scholarly journals Mode Shape Description and Model Updating of Axisymmetric Structures Using Radial Tchebichef Moment Descriptors

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
C. Zang ◽  
H. B. Lan ◽  
D. D. Jiang ◽  
M. I. Friswell
Keyword(s):  
Mode Shape ◽  
Model Updating ◽  
Shape Reconstruction ◽  
Mode Shapes ◽  
Zernike Moment ◽  
Fe Model ◽  
Vibration Data ◽  
Tchebichef Moment ◽  
Axisymmetric Structures ◽  
Modal Vibration

A novel approach for mode shape feature extraction and model updating of axisymmetric structures based on radial Tchebichef moment (RTM) descriptors is proposed in this study. The mode shape features extracted by RTM descriptors can effectively compress the full-field modal vibration data and retain the most important information. The reconstruction of mode shapes using RTM descriptors can accurately describe the mode shapes, and the simulation shows that the RTM function is superior to Zernike moment function in terms of its mathematical properties and its shape reconstruction ability. In addition, the proposed modal correlation coefficient of the RTM amplitude can overcome the main disadvantage of using the modal assurance criterion (MAC), which has difficulty in identifying double or close modes of symmetric structures. Furthermore, the model updating of axisymmetric structures based on RTM descriptors appears to be more efficient and effective than the normal model updating method directly using modal vibration data, avoids manipulating large amounts of mode shape data, and speeds up the convergence of updating parameters. The RTM descriptors used in correlation analysis and model updating are demonstrated with a cover of an aeroengine rig. The frequency deviation between the test and the FE model was reduced from 17.13% to 1.23% for the first 13 modes via the model updating process. It verified the potential to industrial application with the proposed method.

scholarly journals One-Step FE Model Updating Using Local Correspondence and Mode Shape Orthogonality

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Martin Ø. Ø. Jull ◽  
Sandro D. R. Amador ◽  
Anders Skafte ◽  
Jannick B. Hansen ◽  
Manuel L. Aenlle ◽  
...  
Keyword(s):  
Mode Shape ◽  
Model Updating ◽  
Low Frequency ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Assurance Criterion ◽  
Mass Scaling ◽  
The Matrix ◽  
One Step ◽  
Fe Model Updating

In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure.

scholarly journals Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Nizar Faisal Alkayem ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Structural Damage ◽  
Model Updating ◽  
Complex Problem ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Strain Energy ◽  
3D Structures ◽  
Multiobjective Particle Swarm Optimization ◽  
Damage Tracking

Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

L1 Regularized Model Updating for Structural Damage Detection

2018 ◽  
Vol 18 (12) ◽  
pp. 1850157 ◽  
Author(s):  
Yu-Han Wu ◽  
Xiao-Qing Zhou
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Model Updating ◽  
Regularization Parameter ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Modal Data ◽  
Vibration Data ◽  
Stiffness Reduction ◽  
Regularized Model

Model updating methods based on structural vibration data have been developed and applied to detecting structural damages in civil engineering. Compared with the large number of elements in the entire structure of interest, the number of damaged elements which are represented by the stiffness reduction is usually small. However, the widely used [Formula: see text] regularized model updating is unable to detect the sparse feature of the damage in a structure. In this paper, the [Formula: see text] regularized model updating based on the sparse recovery theory is developed to detect structural damage. Two different criteria are considered, namely, the frequencies and the combination of frequencies and mode shapes. In addition, a one-step model updating approach is used in which the measured modal data before and after the occurrence of damage will be compared directly and an accurate analytical model is not needed. A selection method for the [Formula: see text] regularization parameter is also developed. An experimental cantilever beam is used to demonstrate the effectiveness of the proposed method. The results show that the [Formula: see text] regularization approach can be successfully used to detect the sparse damaged elements using the first six modal data, whereas the [Formula: see text] counterpart cannot. The influence of the measurement quantity on the damage detection results is also studied.

