Assessment of vibration-based damage identification techniques
Introduction
Civil infrastructures begin to deteriorate once they are built and used. Maintaining safe and reliable civil infrastructure for daily use is a topic that has received considerable attention in the literature in recent years. Usual inspection techniques require the portion of the structure being inspected to be readily accessible and are therefore not appropriate due to interference with operational conditions. By definition, non-destructive techniques (NDT) are the means by which structures may be inspected without disruption or impairment of serviceability. Many methods have been developed for NDT, and an overview of the various techniques is presented by Witherell [1]. Some techniques are based on visual observations and some are based on the properties of the material. Other techniques are based on the interpretation of the structural condition by observing the change in the global behavior of the structure. The use of vibration test data to determine structural characteristics falls into this last category and are the subject of this paper.
The need of non-destructive and global techniques for structure diagnosis has led to the continuous development of methods examining the changes of dynamic characteristics. Such an approach has been introduced for several years in fields like automotive, aeronautical and mechanical engineering. The basic premise of the global damage detection methods that examine changes in the dynamic properties is that modal parameters, notably resonant frequencies, mode shapes, and modal damping, are a function of the physical properties of the structure (mass, damping, stiffness, and boundary conditions). Therefore, changes in physical properties of the structure, such as its stiffness or flexibility will cause changes in modal properties.
However, as any NDT, vibration-based damage identification techniques (VBDIT) are driven by many factors that can influence the result in the adequate decision as to the absence or presence of a damage. In general, any VBDIT comprises the application of a stimulus to a structure and the interpretation of the response to this stimulus. Repeated inspections of a specific damage will produce different response magnitudes of stimulus response because of minute variations in setup and calibration. This variability is inherent to the process. This is particularly the case when performing dynamic testing: the structural response is first recorded and then analyzed in order to extract, for instance, modal parameters. The data quality (signal-to-noise ratio) and the identification method can affect considerably the results regarding damage detection.
Mazurek [2], Doebling and Farrar [3] are the pioneers in examining the statistical significance of damage identification results. This statistical significance was studied via application to the data from tests performed on the Interstate 40 highway bridge in Albuquerque, New Mexico. Since then, different aspects of these methods have been investigated on the bases of experimental results mostly obtained from existing bridges [4], [5]. It is the intent of this paper to explore further the issue of the statistical significance of the changes for a particular damage indicator. The approach demonstrated in this paper uses random noise simulations to compute probabilities of damage detection and probabilities of false alarm. These probabilities allow to estimate performance qualification of a VBDIT.
Section snippets
Vibration-based damage identification techniques (VBDIT): a review
In this section, the current VBDIT which are validated by a number of experimental results [4], [5] will be reviewed. As in practical damage evaluation it would be always difficult to excite the structural high modal frequencies (need of high quantity of energy), all selected techniques requiring few mode shapes and/or modal frequencies. These methods do not require an analytical model of the structure, only some modal frequencies and mode shapes, before and after damage are necessary which can
Principle of study and noise simulation
In order to study the performance of the presented VBDIT regarding different factors that can have an influence on detection results, a model of a continuous beam was selected as the test model. The model consisted of 20 elements (2 nodes linear elements with 3 degree of freedom per node); for better demonstration the elements are presented in two dimensions (Fig. 3). Values for the material properties of the beam elements were assigned as follows: (1) the elastic modulus ; (2) the
Probabilities of detection and false alarm
The mode shape curvature, change in flexibility and change in flexibility curvature methods present the quantity of variation in each degree of freedom, so the degree of freedom which presents the maximum variation will identify the location of damage. In contrast with the other techniques the strain energy method does not provide the absolute value of variation, therefore as mentioned before, it is necessary to introduce the concept of threshold level. A damage is detected if the normalized
Study procedure
A random force for a period of 40 s (Fig. 6) was applied to node 6 of the presented beam (Fig. 3). To study the influence of the damaged element location in comparison with the force application point, several damaged elements located at different sections along the beam length were considered. Afterwards, the case of simultaneous damaged elements was considered. As presented methods are based on few numbers of mode shapes and/or modal frequencies, in the carried out simulation, only the three
Damaged element far from the source of excitation
Element 11, located near the mid-span of the beam and therefore at a far distance from the point of excitation is first considered as a damaged element (Fig. 3). The probabilities of detection and false alarm provided by the strain energy method for three threshold level are shown in Fig. 8. As we discussed, the results are functions of the selected threshold level; by decreasing the threshold level the probability of detection and false alarm increase. Considering
Simulation results for two damaged elements
In order to evaluate noise effect on the results of the simultaneous damaged elements, two scenarios of damage were considered; first the two damaged elements were positioned relatively far from the supports and the excitation point and in the second, one of these damaged elements were located near a support. The following paragraphs present the details of these scenarios.
Conclusions
The purpose of the present paper has been to illustrate how practically used VBDIT would behave in presence of variability in modal parameters which are often inevitable. As the sources of this variation are often unknown, noise simulations were introduced as a first approach to the problem. Different levels of noise were added to the response signals of a simple supported beam and the modal parameters of the noisy signals were identified. Applying VBDIT to identified modal parameters with
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