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.

scholarly journals Optimal Economic–Environmental Operation of BESS in AC Distribution Systems: A Convex Multi-Objective Formulation

Computation ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 137
Author(s):  
Walter Gil-González ◽  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Andrés Escobar-Mejía
Keyword(s):  
Co2 Emissions ◽  
Power Factor ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Pareto Front ◽  
Reactive Power ◽  
Global Optimum ◽  
Multi Objective ◽  
Objective Model

This paper deals with the multi-objective operation of battery energy storage systems (BESS) in AC distribution systems using a convex reformulation. The objective functions are CO2 emissions, and the costs of the daily energy losses are considered. The conventional non-linear nonconvex branch multi-period optimal power flow model is reformulated with a second-order cone programming (SOCP) model, which ensures finding the global optimum for each point present in the Pareto front. The weighting factors methodology is used to convert the multi-objective model into a convex single-objective model, which allows for finding the optimal Pareto front using an iterative search. Two operational scenarios regarding BESS are considered: (i) a unity power factor operation and (ii) a variable power factor operation. The numerical results demonstrate that including the reactive power capabilities in BESS reduces 200kg of CO2 emissions and USD 80 per day of operation. All of the numerical validations were developed in MATLAB 2020b with the CVX tool and the SEDUMI and SDPT3 solvers.

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 FRF Sensitivity-Based Damage Identification Using Linkage Modeling for Limited Sensor Arrays

2018 ◽  
Vol 18 (08) ◽  
pp. 1840002 ◽  
Author(s):  
Van Vu Nguyen ◽  
Jianchun Li ◽  
Emre Erkmen ◽  
Mehrisadat Makki Alamdari ◽  
Ulrike Dackermann
Keyword(s):  
Degrees Of Freedom ◽  
Damage Identification ◽  
Model Updating ◽  
Sensor Arrays ◽  
Successful Implementation ◽  
Fe Model ◽  
Stiffness Reduction ◽  
Stiffness Matrices ◽  
Novel Method ◽  
Linkage Model

This paper presents a novel method to localize and quantify damage in a jack arch structure by introducing a linkage modeling technique to overcome issues caused by having limited sensors. The main strategy in the proposed Frequency Response Function (FRF)-based sensitivity model updating approach is to divide the specimen into partitions. The Young’s modulus of each partition is then updated to detect stiffness reduction caused by damage. System Equivalent Reduction Expansion Process (SEREP) is used to reduce the full finite element (FE) model to a linkage model. The number of measured degrees of freedom (DOFs) is then expanded to the linkage model using the mass and stiffness matrices of the linkage model for the synthesis of interpolated FRFs. The FRF sensitivities are then formulated using the linkage model along with the interpolated FRFs to iteratively calculate the values of the updating parameters until convergence is achieved. The methodology and theory behind this procedure are discussed and verified using a numerical and experimental study. The successful implementation of this method has the potential to detect the location and severity of damage where sensor placement is limited.

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 Model Updating of Spindle Systems Based on the Identification of Joint Dynamics

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Hongrui Cao ◽  
Songtao Xi ◽  
Wei Cheng
Keyword(s):  
Machine Tool ◽  
Degrees Of Freedom ◽  
Model Updating ◽  
Joint Stiffness ◽  
Iteration Process ◽  
Fe Model ◽  
Receptance Coupling ◽  
Joint Dynamics ◽  
The Difference ◽  
Fe Model Updating

In order to simulate the cutting performance of a spindle mounted in the machine tool, the finite element (FE) model of spindles is required to be coupled with machine tool. However, the unknown joint dynamics (e.g., bolts) between the spindle and machine tool column limit the accuracy of the model. In this paper, an FE model updating method is proposed based on the identification of joint dynamics in both translational and rotational degrees-of-freedom (DOF). The receptance coupling (RC) technique is enhanced to estimate frequency response functions (FRFs) corresponding to rotational DOFs. The joint stiffness is identified through the iteration process by minimizing the difference between the simulated FRF and the measured FRF of the assembly. The proposed method is verified with a machine-tool spindle system. The good agreement between simulation and experiment shows the effectiveness of the method.