Reliable Mode Shape Expansion Method for Error Localisation and Model Updating

1997 ◽  
Author(s):  
Philippe Collignon ◽  
Jean-Claude Golinval
Keyword(s):  
Cantilever Beam ◽  
Mode Shape ◽  
Constitutive Equations ◽  
Structural Model ◽  
Model Updating ◽  
Failure Detection ◽  
Expansion Method ◽  
Relative Performance ◽  
Mode Shapes ◽  
Error Localization

Abstract Failure detection and model updating using structural model are based on the comparison of an appropriate indicator of the discrepancy between experimental and analytical results. The reliability of the expansion of measured mode shapes is very important for the process of error localization and model updating. Two mode shape expansion techniques are examined in this paper : the well known dynamic expansion (DE) method and a method based on the minimisation of errors on constitutive equations (MECE). A new expansion method based on some improvements of the previous techniques is proposed to obtain results that are more reliable for error localisation and for model updating. The relative performance of the different expansion methods is demonstrated on the example of a cantilever beam.

A Method for FE Model Updating of Coupled Vibro-Acoustic Systems Using Constrained Optimization

2013 ◽  
Author(s):  
D. V. Nehete ◽  
S. V. Modak ◽  
K. Gupta
Keyword(s):  
Finite Element ◽  
Constrained Optimization ◽  
Model Updating ◽  
Numerical Study ◽  
Element Model ◽  
Rectangular Cavity ◽  
Mode Shapes ◽  
Fe Model ◽  
Structural Dynamic ◽  
Fe Model Updating

Finite element (FE) model updating is now recognized as an effective approach to reduce modeling inaccuracies present in an FE model. FE model updating has been researched and studied well for updating FE models of purely structural dynamic systems. However there exists another class of systems known as vibro-acoustics in which acoustic response is generated in a medium due to the vibration of enclosing structure. Such systems are commonly found in aerospace, automotive and other transportation applications. Vibro-acoustic FE modeling is essential for sound acoustic design of these systems. Vibro-acoustic system, in contrast to purely structural system, has not received sufficient attention from FE model updating perspective and hence forms the topic of present paper. In the present paper, a method for finite element model updating of coupled structural acoustic model, constituted as a problem of constrained optimization, is proposed. An objective function quantifying error in the coupled natural frequencies and mode shapes is minimized to estimate the chosen uncertain parameters of the system. The effectiveness of the proposed method is validated through a numerical study on a 3D rectangular cavity attached to a flexible panel. The material property and the stiffness of joints between the panel and rectangular cavity are used as updating parameters. Robustness of the proposed method under presence of noise is investigated. It is seen that the method is not only able to obtain a close match between FE model and corresponding ‘measured’ vibro-acoustic characteristics but is also able to estimate the correction factors to the updating parameters with reasonable accuracy.

scholarly journals Rotor Model Updating and Validation for an Active Magnetic Bearing Based High-Speed Machining Spindle

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Adam C. Wroblewski ◽  
Jerzy T. Sawicki ◽  
Alexander H. Pesch
Keyword(s):  
Transfer Functions ◽  
Model Updating ◽  
Dynamic Properties ◽  
Magnetic Bearing ◽  
Mode Shapes ◽  
Model Parameters ◽  
Successful Implementation ◽  
Fe Model ◽  
Rotor Model ◽  
Machining Spindle

This paper presents an experimentally driven model updating approach to address the dynamic inaccuracy of the nominal finite element (FE) rotor model of a machining spindle supported on active magnetic bearings. Modeling error is minimized through the application of a numerical optimization algorithm to adjust appropriately selected FE model parameters. Minimizing the error of both resonance and antiresonance frequencies simultaneously accounts for rotor natural frequencies as well as for their mode shapes. Antiresonance frequencies, which are shown to heavily influence the model’s dynamic properties, are commonly disregarded in structural modeling. Evaluation of the updated rotor model is performed through comparison of transfer functions measured at the cutting tool plane, which are independent of the experimental transfer function data used in model updating procedures. Final model validation is carried out with successful implementation of robust controller, which substantiates the effectiveness of the model updating methodology for model correction.

