Use of LU Decomposition of Modal Flexibility in Structural Damage Detection: Numerical Validation

2013 ◽  
Vol 569-570 ◽  
pp. 986-993
Author(s):  
Yong Hui An ◽  
Jin Ping Ou
Keyword(s):  
Structural Damage ◽  
Numerical Study ◽  
Damage Index ◽  
Triangular Matrix ◽  
Mathematical Tool ◽  
Lu Decomposition ◽  
Flexibility Matrix ◽  
Modal Flexibility ◽  
The Matrix ◽  
Upper Triangular Matrix

The flexibility can be approximately synthesized with the first several measured modal parameters, i.e. the so called modal flexibility. The modal flexibility matrix will change with damage in a structure, and the change of modal flexibility should contain the information of damage. It is important to find a damage index that can pick up damage from the change of modal flexibility. To address this issue, the mathematical tool LU decomposition is introduced to deal with the modal flexibility matrix in order to find damage clearly. After decomposition, the modal flexibility is decomposed into a lower triangular matrix L and an upper triangular matrix U. Numerical results of both single and multiple damage cases under white noise excitation indicate that the matrix U has enough information of damage; and the proposed new technique can be utilized to locate the damage accurately. The present numerical study will lay a foundation for the application of real-time structural health monitoring in experiments and engineering.

FEM Free Damage Detection of Beam Structures Using the Deflections Estimated by Modal Flexibility Matrix

2021 ◽  
pp. 2150128
Author(s):  
Wen-Yu He ◽  
Wei-Xin Ren ◽  
Lei Cao ◽  
Quan Wang
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Damage Index ◽  
Element Model ◽  
Mode Shapes ◽  
Beam Structures ◽  
Flexibility Matrix ◽  
Damage Quantification ◽  
Modal Flexibility ◽  
The Cost

The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

Scaled Acoustics Experiments and Vibration Prediction Based Structural Health Monitoring

2008 ◽  
Author(s):  
Nesrin Sarigul-Klijn ◽  
Israel Lopez ◽  
Seung-Il Baek
Keyword(s):  
Health Monitoring ◽  
Dimensional Reduction ◽  
Structural Damage ◽  
Numerical Study ◽  
Damage Index ◽  
Time Frequency ◽  
Structural Health ◽  
Reduction Techniques ◽  
Vibration Prediction ◽  
Dimensional Reduction Techniques

Vibration and acoustic-based health monitoring techniques are presented to monitor structural health under dynamic environment. In order to extract damage sensitive features, linear and nonlinear dimensional reduction techniques are applied and compared. First, a vibration numerical study based on the damage index method is used to provide both location and severity of impact damage. Next, controlled scaled experimental measurements are taken to investigate the aeroacoustic properties of sub-scale wings under known damage conditions. The aeroacoustic nature of the flow field in and around generic aircraft wing damage is determined to characterize the physical mechanism of noise generated by the damage and its applicability to battle damage detection. Simulated battle damage is investigated using a baseline, and two damage models introduced; namely, (1) an undamaged wing as baseline, (2) chordwise-spanwise-partial-penetration (SCPP), and (3) spanwise-chordwise-full-penetration (SCFP). Dimensional reduction techniques are employed to extract time-frequency domain features, which can be used to detect the presence of structural damage. Results are given to illustrate effectiveness of this approach.

scholarly journals Structural Damage Diagnosis-Oriented Impulse Response Function Estimation under Seismic Excitations

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5413
Author(s):  
Jian-Fu Lin ◽  
Junfang Wang ◽  
Li-Xin Wang ◽  
Siu-seong Law
Keyword(s):  
Damage Detection ◽  
Impulse Response ◽  
Response Function ◽  
Structural Damage ◽  
Numerical Study ◽  
Damage Index ◽  
Impulse Response Function ◽  
Function Estimation ◽  
Seismic Excitations ◽  
Transformation Matrices

