Frequency Domain Decomposition Algorithm Research Articles

Modal identification from turbulence response based on improved frequency domain decomposition

Turbulence excitation is an unavoidable form of excitation in flutter flight tests, and it is also a necessary and effective excitation method in high-speed flights, dives, other high-risk test, and high-frequency modal information mining. However, because the turbulence excitation signals are unmeasurable in the time domain, although the turbulence response contains rich and valuable flutter test information, the randomness and low quality of the data often cause difficulties in modal analysis. Therefore, an improved frequency domain decomposition algorithm for turbulence response processing is proposed in this paper. First, due to the irrelevancy of the atmospheric excitation, the power spectral density function matrix of the multi-channel turbulence response is subjected to singular value decomposition. There is a mathematical relationship between the maximum singular value curve and the system frequency response function. Second, the modal assurance criteria are used to calculate the maximum singular value of a single-degree-of-freedom system. Finally, an orthogonal polynomial method is applied to fit the maximum singular value curve, and the system identification is performed directly in the frequency domain. The simulated data and a certain type of aircraft flutter flight test data are used to verify the proposed method, and the results confirm the effectiveness and engineering applicability of the method developed in this work.

Performance of hybrid decomposition algorithm under heavy noise condition for health monitoring of structure

In this paper, a hybrid damage detection technique involving a combination of variational mode decomposition (VMD) and frequency domain decomposition (FDD) has been applied to study the effectiveness of damage detection in presence of heavily noise contaminated environment. Damage of small magnitude has been tested under Gaussian pulse noise ranging from 0 to 100% for damage analysis. FDD, a signal processing algorithm, has system identification capability in the presence of noise but requires the output acceleration data from all the sensors installed in the nodes of a structure to identify damage. To reduce the number of sensor data needed to identify damage, wavelet-based algorithms have been used to obtain intrinsic mode functions (IMFs) from single sensor output. These IMFs are then fed to FDD algorithm to obtain the natural frequencies of the structure. For comparison purpose, the algorithms (empirical mode decomposition (EMD) + FDD, and VMD + FDD) have been applied to ASCE benchmark building, which has been set as a common platform, using sensor data of first storey. It was observed that the VMD + FDD gives satisfactory damage identification results for 100% noise contamination whereas EMD + FDD was unable to identify damage accurately for noise above 20%. The robustness of VMD + FDD has been established for a different type of noise, random-valued impulse noise, applied on the benchmark structure for detecting the structural parameters. The hybrid algorithm was also checked for system identification using the sensor data of fourth storey to establish its robustness against the sensitivity of the sensor location.

Operational Modal Analysis of Damage Gear

As natural frequencies and mode shapes are often a key to understanding dynamic characteristics of structural elements, modal analysis provides a viable means to determine these properties. This paper investigates the dynamic characteristics of a healthy and unhealthy condition of a commercially used helical gear using the Frequency Domain Decomposition (FDD) identification algorithm in Operational Modal Analysis (OMA). For the unhealthy condition, a refined range of percentage of defects are introduced to the helical gear starting from one (1) tooth being defected (1/60 teeth) to six (6) teeth being defected (6/60 teeth). The specimen is tested under a free-free boundary condition for its simplicity and direct investigation purpose. Comparison of the results of these varying conditions of the structure will be shown to justify the validity of the method used. Acceptable modal data are obtained by considering and accentuating on the technical aspects in processing the experimental data which are critical aspects to be addressed. The natural frequencies and mode shapes are obtained through automatic and manual peak-picking process from Singular Value Decomposition (SVD) plot using Frequency Domain Decomposition (FDD) technique and the results are validated using the established Modal Assurance Criterion (MAC) indicator. The results indicate that OMA using FDD algorithm is a good method in identifying the dynamic characteristics and hence, is effective in detection of defects in this rotating element.

