Modal Identification Algorithm Research Articles

Experimental Investigations of Damage Identification for Aluminum Foam Sandwich Beams Using Two-Step Method

In the experiment, strain gauges and dynamic signal acquisition instruments are used to collect and record data, and the stochastic subspace algorithm is used to extract the first three strain modal parameters of each case. The damage amount identified by the second natural frequency based on the modified Timoshenko beam theory is more in line with the actual situation. The damage depth of case 2 and case 4 is 2 mm, and the identified damage amount is 10% and 9%, respectively. The damage depth of case 3 and case 5 is 4 mm, and the identified damage amount is 16% and 23%, respectively. The damage location information of case 6 is well identified by using the normalized strain modal shape difference index and the enhanced strain modal shape difference index. Taking the strain response signal of case 6 as an example, it is proved that the stochastic subspace strain modal parameter identification algorithm has strong anti-interference ability under the action of 1.5 times, 4 times, and 9 times noise. In addition, the method is verified by theoretical calculation and numerical simulation, and the damage law has a high degree of coincidence with the test. The experimental results show that this method expands the theoretical basis of foam metal damage degree information identification and improves the accuracy of damage location information identification and the anti-interference of parameter identification.

Fully automated operational modal identification of regular and irregular buildings with ensemble learning

Modal identification, a type of system identification that employs modal analysis, can be automated to reduce user interference in extracting modal parameters. Modal analysis is a valuable tool for obtaining a structure's modal parameters, which define its dynamic characteristics. Operational modal identification is a specific type of modal analysis that uses only system outputs to extract modal parameters. The present study aims to introduce a fully automated modal identification algorithm to identify modal parameters for an unknown system based on its output information. The algorithm uses a stochastic subspace algorithm to extract modal parameters, requiring only the appropriate degree of the state-space model estimated using the Singular Value Criterion. Several features are used to create a feature space that separates physical and spurious modes. The Improved Distance Evaluation algorithm selects appropriate features, making the identification process more accurate and flexible. The identification algorithm employs clustering algorithms with different approaches and the Dempster-Shafer data fusion algorithm to integrate clustering algorithm results and avoid divergence among them. Due to limited data diversity for identification in cases where only one dataset is available, statistical resampling methods are used as an alternative. The proposed algorithm can identify modal parameters using only one dataset of the building structure. Signal processing, data collection, clustering, feature extraction, model reduction, and data fusion are all aspects of this algorithm. To assess its performance, four regular and irregular buildings are considered as case studies. The presented modal identification algorithm is highly accurate and robust with the repeatable result as compared to similar algorithms, with extracted modal parameters demonstrating high stability.

A Data-Driven System Identification Method for Random Eigenvalue Problem Using Synchrosqueezed Energy and Phase Portrait Analysis

The primary purpose of this research is to evaluate the uncertainty associated with modal parameter estimation for an inverse dynamic problem in which the structural parameters are random. The random nature of the structure's parameters will be reflected in the modal features of the respected system. However, this may result in additive/subtractive errors in modal parameter identification, affecting the identification technique's efficiency. With this in mind, the present study aims to develop an automated modal identification algorithm for a random eigenvalue problem. This is achieved by a recently developed advanced version of the wavelet transform (i.e., synchrosqueezing), which offers better resolution. Using this technique, the measured responses are transformed into a time-frequency plane, which is further processed by unsupervised learning using K-means clustering for quantification of the modal parameters. This automated identification is repeated for an ensemble of measurements to quantify the random eigenvalues in a statistical sense. The proposed methodology is first tested using simulated time histories of a two degree-of-freedom (dof) system. It is followed by an experimental validation using a beam whose mass matrix is random. The numerical results presented in this work clearly demonstrate the performance (i.e., in terms of efficiency and accuracy) of the proposed output-only automated data-driven identification scheme for random eigenvalue problems.

