Modal Analysis Technique Research Articles

Vibration-based approach for structural health monitoring of ultra-high-performance concrete bridge

Structural Health Monitoring (SHM) is a valuable tool for keeping track of the performance and health of engineering structures over extended periods. The purpose of SHM is to ensure structural safety by relying on information derived from real-time measured data and offer suitable recommendations for the structure's maintenance and management. The fundamental idea of SHM is that the structure's response to vibrations will change noticeably if its mass or stiffness is altered. It is a way to keep tabs on how well a building keeps itself safe and sound with as little human intervention as possible. Throughout this research, a Finite Element (FE) model was updated, and an ambient vibration test was performed on an Ultra-High-Performance Concrete (UHPC) bridge, given its slimmer as well as lighter properties to get modal parameters, including natural frequency and mode shape. Measured modal parameters were acquired and verified with the aid of several Operation Modal Analysis (OMA) techniques, and the FE model has then modified accordingly. The bridge's condition was evaluated and predicted using a mathematical method called simple linear regression, which considered the variations in natural frequency produced by the structure's mass and stiffness. The findings indicate that the stiffness index ratio is a practical and efficient tool for evaluating the bridge's effectiveness. The applied method demonstrated the Sungai Raia bridge's safe functioning in real-world situations.

Dynamic size optimization approach to support railway carbody lightweight design process

The transition to a globalised electrical power supply pushes rolling stock manufacturers to find structural solutions for reducing the power required by the vehicles. Within a market where details can make the difference in economic terms, the concept of design optimization is becoming established. However, current industrial procedure for the evaluation of carbody structural strength, in static field and according to EN 12663-1:2015 standard, does not include any optimization process. More in general, optimization processes, and especially dynamic optimization, are not widely used for designing of railway vehicles. In this framework, the present paper proposes a new dynamic optimization approach to support the design of railway vehicle carbodies subjected to static loads. Proposed methodology aims to minimize the mass of the metallic structure, working on the thicknesses of the optimized components, maintaining the baseline geometry. The constraint function was imposed on the first natural vibration frequency of the system. The optimization strategy is based on a dynamic size optimization process in conjunction with modal analysis techniques, applied on the single carbody shell. The procedure has involved the roof assembly of a single tram vehicle body. The proposed approach is resulted numerically efficient in terms of calculation times. Encouraging results have been achieved in terms of mass saving and mechanical behaviour of the carbody shell. Optimized components were 21% lighter than the original, that corresponds to 3% if evaluated on the total mass of the single carbody metallic structure. The methodology turns out to be a useful tool for supporting designers to reduce the mass of the carbody structures, reducing overdimensioning condition that could affect the carbody structure.

Approximating nonlinear response to harmonic base-excitation using fixed-interface quasi-static modal analysis

The recently developed quasi-static modal analysis (QSMA) technique approximates the amplitude dependent modal characteristics of large-scale finite element models with frictional contact at preloaded interfaces. The nonlinear natural frequencies and damping ratios offer insight into the dynamic behavior of assembled structures, particularly the amount of frictional damping and stiffness loss introduced from an isolated modal oscillation due to the joints. This work presents an approach to approximate the nonlinear steady-state response of a base-excited structure using the nonlinear frequency and damping estimates from QSMA. A Hurty/Craig-Bampton transformation allows for the base-excited system to be expressed in terms of the fixed-interface modal coordinates, thus allowing the extension of previously developed analytical approximations using the prescribed base acceleration and the nonlinear, fixed-interface modes from QSMA. The accuracy and relevance of this non-intrusive approach rely on the applicability of Masing's hypothesis within QSMA to approximate the hysteresis curves from the initial loading curve. The limitations are investigated by considering both Masing and non-Masing joint models. A comparison to reference solutions demonstrates the accuracy of the approximation to efficiently obtain nonlinear steady-state solutions of large-scale models with frictional interfaces for cases that satisfy Masing's hypothesis.

Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method

This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimate provided. • Stabilized finite element method for vibrations of incompressible elastic solids. • Adequacy to solve the eigenvalue problem arising in modal analysis. • Modal analysis of the problem resulting after space discretization. • Stability and convergence estimates for the approximate modal analysis. • Numerical results confirm the accurate and robust behavior of the formulation.

