Parametric model updating with frequency and MAC combined objective function of port crane structure based on operational modal analysis

The vibrational effect is one of the primary considerations during construction due to the ambient excitation from the surrounding environment. Thus, it is necessary to find the most dependable Finite Element (FE) model for the actual structure to improve its quality and life span on site. In this context, the study included a 3-story building model that was analyzed using finite element analysis to determine its dynamic properties such as natural frequency and mode shape to avoid the resonance effect. It is due to the importance of obtaining a reliable and accurate model by verifying with the results of the Operational Modal Analysis (OMA). In general, the goal of this study is to update the FE model so that it is close to the actual scaled model based on the previous OMA study. As a result, an initial linear FE model of the 3-story building scaled model was created using CAD software based on actual geometry to describe the structure's physical properties. The FE model was then imported into CAE software, where the boundary condition and estimated material properties were assigned to determine the effect of random vibration. Through the pairing of Finite Element Analysis results and previous studies, 9 natural frequencies and 9 mode shapes were extracted. The Modal Assurance Criterion (MAC) was used to compare the mode shape of FE results against the OMA to determine the degree of consistency between paired mode shapes. A model updating process was carried out to reduce the discrepancy between the methods. The uncertainties arising from the initial conditions have been discussed in terms of the stiffness of the material used. The updated model allows for an evaluation of the structure's current actions as well as the development of models for a wide range of potential future research scenarios.

This study is to develop a methodology and model to analyze the built-in speakers induced structural acoustic vibration of hard disk drive (HDD) in Notebook PC. First, a structural finite element (FE) model is built for the notebook PC to be analyzed using ANSYS. This FE model is subsequently verified by experiments. Second, the effects of acoustically transmitted and structurally transmitted oscillating forces, induced by the speakers, acting on the HDD, are investigated by acoustic FE model (SYSNOISE) and structural FE model. The acoustic transmission effect on the vibration of HDD is also investigated by experiment, which shows that the simulation results have a good agreement with experimental results. Finally, the effects of stiffness and damping ratio of the HDD supporters on the vibration of HDD are analyzed by the verified FE model.

Modal analysis is an approach to determine the dynamic behavior of a structure through numerical analysis or experimental approach. Nowadays, numerical analysis has been preferred by most researchers and engineers compared to experimental analysis to analyze the structure due to expenditure and time consuming factors of the research. Recently, numerical analysis is done computationally or well known as Finite Element Analysis (FEA) by using finite element (FE) model to replicate the real test structure. Instead of advantage of FE analysis, the trustworthiness of FE model has been questioned since simplification has been made during design stage for complex structure and inaccurate of geometry input of the model. Hence, this paper is carried out to reduce the discrepancies between numerical prediction results with measured test data on FE model of exhaust structure by implementing FE model updating using SOL200 algorithm. Initially, the FE model is running on normal mode analysis SOL103 to extract the modal parameters such as natural frequency and mode shape. Then, the numerical pre-diction result has been correlated and validated with measured test data obtained through Experimental Modal Analysis (EMA). Due to disagreement between numerical result and experimental data in correlation process, the FE model has been updated using SOL200 algorithm. The percentage error between numerical prediction result and measured test data is minimized from 5.67 to 3.23% after been updated. It’s shown the capability SOL200 algorithm in preparing the reliable FE model before been used for further analysis such as structural dynamic modification.KeywordsDynamic studyJoints strategyFinite element analysisExperimental modal analysisFE model updating

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.

In various applications it is important to determine dynamically equivalent spatial finite element (FE) model of complex structures. For instance, obtaining the FE model of an existing aerospace structure is a major requirement for reliable aeroelastic analysis. In such applications a reliable FE model may not be always available, and when this is so a dynamically equivalent FE model derived from modal test will be very useful. This paper presents a noble method to determine spatial FE model of a structure by using experimentally measured modal data along with the connectivity information of measurement points. The method is based on the mass and stiffness orthogonality equations written using experimentally determined mode shapes and natural frequencies. These equations are solved for geometric and material properties constituting global spatial mass and stiffness matrices of an initial FE model. Starting from this initial FE model, mass and stiffness orthogonality equations are updated iteratively employing experimentally obtained natural frequencies and corresponding eigenvectors from the FE model. Iterations are continued until eigensolution of the updated FE model closely correlates with experimentally measured modal data. A simulated case study on GARTEUR scaled aircraft model is presented in order to demonstrate the applicability of the method.

