ABSTRACT
The uncertainty in material properties of an anisotropic plate may influence the acoustic source localization process undertaken for the plate. To study this effect of material uncertainty, the two moduli of elasticity of an orthotropic plate material are considered in this note as independent random variables and the propagation of this material uncertainty through the wave front shape-based acoustic source localization approach is investigated. Assuming lognormal probability distributions for the two random variables, several design points in lognormal spaces are picked using Latin Hypercube Sampling. Finite element analysis is performed for each design point to simulate the elastic wave propagation due to an acoustic event and wave front shape-based approach is applied to estimate the source location. The time-of-arrivals and source localization errors obtained for each design point are considered as separate response functions at that design point and regression kriging metamodels through the responses at the design points are constructed. Monte Carlo simulations are carried out using these metamodels to obtain the distribution parameters (i.e., ranges, means and standard deviations) of the time-of-arrivals and localization errors. A global sensitivity analysis is performed to estimate the effect of each random variable on the localization errors. It is observed that for lognormally distributed moduli of elasticity with same coefficients of variation, uncertainty in the modulus of elasticity in the major direction affects the source localization accuracy more compared to the uncertainty in the modulus of elasticity in the minor direction, particularly when the ellipse-based technique is used.
ABSTRACT
Development of acoustic source localization techniques in anisotropic plates has gained attention in the recent past and still has scope of improvement. Most of such techniques existing in the literature either require known material properties or assume a straight line propagation of wave energy from the acoustic source to a sensor. These limitations have been overcome in recent years by employing wave front shape-based techniques. However, the existing wave front shape-based techniques are applicable in situations where the orientation of the axes of symmetry of the anisotropic plate is known beforehand. In the present study, a modified version of these techniques, namely, elliptical and parametric curve-based techniques, is proposed. This new version is useful when the angle between the axes of symmetry and the reference Cartesian coordinate system is unknown. In the new definition of the objective function, the orientation of the axes of symmetry of the anisotropic plate is treated as an input in the objective function in addition to the other unknowns like the source coordinates and the curve parameters. A numerical study illustrates how the modified new techniques can localize the acoustic source with sufficient accuracy in an anisotropic plate with unknown orientation of the axes of symmetry and its material properties.
ABSTRACT
Estimating the location of an acoustic source in a structure is an important step towards passive structural health monitoring. Techniques for localizing an acoustic source in isotropic structures are well developed in the literature. Development of similar techniques for anisotropic structures, however, has gained attention only in the recent years and has a scope of further improvement. Most of the existing techniques for anisotropic structures either assume a straight line wave propagation path between the source and an ultrasonic sensor or require the material properties to be known. This study considers different shapes of the wave front generated during an acoustic event and develops a methodology to localize the acoustic source in an anisotropic plate from those wave front shapes. An elliptical wave front shape-based technique was developed first, followed by the development of a parametric curve-based technique for non-elliptical wave front shapes. The source coordinates are obtained by minimizing an objective function. The proposed methodology does not assume a straight line wave propagation path and can predict the source location without any knowledge of the elastic properties of the material. A numerical study presented here illustrates how the proposed methodology can accurately estimate the source coordinates.
