Modal Analysis Algorithm Research Articles

Response control of chimneys using tuned mass damper, multi-tuned mass damper and tuned mass inerter system

Growing industry and shifting environmental regulations have made chimneys taller and more flexible, thus making them susceptible to wind forces. Consequently, it becomes necessary to analyze the chimney for undesired wind force causing vortex induced vibration (VIV) and to enhance their performance by the implementation of appropriate countermeasures. In this study, three passive control devices, namely, tuned mass inerter system (TMIS), tuned mass damper (TMD) and multi-tuned mass damper (MTMD), are used to control the VIV of high-rise chimneys. The TMIS comprises a mass element, spring, damper, and inerter subsystem. The MTMD is distributed over the top one-third height of the chimney. The three control devices control the response of the chimneys under random vortex induced forces, and their relative performances are evaluated. The modal spectral analysis and Genetic Algorithm are employed to establish a method for optimizing the damper-structure system for VIV control. The response analysis duly considers the effect of the nonlinear aero-elastic effect. The novelty of the paper lies in the application of TMIS for chimney subjected to vortex induced vibration and comparing its results with other traditional dampers (TMD and MTMD) for the three chimneys of height 120 m, 210 m, and 360 m of varying diameter, taken as illustrative examples. In addition, the study examines the impact of different mass ratios and the mass of the inerter on chimneys. For the three chimneys considered, it is observed that the performance of the TMD is best among the three control techniques adopted. For the tallest chimney (360 m), all three control devices display an optimum mass ratio for which the response reduction is maximum. The performance of the TMIS improves with the increased height of the chimney.

Damage identification in composite structures using high-speed 3D digital image correlation and wavelet analysis of mode shapes

ABSTRACT In this study, the damage identification procedure combining the advantages of high-speed 3D digital image correlation (DIC) that is used for modal analysis and wavelet-based processing algorithm is presented. The proposed procedure has been successfully validated on sandwich composite structures with internal damage of a core and impact damage, and its performance was demonstrated by detection, localisation, and identification of shapes of damage in tested structures, comparable to the results from scanning laser Doppler vibrometry (SLDV). The effectiveness in damage identification was achieved by the development of processing algorithm of acquired mode shapes, which uses a 2D double-density directional wavelet transform with increased sensitivity with entropic weights allowing to automatically select those wavelet coefficients and mode shapes, which are most sensitive to damage. The procedure presented in this paper demonstrates the performance of 3D DIC for damage identification as a cost-effective alternative to the procedures based on SLDV measurements.

A new mesh stiffness determination method in a straight bevel gear system through experimental modal analysis and metaheuristic algorithms

The mesh stiffness plays a crucial role in influencing the performance and behavior of straight bevel gear (SBG) systems. Precisely determining the mesh stiffness enables to assess the SBG system’s dynamic behavior more accurately and anticipate potential concerns such as crack identification and noise reduction. A novel experimental method is developed, employing experimental modal analysis associated with metaheuristic algorithms and an innovative setup. This method effectively determines the mesh stiffness in healthy and cracked systems. Additionally, an analytical method based on the potential energy associated with crack modeling is proposed. Both methods are implemented on SBG systems with varying crack depths. The results obtained from the experimental method are compared with those from the analytical method, revealing good agreement between them. This demonstrates that the newly proposed experimental method effectively considers all parts of mesh stiffness and is appropriate for determining the mesh stiffness in healthy and cracked SBG systems.

A new fully automated operational modal analysis algorithm intended for large civil structures

Abstract A new fully automated operational modal analysis (AOMA) algorithm based on the time-domain covariance-driven stochastic subspace identification (cov-SSI) system identification method is proposed. The new algorithm is intended for large civil structures, such as long-span suspension bridge for which an application example is included. It is shown that the new algorithm is capable of consistently detecting all expected structural modes of the Hardanger bridge, without requiring any prior tuning or parameter selection. The dominating three-step approach to AOMA algorithms in published literature on this topic is highlighted and used as a basis for the new algorithm; it first removes spurious poles using a Gaussian mixture model by analysing their distance to their nearest neighbour. Secondly, hierarchical clustering is used to regroup similar poles, and finally, the groups representing physical modes are selected through a similarity analysis of the size of hierarchical clusters.

