Differentiating damage effects in a structural component from the time response

Abstract

This paper proposes an approach to differentiate the effect of local anomalies on the different load-resisting capacities of a structural component made of elastic isotropic material. The sensitivities of structural dynamic response with respect to different damage indices are derived. They are then used in a time-domain sensitivity-based algorithm for model updating using a gradient-based approach. A planar frame structure is studied in the numerical simulation. Results show that the proposed method can effectively locate and quantify the different types of damage effects, and the proposed method is insensitive to measurement noise. Laboratory verification was performed with a three-dimensional truss structure with the identified results clearly showing how much a local physical damage can change the different physical parameters that lead to the load-resisting capacities of a structural component.

Introduction

Most structures are subject to damage during their lives due to impact, earthquake, typhoon, fatigue, corrosion, etc. In general, structural damage may cause changes in the structural physical properties, and these changes will in turn affect the dynamic responses and characteristics. This fact has been widely utilized for the health monitoring of a structure. The basic idea of vibration-based non-destructive damage detection is to make use of these changes at some specific stages over the lifetime of the structure for damage assessment.

There are many non-destructive methods for damage detection. Housner et al. [1] presented an extensive summary on the state-of-the-art in the control and health monitoring of civil engineering structures. Doebling et al. [2] provided a comprehensive review on the damage detection methods by examining changes in the dynamic properties of a structure. Zou et al. [3] summarized the methods on vibration-based damage detection and health monitoring for composite structures, especially in delamination modeling techniques and delamination detection.

Damage detection usually needs a mathematical model of the structure in conjunction with experimental measurements on the structure. Finite element model (FEM) updating method is a popular tool for damage detection making use of these measurements. A large number of gradient-based model updating methods have been discussed by Friswell and Mottershead [4]. All of them have been used for damage detection [5], [6], [7], [8], [9]. One of the major difficulties in using finite element model updating method lies in the differentiation between the local damages and modeling errors in the structure [10], and a two-stage method has been proposed to overcome this problem [11]. The finite element model of the undamaged structure is firstly updated to remove most of the model errors to have a more accurate model. Then the differences in the modal parameters between the damaged and the intact structures are used to estimate the changes in the system parameters.

The selection of parameters is always a problem with the model updating of a structure [11]. They should exist in the undamaged state of the structure. There may be different types of local damages, e.g. fatigue, crack, seizure of the connection, scaling, loss of material, etc. New measures that are features of the local anomalies appear after the damage occurrence, e.g. the orientation, and length and depth of a crack in a plate. These measures are not known in the damage assessment exercise, and therefore some sorts of parameters that generally describe the load-carrying capacities of the structural components are used. The geometrical and physical parameters of the original finite element model are usually adopted as the parameters for updating. The common practice is to take an equivalent reduction of the elastic modulus of material in the damage detection [12], [13], [14], [15] whereas the real damage could be a hole, a crack or a loss of material in the component. Such an approach would lead to inaccurate identified results with errors smeared throughout the structure.

The identification approaches are mainly based on the changes in the natural frequencies, mode shapes or measured modal flexibility [11]. The major obstacle of using this approach is the requirement of a large number of measuring locations for a better spatial information of the measured data, and the subsequent data processing, which may introduce additional errors in the resulting modal parameters via the Fast-Fourier Transform approach. However, the time-domain approach takes advantage of the time dimension of the plentiful measured data to formulate an over-determined set of equations for finite element model updating and damage detection. The response data at a location at one discretized time instance forms one identification equation in the proposed approach, and only a few accelerometers on the structure are required with minimum measurement activity and disturbance to the structure. The loss of damage information with pre-processing of the measured data can also be avoided. Cattarius and Inman [16] have used the time histories of vibration response of the structure to identify damage in smart structures. Majumder and Manohar [17] have proposed a time-domain approach for damage detection in beam structures using vibration data. The vibration induced by a vehicle moving on a bridge deck was taken to be the excitation force. Also Koh et al. [18] have studied the structural stiffness parameters of a multi-storey framework in a time-domain system identification method. Li and Law [19] proposed a new method for local damages in structures in time-domain using the unit impulse response (UIR) functions obtained from a structure under support excitation. The extraction of the UIR with the aid of discrete wavelet transform from the measured acceleration is described, and a two-step model updating method is adopted for identifying the local damages. Satisfactory identified results can be obtained. However, they modeled the local structural damage as a reduction in Young's modulus without differentiating the damage type. Link and Weiland [20] presented a multi-model updating technique based on a conjunction with modal residuals (eigen-frequencies and mode shapes) and time history residuals.

Engineers would like to know the load-resistance properties of each structural component after an occurrence of damage incidence. And for structures made of isotropic elastic material, such capacity would depend on the properties of the connection and on the different physical and geometric properties of the component, viz. the cross-sectional area, second moments of inertia, polar moment of inertia of cross-section, etc. Therefore, a more satisfactory approach for the damage detection problem should give answers on the location and magnitude of the damage as well as their effects on the different load-carrying-capacities of the structure. One approach was developed by Wu and Law [21] who had differentiated the damage type in a structure using a vector of sensitivities from the eigen-parameters of each structural member.

This paper does not attempt to identity the exact type of local anomalies experienced by the structure, but rather their effect on the different load-carrying capacities of the structural component. The sensitivities of dynamic response with respect to different damage indices of a structure are calculated. The problem of coupling between different indices is addressed and the originally coupled parameters can now be estimated separately. The type of structural damage is differentiated by a gradient-based model updating method based on dynamic response sensitivity. Numerical simulation with a planar frame shows that the proposed method is insensitive to the measurement noise using short duration of data from as few as two accelerometers. The proposed method was further verified with laboratory work carried out on a three-dimensional truss structure. The identified results clearly show how much a local physical damage can affect the different parameters that lead to the load-carrying capacities of a structural component.