A new approach of ensemble learning in fully automated identification of structural modal parameters of concrete gravity dams: A case study of the Koyna dam

This study proposes a new automatic modal identification algorithm that identifies the system's modal parameters based on output-only data. The identification process is based on a stochastic subspace algorithm. Stochastic subspace algorithms only need the model degree to identify the modal parameters of the system. A model degree is an appropriate degree of the state-space model and it is estimated by using the Singular Value Criterion. Several clustering algorithms with different approaches have been used. The most powerful data fusion algorithm, which is called Dempster-Schaffer Theory is applied for integrating the results of the algorithms and preventing divergence of results. Furthermore, it focused on measuring the uncertainty of the identified modal parameters. In the proposed modal identification algorithm, only one data set is used for identification. In this situation, the variety of data is small and limited, and statistical resampling methods seem to be a good option. Establishing the above cycle enables the identification algorithm to identify modal parameters and quantify their uncertainty based only on a data set. This algorithm uses many fields, such as data collection, signal processing techniques, model reduction, feature extraction, clustering and data fusion. The Koyna gravity dam is selected as a case study to evaluate the performance of the developed algorithm. In the first step, a comparative study is carried out to verify the developed finite element model of the Koyna dam. Afterwards, the dam is excited by the Koyna earthquake, and dynamic responses of the dam are collected from the minimum number of points required for system identification. It is noteworthy the number of modes that are identified in this work is equal to 4 vibration modes. The maximum difference between the natural frequencies identified by the present algorithm and the finite element model does not exceed 4.33%. Also, the average difference is less than two percent, which indicates the high accuracy of the system identification algorithm. Also, all the vibration modes in the desired frequency range have been correctly identified. The results indicate that modal parameters with remarkable precision have been extracted by the modified algorithm.

Full-field modal identification using reliability-guided frequency-domain-based digital image correlation method based on multi-camera system

A multi-camera array system was established to address the limitations of traditional measurement methods in full-field modal measurement. According to the principle of binocular vision, two cameras are utilized to form a set of three-dimensional measurement subsystems, and the subsystems are calibrated to establish unity in coordinates. To improve computational efficiency, a reliability-guided frequency-domain-based digital image correlation method is proposed to optimize pixel matching and calculation path. This method incorporates the benefits of a reliability-guided strategy and an integer-pixel search method based on the frequency domain to ensure that the seed point with the optimal matching effect in the calculation area is selected. The zero-mean normalized cross-correlation coefficient is used as the criterion for determining reliability. This approach effectively avoids the problem of error transmission and reduces the need for complex operations and repeated searches in the spatial domain, thus improving computational efficiency. The matching time is reduced, the calculation efficiency of displacement signal extraction under large data volume is improved, and the obtained response signal is substituted into the modal identification algorithm to obtain the modal parameters of the structure. Ultimately, the modal test of a solar panel is performed by constructing a four-camera system, which verifies the correctness of the proposed method and has practical engineering significance.

Instantaneous amplitude and phase signal modeling for harmonic removal in wind turbines

We present a novel approach to harmonic disturbance removal in single-channel wind turbine acceleration data by means of time-variant signal modeling. Harmonics are conceived as a set of quasi-stationary sinusoids whose instantaneous amplitude and phase vary slowly and continuously in a short-time analysis frame. These non-stationarities in the harmonics are modeled by low-degree time polynomials whose coefficients capture the instantaneous dynamics of the corresponding waveforms. The model is linear-in-parameters and is straightforwardly estimated by the linear least-squares algorithm. Estimates from contiguous analysis frames are further combined in the overlap-add fashion in order to yield overall harmonic disturbance waveform and its removal from the data. The algorithm performance analysis, in terms of input parameter sensitivity and comparison against three state-of-the-art methods, has been carried out with synthetic signals. Further model validation has been accomplished through real-world signals and stabilization diagrams, which are a standard tool for determining modal parameters in many time-domain modal identification algorithms. The results show that the proposed method exhibits a robust performance particularly when only the average rotational speed is known, as is often the case for stand-alone sensors which typically carry out data pre-processing for structural health monitoring. Moreover, for real-world analysis scenarios, we show that the proposed method delivers consistent vibration mode parameter estimates, which can straightforwardly be used for structural health monitoring.

Modal Identification of Bladed Disks by Time–Frequency Analysis of the Nonsynchronous Response

Abstract In some circumstances, it is impossible to exploit resonance crossings to identify the modal properties of rotor disks. In these cases, the identification process must rely on nonsynchronous vibrations and becomes challenging for two reasons. First, the signals are weak (compared to the levels measured during resonance crossings) and random, thus an averaging procedure is necessary. Second, the dynamical system is time-variant due to the variation of the rotor speed. This paper presents a modal identification procedure formulated in the framework of the time–frequency analysis. A region of the time–frequency plane is stretched to map the system into a fictitious linear time-invariant (LTI) system. Then, the power spectral density function (PSD) of the response is computed by an averaging procedure. Finally, the modal properties are estimated through an output-only modal identification algorithm. The procedure is applied to simulated and experimental data regarding a bladed disk of a steam turbine.