Experimental comparison of three automatic operational modal analysis algorithms on suspension and floating bridges

Automatic operational modal analysis is necessary for long-term monitoring of structures when using modal information. Many algorithms have been proposed to accomplish this task; two examples are the fully automatic algorithm by Reynders et al. in 2012 and the semi-automatic algorithm by Kvåle and Øiseth in 2020; however, few in-depth direct comparisons exist. This work compares the two algorithms mentioned above with a new fully automatic algorithm recently developed by the authors, inspired by the best functioning elements from algorithms published since 2008 and following the standard three-step framework. The comparison is performed using 3600 experimental datasets from three real bridges – the Hardanger and Hålogaland suspension bridges and the Bergsøysund floating pontoon bridge – where the detections made by the algorithms are compared to the pre-defined reference modes of the bridges. The new algorithm (Dederichs 2023) performs equally to the Kvåle 2020 algorithm in correct detections and better than the Reynders 2012 algorithm. The two best algorithms detect the easily excited structural modes in over 90 % of the datasets. The Reynders 2012 algorithm is shown to have a more cautious approach to mode detections, making few correct detections and fewer errors. A sensitivity analysis of the criteria to compare detected modes to reference modes shows that this does not impact the comparison’s conclusions.

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.

A robust probabilistic approach to stochastic subspace identification

Modal parameter estimation of operational structures is often a challenging task when confronted with unwanted distortions (outliers) in field measurements. Atypical observations present a problem to operational modal analysis (OMA) algorithms, such as stochastic subspace identification (SSI), severely biasing parameter estimates and resulting in misidentification of the system. Despite this predicament, no simple mechanism currently exists capable of dealing with such anomalies in SSI. Addressing this problem, this paper first introduces a novel probabilistic formulation of stochastic subspace identification (Prob-SSI), realised using probabilistic projections. Mathematically, the equivalence between this model and the classic algorithm is demonstrated. This fresh perspective, viewing SSI as a problem in probabilistic inference, lays the necessary mathematical foundation to enable a collection of new OMA approaches. To this end, a statistically robust SSI algorithm (robust Prob-SSI) is developed, capable of providing a principled and automatic way of handling outlying or anomalous data in the measured timeseries, such as may occur in field recordings, e.g. intermittent sensor dropout. Robust Prob-SSI is shown to outperform conventional SSI when confronted with ‘corrupted’ data, exhibiting improved identification performance and higher levels of confidence in the found poles when viewing stabilisation diagrams. Similar benefits are also demonstrated on the Z24 Bridge benchmark dataset, highlighting enhanced performance on measured systems.

A non-parametric algorithm for time-dependent modal analysis of civil structures and infrastructures

Vibration-based monitoring strategies have been demonstrated to be effective tools in providing – in nearly real-time – reliable information regarding the integrity of structures and infrastructure systems. However, commonly used methods for vibration analysis and modal identification are not able to capture the time variation of the modal properties during single acquisitions, hence they cannot perform dynamic identification in the presence of nonlinearities or non-stationary input excitations. To overcome this limitation, a novel non-parametric algorithm for automatic time-dependent modal analysis is hereby presented and discussed. This Enhanced Modal Identification for Long-term Integrity Assessment (EMILIA) algorithm can compute time-dependent estimations of the natural frequencies and mode shapes that can be critical to the early identification of hidden damage. The dynamic characterization of a beam-like structure in sound and damaged conditions is carried out for numerical validation purposes, allowing to evaluate the reliability of the proposed method over different scenarios and comparing its efficiency against traditional algorithms. Finally, further tests are conducted to analyse the sensitivity of the EMILIA algorithm to its main parameters and components.