Parameter Adaptation With Automatically Selected Co-Ordinates From Measured Eigenvectors As a Way to a Validated FE Model

1997 ◽  
Author(s):  
Manfred W. Zehn ◽  
Gerald Schmidt ◽  
Oliver Martin
Keyword(s):  
Mode Shape ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
High Sensitivity ◽  
Mode Shapes ◽  
Problem Solver ◽  
Fe Model ◽  
Parameter Adaptation ◽  
Fine Mesh ◽  
Reduction Techniques

Abstract This paper considers an algorithm on the basis of parameter adaptation for mass and stiffness embedded in the eigenvalue problem solver. The algorithm is intended for large finite element (FE) models. The errors, which can be reduced by the procedure described in this paper, occur due to detailed features, which would require an unduly fine mesh to be included in the model, or in uncertainties in the description of mechanical behaviour, material properties, etc. Another source for errors are model reduction techniques (superelement technique) necessary for the application of the model structure in an automatic control circuit (smart structures). It is a well-known fact that the natural frequencies can be measured much more accurately than mode shapes, for mode shapes can only be measured for accessible regions and normally for translational degrees of freedom (DOF). Therefore the algorithm uses only measured natural frequencies (frequency differences) and the calculated mode shape vectors to determine the parameter changes. In a new approach it is also possible to select automatically, or by experience, those co-ordinates from the measured mode shape vectors that correspond to points with high sensitivity or other very reliable points. An interface system designed to exchange data between the experimental modal analysis system (EMA) and the FE program ensures, that the measured and calculated mode shape vectors are orthonormalised in the same way and the points of the FE mesh correspond to the pick up points for the measurement. Examples of industrial parts at the end of the paper illustrate how the procedure works and what influence we can obtain by inclusion of some co-ordinates of measured mode shape vectors.

Modal Identification and Finite Element Model Updating by Adding Known Masses

2013 ◽  
Vol 405-408 ◽  
pp. 808-815 ◽  
Author(s):  
Chang Deng ◽  
Shao Wei Hu ◽  
Pei Ying Gu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Objective Function ◽  
Mode Shape ◽  
Model Updating ◽  
Element Model ◽  
Modal Identification ◽  
Test Method ◽  
Fe Model ◽  
Modal Test

This paper focus on the model updating of civil structural systems. Traditional modal test method can identify the frequency of the civil structure accurate, but it is difficult to identify the mass-normalized mode shape. By adding a series of known masses to the structure, measuring the frequency of this mass-modified system, and only using this set of frequency data, the mass-normalized mode shape of the structure can be identified. And the model updating method was developed, which constructed an objective function through the frequency of the measurement and the FE model, corrected the FE model's parameters to minimize the objective function. The example was included to show the capabilities of the technique. The finite element model of the fixed-free beam was updated by the dynamic characteristics which was identified from the modal test, the results show that updated results coincided with the experience of the analyst.

Representation of bolted joints in a structure using finite element modelling and model updating

2020 ◽  
Vol 14 (3) ◽  
pp. 7141-7151 ◽  
Author(s):  
R. Omar ◽  
M. N. Abdul Rani ◽  
M. A. Yunus
Keyword(s):  
Finite Element ◽  
Dynamic Behaviour ◽  
Model Updating ◽  
Complex Structure ◽  
Bolted Joints ◽  
Model Parameters ◽  
Fe Model ◽  
Bolted Joint ◽  
Fe Modelling ◽  
Joint Structure

Efficient and accurate finite element (FE) modelling of bolted joints is essential for increasing confidence in the investigation of structural vibrations. However, modelling of bolted joints for the investigation is often found to be very challenging. This paper proposes an appropriate FE representation of bolted joints for the prediction of the dynamic behaviour of a bolted joint structure. Two different FE models of the bolted joint structure with two different FE element connectors, which are CBEAM and CBUSH, representing the bolted joints are developed. Modal updating is used to correlate the two FE models with the experimental model. The dynamic behaviour of the two FE models is compared with experimental modal analysis to evaluate and determine the most appropriate FE model of the bolted joint structure. The comparison reveals that the CBUSH element connectors based FE model has a greater capability in representing the bolted joints with 86 percent accuracy and greater efficiency in updating the model parameters. The proposed modelling technique will be useful in the modelling of a complex structure with a large number of bolted joints.

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