An automatic real-time cable modal frequency identification and tracking algorithm by combining recursive band-pass filter and recursive Hilbert transform

Cables are essential elements in bridge engineering. The cable force is usually determined by the vibration method using the cable modal frequency. This paper proposes a real-time online identification method of cable modal frequency based on band-pass filter and Hilbert transform. A recursive form of band-pass filtering (RBF) is employed so that the original signal can be filtered for the target frequency band to obtain a single modal signal of the target order of the cable. The recursive Hilbert transform (RHT) is then used to obtain a real-time resolved signal for real-time frequency identification, allowing for real-time identification and tracking of the time-varying modal frequencies at the cable's target order. This method is more efficient than traditional time–frequency analysis methods. According to numerical simulations and actual measurement data. The method is noise-resistant and does not necessitate priori information of the order. The method allows online identification and tracking of time-varying frequency of interest at a specific order. The procedure can be applied to the real-time identification of cable incident frequencies in an online monitoring system, and can also provide a basis for further real-time identification of time-varying cable forces.

Raspberry Shake-Based Rapid Structural Identification of Existing Buildings Subject to Earthquake Ground Motion: The Case Study of Bucharest.

The Internet of things concept empowered by low-cost sensor technologies and headless computers has upscaled the applicability of vibration monitoring systems in recent years. Raspberry Shake devices are among those systems, constituting a crowdsourcing framework and forming a worldwide seismic network of over a thousand nodes. While Raspberry Shake devices have been proven to densify seismograph arrays efficiently, their potential for structural health monitoring (SHM) is still unknown and is open to discovery. This paper presents recent findings from existing buildings located in Bucharest (Romania) equipped with Raspberry Shake 4D (RS4D) devices, whose signal recorded under multiple seismic events has been analyzed using different modal identification algorithms. The obtained results show that RS4D modules can capture the building vibration behavior despite the short-duration and low-amplitude excitation sources. Based on 15 RS4D device readings from five different multistorey buildings, the results do not indicate damage in terms of modal frequency decay. The findings of this research propose a baseline for future seismic events that can track the changes in vibration characteristics as a consequence of future strong earthquakes. In summary, this research presents multi-device, multi-testbed, and multi-algorithm evidence on the feasibility of RS4D modules as SHM instruments, which are yet to be explored in earthquake engineering.

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.

An Improved Monitoring System via the Integration of Structural Health Monitoring and Earthquake Emergency Alert Technologies

As a result of the advantages it offers in construction management and maintenance, structural health monitoring for civil structures is becoming more popular in Europe and throughout the world. The main advantages of using such methods include cheaper inspections, more accurate research into the behavior of structures under dynamic loads, better seismic protection, and real-time or near-real-time observation of structural response and evolution of damage, which helps with post-earthquake scenario production and rescue efforts. As a result, Structural Monitoring Systems is a very multidisciplinary field, in which researchers from a wide variety of fields and institutions may work together to improve the effectiveness and reliability of these systems, the benefits of which are almost self-evident. Nowadays, developments in wireless sensor networks, techniques for determining modal properties, and damage detection systems are among the most urgent issues in the sector. Although modal identification and damage detection algorithms have improved, sensor technology has advanced at a faster rate.

Trend Analysis of Modal Identification based Real-time Power System Oscillations using L1 Trend Filtering

This paper is looking to show to use of system data collected from wide-area monitoring systems (WAMS). They allow monitoring of the dynamics of power systems. Among the WAMS applications, there is the modal identification algorithm, which identifies critical oscillatory modes from PMU measurements. This application permits using data processors for estimating of frequency, damping, and amplitude of dominant mode oscillations observable in a specific electric signal (e.g., active power, frequency) recorded for the analyzed period. However, since modal identification of real-time measurements is based on an online optimization, the results usually have considerable fluctuations. Thus, it is essential to consider the complementary implementation of trend analysis for acquiring convenient early-warning indicators of oscillatory problems. This consideration allows avoiding erroneous information of the systems oscillatory behavior of the system real-time that modal identification of crude results could deliver. In this paper, the application of a l1 filter for determining the trend analysis of high-dimensional data set resulted from a commercial modal identification is explored. The algorithm is applied to an oscillatory event registered by the WAMS of the Ecuadorian National Interconnected System with promising results.