Localization of Impulsive Sound Source in ShallowWaters using a Selective Modal Analysis Algorithm

Localization of Impulsive Sound Source in ShallowWaters using a Selective Modal Analysis Algorithm

Experimental comparison of automatic operational modal analysis algorithms for application to long-span road bridges

Operational modal analysis (OMA) of long-span road bridges from vibration measurements is a topic of interest due to its potential applications within structural health monitoring. Algorithms for the automation of OMA (AOMA) have been proposed since around 2005, relying on machine learning to automate previously manual tasks. The fundamental principles of AOMA are explained in the theory of this work, as are the functioning principles of the clustering algorithms employed by most AOMA algorithms. A performance comparison of six AOMA algorithms (Magalhaes 2009, Reynders 2012, Zhang 2014, Neu 2017, Yang 2019, Kvåle 2020) is provided using real-world data from the Hardanger suspension bridge. To the authors’ best knowledge, it is the first comparison of AOMA algorithms for bridges. While Reynders 2012 is shown to be the only fully automated algorithm, Magalhaes 2009, Zhang 2014, and Kvåle 2020 are the algorithms with the highest successful detection rate. Neu 2017 and Yang 2019, however, make the least detection errors, respectively, the least false detections and the least duplicate detections. The variability amongst datasets is shown not to impact the algorithms’ comparison. An outright recommendation on which algorithm to use is impossible due to the multitude of potential use cases, but Neu 2017 seems to provide the best performance compromise for the tested case.

A DBSCAN-based automated operational modal analysis algorithm for bridge monitoring

Advanced data analysis techniques are of paramount importance for the Structural Health Monitoring (SHM) of civil buildings and infrastructures. In particular, Automated Operational Modal Analysis (AOMA) algorithms are necessary for the output-only monitoring of such massive and large structures. The unsupervised estimation of their modal parameters from ambient vibrations enables assessing their integrity efficiently and continuously. This is particularly important for reinforced concrete (RC) bridges, which need constant maintenance. In this context, the classic cluster-based, multi-stage approach is effective in cleaning the stabilisation diagram and discerning stable and unstable modes. However, due to the shortcomings of binary classification with (k = 2)-means clustering, the labelling between ‘possibly physical’ and ‘certainly spurious’ modes may not be completely reliable. The procedure described here applies Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to bypass this limitation. This allows, among other advantages, to automatically detect and remove outliers, differently from the traditional techniques. The algorithm is fully automated, including the data-driven setting of DBSCAN parameters. Its viability is tested here on a real, full-scale case study, the Z24 road bridge dataset.

In-situ test and model updating of an RC tied-arch bridge

The Italian bridge asset is dated, and the functionality of many bridges is jeopardised by degradation due to ageing and environmental effects, as well as by increasing traffic loads. An adequate operational monitoring and maintenance program is essential for ensuring the safety condition of these critical structures. Administrations in charge and policymakers must clearly understand the actual condition of the infrastructure asset in order to optimise maintenance and retrofit planning. For this purpose, visual inspections might fail to reflect the current condition accurately; thus, additional experimental investigation campaigns are desirable. In the knowledge process for existing bridges, valuable information can be obtained through appropriate experimental tests, such as material testing and dynamic identification. Moreover, the potential of on-site test results in updating structural modelling has been demonstrated, successfully improving the performance assessment of bridges. However, sensitivity-based Finite Element model updating requires a deep knowledge of the examined structure to determine which parameters mainly affect the dynamic response.In this framework, the contribution of this paper consists of a typological analysis and model updating of an existing RC tied-arch bridge dating back to the 1930s. The structural condition was assessed by an on-site investigation campaign, including a geometric survey, material testing, and ambient vibration test (AVT). For the latter, three algorithms for operational modal analysis were performed to extract the bridge's modal parameters and then compare outcomes. Lastly, results from experimental tests were used to update a 3D finite element model.

