System Equivalent Reduction Expansion Process Research Articles

Damage Detection Based on Damage Force Indicator Using Reduced-Order FE Models

Damage measures, one of the important parameters in Structural Health Monitoring (SHM), and useful in detecting the presence and location of cracks in beams, are developed in this article. This development is based on the reduced Finite element models for healthy and damaged structures. Finite element reduced-order model (ROM) methods like static condensation, system equivalent reduction expansion process (SEREP) and dynamic condensation have been used to generate reduced order models. ROM generated by static condensation are used to analyze beams under static loading while SEREP and dynamic condensation methods are used for dynamic loading. The developed damage measure is the force residue obtained from the stiffness relationship of healthy and damaged beam, which we call damage force indicator (DFI). For dynamic load cases, the measure is evaluated in the frequency domain. Sensitivity of orientation of crack prediction is performed by using different orientations of crack and comparing it with a crack of standard orientation. A general method to determine the approximate region of damage for a structure with no a priori knowledge of damage is also explained. Damage measures are verified using experimentally measured responses, to prove the efficiency of the approach.

Condensed Model Identification and Recovery for Structural Damage Assessment

This study aims to develop a system identification methodology for determining structural parameters of linear dynamic system, taking into consideration of practical constraints such as insufficient sensors. A new methodology called the condensed model identification and recovery method is presented for identification of full stiffness matrices for damage assessment based on incomplete measurement. With the proposed methodology, it is possible to obtain several condensed stiffness matrices, so as to identify individual stiffness coefficients for the structure. Three different model condensation methods, namely static condensation, dynamic condensation, and system equivalent reduction expansion process, are adopted. Having identified the condensed model, the stiffness parameters in the entire system are recovered by extracting sufficient information with either fixed sensor or repositioned sensor approach. The efficiency of the proposed technique is shown by numerical simulation study for multistory shear buildings subjected to random forces, accounting for effects of signal noise. In addition, laboratory experiments are carried out to illustrate the performance of the proposed method. It is shown both numerically and experimentally that the proposed methodology gives reasonably accurate identification in terms of locating and quantifying structural damage.

Vibration control in a composite box beam with piezoelectric actuators

This work presents a theoretical and experimental investigation of vibration control ofcomposite box beams using distributed, surface mounted piezoelectric (PZT) patches asactuators. The finite element modeling of the box beam is done by formulating a first-ordershear deformable active composite thin walled beam element. The degrees offreedom at each node are axial, bending in spanwise and chordwise directions,corresponding shears and twist. The superconvergent element derived uses higherorder interpolating polynomials obtained by solving electromechanically coupledstatic governing differential equations. The open loop response is validated withexperimental and analytical results available in the current literature. A systemequivalent reduction expansion process (SEREP) is implemented for reduced ordermodeling. Open and closed loop responses to electrical bending actuation areobtained both experimentally and analytically using state space modeling. Aproportional-integral (PI) controller using acceleration feedback is implementedfor control of vibration due to single-frequency excitations. Experimental andnumerical results correlate very well in the above cases. Eigenstructure assignmentthrough output feedback is designed for multimodal control of transient responses.

Model order reduction of unsteady flow past oscillating airfoil cascades

This study focuses on developing reduced-order models for unsteady aerodynamic flows past a cascade of two-dimensional airfoils. A reduction method known as System Equivalent Reduction Expansion Process (SEREP) is used. The computational efficiency of the SEREP reduced-order model is compared with a reduced-order model formed using the Proper Orthogonal Decomposition (POD) technique. The present study shows that the SEREP is computationally more efficient than POD.

An iterative system equivalent reduction expansion process for extraction of high frequency response from reduced order finite element model

An iterative system equivalent reduction expansion process (SEREP) is proposed for extraction of high frequency response from a reduced-order model (ROM) under frequency band-limited excitation. Various model order reduction methods are discussed. To alleviate the present drawback of the SEREP, which requires computation of full system modal matrix, an iterative method based on Sturm sequence check is proposed. The method uses eigenvalue separation properties on the excitation frequency band to identify the optimal number of the eigenpairs required to capture the accurate response. The basic steps for numerical implementation are given. Numerical results are presented to validate the predicted response. Comparison is also made to explain the reasons for the instability of the ROM based on dynamic condensation to capture the high frequency dynamics. Case studies are carried out to demonstrate the effect of the chosen frequency band for response extraction. Also, it is shown that accurate results are obtained while using the proposed method when the chosen frequency band encompass the excitation frequency band.

Comment on "Improvement in Model Reduction Schemes Using the System Equivalent Reduction Expansion Process"

1 0.000001 0.000000 0.000072 0.000000 0.025081 0.000056 2 0.000417 0.000000 0.026975 0.000012 0.311917 0.534706 3 0.003388 0.000000 0.335096 1.08737 0.917563 1.51624 4 0.014125 0.000023 0.946580 1.40021 1.50816 1.50714 5 0.037918 0.000387 1.67978 1.88315 2.15232 2.82557 6 0.040935 0.005863 2.51075 2.50444 2.92630 3.33190

Comment on 'Improvement in model reduction schemes using the system equivalent reduction expansion process'

Comment on 'Improvement in model reduction schemes using the system equivalent reduction expansion process'

Improvement in model reduction schemes using the system equivalent reduction expansion process

The SEREP produces an exact reduced model. However, this method requires knowledge of the full system eigenvectors. An extension of this method was presented that uses only the mode shapes of a reduced system. The reduced system mode shapes can be obtained from any reduction procedure, including Guyan, for example. Results from a simulation of a cantilevered Euler Bernoulli beam validated the technique. It was shown that the method improved upon the Guyan and the IRS reduction methods provided that a proper set of master DOF were chosen