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Signal Processing of Ultrasonic Backscattered Echoes for Evaluating the Microstructure of Materials — a Review
Abstract
The microstructure evaluation of materials using ultrasonic backscattered echoes has significant practical implications. Ultrasonic backscattered grain echoes are random signals which bear information related to the attenuation caused by scattering and absorption. The variation of attenuation as a function of position and frequency represents changes in the scattering cross-section and absorption effects of grains. We present a statistical model of backscattered signals which is used for developing signal processing techniques in both time and frequency domain. The attenuation in the backscattered signal is evaluated by performing temporal and spatial averaging. The spectral shift in the backscattered signal is characterized using moment analysis. Furthermore, frequency-dependent attenuation is estimated by applying cepstral processing. Experimental results using steel samples of different grain sizes are in close agreement with theoretical predictions.
... These include not only material-but also tissueoriented applications. In345 the authors considered measuring the attenuation from the time domain envelope, not taking into account the frequency dependence. In [3] the possibility of measuring the frequency dependent attenuation by computing the logspectral difference at different depths was also considered. ...
... In345 the authors considered measuring the attenuation from the time domain envelope, not taking into account the frequency dependence. In [3] the possibility of measuring the frequency dependent attenuation by computing the logspectral difference at different depths was also considered. Assuming a linear dependence on frequency, the attenuation slope may be estimated by a linear fitting to the log-spectral difference678. ...
... In some cases [7, 8, 10, 11], under the linear dependence hypothesis and assuming a Gaussian envelope pulse, explicit relations between the attenuation slope and the representative frequency can be obtained. In other cases [3, 12, 13], there are experiments directly showing correlations between the centroid frequency and properties of the material such as the grain size. In this paper we present some new contributions to the problem of estimation of attenuation by means of time– frequency analysis of the backscattering noise. ...
We consider in this paper the general problem of ultrasonic characterization of materials by means of analysing the dependence of attenuation on the frequency and depth of the backscattering noise. Some theoretical analysis is included to define the procedure and to gain insights into the suitability of the approach. From the depth-and frequency-dependent attenuation diagrams we may derive material signatures to be used for classification-oriented problems or derive parameters to be correlated with material properties. A particular case is considered: the characterization of cement pastes. For this case we propose the use of attenuation profiles as material signatures, and we show that the area of the profile exhibits good correlation with the porosity measured by destructive methods.
... A tentative alternative is to characterize the material by using the many superimposed echoes scattered by the inner microstructure of the material. This generates the so called grain noise (GN) [2], [3], [5], [6], [10]- [12], [15]. The only constraint to obtain GN is to use an adequate excitation frequency so that [ ] 3 . ...
... Linear dependence is a realistic hypothesis in tissue analysis, but it is not valid in general for all materials. Instead, in [10], [11], [12], [15], the representative frequency variations are directly correlated with material properties, in a purely experimental manner, with no special constraints about the attenuation dependence on frequency. In [5], the maximum energy frequency profiles are considered for flaw detection. ...
In this paper, we propose a technique for material characterization by using centroid frequency profiles (CFP) of ultrasound echo signals. These echo signals are composed by grain noise due to the superposition of many small echoes from the inner microstructure plus observation noise. A CFP indicates the centroid frequency dependence on depth, corresponding to power spectrum density assessments at different depths. We show in the paper the relation between the mean and variance of the CFP and the grain-to-observation-noise-ratio (GOR) at every depth. The GOR depends on the material ultrasound attenuation, so that CFP may be used for material characterization. Although we consider here the estimation of cement paste porosity, the proposed technique may have general applicability. Cement paste is the main component of mortar and concrete. Therefore, cement porosity is an important problem because the vulnerability (and thence the durability) of these construction materials to external agents depends heavily on it. Experiments have been made to show the correlation between cement paste porosity and a penetration parameter obtained from the CFP.
... En [1] y [3] los autores consideran la medida de la atenuación en el dominio temporal dejando de lado la dependencia de este parámetro con la frecuencia. La dependencia de la atenuación con la frecuencia se considera en [4] aunque de manera muy simplificada, donde se supone una dependencia lineal del coeficiente de atenuación con la frecuencia. ...
Ultrasonic backscattering noise appears in a large number of nondestructive testing applications, in the general area of tissue or materials characterization. We consider in this contributions the time-frequency analysis of backscatterin g noise with aim of obtaining depth profiles of some parameters related to the attenuation. The proposed analysis may have general applicability in the characterization of materials or tissues having depth dependent properties. For example, it may be useful for measuring the penetration of repairing substances in deteriorated building elements. Also it may be of interest to obtain signatures of the material for classification purposes.