Robust Synchronization of Ambient Vibration Time Histories Based on Phase Angle Compensations and Kernel Density Function.

The output-only modal analysis is ubiquitously used for structural health monitoring of civil engineering systems. The measurements for such applications require the use of multiple data acquisition systems (DAS) to avoid complicated meshes of cables in high-rise buildings, avoid traffic constriction on a bridge during measurements, or to avoid having limited channels in a single DAS. Nevertheless, such requirements introduce time synchronization problems which potentially lead to erroneous structural dynamic characterization and hence misleading or inconclusive structural health monitoring results. This research aims at proposing a system-identification-based time synchronization algorithm for output-only modal analysis using multiple DAS. A new procedure based on the compensation of the phase angle shifts is proposed to identify and address the time synchronization issue in ambient vibration data measured through multiple DAS. To increase the robustness of the proposed algorithm to the inherent inconsistencies in these datasets, the kernel density function is applied to rank multiple time-shift estimates that are sometimes detected by the algorithm when inaccuracies exist in the data arising from low signal-to-noise ratio and/or presence of colored noise in the ambient excitations. First, the synchronized ambient vibration dataset of a full-scale bridge is artificially de-synchronized and used to present a proof of concept for the proposed algorithm. Next, the algorithm is applied to ambient vibration data of a 30-story, reinforced concrete building, where the synchronization of the data could not be achieved using two DAS despite best efforts. The application of the proposed time synchronization algorithm is shown to both detect and correct the time synchronization discrepancies in the output-only modal analysis.

A fast collapsed Gibbs sampler for frequency domain operational modal analysis

This paper introduces a fast Gibbs sampler for solving a fully Bayesian problem in operational modal analysis. The proposed method is able to infer modal properties from the FFT of well-separated modes. System identification and related uncertainties are captured by a posterior distribution. The classical resonance description is wrapped into a hierarchical probabilistic model. The model is sampled through an enhanced Gibbs sampler including a Metropolis–Hasting step. The entire sampling scheme is new and the fast convergence of the algorithm is enabled by two strategies. First, the use of a collapsed Gibbs algorithm allows for an efficient sampling of the mode shape. Second, the use of adequate candidate distributions in the Metropolis–Hasting step provides excellent acceptance ratios, around 75%. Eventually, the numerical inference procedure is compared to the state-of-the-art Fast Bayesian FFT Algorithm (Fast-BFFTA), which is the most commonly used algorithm for Bayesian operational modal analysis. The sampler surpasses the Fast-BFFTA for small data-based identification, while remaining sustainable in terms of computing requirements.

An automated operational modal analysis algorithm and its application to concrete dams

With the increasing application of long-term dynamic monitoring systems to civil engineering structures, automated operational modal analysis (OMA) has become a fascinating research area for structural health monitoring. In recent years, different automated approaches based on the existing parametric or nonparametric OMA algorithms have been developed. However, they usually perform less well in large complex structures with weak excitation because of inherent limitations of those algorithms. In this work, a three-stage automated OMA algorithm based on a combination of the second-order blind identification (SOBI) and the covariance-driven stochastic subspace identification (SSI-COV) is proposed, which takes full advantage of both parametric and nonparametric algorithms while overcoming the limitations. The automated approach avoids the ambiguous work related to interpreting stabilization diagrams without losing accuracy and thus obtains more reliable modal parameters. The proposed method is fully validated by simulated data from an 8-DOF system and data recorded on a concrete arch-gravity dam in view of single and continuous monitoring. The results show that all physical modes can be well-separated and reliably identified by the proposed method with high accuracy, confirming the excellent performance of the method, especially for continuous monitoring.

