Rough surface reconstruction of real surfaces for numerical simulations of ultrasonic wave scattering

Abstract

The scattering of waves by rough surfaces plays a significant role in many fields of physical sciences including ultrasonics where failure surfaces are often rough and their accurate identification is critical. The prediction of the strength of scattering can be hampered when the roughness is not adequately characterised and this is a particular issue when the surface roughness is within an order of the incident wavelength. Here we develop a methodology to reconstruct, and accurately represent, rough surfaces using an AutoRegressive (AR) process that then allows for rapid numerical simulations of ultrasonic wave rough surface scattering in three dimensions. Gaussian, exponential and AR surfaces are reconstructed based on real surface data and the statistics of the surfaces are compared with each other. The statistics from the AR surfaces agree well with those from actual rough surfaces, taken from experimental samples, in terms of the heights as well as the gradients, which are the two main factors in accurately predicting the wave scattering intensities. Ultrasonic rough surface scattering is simulated numerically using the Kirchhoff approximation, and comparisons with Gaussian, exponential, AR and real sample surfaces are performed; scattering intensities found using AR surfaces show the best agreement with the real sample surfaces.

Prediction of reflection amplitudes for ultrasonic inspection of rough planar defects

“…The samples were obtained via specimen separation or 50% load drop, with the resulting datasets processed and statistically characterised. The values obtained for ( V , ) for fatigue in steel are consistent with previous literature [2,21]. Values from 0.01 up to 0.5mm were reported for RMS height in A533B samples by [2], and [21] reported an average correlation length of 0.563mm in A533B.…”

“…The values obtained for ( V , ) for fatigue in steel are consistent with previous literature [2,21]. Values from 0.01 up to 0.5mm were reported for RMS height in A533B samples by [2], and [21] reported an average correlation length of 0.563mm in A533B.…”

“…As noted by Ogilvy [3], both statistical and experimental studies identified classes of rough surfaces for which distributions are close to Gaussian. Fatigue and corrosion measurements [18][19][20] have also supported this conjecture and recently, Choi et al [21] identified specific regimes for which Gaussian distributions approximate real rough surfaces well.…”

Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects

“…As well as the analytical benefits of using a well-understood statistical distribution, experimental evidence has indicated that rough surfaces possess Gaussian spectra when arising from natural processes, such as thermal fatigue [15,17]. However, recent work [18] advocates an autoregressive method to accurately represent real rough surfaces in 3D and recommends caution when assuming Gaussian roughness, advising that it performs well under certain conditions, but not universally.…”

Hidden Markov model-based digital twin construction for futuristic manufacturing systems

“…As far as the data processing is concerned, the surface heights data are a piece of time series. These data can be processed by using different approaches for the reconstruction of the surface heights [e.g., fractional Brownian motion-based simulation (Higuchi et al ., 2001), rule-based systems (Ullah and Harib, 2006), autocorrelation analysis (Chui et al ., 2013; Choi et al ., 2018), feature-based simulation (Ullah et al ., 2010), and integer-sequencedbased dynamical systems (Ullah, 2017)]. The methodologies mentioned above are highly customized, and require a large set of user-defined parameters.…”