... We assume the number of grains within the material is high and there is no regularity, neither in the grain size nor in the distances between grains. In such case, it can be considered that grain noise amplitudes can be modelled by a Gaussian distribution [17,18]. When the number of grains is not high enough and there is a lower chaos in the material microstructure, other distributions fit better, such as K or Gamma distributions. ...
In this paper, a fast and efficient matching pursuit-based approach is proposed to detect ultrasonic flaw echoes in strongly scattering materials. Matching pursuit requires a dictionary composed of elements well matched with the ultrasonic pulse echoes obtained from the transducer. The method proposed in this paper utilizes time-shifted Morlet functions as dictionary elements because they are well matched with the ultrasonic pulse echoes obtained from the transducer used in the experiments. Our method is fast enough to be used in the signal processing stage of real-time inspection systems. Computer simulation was performed to verify flaw detection for diverse ultrasonic waves embodied in high-level synthetic grain noise. Flaw detection is also experimentally verified using ultrasonic traces acquired from a carbon fibre reinforced plastic material. Numerical results show meaningful SNR improvements for low input SNR (below 0 dB).
... If the attenuation may be considered to be linearly dependent on frequency , the center frequency estimates are used for estimating the attenuation coefficient1234. In other cases the center frequency estimates are correlated with properties of material567, or for flaw detection [8]. There are different alternatives for computing the center frequency. ...
In this paper we propose a new technique for estimating the center frequency of the ultrasound pulse from records of backscattering noise. We start by considering that the conventional maximum frequency method can be seen as a filtering (differentiator) of the pulse spectrum magnitude followed by a searching for the zero-crossing value. The new approach replaces the differentiator by a Hilbert transformer. We show in the paper that the proposed method has less variance than the maximum frequency method. In particular, we analyse the performance assuming that the real cepstrum method is used for extracting pulse spectrum magnitude. We give an upper bound for the variance reduction when practical criteria are applied for fitting the cepstrum cut-off frequency. The analytical work is verified by real and simulated data.
The ultrasonic backscattered grain signal consists of interfering multiple echoes with random amplitude and phase corresponding to a highly complex grain structure. Among the various inherent features of the grain signal, attenuation is a measurable feature resulting from the effect of scattering and absorption. The concept of ergodicity of the ultrasonic backscattered grain signal and its usefulness for measuring attenuation is presented in this report. A mathematical model of the grain signal describing both spatial and temporal averaging is developed. Experimental results using steel samples with different grain sizes along with the discussion of reproducbility and sensitivity of spatial and temporal averaging for measuring attenuation is presented.
The paper proposes the use of the ultrasonic attenuation due to grain boundary scattering as proxy for grain size in the well-known Hall-Petch relations, which predict mechanical properties of steel. A laboratory experimental program was carried out on plain carbon steels to determine the range of applicability of the method, what information in addition to attenuation would be necessary, the effects of alloy and microstructure, and the accuracy of such predictions. The results of testing 46 plain carbon steel plates indicate that ultrasonic attenuation and chemical composition in combination serve to adequately predict some of the mechanical properties. Although the experimental work was conducted under laboratory conditions, the results to date point to the possibility of developing an ultrasonic attenuation-based-on line method for predicting the mechanical properties of steel.
This chapter examines the scattering in polycrystalline media. A polycrystalline medium consists of grains of the constituent material. The grain boundaries themselves are flat curved surfaces. The grains formed by crystallization from the melt or by recrystallization during heat treatment, as in a metal, or they may be brought together by pressure and sintering, as in a ceramic. The attenuation of a polycrystalline material, in most cases, is determined almost entirely by grain scattering, which disperses the energy in the traveling wave. The velocity is determined by the elastic moduli and the preferred orientation of the grains, the latter property making the medium completely elastically anisotropic, so that the velocity is a function of the direction of propagation. Scattering by single inhomogeneities, particularly spheres and cylinders, has been studied extensively. It is found that an inhomogeneity will scatter elastic waves if it differs in modulus or density from the surrounding medium. It is observed that in a diffusionless transformation such as the martensitic transformation, in which the rearrangement of atoms comes about by shearing strains, there is a difference in orientation among the small sections of the microstructure.
