Structural Damage Detection Using Linear Matrix Inequality Methods

2000 ◽  
Vol 122 (4) ◽  
pp. 448-455 ◽  
Author(s):  
M. O. Abdalla ◽  
K. M. Grigoriadis ◽  
D. C. Zimmerman
Keyword(s):  
Experimental Data ◽  
Linear Matrix Inequality ◽  
Damage Detection ◽  
Structural Damage ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Structural Damage Detection ◽  
Test Bed ◽  
Stiffness Reduction

In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]

scholarly journals A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

2020 ◽  
Vol 10 (17) ◽  
pp. 5859
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
State Feedback ◽  
Optimization Problems ◽  
Seismic Protection ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Static State ◽  
Fluid Viscous Dampers ◽  
Iterative Linear Matrix Inequality

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

Flexibility-Based Objective Functions for Constrained Optimization Problems on Structural Damage Detection

2011 ◽  
Vol 186 ◽  
pp. 383-387 ◽  
Author(s):  
Xi Chen ◽  
Ling Yu
Keyword(s):  
Damage Detection ◽  
Constrained Optimization ◽  
Objective Function ◽  
Structural Damage ◽  
Optimization Problems ◽  
Objective Functions ◽  
Structural Damage Detection ◽  
Constrained Optimization Problems ◽  
Modal Assurance Criterion ◽  
Damage Scenarios

Based on concepts of structural modal flexibility and modal assurance criterion (MAC), a new objective function is defined and studied for constrained optimization problems (COP) on structural damage detection (SDD) in this paper. Compared with traditionally objective function, which is defined based on natural frequencies and MAC, effect of objective functions on robustness of SDD calculation is evaluated through numerical simulation of a 2-storey rigid frame. Structural damages are identified by solving the COP on SDD based on an improved particle swarm optimization (IPSO) algorithm. Weak and multiple damage scenarios are mainly considered in various noise conditions. Some illustrated results show that the newly defined objective function is better than the traditional ones. It can be used to identify the damage locations but also to quantify the severity of weak and multiple damages in measurement noise conditions.

An Optimal Hybrid Expansion—Reduction Damage Detection Method

2003 ◽  
Vol 9 (8) ◽  
pp. 983-995 ◽  
Author(s):  
M. Abdalla ◽  
K. Grigoriadis ◽  
D. Zimmerman
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Linear Matrix ◽  
Test Bed ◽  
Detection Problem ◽  
Lmi Optimization ◽  
Modal Data ◽  
Stiffness Matrices

In this paper, we examine the structural damage detection problem with an incomplete set of measurements. Linear matrix inequality (LMI) optimization methods are proposed to solve this hybrid damage detection problem that integrates modal data expansion and model reduction with an LMI based damage detection procedure. In the proposed hybrid approach, the transformation matrix is based on the measured data avoiding the use of the healthy mass and stiffness matrices. The method is demonstrated using experimental modal data obtained from the NASA eight-bay cantilevered truss test bed. The experimental results of this hybrid approach are shown to provide a clearer indication of damage than using stand-alone expansion or reduction techniques.

Application of an Implicit Redundant Genetic Algorithm for Structural Damage Identification of Flexible Structures

2004 ◽  
Author(s):  
T. R. Liszkai
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Damage Identification ◽  
Optimization Problems ◽  
Flexible Structures ◽  
Nuclear Industry ◽  
Superior Performance ◽  
Structural Damage Detection ◽  
Measuring Device ◽  
Structural Damage Identification

Detecting structural damage is critical in assessing current condition, calculating remaining life, and developing rehabilitation strategies for existing structures. Many structural damage identification methods (SDIM) use vibration data to localize and identify deterioration of structural members. Due to practical constraints, such as cost, number of input channels of the measuring device, or lack of access of parts of the structure, the actual number of sensors used to collect measurement data is much smaller then the number of possible sensor locations. Therefore, the inverse problem associated with structural damage identification is ill formulated and often difficult to solve explicitly. This research addresses the problem of structural damage detection using the linear vibration information contained in frequency response functions (FRF). A structural damage identification method (SDIM) is proposed, which minimizes the error between the analytically computed and measured vibration signatures of structures. The SDIM is formulated as an unconstrained optimization problem, which is solved using genetic algorithms (GA). The implicit redundant representation (IRR) of genes allows the formulation of unstructured optimization problems in which the number of unknown variables is indefinite. The IRR GA efficiently exploits the unstructured nature of structural damage detection by allowing the number of assumed damaged elements to change throughout the optimization. The accuracy and efficiency of SDIM is increased when the IRR GA is used instead of the simple fixed representation GA. The procedure is applied to flexible structures to show that the proposed SDIM is capable of identifying damages in structures often used in the nuclear industry. Noisy measurements are also considered in the simulations to investigate their effect on the proposed SDIM accuracy. Test case results using different measurement noise levels show that the IRR GA has superior performance over the standard fixed representation GA in correctly identifying both the location and extent of damages.

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