110 G.N. Stevens et al. Fig. 10.4 Experimental variability in wavenumber where spurious peaks are observed in the LDV measurements. (a) SLGU measurements. (b) LDV measurements causing corrosion, would exhibit an increase in wavenumber (recall Fig. 10.2a) in the presence of damage. A change in the effective thickness may also result from cases where materials in a structure separate, such as delamination in composites and debonding in pipes with protective coating, resulting in an increased wavenumber (recall Fig. 10.2b). 10.4 Methodology 10.4.1 Damage Detection Through Inverse Analysis Damage detection methods can be separated into two distinct categories: model-based and nonmodel-based. Model-based methods compare experimental measurements to analytical, physics-based model predictions to localize and quantify the severity of damage in a structure. Nonmodel-based methods correlate data from undamaged and damaged scenarios to detect the presence of damage and are typically only capable of damage localization [5], meaning that they cannot quantify the severity of damage. Model-based methods result in an inverse analysis, where observed measurements are used to infer model parameters related to the damage feature [17]. While model-based methods tend to be more computationally expensive, they carry the distinct advantage of quantifying the severity of damage. The focus herein is a model-based method for NDE. For model-based damage detection, a numerical model that mathematically describes the phenomenon of interest is used to predict the behavior of a physical process at a specified control setting. Numerical models seek to represent engineering principles defining the underlying physics of the problem, (x,t), where t is the true value of physical parameters (material properties in this application) and x is the control settings that define the domain of the application (excitation frequency in this application). True parameter values are often unknown and as such, best estimates of these parameter values, , areused in the model. Incomplete representation of these engineering principles results in model form error (or model bias), (x). Model form error is only known at settings where experiments have been conducted. Thus, an estimate of model form error is necessary for untested settings of the domain. Model form error can be estimated at untested settings using an empirically trained function, referred to as discrepancy, ı(x). Similarly, experimental measurements, y(x), contain experimental error, ", as they are noisy representations of reality. Thus, experimental measurements are related to the numerical model accordingly: y.xi/ D˜.xi; i/ C•.xi/ C"i where i D1;2; : : : ; n (10.5) Said differently, experiments, y(x), can be described as the sum of the best estimate numerical model predictions, (x, ), discrepancy, ı(x), and experimental error, " for n unique experimental settings within this framework. Table 10.1 details the parameters of the guided Lamb wave propagation (LWP) model for the application of the model within this framework.
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