Damage Detection in Structures Based on Principal Component Analysis of Forced Harmonic Responses

peer reviewedAn approach based on principal component analysis (PCA) is considered here to tackle the problem of structural damage detection. The key idea of PCA is to reduce a large number of measured data to a much smaller number of uncorrelated variables while retaining as much as possible of the variation in the original data. PCA is applied here to the problem of damage detection in structures submitted to harmonic excitation. When processing vibration measurements, it can be shown that the basis of eigenvectors (called the proper orthogonal modes) span the same subspace as the mode-shape vectors of the monitored structure. Thus the damage detection problem may be solved using the concept of subspace angle between a reference subspace spanned by the eigenvectors of the initial (undamaged) structure and the subspace spanned by the eigenvectors of the current (possibly damaged) structure. The method is illustrated on the example of a real truss structure for damage detection and is combined to a model updating technique for damage localization

Electro-mechanical Coupling in MEMS: Modeling and Experimental Validation

This paper presents the advantages of a strong coupled formulation to model the electro-mechanical coupling appearing in MEMS. The classical modeling approach is to use a staggered methodology iterating between two different programs to obtain the solution of the coupled problem. In this research a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed. Using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and accurately determine the static pull-in voltage. Moreover, the natural frequencies may be computed around each equilibrium positions. The dynamic behavior of the structure may also be studied and two new parameters are defined: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimization and extended finite elements

Development of numerical algorithms for practical computation of nonlinear normal modes

When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a nonlinear bladed disk is considered to demonstrate the developments

Model Updating Based on Frequency Response Functions Using A General Finite Element Code

peer reviewedModel updating techniques using frequency response function (FRF) data are studied in this paper. The numerical techniques are discussed for implementation with a large commercial finite element (FE ) code. System equivalent reduction expansion process is adopted to reduce the complete FE solutions onto the experimental degrees of freedom. The rank-deficiency difficulty with this method is overcome using either of two numerical techniques: diagonal perturbation and singular value decomposition. This second technique is also used in solving the updating equation. Experimental FRF data are compared with the FE solutions, and the updated model parameters are obtained via an iteration procedure. A simplified frequency domain assurance criterion is proposed to evaluate the correlation between the FE model and the measured structure at the chosen frequencies. After verifying the efficiency of the methods with several benchmark tests, the program is applied to an aeroplane model test. Some conclusions are given and remaining problems illustrated

Application of ARMAV models to identification and damage detection of mechanical and civil engineering structures

peer reviewedIn this paper, the application of auto-regressive moving average vector models to system identification and damage detection is investigated. These parametric models have already been applied for the analysis of multiple input-output systems under ambient excitation. Their main advantage consists in the capability of extracting modal parameters from the recorded time signals, without the requirement of excitation measurement. The excitation is supposed to be a stationary Gaussian white noise. The method also allows the estimation of modal parameter uncertainties. On the basis of these uncertainties, a statistically based damage detection scheme is performed and it becomes possible to assess whether changes of modal parameters are caused by, e.g. some damage or simply by estimation inaccuracies. The paper reports first an example of identification and damage detection applied to a simulated system under random excitation. The `Steel-Quake' benchmark proposed in the framework of COST Action F3 `Structural Dynamics' is also analysed. This structure was defined by the Joint Research Centre in Ispra (Italy) to test steel building performance during earthquakes. The proposed method gives an excellent identification of frequencies and mode shapes, while damping ratios are estimated with less accuracy

Dynamic investigations of paddle MEMS cantilevers used in mass sensing applications

The dynamic behaviour of paddle MEMS cantilever oscillators under electrostatic actuation is investigated and presented in this paper. The scope is to estimate the influence of the geometrical dimensions and operating conditions on the frequency response of mechanical paddle cantilevers fabricated from polysilicon. Theoretical approach and finite element analysis are developed considering the multiphysics coupling between the electrical field and the mechanical structure of oscillators. The;experimental tests are performed under ambient condition and in vacuum in order to characterize the effect of operating condition on the frequency response of paddle cantilevers

Detection of nonlinearity in a dynamic system using deformation modes obtained from the Wavelet Transfrom of measured responses

An efficient approach to Structural Health Monitoring of dynamical systems based on the Wavelet Transform (WT) and the concept of subspace angle is presented. The objective is to propose a detection method that is sensitive to the onset of nonlinear behaviour in a dynamic system. For this purpose, instantaneous frequencies are identified first from output-only vibration signals using the Wavelet Transform. Time varying deformation shapes are then extracted by analyzing the whole measurement data set on the structure. From this information, different dynamic states of the structure may be detected by inspecting time variations of ‘modal’ features. The experimental structure considered here as application example is a clamped beam with a geometric nonlinearity. Detection of nonlinearity is carried out by means of the concept of subspace angles between instantaneous deformation modes extracted from measurement data using the continuous Wavelet Transform. The method consists in controlling the angular coherence between active subspaces of the current and reference states respectively. The proposed technique, which shows a good sensitivity to small changes in the dynamic behaviour of the structure, may also be used for damage detection

On the Use of Principal Component Analysis for Parameter Identification and Damage Detection in Structures

In this lecture, an approach based on principal component analysis (PCA) is considered for three purposes, namely damage detection, structural health monitoring and identification of nonlinear parameters in structural dynamics. The key idea of PCA is to reduce a large number of measured data to a much smaller number of uncorrelated variables while retaining as much as possible of the variation in the original data. The first problem to which PCA is applied here is the damage detection problem. When applied to vibration measurements, it can be shown that the basis of eigenvectors (called the proper orthogonal modes) span the same subspace as the mode-shape vectors of the monitored structure. Thus the damage detection problem may be solved using the concept of subspace angle between a reference subspace spanned by the eigenvectors of the initial (undamaged) structure and the subspace spanned by the eigenvectors of the current (possibly damaged) structure. The second problem concerns structural health monitoring of civil engineering structures when environmental effects (e.g. the influence of the variation of the ambient temperature) have to be removed from the structural changes. In this case, PCA may be applied on identified modal features (e.g. the natural frequencies) to separate the changes due to environmental variations from the changes due to damage sources. The third problem is related to the estimation of nonlinear parameters using model updating techniques. In this case, the most interesting property of PCA is that it minimizes the average squared distance between the original signal and its reduced linear representation. When applied to nonlinear problems, PCA gives the optimal approximating linear manifold in the configuration space represented by the data. The linear nature of the method is appealing because the theory of linear operators is still available. However, it should be borne in mind that it also exhibits its major limitation when the data lie on a nonlinear manifold