Bridge Modal Parameter Identification from UAV Measurement Based on Empirical Mode Decomposition and Fourier Transform

This paper proposes two approaches, Empirical Mode Decomposition (EMD) and Fourier Transform (FT), to correct the vibration signals measured by an Unmanned Aerial Vehicle (UAV), which overcomes the difficulty of selection of reference points used in other correction methods, such as homography transformation and three-dimensional reconstruction. In the method of this paper, a UAV is used to collect the video of a vibrated bridge, and the displacement signal of the bridge is obtained from the video by Kanade–Lucas–Tomasi (KLT) optical flow method, which contains false displacement caused by the ego-motion of the UAV during the measurement. The false displacement can be effectively eliminated by EMD and FT to obtain the real displacement signal. Finally, the displacement signal is processed by the Operational Modal Analysis (OMA) technique to obtain the bridge modal parameters. The performance of correcting vibration signals and extracting bridge modal parameters from the vibration signals based on EMD, FT, and Differential Filtering (DF) are compared by taking the fixed camera measurement as a reference (the accuracy of measuring bridge vibration with fixed cameras has been verified) in this paper, and it is demonstrated that EMD has better reliability in processing signal measured by UAVs, which is mainly due to the absence of random factors and too much noise in the signal processing process of EMD.

Laser Doppler Vibrometry for Evaluating the Quality of Welds in Lithium-Ion Supercells

The inspection of the quality of welds in battery packs plays an important role in ensuring safety during the manufacturing and operation of energy-storage devices in automotive vehicles during service. This research investigated the novel application of laser Doppler vibrometry, a widely used non-destructive optical technique for modal analysis, to the post-weld evaluation of micro-TIG-welded interconnections in lithium-ion supercells. The experimental modal analysis showed features in the modal models of the supercells that were unique to their welding conditions. The comparisons between the supercells showed an absence of linear correlations between the modal parameters and the welding current, as well as differences in the welding parameters obtained from the negative and positive terminals of the cylindrical cells. These findings suggested that the modal parameters of the supercells were more strongly influenced by the rigidity of the structural materials than by the localized compliance of the welded interconnections. While this investigation demonstrated a method for using laser Doppler vibrometry to distinguish between different welding conditions in lithium-ion supercells at a structural level, further development is needed to identify the weld quality of individual interconnections.

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. We show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

An investigation on structural dynamic modification of a machine casing

Investigation on structural dynamic characteristic is a crucial step in the noise, vibration and harshness (NVH) analysis in order to enhance the structural vibration, which subsequently contribute to improving the acoustical environment. The excitation of the structure can produce high vibration which could be transferred to the other parts of the body, then lead to high noise radiating components. Structural dynamic modification is one of the important techniques in the design of mechanical structures. It is an application of experimental modal analysis technique to investigate the effect of the physical and geometrical parameters on the dynamic properties of the structures such as frequencies and mode shapes. This paper investigates the dynamic properties of a machine casing structure which is extensively used in industrial applications. This investigation had successfully produced natural frequencies and their associated mode shapes of such open box for the original structure and modified structure. The study establishes the step-by-step procedures to carry out experimental modal analysis on the structures, using single input excitation and single output responses (SISO) technique. To ensure the validity of the results obtained an inverse method was done by fixing the response and moving the excitation. The results found were absolutely the same. Finally, comparison between results obtained from analysis showed significant differences on both frequencies and mode shapes.

Elastic wave attenuation in a metaplate with periodic hollow shapes for vibration suppression

Low noise and vibrations are requirements for engineering structures to realize comfort and ensure systems are environmental friendly. Periodic structures such as phononic crystals have been investigated to suppress noise and vibrations because they inhibit elastic wave propagation in the frequency ranges referred to as the band gap. This study led to the proposal of a metaplate (MP) with periodic hollow structures to form band gaps by changing the surface shapes of the thin plates. MPs such as this can be beneficial from the viewpoints of manufacturing cost and structural reliability when applied to engineering structures. To evaluate the potential ability of the proposed MP to suppress vibrations, we obtained the band gap frequency of out-of-plane deformation waves using the wave finite element method. To efficiently evaluate the band gaps, the internal degrees of freedom in a unit cell are reduced based on the modal analysis technique. Furthermore, the out-of-plane and in-plane deformation waves are separated using kinematic energy to extract the band gap related to the out-of-plane deformation waves. Based on this numerical framework, we demonstrate that periodic hollow shapes can form a band gap in the frequency range of interest in engineering problems. Moreover, the potential of the MP was investigated using hollow shape design and material selection, and the results indicate that the proposed MP is beneficial for tuning the band gap frequency in a unit cell of which the size is acceptable for engineering structures. Finally, vibration suppression caused by band gap is experimentally demonstrated via impact testing of an MP fabricated using additive manufacturing.

