Abstract: Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.
Abstract: Model updating method has received increasing
attention in damage detection structures based on measured modal
parameters. Therefore, a probability-based damage detection
(PBDD) procedure based on a model updating procedure is
presented in this paper, in which a one-stage model-based damage
identification technique based on the dynamic features of a structure
is investigated. The presented framework uses a finite element
updating method with a Monte Carlo simulation that considers the
uncertainty caused by measurement noise. Enhanced ideal gas
molecular movement (EIGMM) is used as the main algorithm for
model updating. Ideal gas molecular movement (IGMM) is a multiagent
algorithm based on the ideal gas molecular movement. Ideal
gas molecules disperse rapidly in different directions and cover all
the space inside. This is embedded in the high speed of molecules,
collisions between them and with the surrounding barriers. In IGMM
algorithm to accomplish the optimal solutions, the initial population
of gas molecules is randomly generated and the governing equations
related to the velocity of gas molecules and collisions between those
are utilized. In this paper, an enhanced version of IGMM, which
removes unchanged variables after specified iterations, is developed.
The proposed method is implemented on two numerical examples in
the field of structural damage detection. The results show that the
proposed method can perform well and competitive in PBDD of
structures.
Abstract: This paper presents an effective model updating strategy for damage localization and quantification in frames by defining damage detection problem as an optimization issue. A generalized version of the Modal Residual Force (MRF) is employed for presenting a new damage-sensitive cost function. Then, Grey Wolf Optimization (GWO) algorithm is utilized for solving suggested inverse problem and the global extremums are reported as damage detection results. The applicability of the presented method is investigated by studying different damage patterns on the benchmark problem of the IASC-ASCE, as well as a planar shear frame structure. The obtained results emphasize good performance of the method not only in free-noise cases, but also when the input data are contaminated with different levels of noises.
Abstract: Structures such as buildings, bridges, dams, wind turbines etc. need to be maintained against various factors such as deterioration, excessive loads, environment, temperature, etc. Choosing an appropriate monitoring system is important for determining any critical damage to a structure and address that to avoid any adverse consequence. Structural Health Monitoring (SHM) has emerged as an effective technique to monitor the health of the structures. SHM refers to an ongoing structural performance assessment using different kinds of sensors attached to or embedded in the structures to evaluate their integrity and safety to help engineers decide on rehabilitation measures. Ability of SHM in identifying the location and severity of structural damages by considering any changes in characteristics of the structures such as their frequency, stiffness and mode shapes helps engineers to monitor the structures and take the most effective corrective actions to maintain their safety and extend their service life. The main objective of this study is to review the overall SHM process specifically determining the natural frequency of an instrumented simply-supported concrete beam using modal testing and finite element model updating.
Abstract: Model updating is an inverse eigenvalue problem which
concerns the modification of an existing but inaccurate model with
measured modal data. In this paper, an efficient gradient based
iterative method for updating the mass, damping and stiffness
matrices simultaneously using a few of complex measured modal
data is developed. Convergence analysis indicates that the iterative
solutions always converge to the unique minimum Frobenius norm
symmetric solution of the model updating problem by choosing a
special kind of initial matrices.
Abstract: A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.
Abstract: In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.
Abstract: The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p
Abstract: One of the difficulties of the vibration-based damage identification methods is the nonuniqueness of the results of damage identification. The different damage locations and severity may cause the identical response signal, which is even more severe for detection of the multiple damage. This paper proposes a new strategy for damage detection to avoid this nonuniqueness. This strategy firstly determines the approximates damage area based on the statistical pattern recognition method using the dynamic strain signal measured by the distributed fiber Bragg grating, and then accurately evaluates the damage information based on the Bayesian model updating method using the experimental modal data. The stochastic simulation method is then used to compute the high-dimensional integral in the Bayesian problem. Finally, an experiment of the plate structure, simulating one part of mechanical structure, is used to verify the effectiveness of this approach.
Abstract: In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw