Structural Damage Detection Using Digital Video Imaging and Wavelet Transformation

Non-contact measurement offers convenient and less expensive setup. Sometimes, they may also be the only resort because the structure is too small to be instrumented with contact sensors and/or the additional mass of the sensor is too large to use. In other cases, the structure is inaccessible due to obstruction for the case of tall/large structures such as bridges or towers. The digital imaging techniques offer an alternative to contact measurement. In this paper, use of digital video imaging is proposed for detecting damage in structures. The theory of measuring structural vibration using high-resolution images based on sub-pixel edge detection technique is demonstrated with extraction of displacement time series from video images. From displacement time series, characteristic dynamic properties, i. e., natural frequency, damping and mode shapes, are established. Mode shape difference function is introduced and derived for damage detection purpose. These mode shape difference functions are subjected to continuous wavelet transformation for determining their singularity (discontinuity) at locations of damage. A laboratory test program was carried out to implement the concepts using a high-speed digital video camera. Results show that the proposed approach of data acquisition using digital video camera is effective to provide spatially intensive time-series data for non-contact structural testing. Furthermore, it is shown that the wavelet transformation of mode shape difference functions to isolate locations of singularity is able to identify the damage and their locations. INTRODUCTION Many structures in the civil infrastructure system need constant monitoring for deciding repair, maintenance, and rehabilitation. Research efforts have been reported in the past for monitoring these structures using their dynamic characteristics (Doebling et al [24]), such as the natural frequencies and mode shapes. Previously proposed approaches overwhelmingly used accelerometers for measurement, attached to the structure at a limited number of points. The effectiveness of these approaches still needs to be demonstrated because the resolution of the acquired data is limited. Such approaches also require access to the structure, which may be costly or impractical. To circumvent these difficulties, dynamic digital imaging is proposed here for structural health monitoring. Aspects related to this approach are briefly reviewed next, before it is fully presented later. Damage and alteration to structures change their behaviors. If these changes are accurately measured, they can be used to identify and locate the structural damage and alteration. This process of identification is referred to as damage detection. Such detection should cover at least two key aspects: 1) detecting presence of damage, and 2) identifying the damage locations or neighborhoods. Doebling et al [24] presented a review for damage detection of civil structures using vibration measurement, and Dimarogonas [1] for vibration based methods for detecting cracks in particular. A number of previously proposed methods require a comprehensive dynamic analysis of the structure including a finite element analysis. This analysis is meant to establish a reference to be compared with measured results for damage identification. There are two main issues associated with this approach. 1) It is not always cost-effective to conduct dynamic analysis of a structure. 2) It is always very costly, if not impossible, to obtain valid models of finite element analysis for as-built civil structures. Without physical testing, the validity of these models cannot be confirmed. During the last two decades, structural dynamic system parameters such as natural frequencies, damping, and mode shapes have been investigated for their possible use in structural damage identification and localization. While changes in natural frequencies may be used to detect the existence of damage, the mode shapes are more important indices for damage location identification. However, measurements using traditional sensors, such as accelerometers, offer low spatial resolution for mode shapes. Hence, digital imaging as alternative to traditional measurement sensor is proposed in this research. Edge detection algorithms at sub-pixel level use information from neighboring pixels to determine the edge location within a pixel (Lan and Mohr [26]). Typical approaches of sub-pixel edge detection are as follows. 1) Fitting a predetermined edge model to that of image data (Aghajan et al [9]). 2) Convolving image data with predefined filters having sub-pixel accuracy (Huertas et al [3]). 3) Non-linearly interpolating the image data (Jensen and Anastassiou [14]). 4) Equalizing spatial moments of a selected edge model and the image data to solve for the edge parameters in the model (Lyvers et al[8]). However, these previously proposed approaches still do not meet the resolution requirement for civil structural health monitoring and damage detection. The work reported in this paper attempts to address this issue, by developing a new edge detection algorithm at sub-pixel level for high accuracy. For damage presence detection and their location determination, previous research efforts have been reported on using the difference between the mode shape’s derivatives of intact and damaged states of the structure, which result in spikes at the location of damage (Gentile and Messina [2], Pandey et al [5], Chance et al [12], Yuen [18]). It is inferred that lower modes can be more useful than higher ones in such application (Wahab and Roeck [17]). However, for using the mode shape’s derivatives, the measured data need to have high spatial resolution and low noise for reliable estimation of damage location. Hence, the difference in mode shapes for the damaged and reference states is to be used here in damage location identification, because mode shapes are less sensitive to noise. Recently, wavelet transformation has found wider application in decomposing data to localize and zoom in their local characteristics (Daubechies [10], Mallat [22]). A review is provided by Peng and Chu [27] of available wavelet transformation methods and their application to machine condition monitoring. Liew and Wang [15] found that crack location could be indicated by the variation of some wavelet coefficients along the length of a structural component. Furthermore, Wang and Deng [21] and Quek et al [23] demonstrated the potential of Haar Wavelet transformation for damage detection. Hong et al [11] presented damage detection for a beam structure using the Lipschitz exponents estimated by wavelet transform. The magnitude of Lipschitz exponent was used as an indicator of damage extent. Both numerical and experimental verification were shown utilizing continuous Mexican Hat Wavelet transformation having two vanishing moments for determining the Lipschitz exponent. It was concluded that the first mode shape is more useful than higher ones in the exponent estimation and thus in detecting damage. Lu and Hsu [13] presented a wavelet transform based method for the detection of structural damage, by comparison of the discrete wavelet transforms of the signals before and after damage in the spatial domain. THEORETICAL DEVELOPMENT A. Sub-pixel Edge Detection In digital images, traditionally an edge is defined as the location of sharp change in gray value. On the other hand, sudden changes of gray level as step function are rarely seen in real life. Instead, the change usually occurs over several neighboring pixels. Depending on the characteristics of the edge several model have been proposed, step edges, roof edges, and ramp edges. Edges convey information on the images objects and scene content, which is used extensively in visual recognition. Thus, edge detection is important for feature detection, segmentation, and motion analysis. To realistically model edges, it is critical to understand the process of image formation. This process along with sub-pixel edge detection is discussed in length and can be found in the paper [25]. Two dimensional light intensity variation model around edge is modeled as: ( ) ) ( ) , ( 2 R Qx Px y k h y x W a + + − Φ + = ′ (1) where, = Edge’s curvature at P 2 0 = x R = Edge’s Interception (edge location at y 0 = x ) Q = Edge’s slope at 0 = x = Blurring factor of edge a = Gray value of background h = Difference of gray value between dark and bright area (contrast) k = Cumulative Gaussian probability function (.) a Φ Accordingly, the gray value G is modeled as the result of photon accumulation within the pixel of image sensor as: ) , ( j i ) , ( ) , ( ) , ( 5 . 0