# Focus: Ultrasound Signal Reveals Microstructure

Physics 6, 41
A model for analyzing materials using ultrasound shows that the seemingly random fluctuations in the data may contain information about the microscopic structure.

As a steel girder or concrete slab ages, its internal microstructure may change and lead to catastrophic failure. A proposed technique for analyzing the noise in ultrasound signals, described in Physical Review E, could provide an early warning system. The method is an adaption of an analysis previously used to characterize DNA. In the new computer simulations, the technique was able to correctly identify a wide range of microstructures in a one-dimensional material.

The flooding of a river or a stock market crash may seem unpredictable, but often these events have some hidden relation to the past. The level of the river may be more likely to go up if it went up the week before, for example. It’s as if these systems retain some memory of past fluctuations, rather than having totally independent fluctuations from one moment to the next. One of the mathematical techniques for identifying such long-term memory in seemingly random data is called detrended fluctuation analysis (DFA). It has been used in the study of long-range correlations in DNA sequences [1], heart rates, human stride lengths, and temperature records.

DFA could also be useful in ultrasonic evaluation of materials. Engineers currently use the scattering of ultrasound signals in a material as a way to nondestructively test for cracks or other large-scale features. However, research in 2004 showed that DFA performed on ultrasound signals from a cast-iron sample could reveal the fractal nature of the microstructure [2]. André Vieira of University of São Paulo in Brazil and his colleagues at the Federal University of Ceará in Brazil have now developed a more general DFA framework for ultrasound inspection.

To evaluate their model, the team simulated a 2-centimeter-long chunk of a one-dimensional material made up of a series of microscale domains. Each of these domains had a distinct size and density, and the boundaries between domains acted as scattering sites for sound waves. When an ultrasonic pulse entered the sample from the left, parts of the pulse either passed through or reflected back from each domain boundary. Essentially, the different sound waves that made up the pulse performed a random walk through the material, sometimes interfering with each other along the way. The sound waves that eventually walked their way back to the left edge represented the ultrasound signal. The team generated this back-scattered signal from $1600$ simulated samples with a wide range of domain sizes and densities. Each sample had one of four possible average densities and one of four possible average domain sizes, for a total of $16$ different microstructure classes.

The simulated data appeared to be random noise, but the team used the DFA technique to check for long-range correlations that might be caused by the combination of scattering and interference. The analysis showed that for short time scales, the fluctuations were correlated, but for longer ones, they were anticorrelated (the long-range fluctuations were smaller than would be expected for purely random noise). Vieira believes this anticorrelation is due to destructive interference between different waves.

For a more sophisticated analysis, the researchers turned to tools from the field of pattern recognition, which aims to identify patterns in noisy data. For each simulated sample, they defined a 37-component “DFA vector” based on the signal’s degree of fluctuations on $37$ different time scales, from tens of nanoseconds up to tens of microseconds. The team then took a subset of these vectors to form a “training set” representing all $16$ microstructure classes. Next, they compared “test” vectors from other samples with averages of the training vectors using a technique called Gaussian discriminants. The team was able to correctly identify the class of a test sample with an error rate of less than $2$ percent.

“The technique is new in that it claims to extract far more detail from the microstructure than is currently thought possible,” says Bruce Drinkwater of the University of Bristol in the UK. “However, the underlying model is one-dimensional and hence a significant simplification over reality.” Assuming this and other simplifications can be addressed, Drinkwater suspects this technique could work for composite materials (as found in devices such as wind turbines), “where it would be really useful to be able to accurately check the various layers within such systems.”

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics based in Lyon, France.

## References

1. C-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, “Mosaic Organization of DNA Nucleotides,” Phys. Rev. E 49, 1685 (1994)
2. J. M. O. Matos, E. P. de Moura, S. E. Krüger, and J. M. A. Rebello, “Rescaled Range Analysis and Detrended Fluctuation Analysis Study of Cast Irons Ultrasonic Backscattered Signals,” Chaos, Solitons & Fractals 19, 55 (2004)

Acoustics

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