation technique which requires no artificial excitation applied to SSI system and to measure output-only. The damping ratio identification is then performed by combining the improved random decrement method and Ibrahim time domain method. To demonstrate the validity of the proposed approach, a case study is performed and the results are compared with the conventional peak-peaking method results. The results show the proposed method can effectively identify the modal parameter of either frequencies or damping ratios of in-situ buildings subjected to ambient excitation.

An Identification Method for Damping Ratio of <i>In Situ</i> Building

Damping evaluation is of great importance in predicting the dynamic response of systems. To get the accurate damping ratios of a system, many identification methods have been proposed and developed. But only few of them achieved accurate results for in-situ buildings due to the fact that the responses are significantly influenced by noise. This paper proposes a new method to accurately identify the damping ratios of in-situ buildings. The method is based on ambient excitation technique which requires no artificial excitation applied to SSI system and to measure output-only. The damping ratio identification is then performed by combining the improved random decrement method and Ibrahim time domain method. To demonstrate the validity of the proposed approach, a case study is performed and the results are compared with the conventional peak-peaking method results. The results show the proposed method can effectively identify the modal parameter of either frequencies or damping ratios of in-situ buildings subjected to ambient excitation.

Some Remarks on Experimental Estimation of Damping for Seismic Design of Civil Constructions

Experimental estimation of damping is currently not a comprehensively solved problem. Although modal frequencies and mode shapes can be measured confidently and quite easily by means of dynamic tests on civil structures, an accurate identification of damping ratios needs further development. Experimental values can be characterized by large error bounds mainly because damping is strongly influenced by the magnitude of the dynamic response of a structure.In this paper, the main issues concerning identification of modal damping ratios are discussed in order to define methods for their reliable estimation, to reduce uncertainties and characterize error bounds. According to this aim, a procedure for optimized modal parameter estimation via Stochastic Subspace Identification is also proposed. Then data collected from an extensive literature review are analyzed depending on the type of structure in order to point out the main factors affecting damping. Moreover, a comparison with provisions about structural damping given in National and International seismic codes for structural design of civil structures is reported. This process demonstrates that the development of a damping database based on homogeneous and reliable estimates is required for calibration of predictive formulations to be used in the framework of performance-based seismic design.

Identification of modal damping ratios of structures with closely spaced modal frequencies

This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.