Updating the Mathematical Model of a Structure Using Vibration Data

2005 ◽  
Vol 11 (12) ◽  
pp. 1469-1486 ◽  
Author(s):  
Ashutosh Bagchi
Keyword(s):  
Mathematical Model ◽  
Model Updating ◽  
Three Dimensional ◽  
Field Tests ◽  
Mode Shapes ◽  
Actual Structure ◽  
Shell Elements ◽  
Vibration Data ◽  
The Difference ◽  
The Mathematical Model

Model updating is an important step for correlating the mathematical model of a structure to the real one. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper concentrates on the model updating techniques using the natural frequencies or frequencies and mode shapes of a structure. An iterative technique is developed based on the matrix update method. The method hasbeenappliedtothefiniteelement models of a three span continuous steel free deck bridge located in western Canada. The finite element models of the bridge have been constructed using three-dimensional beam and facet shell elements and the models have been updated using the measured frequencies. From the study it is clear that the initial model needs to be built such that it represents the actual structure as closely as possible. The results demonstrate that the difference between the modal parameters from the model and field tests affect the quality of the model updating process.

Multi-Objective Model Updating Optimization Considering Orthogonality

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Braden T. Warwick ◽  
Il Yong Kim ◽  
Chris K. Mechefske
Keyword(s):  
Mode Shape ◽  
Degrees Of Freedom ◽  
Pareto Front ◽  
Model Updating ◽  
Current Model ◽  
Physical Reality ◽  
Frequency Error ◽  
Fe Model ◽  
Multi Objective ◽  
Objective Model

The coordinate orthogonality check (CORTHOG) and multi-objective optimization considering pseudo-orthogonality as an objective function are introduced to overcome several limitations present in current model updating methods. It was observed that the use of the CORTHOG to remove four inaccurate degrees-of-freedom (DOF) was able to increase the orthogonality between mode shape vectors. The multi-objective model updating process generated a Pareto front with 38 unique optimal solutions. Four critical points were identified along the Pareto front, of which decreased the natural frequency error by greater than 2.84% and further increased the orthogonality between mode shape vectors. Therefore, it has been demonstrated that both steps of the methodology are critical to significantly reduce the overall errors of the system and to generate a finite element (FE) model that best describes physical reality. Additionally, the methodology introduced in this work generated a feasible computational runtime allowing for it to be easily adapted to widespread applications.

Structural Identification and Numerical Models for Slender Historical Structures

2015 ◽  
pp. 674-703 ◽  
Author(s):  
Dora Foti ◽  
Mariella Diaferio ◽  
Nicola Ivan Giannoccaro ◽  
Salvador Ivorra
Keyword(s):  
Model Updating ◽  
Numerical Models ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Fe Model ◽  
Detailed Structural Analysis ◽  
Ambient Vibration Tests ◽  
Great Confidence ◽  
Vibration Tests ◽  
The Time Domain

In the present chapter the theoretical basis of different methods developed for the calibration of FEMs are discussed. In general, Model Updating techniques are based on the use of appropriate functions that iteratively update selected physical properties (characteristics of the materials, stiffness of a link, etc.). In this way the correlation between the simulated response and the target value could improve if compared to an initial value. The FE model thus obtained can be used for a detailed structural analysis with a great confidence. The technique described in the first part of the chapter is applied to the evaluation of the structural properties of the tower of the Provincial Administration Building in Bari (Italy).The final purpose is to predict the performance of the tower to different combinations of static and dynamic loads, i.e. earthquakes or other induced vibrations. Ambient vibration tests have been performed on the above mentioned tower with the aim of determining its dynamic response and developing a procedure for modeling this building (Foti et al., 2012a). The Operation Modal Analysis (OMA) has been carried out both in the frequency domain and in the time domain to extract the dominant frequencies and mode shapes of the tower.

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