Soil damping calculation of the offshore wind turbine supported by wide-shallow bucket foundation

The soil damping, which shows an obvious relationship with the foundation type and soil parameters, has a very important effect on the dynamic response and fatigue characteristics of Offshore Wind Turbine (OWT) structure. Known as a novel type of foundation, the Wide-Shallow Bucket Foundation (WSBF) has been gradually applied in a few Offshore Wind Farms (OWF) of China during the past five years. Due to the shallow bucket skirt and the more contact area between soil and foundation, the soil damping of the OWTs supported by WSBF may reflect different foundation-soil interaction characteristics compared with monopile and jacket foundation. There, the calculation of soil damping for the OWTs supported by WSBF was focused on and discussed in this paper. Firstly, the rotation and swing theoretical model of OWT supported by WSBF was established and then the theoretical model of natural frequency calculation was also presented based on the transfer matrix method. Further, one new theoretical calculation method of soil damping for the OWT supported by WSBF was proposed considering soil hysteresis characteristics. Secondly, taking an OWT of one actual OWF as the research object, accurate theoretical estimation of soil damping for WSBF was achieved combined prototype observation, modal frequency identification and Genetic Algorithm (GA) with a value around 0.120%. Then, three different geological conditions and soil parameters of another actual OWF were selected to complete the comparison between the results obtained from the proposed theoretical calculation method and numerical simulation method, and verify the general applicability of the new model and method based on the engineering error within 5%. Finally, the influence on the soil damping of OWT structure considering different factors (compression modulus and Plasticity Index (PI)) was discussed by using the new theoretical calculation method. It is concluded that the soil damping rises with the increase of the compression modulus, while it decreases as the PI increases.

Single Output and Algebraic Modal Parameters Identification of a Wind Turbine Blade: Experimental Results

This paper describes the evaluation of a single output, online, and time domain modal parameters identification technique based on differential algebra and operational calculus. In addition, an analysis of the frequency response function (FRF) of the system is conducted in a specific set up, emulating its nominal or operational conditions to determine the influence of the non-linearities over the dynamic behavior of the system in those particular magnitudes of deformations; thus, this influence is quantified by a numerical index. This methodology is applied to a wind turbine blade submitted to wind tunnel experiments. The natural frequencies and modal damping ratios of six bending modes associated with the blade are estimated using real-time velocity measurements from one single point of the blade. A comparison with the usual impact hammer modal testing is performed to evaluate and establish the proposed approach’s main contributions. The developed modal parameter identification algorithms are implemented to run into a standard personal computer (PC) where the data acquisition system’s measurements are conditioned and processed. The results show the performance and the fast parametric estimation of the proposed algebraic identification approach.

Modal identification of concrete arch dam by fully automated operational modal identification

Modal identification is a type of system identification, which studies on the modal parameters of systems by using modal test. In the case of using operational or ambient modal analysis, there is no need to measure excitation, and the system output data are adequate for identification purposes. These modal parameters of system are of great importance from the engineering point of view particularly in the area of system identification, damage detection, and condition monitoring. In a fully-automated identification approach, the modal parameters are extracted without intervention of a specialized user. In this study, a Fully Automated Operational Modal Identification algorithm is developed to identify modal parameters of an arch dam. For this purpose, Morrow point arch dam is selected, and a 3-D finite element of the dam is established. In the first step, the computed natural frequencies of the dam based on the forced vibration tests are utilized to verify the developed finite-element model of the dam. Afterwards, the dam is excited by El-Centro earthquake, and its seismic response is recorded. The collected signals are presented to the proposed identification algorithm. The proposed algorithm presents a methodology to classify the physical mode shapes from spurious modes using the Stochastic Subspace framework. The results indicate acceptable identification via the proposed algorithm using a dataset and non-repetitive data acquisition. Moreover, the identification process is automated and it does not require any user interaction. It is noteworthy to state that the algorithm can identify any dam with any number of mode shapes, and it is practical and straightforward to apply.

Modal parameter identification of subsynchronous oscillation based on stochastic subspace algorithm

At present, under the general trend of interconnection of power grid systems, the problem of sub-synchronous oscillation of power systems has gradually become the focus of attention. Stochastic subspace modal identification (SSI) algorithm plays an important role in vibration detection and damage identification of large motors. Finally, experiments are performed on the data collected in the field, and the results show that the SSI algorithm can better identify the mode of the signal. Compared with the traditional Prony algorithm and ARMA algorithm, the recognition accuracy of the stochastic subspace algorithm constructed in this paper is higher than that of Prony algorithm and ARMA algorithm, which has the advantage of strong anti-noise.

