scholarly journals Two-stage Bayesian system identification using Gaussian discrepancy model

2020 ◽  
pp. 147592172093352
Author(s):  
Feng-Liang Zhang ◽  
Siu-Kui Au ◽  
Yan-Chun Ni
Keyword(s):  
System Identification ◽  
Structural Model ◽  
Structural Parameters ◽  
Stage Ii ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Model Parameters ◽  
Modeling Error ◽  
Two Stage ◽  
Classical Statistics

System identification aims at updating the model parameters (e.g. mass and stiffness) associated with the mathematical model of a structure based on measured structural response. In this process, a two-stage approach is commonly adopted. In Stage I, modal parameters including natural frequencies and mode shapes are identified. In Stage II, the modal parameters are used to update structural parameters such as those related to stiffness, mass, and boundary conditions. A recent Bayesian formulation allows the identification results in the first stage to be incorporated in the second stage directly via Bayes’ rule without using a heuristic model (often based on classical statistics) that transfers the information from Stages I to II. This opens up opportunities for explicitly accounting for modeling error in the structural model (Stage II) through the conditional distribution of modal parameters given structural model parameters. Following this approach, this article investigates a methodology where the modeling error between the two stages is incorporated with Gaussian distributions whose statistical parameters are also updated with available data. Leveraging on special mathematical structure induced by the model, computational issues are resolved and an analytical investigation is performed that yields insights on the role of modeling error and whether its statistics can be distinguished from those of identification uncertainty (defined for given structural model). The proposed methodology is verified using synthetic data and applied to a laboratory-scale structure.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Identification of Structural Parameters in Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 428-438 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Structural Model ◽  
Structural Parameters ◽  
Model Parameters ◽  
Disk Model ◽  
Response Data ◽  
State Response ◽  
Bladed Disk ◽  
True Model

The present investigation focused on the estimation of the parameters of a structural model to represent “at best” a set of measurements of the steady state response of a mistuned bladed disk. The applicability of the least squares and maximum likelihood approaches to the identification of the bladed disk model from this data is first investigated. The advantages and drawbacks of these techniques motivate the introduction of a new mixed least squares-maximum likelihood formulation which is shown to recover well the true model parameters from noisy simulated response data.

scholarly journals Determination of characteristic Parameters of masonry Structures via Operational Modal Analysis

2019 ◽  
Vol 12 (3) ◽  
Author(s):  
Ali Koçak ◽  
Burak Toydemir ◽  
Melih Bulgur
Keyword(s):  
Modal Analysis ◽  
Operational Modal Analysis ◽  
Physical Models ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Model Parameters ◽  
Masonry Structures ◽  
Characteristic Parameters ◽  
Characteristic Model

Commonly, material and vibration characteristics of masonry structures remain uncertain in the evaluation of existing structures under external loads such as earthquake, heat, wind, etc. In addition, determination of compressive and tensile strength of a masonry walls is not straightforward. However, it is very important to know the characteristic parameters such as eigen values, periods and mode shapes of a structure beforehand in order to create accurate and reliable physical models. Since each historical structure has its own unique wall and bearing characteristics, it is not possible to accept random initial values for the bearing capacity and other parameters of the structure. Besides, conducting vertical and lateral loading experiments is costly and time consuming. An alternative way to determine these parameters that govern the structural behavior is to carry out experimental vibration tests using accelerometers. This method, which is also called as Operational Modal Analysis (OMA), is used to obtain the free and forced vibration response of structures by experimental means and to determine the modal parameters of the structure. OMA is very important for the appropriate use of an analysis method and the model parameters used in the analysis. In this study, two masonry buildings, one of which is historical, are discussed and the modal parameters of buildings are determined experimentally with OMA. Characteristic values obtained from OMA were compared with the three dimensional finite element method by adjusting characteristic model parameters.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1996 ◽  
Vol 118 (1) ◽  
pp. 28-35 ◽  
Author(s):  
K. M. Gorrepati ◽  
M. D. Rao
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Novel tensor subspace system identification algorithm to identify time-varying modal parameters of bridge structures

2021 ◽  
pp. 147592172110360
Author(s):  
Erhua Zhang ◽  
Di Wu ◽  
Deshan Shan
Keyword(s):  
System Identification ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Identification Algorithm ◽  
Time Varying ◽  
Advanced Technique ◽  
Stabilization Diagram ◽  
Bridge Structures ◽  
Tensor Subspace

Subspace-based system identification algorithms have been developed as an advanced technique for performing modal analysis. We introduce a novel tensor subspace-based algorithm to identify the time-varying modal parameters of bridge structures. A new time dimension is introduced in the traditional Hankel matrix, and a mathematical model of tensor subspace decomposition is established. Combined with the stabilization diagram, tensor parallel factor decomposition is used to estimate the frequencies, mode shapes, and modal damping ratios. The effectiveness of the proposed algorithm is validated by comparing it with the classical sliding-window–based stochastic subspace algorithm on a model cable-stayed bridge dynamic test. The proposed algorithm is further applied to process the dynamic responses of a real bridge health monitoring system to identify its time-varying modal frequencies. Our results demonstrated that the proposed algorithm significantly reduces computational efforts and extends the range of solution ideas for future out-only time-varying system identification problems.