Physically meaningful Lyapunov modal contributions in linear systems

This paper introduces a finite-time generalization of Lyapunov modal contributions (LMC) – a technique for energy-based selective modal analysis. The main focus is a case study involving a system with physically meaningful squared output and considering its unforced movement as transferring excessive energy towards its environment. This problem statement leads to LMCs estimating energy transfers measured in joules. The results facilitate solutions to several issues that occur in applications of methods based on Gramian spectral decomposition.

Reducing coherent filtering artefacts in time‐domain operational modal analysis

Signals collected for modal analysis are often filtered in order to reduce sensor noise, out-of-band oscillations, or for dealing with closely-spaced modes. This filtering introduces filtering artefacts into the data due to the non-ideal filter response and is well understood for impulse excitation. However, for ambient vibration data filtering, artefacts become superimposed, preventing their visual identification, and will corrupt the correlation function of the data used in time-domain operational modal analysis (OMA) techniques such as covariance-driven stochastic subspace identification and the random decrement technique. This corruption leads to inaccurate, misleading, biased or spurious frequency and damping estimates, with the inaccuracy increasing for systems with higher damping or lower signal-to-noise ratios. Counter-intuitively, the error in damping estimates is as large for modes with natural frequencies far from the filter cutoff frequency as for modes which are close to the cutoff frequency. In this paper, an alternative to filtering for time-domain OMA, trimming of the correlation of noise from unfiltered correlation functions, is introduced and tested using 10,000 numerically generated ambient vibration data sets. It has been shown that this technique reduces the mean absolute error in the frequency estimates by over 200% and the mean absolute error in the damping estimates by over 400%. Additionally, a new technique which incorporates fitting of filtering artefacts as part of the modal analysis is introduced for where filtering of ambient vibration data is unavoidable and is demonstrated using real-world acceleration data collected from a two-way spanning concrete slab subject to footfall excitation.

Structural Identification of a 90 m High Minaret of a Landmark Structure under Ambient Vibrations

This paper presents the operational modal analysis of a 90-m-high RC minaret of an iconic mosque considered as a landmark of the city. The minaret was monitored for three days with 11 tri-axial MEMS accelerometers. The purpose of the study was to observe the behavior, develop a representative finite element (FE) model, and establish baseline data for health monitoring studies. The modal properties were extracted using three operational modal analysis techniques (OMA): Enhanced Frequency Domain Decomposition (EFDD), Stochastic Subspace Identification (SSI), and Natural Excitation Technique with Eigensystem Realization Algorithm (NExT-ERA). The first 10 identified modes were below 7 Hz. Eight modes out of the ten were bending-dominant, while the remaining two were torsion-dominant. A FE model was also developed in ETABS to ascertain and compare the response of the structure with the identified results. From the FE model, the modes corresponding to the first ten identified modes were considered for comparison with the identified frequencies from ambient monitoring. The maximum 7.71% error was observed between the experimental and numerical frequencies. The error was minimized by using the manual updating the material properties and adding the weight of nonstructural elements. The variation of identified modal frequencies with ambient temperature was observed to be linearly dependent to a reasonable degree. A general trend of decreasing identified frequencies was observed with the rise in temperature.

Damping identification of offshore wind turbines using operational modal analysis: a review

