Operational Acoustic Modal Analysis: Sensitivity-Based Mode Shape Normalisation

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

This paper substantially advances Nieter and Singh’s acoustic modal analysis technique [J. Acoust. Soc. Am. 72, 319–326 (1983)] which used the coincident-quadrature response method to extract acoustic global properties of one-dimensional systems. Here a technique to identify modal parameters including damping of a three-dimensional cavity is proposed. The cavity is excited by a convertible acoustic driver whose volume velocity is monitored. Acoustic transfer impedance database is obtained for a number of cavity boundary locations which are chosen such that all modes of interest can be adequately described. The vector diagram method is used to fit the measured database in the neighborhood of each resonance frequency with a circle. The experimental technique proposed here has been verified by applying it first to a cylindrical cavity whose exact eigensolutions are known. Then for an annularlike cavity, experimentally extracted natural frequencies and pressure mode shapes are found to agree well with the results of a finite element model. The significance of this paper lies in the successful demonstration of an experimental technique which can be used for diagnosing the acoustics of irregular shaped cavities. The proposed technique also offers an alternative to the finite element method for acoustic modal analysis of three-dimensional ducts and resonators of irregular shapes and/or with complicated boundary conditions.

This paper presents an application of the Experimental Acoustic Modal Analysis (AMA) on a vintage 10 M Conn tenor saxophone. This technique originates from the traditional Modal Analysis which is commonly adopted to determine the dynamic behaviour of solid structures. The methodology is based on the measurement of Frequency Response Functions (FRFs) as a ratio of the acoustic pressure, measured by means of a set of microphones positioned along the saxophone body, and the volume velocity produced by an acoustic source and measured at the instrument input. The microphones are housed on the stripped saxophone keys by means of tailored three-dimensional printed adapters. The AMA makes use of the FRFs to extract modal parameters, such as resonance frequencies, loss factors, and mode shapes. These parameters pertain to the cavity modes of the saxophone passive resonator. The analysis has been performed for three different notes (B ♭, B, and C) and for two registers of the instrument in order to show the potential of the technique. Moreover, the influence of the mouthpiece volume on the cavity modes has been shown. The information obtained by AMA can find useful application in the validation of analytical or numerical models of this kind of musical instruments.

It is a very difficult engineering issue to assess the earthquake performance levels of existing masonry structures and determine whether they require strengthening or retrofitting. The materials used in the production of masonry structures vary from region to region, even within the same structure, and the lack of standard mechanical properties of these materials makes it difficult to define the material model in the numerical models of such structures. It is known that these problems are eliminated by the Operational Modal Analysis (OMA) technique because it does not damage the structure and accelerates the process. In the framework of this research, experimental measurement of the 5-story masonry structure was taken with OMA, and numerical modeling was made by SAP2000v14 software. The damping ratio, natural frequencies, and mode shapes of the structure were determined. Frequency-domain-based methods were used in the analysis and evaluation of OMA responses from the Enhanced Frequency Domain Decomposition Method (EFDDM), while the Stochastic Subspace Identification Method (SSIM) was used for time-domain-based methods.

Despite its importance in structural dynamics and vibration, modal analysis is rarely performed in acoustics due to the high modal density of sound fields. A novel acoustic modal analysis (AMA) approach is proposed in this paper for enclosed acoustic fields, such as a room, from the perspective of state-space formulation of control systems. A single-input-multiple-output (SIMO) state-space model is established in light of the balanced realization (BR), given impulse response measurements. The BR model is then converted to a modal form such that the modal parameters, including natural frequencies, damping ratios, and mode shapes, can be estimated. To reconstruct mode shapes, plane wave decomposition (PWD) and compressive sensing (CS) techniques are exploited to solve the underdetermined problem for a spatially sparse representation of mode shapes under the Schroeder frequency. As a result, a model of a continuous system can be "interpolated" for any arbitrary source-receiver positions on the basis of the estimated mode shapes. With the identified modal parameters, the low-frequency and early reflection part of room impulse responses (RIRs) can be synthesized for arbitrary source-sensor pairs. The proposed AMA acoustic field interpolation is validated by extensive simulations and experiments.