Impulse response function (IRF) is an ideal structural damage index for the identification of structural damage associated with changes in modal properties. However, IRFs from multiple excitations applied at different degrees-of-freedoms jointly contribute to the dynamic response, and their estimation is often underdetermined. Although some efforts have been devoted to the estimation of IRF for a structure under single excitation, the case under multiple excitations has not been fully investigated yet. The estimation of IRF under multiple excitations is generally an ill-conditioned inverse problem such that an incorrect or non-feasible solution is common, preventing its application to damage detection. This work explores this problem by introducing dimensionality reduction transformation matrices relating two sets of IRFs of a structure with discussions on the performance of the non-unique transformation matrices. Then, the extraction of IRF via wavelet-based and Tikhonov regularization-based methods are compared. Finally, a numerical study with a truss structure is conducted to validate the estimation of the IRFs and to demonstrate their applicability for damage detection under seismic excitations. Both the damage locations and severity are accurately identified, indicating the proposed methodology can enable the IRFs estimation under multiple excitations for successful damage detection.

scholarly journals A New Flexibility Based Damage Index for Damage Detection of Truss Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
M. Montazer ◽  
S. M. Seyedpoor
Keyword(s):  
Damage Detection ◽  
Modal Analysis ◽  
Structural Damage ◽  
Damage Index ◽  
Truss Structures ◽  
Structural Elements ◽  
Reliable Tool ◽  
Flexibility Matrix ◽  
Strain Change ◽  
Flexibility Index

A new damage index, called strain change based on flexibility index (SCBFI), is introduced to locate damaged elements of truss systems. The principle of SCBFI is based on considering strain changes in structural elements, between undamaged and damaged states. The strain of an element is evaluated using the columnar coefficients of the flexibility matrix estimated via modal analysis information. Two illustrative test examples are considered to assess the performance of the proposed method. Numerical results indicate that the method can provide a reliable tool to accurately identify the multiple-structural damage for truss structures.

scholarly journals Online Monitoring of Flexural Damage Index of a Cable-Stayed Bridge

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Byeong Hwa Kim
Keyword(s):  
Structural Damage ◽  
Damage Index ◽  
Assessment System ◽  
Modal Parameters ◽  
Time Signal ◽  
Central Difference ◽  
Cable Stayed Bridge ◽  
Modal Flexibility ◽  
Deck Plate ◽  
Difference Formula

This work introduces a recent application of the online nondestructive damage assessment system into a cable-stayed bridge. A set of ambient modal parameters are automatically extracted every 20 minutes using real-time signal data collected from a total of 26 accelerometers attached on the deck plate of the bridge. Then, a set of modal flexibilities are reconstructed by the combination of the extracted modal parameters with the approximated modal mass of the girder. Next, the curvature of the modal flexibility is approximated by a central difference formula. Finally, the set of flexural damage index equations is constructed by comparing the modal curvature of the damaged state to that of the undamaged state. Solving the overdetermined flexural damage index equations, the desired damage index is finally quantified. The resulting index clearly indicates the location and severity of the potential structural damage on the girder. Based on the overall performance of the implemented health monitoring system, the bridge operator’s damage index control criteria are set to ±20% of the undamaged state.

scholarly journals On two open problems about strongly clean rings

2004 ◽  
Vol 70 (2) ◽  
pp. 279-282 ◽  
Author(s):  
Zhou Wang ◽  
Jianlong Chen
Keyword(s):  
Matrix Ring ◽  
Triangular Matrix ◽  
Open Problems ◽  
Clean Rings ◽  
Clean Ring ◽  
The Matrix ◽  
Triangular Matrix Ring ◽  
Semiperfect Ring ◽  
Upper Triangular Matrix ◽  
Upper Triangular Matrix Ring

A ring is called strongly clean if every element is the sum of an idempotent and a unit which commute. In 1999 Nicholson asked whether every semiperfect ring is strongly clean and whether the matrix ring of a strongly clean ring is strongly clean. In this paper, we prove that if R = {m/n ∈ ℚ: n is odd}, then M2(R) is a semiperfect ring but not strongly clean. Thus, we give negative answers to both questions. It is also proved that every upper triangular matrix ring over the ring R is strongly clean.