Abstract. To increase the contribution of offshore wind energy to the global energy mix in an economically sustainable manner, it is required to reduce the costs associated with the production and operation of offshore wind turbines (OWTs). One of the largest uncertainties and sources of conservatism in design and lifetime prediction for OWTs is the determination of the global damping level of the OWT. Estimation of OWT damping based on field measurement data has hence been subject to considerable research attention and is based on the use of (preferably operational) vibration data obtained from sensors mounted on the structure. As such, it is an output-only problem and can be addressed using state-of-the-art operational modal analysis (OMA) techniques, reviewed in this paper. The evolution of classical time- and frequency-domain OMA techniques has been reviewed; however, the literature shows that the OWT vibration data are often contaminated by rotor speed harmonics of significantly high energy located close to structural modes, which impede classical damping identification. Recent advances in OMA algorithms for known or unknown harmonic frequencies can be used to improve identification in such cases. Further, the transmissibility family of OMA algorithms is purported to be insensitive to harmonics. Based on this review, a classification of OMA algorithms is made according to a set of novel suitability criteria, such that the OMA technique appropriate to the specific OWT vibration measurement setup may be selected. Finally, based on this literature review, it has been identified that the most attractive future path for OWT damping estimation lies in the combination of uncertain non-stationary harmonic frequency measurements with statistical harmonic isolation to enhance classical OMA techniques, orthogonal removal of harmonics from measured vibration signals, and in the robustification of transmissibility-based techniques.

The Demonstrator of Structural Health Monitoring System of Helicopter Composite Blades

The health and usage monitoring systems are widely used for the monitoring of vibrations of power plant units on helicopters. At the same time critical helicopter structures like main and tail rotors or tail boom are still out of permanent monitoring. Practically all non-destructive techniques (NDT), like ultrasound, eddy current, X-ray and others make the inspection of structural components available on the ground only, during the maintenance check or overhaul. The article considers the promising technique for structural health monitoring (SHM) of a helicopter in flight, inter alia, of rotating blades. Actively developing methods of modal analysis, especially “operational” one, open the new opportunity for structural monitoring and its attendant issues. The Operational Modal Analysis (OMA) techniques and the methods of its data application are the basis of the novel concept of “modal passport” for monitoring of helicopter’s blades. There is brief description of basic principles of the modal passport and its trial application. The paper discusses the problems associated with practical application of modal passport to rotating helicopter blades and ways to overcome it. The light coaxial helicopter Ka-26 became the operating platform for experimental study of OMA application and works as the demonstrator of advance SHM techniques. Brief description of measurement system, including equipment and transducers on the blades is presented. The discussed research stage aims to demonstrate the potential of OMA techniques for monitoring of rotating blades, applying the seeded faults to estimate sensitivity of the SHM system. The paper discusses analytical and experimental study of the blade, including FE modelling and comparative analysis with the experimental data. The conclusions of the paper summarize the results of the research stage, outline the novelties and its practical application. The tasks of further works for SHM research stages using the demonstrator are formulated.

Tracking the variation of complex mode shapes for damage quantification and localization in structural systems

Real structures mode shapes estimated by modal analysis techniques have a common feature: in most cases they are complex, and their level of complexity can be soundly influenced by the presence and extent of physical damage, which also affects the distribution of energy dissipation mechanisms within the structures. Starting from the contributions available in the literature, the present paper investigates, from a numerical and experimental point of view, the correlation existing between localized damage and variation of global modal complexity indices conventionally employed to quantify the nonproportionality of damping in structural systems. Finally, driven by the inferences made through numerical and experimental test cases by tracking the variation of complex modes over multiple and progressive damage scenarios, a new index for damage localization and quantification is formulated and validated against real data.

Multistep Experimental Calibration of Mechanical Parameters for Modelling Multilayer Antishatter Safety Films in Structural Glass Protection

Glass material is largely used in buildings and facilities due to various motivations. Besides, glass still represents a vulnerable component for building occupants. Careful attention is required especially for glass elements that may be subjected to extreme design loads, such as impact, vibrations, etc. Among various approaches and techniques to prevent danger for people in case of glass breakage, multilayer antishatter safety films (ASFs) are commercially available for the retrofit of existing monolithic glass members. In the present research study, a multistep experimental program is presented to obtain the characterization of key input mechanical parameters that are required for the numerical analysis of glass elements protected by ASFs. Relevant characteristics are derived for the definition of an equivalent material and monolithic tape able to reproduce the ASF experimental outcomes. On the side of experiments, artificially aged specimens (healing process) are investigated. A major advantage is taken from small-scale peel and tensile tests on ASF samples, as well as Operational Modal Analysis (OMA) techniques for nondestructive vibration measurements on preliminary fractured specimens of ASF-bonded glass elements. Efficient Finite Element (FE) numerical models calibrated with the support of experimental data and Cohesive Zone Modelling (CZM) techniques are presented for discussion of comparative results, giving evidence of rather good estimates and possible extension of the multistep experimental procedure.