Ambient Vibration Testing of a Pedestrian Bridge Using Low-Cost Accelerometers for SHM Applications

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

Enhanced frequency domain decomposition algorithm: a review of a recent development for unbiased damping ratio estimates

Enhanced frequency domain decomposition (EFDD) is one of OMA methods and has received significant interest from the engineering community involved in the identification of the modal structure. The great attention towards this method is driven by its capability as a user-friendly and fast processing algorithm. However, this method has drawbacks in providing accurate identification of damping ratios, despite natural frequencies and mode shapes can be computed through assuredly and reasonably accurate estimates. The exact practical computation of modal damping is still an open issue, often leading to biased estimates since the errors are coming from every step in EFDD procedures and mainly due to signal processing. Thus, the computation of modal damping becomes tremendously vital in structural dynamics because modal damping is one of the critical parameters of resonance. This review aims to provide relevant essential information on modal damping for a reliable estimation, reduce uncertainties and define error bounds. A literature review has been carried out to find the best practice criteria for modal parameter identification, in particular, modal damping ratio.

Assessment of Frequency versus Time Domain enhanced technique for response-only modal dynamic identification under seismic excitation

In the present study, response-only system identification is explored towards estimating modal dynamic properties of buildings under earthquake excitation. Seismic structural response signals are adopted with two different implemented Operational Modal Analysis (OMA) techniques, namely a refined Frequency Domain Decomposition algorithm and an improved data-driven Stochastic Subspace Identification (SSI-DATA) procedure, working in the Frequency Domain and in the Time Domain, respectively. These algorithms are specifically conceived to operate with seismic structural responses and at simultaneous heavy damping (in terms of identification challenge), towards achieving consistent estimations of natural frequencies, mode shapes and modal damping ratios. Classical OMA assumptions shall not contemplate short-duration, non-stationary earthquake-induced response signals. Nevertheless, the present enhanced output-only algorithms allow for estimating all strong ground motion modal parameters. First, a linear three-storey frame structure under ten selected earthquake base-excitations is considered, in order to assess the two OMA techniques at synthetic seismic response input. Comprehensive results are presented, by comparing the two developed methods, between achieved modal estimates and sought target values. Second, an existing instrumented building (CESMD database) is analyzed, by adopting real seismic response signals, reaching again effective modal estimates and corroborating the previous necessary condition analysis. According to this investigation, best up-to-date, re-interpreted, output-only techniques may effectively be used for potential Structural Health Monitoring purposes in the Earthquake Engineering range.

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This article assesses numerically the potential of two different spectral estimation approaches supporting non-uniform-in-time data sampling at sub-Nyquist average rates (i.e. below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks for operational modal analysis of civil engineering structures. This consideration relaxes transmission bandwidth constraints in wireless sensor networks and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements, and structural mode shapes are extracted using the frequency-domain decomposition algorithm. The first approach relies on the compressive sensing theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e. have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given compression rate, the performance of the compressive sensing–based approach is detrimentally affected by signal sparsity, while the power spectrum blind sampling–based approach achieves modal assurance criterion >0.96 independently of signal sparsity for compression ratios as low as 22% the Nyquist rate. It is concluded that the power spectrum blind sampling–based approach reduces effectively data transmission requirements in wireless sensor networks for operational modal analysis, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity.

Damping estimation of large wind-sensitive structures

The adequacy of two identification techniques to accurately estimate the modal damping ratios (MDRs) from ambient vibration records is assessed for long-span suspension bridges with eigen frequencies close to or below 0.1 Hz. The first method is an automated covariance driven stochastic subspace identification (SSI-COV) algorithm and the second one is an automated Frequency domain decomposition algorithm (AFDD). The bias and the dispersion of the identified MDRs are first assessed using simulated bridge vibration records and then investigated using full-scale acceleration data obtained on the Lysefjord Bridge, Norway.The simulated data showed that record durations of 60 min provided up to three times more accurate estimates of the MDRs than if the more common record duration of 10 min is used. For the full-scale acceleration records and a duration of 60 min, the MDR estimates showed a relatively large dispersion with a non-Gaussian distribution, suggesting that the median value of the MDR may be more reliable than the arithmetic mean. The AFDD algorithm was observed to estimate the MDRs with a larger bias than the SSI-COV method. This suggests that the frequency-domain based approach is not well suited for the modal parameters identification of long suspension bridges with eigen-frequencies around and below 0.1 Hz.