Cyclostationarity and the cepstrum for operational modal analysis of MIMO systems—Part II: Obtaining scaled mode shapes through finite element model updating

In order to derive mass normalized mode shapes from Operational Modal Analysis (OMA) techniques, additional experiments have to be conducted in the interest of scaling the determined mode shapes. Various investigations have been carried out based on the deterministic perturbed mass matrix, also known as the mass change method. However, the conventional form of this method requires a number of rather costly and sometimes impractical experiments on the structure. In this article, it is intended to use traffic as a stochastic source of mass change to calculate mass scaling factors. Adequate traffic stream on bridges can affect the Eigen properties of the structure efficiently. The vehicles on the bridge are only considered to affect the mass properties, and vehicle-bridge interaction is neglected. A simplified structural model of a bridge is considered and the traffic is modeled as lognormal distribution. Nodal masses induced by the vehicles are converted to time histories to avoid difficulties based on the moving mass problem. Consequently, a method is proposed to produce the modified mass matrix which can be used in the scaling factor equations. Finally, scaling factors of mode shapes are proposed by comparing the unperturbed structure and the perturbed mass matrix structure.

Successful osseointegration of orthopedic implants relies on achieving mechanical stability of screw fixation. Various techniques have been utilizing to assess screw stability; however, some of these methods are destructive or time-consuming. Non-destructive techniques, such as modal analysis, have gained interest in evaluating screw stability. This study aimed to assess the primary and secondary stability of screws in an in-vivo animal experiment by comparing conventional methods with two modal methods, namely Periotest® and acoustic modal analysis (AMA). To achieve this goal, eight rabbits were implanted with cylindrical threaded screws. The screw fixation stability was evaluated using four different test methods. Initially, the peak insertion torque (PIT) was measured for each bone screw during the implantation process. Additionally, AMA and Periotest® were employed to assess the natural frequency (NF) and Periotest® value (PTV) of the bone-screw structure, respectively. Finally, a destructive pull-out test was conducted to determine the peak pull-out force (PPF). The average primary stability values were measured 5.15 N.cm for PIT, 2507±59 Hz for NF, 21.85±4.1 for PTV, and 94.45±12 for PPF. In contrast, the secondary stability showed varying results with an average increase of 39% for NF, 101% for PTV, and 194% for PPF. The research also compared the non-destructive AMA with the destructive pullout test, considered the gold standard for stability evaluation of bone screws. The study found that AMA exhibited a linear relationship with the pullout test, making it an accurate method for assessing orthopedic and spinal screw applications.

This paper investigates the use of conventional operational modal analysis (OMA) techniques for modal parameters identification of a rotating system supported by roller bearings. Although largely applied in civil engineering, in-depth studies on different types of systems are still limited in the literature. The novel of the paper is to address such issue by applying conventional OMA methods, such as enhanced frequency domain decomposition (EFDD) and stochastic subspace identification (SSI-data), to identify the modal parameters of a rotating machine, investigating the challenging particularities of these systems due to their inherent operating conditions, especially regarding the presence of harmonic forces, eventually closed-spaced modes, and non-proportional damping due to the bearings. The results presented in the experimental tests showed that, with the use of specific tools, in comparison with traditional experimental modal analysis (EMA), the used OMA methods have managed to successfully identify the modal parameters of a roller bearing supported rotor.

\nThis work presents a summary of the research study of operational modal analysis (OMA) application for condition monitoring of operating pipelines. Special focus is on the topicality of OMA for definition of the dynamic features of the pipeline (frequencies and mode shapes) in operation. The research was conducted using two operating laboratory models imitated a part of the operating pipeline. The results of finite-element modeling, identification of pipe natural modes and its modification under the influence of virtual failure are discussed. The work considers the results of experimental research of dynamic behavior of the operating pipe models using one of OMA techniques and comparing dynamic properties with the modeled data. The study results demonstrate sensitivity of modal shape parameters to modification of operating pipeline technical state. It is resumed about ability of operating pipeline condition monitoring by measuring dynamic deformations of the operating pipe and OMA techniques application for dynamic properties extraction.\n

On the application of correlation function matrices in OMA

Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring (SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3 damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes (quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression) and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration measurements.