A recent development in operational modal analysis (OMA) is the possibility of using measured, artificial loads in addition to the unmeasured, ambient excitation, while the ratio between forced and ambient excitation can be low compared to classical experimental modal analysis (EMA). Most of these so-called OMAX algorithms lack the intuitiveness of their EMA and OMA counterparts, since they fit a system model that takes both the measured and the operational excitation into account directly to the measured signals. A more physically intuitive subspace algorithm for OMAX, that starts with an accurate decomposition of the measured joint response in a forced and an ambient part, was recently introduced. In this paper, the performance of this algorithm, which is called CSI-ic/ref, is assessed by means of a case study, where a two-span steel arch footbridge is tested in operational conditions, with and without using additional actuators. From a comparison of the modal parameters with results from a finite elementmodel, an OMA algorithm, and an alternative OMAX algorithm, it can be concluded that CSI-ic/ref yields accurate modal parameter estimates.KeywordsMode ShapeModal ParameterBridge DeckModal Assurance CriterionExperimental Modal AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The MX3D Bridge is the world’s first additively manufactured metal bridge. It is a 10.5 m-span footbridge, and its dynamic response is a key serviceability consideration. The bridge has a flowing, sculptural form and its response to footfall was initially studied using a 3D finite element (FE) model featuring the designed geometry and material properties obtained from coupon tests. The bridge was tested using experimental modal analysis (EMA) and operational modal analysis (OMA) during commissioning prior to installation. The results have shown that the measured vibration response of the bridge under footfall excitation is 200% greater than predictions based on the FE model and contemporary design guidance. The difference between predicted and measured behaviour is attributed to the complexity of the structure, underestimation of the modal mass in the FE model, and the time-variant modal behaviour of the structure under pedestrian footfall. Both OMA and EMA give a dominant natural frequency for the bridge of between 5.19 Hz and 5.32 Hz, higher than the FE model prediction of 4.31 Hz, and average damping estimates across all modes of vibration below 15 Hz of 0.61% and 0.74% respectively, higher than the 0.5% assumed within the design guidance, slightly reducing the peak response factor predicted for the bridge.

The investigation of dynamic behavior of aerospace structures is a challenging task due to the interaction of different types of aerodynamic and structural parameters. The identification of operational loads is essential for accurate investigation of the fatigue life especially in case of composite structures. In the present work, a mixed experimental and numerical approach is used for indirect identification of operational loads for composite structures using model correlation and updating technique. In the first step, the operational modal analysis using the response of accelerometers is performed for an anisotropic spar in cantilever position by using poly reference least square complex frequency (pLSCF) algorithm. Model correlation and updating of the FE model with the operational mode shapes is performed using Modal Assurance Criteria (MAC). The updated FE model is used for extraction of system matrices using Frequency Response Functions (FRFs). The physical response of accelerometers and transfer functions in the form of FRFs from the FE are used for identification of the operational loads at different locations of the structure. Finally, the proposed approach is validated by applying the extracted loads on the FE model and comparing the response at different locations.

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

Uncertainties in finite element (FE) model updating arise from two main sources: measurement noise and modeling errors. The latter includes model parameter uncertainty and model uncertainty itself. Among these sources of uncertainty, model uncertainty has been proven to be the most influential source of error in FE model updating, which is particularly important when using the updated model for damage identification (DID) purposes. This paper investigates the effects of model uncertainty when updating mechanics-based nonlinear FE models of building structures subjected to earthquake excitation. To solve the parameter estimation problem, the unscented Kalman filter is used as parameter estimation tool. Numerically simulated response data of two state-of-the-art nonlinear FE models of building structures designed according to modern design codes are used as application examples. A two-dimensional steel building and a three-dimensional reinforced concrete building, both subjected to seismic base excitation, are analyzed for different types and levels of model uncertainty. The results show that model uncertainty may have significant detrimental effects when using the updated FE model for DID, chiefly in the case of large modeling uncertainty. Although a good match between the measured (observed) and FE predicted responses is usually achieved, unobserved responses at global and local levels often show significant errors.

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.

Safety assessment of structures for near-field blast-induced ground excitations using operational modal analysis

Operational modal analysis (OMA) is a procedure that allows the modal parameters of a structure to be extracted from the measured response to an unknown excitation generated during operation. Nonlinearity is inevitably and frequently encountered in OMA. The problem: The traditional OMA method based on linear modal theory cannot be applied to a nonlinear oscillation system. The solution: This paper aims to propose a nonlinear OMA method for nonlinear oscillation systems. The new OMA method is based on the following: (1) a self-excitation phenomenon is caused by nonlinear components; (2) the nonlinear normal modes (NNMs) of the system appear under a single-frequency harmonic excitation; and (3) using forced response data, the symbolic regression method (SR) can be used to automatically search for the NNMs of the system, whose modal parameters are implicit in the expression structure expressing each NNM. The simulation result of a three-degree-of-freedom (3-DOF) nonlinear system verifies the correctness of the proposed OMA method. Then, a disc-rod rotor model is considered, and the proposed OMA method’s capability is further evaluated.

Rotating machines are key components in energy generation processes, and faults can lead to shutdowns or catastrophes encompassing economic and social losses. Structural Health Monitoring (SHM) of structures in operation is successfully performed via Operational Modal Analysis (OMA), which has advantages over traditional methods. In OMA, white noise inputs lead to the accurate extraction of modal parameters without taking the system out of operation. However, this excitation condition is not easy to attain for rotating machines used in power generation, and OMA can provide inaccurate information. This research investigates the applicability of machine learning as a pre-stage of OMA to differentiate adequate from inadequate excitations and prevent inaccurate extraction of modal parameters. Data from a rotor system was collected under different conditions and OMA was applied. In a training stage, measurements were characterized by statistical features and K-means was used to determine which features provided information about the excitation condition, that is, which excitation was adequate to extract the rotor’s modal parameters via OMA. In a testing stage, data were successfully classified as adequate or not adequate for OMA, achieving 100% accuracy and revealing the technique’s potential to support SHM of rotating machines. The technique is extendable to other monitoring systems based on OMA.