Earthquake structural modal estimates of multi-storey frames by a refined Frequency Domain Decomposition algorithm

This paper targets the frequency domain identification of current structural modal properties under earthquake excitation. A new refined Frequency Domain Decomposition (rFDD) algorithm is implemented towards the output-only modal dynamic identification of heavy-damped frame structures, which are subjected to a wide set of strong ground motions. In fact, both seismic excitation and/or high damping values shall not fulfil traditional FDD assumptions. Despite that, with the present rFDD implementation quite limited errors in the modal parameter estimates have been achieved, including for the modal damping ratios (ranging from 1% to 10%). At first, the identification technique is formulated and explored analytically, by proving its potential effectiveness with seismic response input. Then, all strong motion modal parameters are consistently identified. As a fundamental necessary condition, synthetic response signals are adopted. These have been generated prior to dynamic identification from computed numerical seismic responses of a set of shear-type frames. The efficiency of the present original implementation is highlighted, by proving that consistent rFDD modal dynamic identification of structures at seismic input and simultaneous heavy damping looks feasible. Thus, the paper delivers a robust method for inspecting current structural modal properties of frame buildings under earthquake excitation and for observing their possible variation along experienced seismic histories.

Experimental Studies on Damage Detection in Frame Structures Using Vibration Measurements

This paper presents an experimental study of frequency and time domain identification algorithms and discusses their effectiveness in structural health monitoring of frame structures using acceleration input and response data. Three algorithms were considered: 1) a frequency domain decomposition algorithm (FDD), 2) a time domain Observer Kalman IDentification algorithm (OKID), and 3) a subsequent physical parameter identification algorithm (MLK). Through experimental testing of a four-story steel frame model on a uniaxial shake table, the inherent complications of physical instrumentation and testing are explored. Primarily, this study aims to provide a dependable first-order and second-order identification of said test structure in a fully instrumented state. Once the characteristics (i.e. the stiffness matrix) for a benchmark structure have been determined, structural damage can be detected by a change in the identified structural stiffness matrix. This work also analyzes the stability of the identified structural stiffness matrix with respect to fluctuations of input excitation magnitude and frequency content in an experimental setting.

Experimental Studies on Damage Detection in Frame Structures Using Vibration Measurements

This paper presents an experimental study of frequency and time domain identification algorithms and discusses their effectiveness in structural health monitoring of frame structures using acceleration input and response data. Three algorithms were considered: 1) a frequency domain decomposition algorithm (FDD), 2) a time domain Observer Kalman IDentification algorithm (OKID), and 3) a subsequent physical parameter identification algorithm (MLK). Through experimental testing of a four-story steel frame model on a uniaxial shake table, the inherent complications of physical instrumentation and testing are explored. Primarily, this study aims to provide a dependable first-order and second-order identification of said test structure in a fully instrumented state. Once the characteristics (i.e. the stiffness matrix) for a benchmark structure have been determined, structural damage can be detected by a change in the identified structural stiffness matrix. This work also analyzes the stability of the identified structural stiffness matrix with respect to fluctuations of input excitation magnitude and frequency content in an experimental setting.

Identification and Damage Detection in Structures Subjected to Base Excitation

This paper presents an experimental study of different algorithms for the health monitoring of frame structures subjected to base excitation (e.g. earthquake ground motion). These algorithms use only the acceleration time histories of the input and of the response output and are tested for the identification of the dynamic characteristics of the structure (natural frequencies and damping ratios) and for detecting and quantifying any possible structural damage that occurs in the frame. Three algorithms were considered: (1) a frequency domain decomposition algorithm, (2) a time domain Eigensystem Realization Algorithm together with Observer Kalman Identification algorithm, and (3) a subsequent physical parameter identification algorithm (MLK). Through extensive experimental testing of a four-story steel frame model on a uniaxial shake table, the performance of the various methods as well as the inherent complications of physical instrumentation and testing are explored.