The accuracy of modal parameter estimates from estimation methods built in the framework of experimental modal analysis (EMA) can be assessed by several methods provided the information of input loadings and output responses. However, a deeper investigation is necessary for estimation methods built in the operational modal analysis (OMA) framework to establish confidence boundaries for the modal parameter estimates. This paper aims to estimate uncertainties of the modal parameter estimates by testing the sensitivity of the damped natural frequencies, damping ratios, and mode shapes to the choice of the estimation method and data acquisition settings used in this method. The uncertainty estimates of the modal parameter estimates are tested for changes in the boundary conditions. The tests provide insights into tendencies for the accuracy of the modal parameter estimates when the boundary conditions provide a different set of “true” modal parameter values. A simple cantilever beam experimental setup is used to obtain benchmark modal parameter estimates from EMA that are used to estimate the accuracy of the modal parameter estimates from OMA. The method’s robustness in estimating uncertainties and accuracies for modal parameter estimates is tested for several independent experiments. The boundary conditions for the cantilever beam are changed to test the influence of altering modal parameter estimates on the estimated uncertainties and accuracies. The boundary conditions are changed using materials with different elastic properties and the connection pressure between the clamping device and beam. A method presented in Paulsen et al. (Proceedings of the 9th International Operational Modal Analysis Conference, IOMAC, 2022) calculates a representative modal parameter estimate from a set of modal parameter estimates based on weightings obtained from the modal assurance criterion. The method’s ability to reduce uncertainties and increase accuracies of the representative estimate is demonstrated by repeating a test setup ten times. The results present simultaneously a reduction of uncertainties and an increase of accuracies for the representative modal parameter when the weighting method is used. An evaluation of dependencies between the estimated uncertainties and accuracies finds a proportional relation for the damped natural frequency when the uncertainties are described as a relative standard deviation. The analysis presents higher accuracy for the damped natural frequency and mode shape estimates compared to the damping factor, and the accuracy of the damping factor is dependent on the actual value of the damping factor. These phenomena for accuracy are well known and indicate that the uncertainties of modal parameter estimates can be assessed through a sensitivity test of estimation methods and data acquisition parameters.

This paper will evaluate different automated operational modal analysis techniques for the continuous monitoring of offshore wind turbines. The experimental data has been obtained during a long-term monitoring campaign on an offshore wind turbine in the Belgian North Sea. State-of-the art operational modal analysis techniques and the use of appropriate vibration measurement equipment can provide accurate estimates of natural frequencies, damping ratios and mode shapes of offshore wind turbines. To allow a proper continuous monitoring the methods have been automated and their reliability improved. The advanced modal analysis tools, which will be used, include the poly-reference Least Squares Complex Frequency-domain estimator (pLSCF), commercially known as PolyMAX, the polyreference maximum likelihood estimator (pMLE), and the frequency-domain subspace identification (FSSI) technique. The robustness of these estimators with respect to a possible change in the implementation options that could be defined by the user (e.g. type of polynomial coefficients used, parameter constraint used…) will be investigated. In order to improve the automation of the techniques, an alternative representation for the stabilization charts as well as robust cluster algorithms will be presented.

Two research projects have been conducted to study the possibility of using acoustic emission and modal analysis techniques for in situ surveillance of offshore platforms. For acoustic emission, experiments onshore, in sheltered area and on platforms have been conducted. The experimental part of the program terminated with a test on a pre-cracked T-joint on a platform in the southern North Sea. A prototype industrial system and the corresponding interpretation software have been developped. The various tests show that acoustic emission allows detection of cracks and monitoring of crack growth in a limited area of a platform. Modal analysis has been studied through theoretical analysis, small scale tests and field tests on an operational platform. Two slightly different techniques have evolved from the study: – modal analysis per se which gives global information on the overall structure. – vibrodetection which provides more accurate measurements on individual bracings.