On a hybrid use of structural vibration signatures for damage identification: a virtual vibration deflection (VVD) method

2016 ◽  
Vol 23 (4) ◽  
pp. 615-631 ◽  
Author(s):  
Hao Xu ◽  
Zhongqing Su ◽  
Li Cheng ◽  
Jean-Louis Guyader
Keyword(s):  
Structural Damage ◽  
Damage Identification ◽  
Numerical Study ◽  
Damage Index ◽  
Structural Vibration ◽  
Single Type ◽  
Structure Identification ◽  
Detection Accuracy ◽  
Beam Model ◽  
Vibration Signatures

A damage identification method named virtual vibration deflection (VVD) was developed, the principle of which was formulated based on the “weak” modality of the pseudo-excitation (PE) approach previously established. In essence, VVD is based on locating structural damage within a series of “sub-regions” divided from the entire structure under inspection, and each sub-region was considered as a “virtual” structure undergoing independent vibration. The corresponding vibration deflection of the “virtual” structure was then used to derive the damage index of VVD. Besides various advantages inheriting from the PE approach, for example, capability of detecting damage without baseline signals and pre-developed benchmark structures, VVD exhibits improved detection accuracy and particularly enhanced noise immunity compared with the PE approach, attributed to a hybrid use of multi-types of vibration signatures (MTVS). As a proof-of-concept investigation, a beam model was used in a numerical study to examine the philosophy of VVD. And the influences from different factors (i.e., level of measurement noise and measurement density) on the detection accuracy of VVD were discussed based on the numerical model. An experiment was carried out subsequently to identify the locations of multiple defects contained in an aluminum beam-like structure. Identification results constructed by the PE approach, VVD using single-type of vibration signatures, and VVD using MTVS, were presented, respectively, for the purpose of comparison.

scholarly journals An Exact Approach for Structural Damage Assessment

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Q. W. Yang
Keyword(s):  
Damage Assessment ◽  
Structural Damage ◽  
Damage Identification ◽  
Structural Stiffness ◽  
Static Displacement ◽  
Exact Approach ◽  
Flexibility Matrix ◽  
Before And After ◽  
The Matrix ◽  
Exact Relationship

An exact approach is proposed for damage identification in statically determinate structures. The contribution of this study is twofold. Firstly, a rigorous disassembly formulation of structural global flexibility matrix is presented based on the matrix spectral decomposition, which can provide an exact relationship between the modifications of structural stiffness parameters and the associated flexibility matrix. Secondly, the static minimum-rank flexibility change is derived to obtain the exact flexibility change before and after damage. The proposed method is economical in computation and is simple to implement. For the statically determinate structures, the proposed method can exactly compute the elemental perturbed stiffness parameter only using a few of incomplete static displacement data. The efficiency of the proposed method is demonstrated by two statically determinate structures.

scholarly journals Design and implementation of dual-core MIPS processor for LU decomposition based on FPGA

2021 ◽  
Vol 11 (2) ◽  
pp. 1476
Author(s):  
Rusul Khalil Saad ◽  
Safaa S. Omran
Keyword(s):  
Control Systems ◽  
Communication Systems ◽  
Triangular Matrix ◽  
Good Alternative ◽  
Matrix Inversion ◽  
Lu Decomposition ◽  
Lower Triangular Matrix ◽  
Upper Triangular Matrix ◽  
Time Required ◽  
Dual Core

Many systems like the control systems and in communication systems, there is usually a demand for matrix inversion solution. This solution requires many operations, which makes it not possible or very hard to meet the needs for real-time constraints. Methods were exists to solve this kind of problems, one of these methods by using the LU decomposition of matrix which is a good alternative to matrix inversion. The LU matrices are two matrices, the L matrix, which is a lower triangular matrix, and the U matrix, which is an upper triangular matrix. In this paper, a design of dual-core processor is used as the hardware of the work and certain software was written to enable the two cores of the dual-core processor to work simultaneously in computing the value of the L matrix and U matrix. The result of this work are compared with other works that using single-core processor, and the results found that the time required in the cores of the dual-core is more less than using single-core. The designed dual-core processor is invoked using the VHDL language.

Sign in / Sign up

Export Citation Format

Share Document