Operational modal parameter identification with correlated colored noise excitation

Operational modal analysis refers to the modal analysis of a structure in its operating state. The advantage of operational modal analysis is that only the output vibration signal of a system is used. The classical operational modal analysis algorithm is based on the white noise excitation assumption, and it is considered that there is no correlation between the excitations; several identification methods have been developed in time and frequency domains. But excitations are not completely independent with each other and not pure white. In this article, the matrix theory is used to prove that the operational modal analysis algorithm can still be used to identify modal parameters when the excitation is correlated. In the simulation, five kinds of colored noise excitations are applied to the cantilever beam with correlated excitations, which shows that the idea proposed in this article is rational. In the experiment, the foundation excitation of colored noise is added to the cantilever beam, which can be regarded as applying several related excitations. It also shows the rationality of this idea.

Частотная отстройка элементов конструкции планера воздушного судна

The paper emphasizes the relevance of the problem of resonance in aircraft airframe structural elements, and relying on the operating experience shows the consequences of this phenomenon in terms of fatigue cracks occurring in the details of the aircraft airframe during vibration load. The types and consequences of failures in aviation equipment airframe structural elements arising from vibration load are analyzed. On the example of the slat, the forms of natural oscillations of high-lift devices are investigated, their relationship with the rotational frequencies of the high and low pressure rotors of the lift-propulsion system is shown. The study introduces the method of frequency offset of the structural pattern of the object under consideration, and implements the algorithm for modal analysis of a metal structure on the basis of modern applied packages of three-dimensional modeling and engineering analysis. The place of analytical calculations in the structure of the entire product life cycle is noted.

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting of flexible beams and rigid bodies. The theory is sufficiently general in that the rigid bodies can be of any shape or size, but importantly, the theory permits connections of the rigid bodies to any number beams at any arbitrary points and oriented at any arbitrary angles. For beam members, a range of theories including the Bernoulli-Euler and Timoshenko theories are applied. The assembly procedure for the beam and rigid body properties is simplified without resorting to matrix inversion. The difficulty generally encountered in computing the problematic J0 count when applying the Wittrick-Williams algorithm for modal analysis has been overcome. Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multi-body system's dynamic behaviour. Some exact benchmark results are provided and compared with published results and with finite element solutions. This research provides an exact and highly efficient analysis tool for multibody system dynamics which is for the free vibration analysis, ideally suited for optimization and inverse problems such as modal parameter identification.

An online and real-time adaptive operational modal parameter identification method based on fog computing in Internet of Things

A large number of smart devices make the Internet of Things world smarter. However, currently cloud computing cannot satisfy real-time requirements and fog computing is a promising technique for real-time processing. Operational modal analysis obtains modal parameters that reflect the dynamic properties of the structure from the vibration response signals. In Internet of Things, the operational modal analysis method can be embedded in the smart devices to achieve structural health monitoring and fault detection. In this article, a four-layer framework for combining fog computing and operational modal analysis in Internet of Things is designed. This four-layer framework introduces fog computing to solve tasks that cloud computing cannot handle in real time. Moreover, to reduce the time and space complexity of the operational modal analysis algorithm and support the real-time performance of fog computing, a limited memory eigenvector recursive principal component analysis–based operational modal analysis approach is proposed. In addition, by examining the cumulative percent variance of principal component analysis, this article explains the reasons behind the identified modal order exchange. Finally, the time-varying operational modal identification results from non-stationary random response signals of a cantilever beam whose density changes slowly indicate that the limited memory eigenvector recursive principal component analysis–based operational modal analysis method requires less memory and runtime and has higher stability and identification effect.

Resonance Monitoring of a Horizontal Wind Turbine by Strain-Based Automated Operational Modal Analysis

A strain-based automated operational modal analysis algorithm is proposed to track the long-term dynamic behavior of a horizontal wind turbine under operational conditions. This algorithm is firstly validated by a scaled wind turbine model, and then it is applied to the dynamic strain responses recorded from a 5 MW wind turbine system. We observed variations in the fundamental frequency and 1f, 3f excitation frequencies due to the mass imbalance of the blades and aerodynamic excitation by the tower dam or tower wake. Inspection of the Campbell diagram revealed that the adverse resonance phenomenon and Sommerfeld effect causing excessive vibrations of the wind tower.