An update on techniques to assess normal-mode behavior of rock arches by ambient vibrations

Abstract. Natural rock arches are rare and beautiful geologic landforms with important cultural value. As such, their management requires periodic assessment of structural integrity to understand environmental and anthropogenic influences on arch stability. Measurements of passive seismic vibrations represent a rapid and non-invasive technique to describe the dynamic properties of natural arches, including resonant frequencies, modal damping ratios, and mode shapes, which can be monitored over time for structural health assessment. However, commonly applied spectral analysis tools are often limited in their ability to resolve characteristics of closely spaced or complex higher-order modes. Therefore, we investigate two techniques well-established in the field of civil engineering through application to a set of natural arches previously characterized using polarization analysis and spectral peak-picking techniques. Results from enhanced frequency domain decomposition and parametric covariance-driven stochastic subspace identification modal analyses showed generally good agreement with spectral peak-picking and frequency-dependent polarization analyses. However, we show that these advanced techniques offer the capability to resolve closely spaced modes including their corresponding modal damping ratios. In addition, due to preservation of phase information, enhanced frequency domain decomposition allows for direct and convenient three-dimensional visualization of mode shapes. These techniques provide detailed characterization of dynamic parameters, which can be monitored to detect structural changes indicating damage and failure, and in addition have the potential to improve numerical models used for arch stability assessment. Results of our study encourage broad adoption and application of these advanced modal analysis techniques for dynamic analysis of a wide range of geological features.

PMU-Based Power System Stabilizer Design: Optimal Signal Selection and Controller Design

Phasor measurement unit (PMU) provides beneficial information for dynamic power system stability, analysis, and control. One main application of such useful information is data-driven analysis and control. This article presents an approach for optimal signal selection and controller structure determination in PMU-based power system stabilizer (PSS) design. An algorithm is suggested for selecting the optimal input and output signals for PSS, in which a combination of system clustering, modal analysis, and principal component analysis techniques is used. The solution for the optimal PSS input–output selection is determined to increase the observability and damping of the power system. The approach can efficiently reduce the number of input–output signals, while the overall performance is not deteriorated. Then, a linear matrix inequality-based technique is elaborated to design the PMU-based PSS parameters. The stabilizer design approach is formulated as a convex optimization problem and the appropriate stabilizer for pole allocation of the closed-loop model is designed. This method is simulated on two sample power systems. Also, to compare the results with the previous methods, the system is simulated and the results of two previously developed algorithms are compared with the proposed approach. The results show the benefit of the suggested method in reducing the required signals, which decreases the number of required PMUs, while the system damping is not affected.

Beam mode characterization by applying operational modal analysis to neutron detectors data

Operational Modal Analysis techniques are widely used in civil, aerospace and industrial applications. There are several methods and one of the most utilized is Enhanced Frequency Domain Decomposition (EFDD). In the nuclear sector, part of this method was applied to analyze simulated neutron detectors data with promising results in the framework of CORTEX project. Given the possibilities of this methodology, in this work, EFDD was fully implemented to characterize the Beam Mode frequency region in plant data from two KWU reactors. The results show that closely spaced resonances can be separated and that three modes of vibration are found. The mode shapes obtained for each resonance give information on the physical origin of the vibration and with them it was proved that the dominant resonance in the Beam Mode region is not connected to a pendular motion.

Improving damping performance of fiberglass-reinforced resin matrix composites by designing viscoelastic sandwich layer

A new type of damping composite structure was fabricated by embedding polymer materials into the phenolic resin matrix fiberglass-reinforced laminates. The damping layer of novel damping composites shows the characteristics of anti-aging and strong adhesion compared with the traditional damping composites. The ingredients of the polymer material were studied according to the orthogonal test method. The curing mechanism of resin matrix and vulcanized characteristics of polymer damping material were combined in the design process. The damping composite structures were researched by single cantilever beam vibration and modal analysis techniques to determine its damping characteristics. The least square method was used to calculate the loss factor of the damping composites. It was observed that the damping performance of co-cured composites was significantly enhanced compared to traditional damping composites. When the thickness of damping layer is only 0.1 mm, the composite loss factor increases by as much as 49%. The embedding of damping layer has a positive effect on structural stiffness. The work indicates that the low-temperature co-cured phenolic resin matrix damping composite has broad application prospects in vibration reduction.