A Method of Modal Parameter Identification for Wind Turbine Blade Based on Binocular Dynamic Photogrammetry

The identification of operational modal parameters of a wind turbine blade is fundamental for online damage detection. In this paper, we use binocular photogrammetry technology instead of traditional contact sensors to measure the vibration of blade and apply the advanced stochastic system identification technique to identify the blade modal frequencies automatically when only output data are available. Image feature extraction and target point tracking (PT) are carried out to acquire the displacement of labeled targets on the wind turbine blade. The vibration responses of the target points are obtained. The data-driven stochastic subspace identification (SSI-Data) method based on the Kalman filter prediction sequence is explored to extract modal parameters from vibration response under unknown excitation. Hankel matrixes are reconstructed with different dimensions, so different modal parameters are produced. Similarity of these modal parameters is compared and used to cluster modes into groups. Under appropriate tolerance thresholds, spurious modes can be eliminated. Experiment results show that good effects and stable accuracy can also be achieved with the presented photogrammetry vibration measurement and automatic modal identification algorithm.

Research on modal analysis method of CNC machine tool based on operational impact excitation

With the rapid development of modern industry and industrial upgrading, machine tool performances such as high machining speed, high machining accuracy, and high reliability have gradually become the development trend of high-end CNC machine tools. The vibration characteristics of the machine structure become an important factor affecting the machining quality and processing efficiency of the machine tool. Since the movable parts of the CNC machine tool will impact the machine structure itself during the acceleration and deceleration process, by identifying the structural vibration response signal, the modal parameters of the machine tool in the running state can be obtained, called active excitation mode analysis. However, this method still has certain defects in theory and experiment. For example, the excitation principle is not theoretically explained, and the excitation energy and the frequency band of the method are limited. To solve these problems, this paper conducts more comprehensive research on the modal analysis method of CNC machine tools based on operational impact excitation. The main research contents are as follows: considering the rigid body motion of the table and the elastic collision of the screw nut pair, the impact excitation is modeled and analyzed. We have introduced a response-based modal identification algorithm. The influence factors of impact excitation energy and frequency band were studied from both theoretical and experimental aspects. Design three excitation sequences for workbench excitation and spindle excitation, respectively, analyze the vibration response and modal identification of the machine tool structure under different excitation sequences. It is verified that the method does not depend on the specific excitation sequence, as long as it satisfies the random characteristics. Aiming at the problem of insufficient excitation energy of the machine tool structure for single-component impact excitation, a multi-component joint impact excitation method based on the principle of multi-point excitation technology is proposed. The design experiment is carried out to verify the impact excitation method, which shows that the joint excitation has better excitation effect than single-axis excitation.

Novel Nonstationarity Assessment Method for Hypersonic Flutter Flight Tests

Hypersonic aircraft have been rapidly developed in recent years both theoretically and experimentally. Aerothermoelastic simulation is very challenging due to its inherent complexity, but physical tests are a workable approach. Flutter tests with variable speed are a popular alternative to hypersonic tests which provide nonstationary structural response data. This paper proposes a nonstationarity assessment method based on energy distribution in the time-frequency domain. The proposed method reveals the nonstationarity level corresponding to the appropriate modal identification algorithm or flutter boundary prediction (FBP) method. Several classic flutter criteria are utilized to build a hypersonic aircraft FBP framework. Numerical simulation and experimental applications demonstrate the effectiveness and feasibility of the proposed method, which facilitates accurate flutter predictions for the subcritical turbulence response during hypersonic flutter flight.

Failure Identification of Dump Truck Suspension Based on an Average Correlation Stochastic Subspace Identification Algorithm

This paper proposes a fault identification method based on an improved stochastic subspace modal identification algorithm to achieve high-performance fault identification of dump truck suspension. The sensitivity of modal parameters to suspension faults is evaluated, and a fault diagnosis method based on modal energy difference is established. The feasibility of the proposed method is validated by numerical simulation and full-scale vehicle tests. The result shows that the proposed average correlation signal based stochastic subspace identification (ACS-SSI) method can identify the fluctuation of vehicle modal parameters effectively with respect to different spring stiffness and damping ratio conditions, and then fault identification of the suspension system can be realized by the variation of the modal energy difference (MED).