based on the differences in arrival times to each element. This widely used method has been applied to damage detection methods in the active pitch-catch applications [13, 14]. However, the interference of reflections and dispersion are a major drawback in conventional time-of-arrival beamforming applications. The same issue is observed in ocean acoustic applications where multiple arrivals are seen due to reflections off the surface and sea bottom. An alternate approach was developed. Instead of using one particular wave path, the entirety of the arrival structure is used in what is known as matched-field processing (MFP) [15–17]. In this method the look direction is constructed through a known full-field result. Because of the multiple arrival structure in the time domain it is more appropriate to work in the frequency domain. Returning to the passive long-time correlations, the full-field impulse response function is simply the long-time averaged cross correlation function in a diffuse field. This powerful result means array signal processing methods can be used on the passive reconstructed impulse response function. This technique has been demonstrated in ocean acoustics [18]. This method is studied in this paper as applied to damage detection in a composite wind turbine blade. Rotor blades in utility sized wind turbines are a very attractive structure for passive monitoring because they see significant as well as stochastic loads and pressure waves during operation. 8.2 Background 8.2.1 Correlation Function in Diffuse Fields The derivation of the extraction of the impulse response function from long-time averaged cross correlations can be found in literature [3, 7]. The basic result is expressed as a cross correlation function with two components, a causal and anticausal function (Eq. 8.1). The positive and negative time components correspond to the two directional impulse response functions between the two sensors. In a linear system, these two equal each other by the reciprocity principle. This similarity has been previously studied as a metric for damage detection in both an active-passive approach and a passive approach [9, 19]. In this experiment, each side represents the two impulse response functions for the sensor pair used in the array signal processing approach. dCi j tð Þ dt hji tð Þ hi j t ð Þ ð8:1Þ It is important to note that the forward and backward impulse response functions are only estimated to the degree that the noise sources are diffuse and broadband. A diffuse field requires spatially and temporally random sources. Because this is practically impossible to obtain in any application, care needs to be taken when observing the similarity between the forward and backwards portions of the cross-correlation function. For example, if noise sources are biased towards the side of one sensor then the two impulse response functions will differ by some amount. In addition to noise distribution, other factors to consider are frequency dependent attenuation in structure and sensor spacing. 8.2.2 Matched-Field Processing The MFP method is the spatial representation of the plane-wave beamforming because it uses the full-field solution at a spatial point for determining the look direction [17]. The algorithms for improving the look-direction, such as the minimumvariance and a constraint on white-noise, can still be used [20, 21]. MFP x; y; ð Þ¼ w* x; y; ð ÞsðÞ 2 ¼ w* x; y; ð ÞsðÞs*ðÞw x; y; ð Þ ð 8:2Þ The MFP ambiguity output can be written as a function of spatial position, where the replica vector, w(x,y ), is of length of the number of sensors in the array and the cross spectral density matrix (CSDM), K()¼s()s*(), is simply the hermitian product of the data vector. The replica vector can be formed through numerical simulation or by experiment. In this paper, the replica vector is obtained through experiment. The benefits of obtaining a replica vector through an experiment is it is the most 68 J.D. Tippmann and F.L. di Scalea
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