Correlation of the SPICE Beam Expander Structural Model With Component and System Level Modal Test Results

1993 ◽  
Author(s):  
Mark E. Mimovich
Keyword(s):  
Structural Model ◽  
Structural Parameters ◽  
System Level ◽  
Mode Shapes ◽  
Test Results ◽  
Modal Assurance Criterion ◽  
Test Analysis ◽  
Measurement Systems ◽  
Modal Test ◽  
Beam Expander

Abstract A full scale experimental beam expander structure is modeled and correlated with modal test results on a component and system level. Correlation of the FE models is completed using the LINK module of the Leuven Measurement Systems (LMS) software which is also used to acquire and reduce the modal test data. The correlation tools used to measure the agreement between test and analytic mode shapes are the Modal Assurance Criterion (MAC), Coordinate Modal Assurance Criterion (CoMAC), and mass cross-orthogonality. In addition to the tools used to measure agreement between test and analysis modal parameters, sensitivity and optimization algorithms are used to identity structural parameters which influence a particular mode and what the minimum change(s) must be in the parameter(s) to bring about the desired agreement. As part of a system level pre-test analysis, the theoretical mode shapes along with a normalized line-of-sight error associated with each mode are used to select the best measurement and excitation locations.

Self-Identification Experiments Using Variable Inertia Systems for Flexible Beam Structures

Aerospace ◽  
2006 ◽  
Author(s):  
Atsuhiko Senba ◽  
Hiroshi Furuya
Keyword(s):  
Spline Interpolation ◽  
Structural Parameters ◽  
The Self ◽  
Identification Accuracy ◽  
Sensitivity Analyses ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Flexible Beam ◽  
Control Input ◽  
Test Beam

The concept of self-identification and its feasibility are experimentally investigated. The modal parameters changed multiple times by the control input of variable inertia parameter are used to obtain linear equations about unknown structural parameters to overcome the lack of modes. We derive the controllability of the modal parameters as the requested conditions for implementing self-identification using sensitivity analyses of the modal parameters with respect to the control input. Also, a criterion for the self-identification is proposed to measure the controllability. Then, the self-identification experiments are performed to examine the present method using a flexible cantilevered beam structure with variable inertia systems, which include controllable additional mass attached to the beam. As a result, the bending stiffness and mass per unit length of the test beam are accurately identified when the controllable and observable lower modes are appropriately excited by input force and their changes due to the variable inertia are accurately estimated from the combinations of a few strain gage sensors output and a cubic spline interpolation technique. The results also indicate that the identification accuracy of higher modes is affected by the accuracy of the estimated controllable mode shape, which is sensitive to the locations of sensors. As the proposed criterion is larger, the identification accuracy becomes more insensitive to the estimation error of the mode shapes.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).

scholarly journals Comparison of Mode Shapes of Carbon-Fiber-Reinforced Plastic Material Considering Carbon Fiber Direction

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 311
Author(s):  
Chan-Jung Kim
Keyword(s):  
Carbon Fiber ◽  
Modal Analysis ◽  
Dynamic Behavior ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Carbon Fiber Reinforced Plastic ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Fiber Reinforced Plastic ◽  
Reinforced Plastic

Previous studies have demonstrated the sensitivity of the dynamic behavior of carbon-fiber-reinforced plastic (CFRP) material over the carbon fiber direction by performing uniaxial excitation tests on a simple specimen. However, the variations in modal parameters (damping coefficient and resonance frequency) over the direction of carbon fiber have been partially explained in previous studies because all modal parameters have only been calculated using the representative summed frequency response function without modal analysis. In this study, the dynamic behavior of CFRP specimens was identified from experimental modal analysis and compared five CFRP specimens (carbon fiber direction: 0°, 30°, 45°, 60°, and 90°) and an isotropic SCS13A specimen using the modal assurance criterion. The first four modes were derived from the SCS13A specimen; they were used as reference modes after verifying with the analysis results from a finite element model. Most of the four mode shapes were found in all CFRP specimens, and the similarity increased when the carbon fiber direction was more than 45°. The anisotropic nature was dominant in three cases of carbon fiber, from 0° to 45°, and the most sensitive case was found in Specimen #3.

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