Using the Kerr magneto‐optic effect, domain structure was observed during dc and 60‐Hz magnetization in 3% Si☒Fe bi‐crystals and commercial samples with (100) [001] grain orientation. High‐speed movies were taken at 3600 frames∕sec using a stroboscopic light source. A significant influence of grain boundary demagnetizing fields on domain structure was found. Reverse spikes and complex V‐line structures were observed which reduced the normal component of magnetization at grain boundaries. These structures did not appear in the demagnetized state and occurred only when the sample was magnetized.
Grain size characterization using ultrasonicbackscattered signals is an important problem in nondestructive testing of materials. In this paper, a heuristic model which relates the statistical characteristics of the measured signal to the mean ultrasonicwavelet and attenuation coefficient in different regions of the sample is investigated. The losses in the backscattered signal are examined using temporal averaging, correlation, and probability distribution functions of the segmented data. Furthermore, homomorphic processing is used in a novel application to estimate the mean ultrasonicwavelet (as it propagates through the sample) and the frequency‐dependent attenuation. In the work presented, heat‐treated stainless steel samples with various grain sizes are examined. The processed experimental results support the feasibility of the grain size evaluation techniques presented here using the backscattered grain signal.
Grain size in metals decides the smallest defect that can be detected in them. The research reported here aimed at minimizing the back-scattered energy-“grass” to the flaw detector operator—and extracting information from it about grain size. Detailed experiment supports the original statistical analysis
The nondestructive testing of multi-layered targets and targets with inhomogeneous and randomly distributed scatterers as in large grained materials have many important applications. Ultrasonic examination of such targets results in interfering multiple ecohes (reverberation) which complicates their evaluation by conventional techniques. This research consists of the analytical evaluation of backscattered echoes from sample targets coupled with the development of suitable digital signal processing techniques for their characterization. By decoupling the components of the backscattered echoes, an appropriate identification and classification technique is introduced which allows the characterization of the layered structure using detected echoes of significant intensities. Computer simulation was developed to verify the significance of the classification technique. The classification procedure allows the application of signal processing techniques such as subtraction, correlation, spectral analysis, and cepstral analysis. The subtraction technique is applied in order to separate various classes of echoes. This technique necessitates interpolation and synchronization of the digitized data. In this study an appropriate method of interpolation is presented based on the time-shift property of Fourier transforms. Correlation techniques are applied to the backscattered signal in order to improve the visibility of various classes of echoes. The correlation techniques improves the signal-to-noise ratio at the expense of resolution. The presence of the periodicity in the power spectrum can be related to layer thickness which is experimentally verified. Cepstral analysis is also appropriate for the processing of reverberant echoes in order to extract desired features. In this study, cepstral processing is used for separation of echoes, and extraction of the averaged echo waveshape for use in deconvolution. Results demonstrate that the power cepstrum provides good resolution. Various signal processing techniques, in both the time and frequency domains, have been applied to backscattered signals for grain size evaluation. Time domain analysis consists of time averaging, autocorrelation functions, and determination of the probability density function of the backscattered signals. Time averaging demonstrates significant sensitivity to grain size variation and also provides good reproducibility. Autocorrelation functions of the data were not informative since no periodicity exists in solids. It is shown that relative changes in statistical parameters (e.g., mean and standard deviation) of the probability density functions are also feasible for grain size evaluation. Quantitative evaluation of the magnitude spectra of backscattered signals were assessed by moment analysis. Moment values show inadequate sensitivity to grain sizes due to the presence of random peaks and valleys in the spectra. Furthermore, the magnitude spectrum were cepstrally smoothed in order to obtain an estimate of attenuation in the backscattered signals as a function of frequency. Results demonstrate a moderate performance of this technique for grain size evaluation.
An attempt has been made to equate quantitatively the coercive force as a function of the grain size and the concentration of nonmagnetic inclusions. It was found that the coercive force H c of recrystallized 47.5% nickel-iron can be completely described, independent of the final anneal temperature, by the grain size d K and the inclusion content N F . Only nonmagnetic inclusions of sub-micron size (0.02- 0.5 μm) were found to be of significance. A definite correlation between the coercive force of 47.5% nickel-iron and those inclusions visible using an optical microscope (> 1μm) was not observed. Furthermore, there was no clear dependence of the coercive force on the sulfur and oxygen content. The grain size term H cK was found to be in good agreement with the theory of A. Mager [1]. Surprisingly, there was no difference between the low-angle grain boundaries of strip with cube texture and the large-angle grain boundaries of un-textured strip with respect to H cK .
Scattering in Polycrystalline Media”, Method of Experimental Physics
- E P Papadakis
Performance Evaluation of Temporal and Spatial Averaging”, To be published in Acoustical Imaging
- T J Saniie
- N M Wang
- Bilgutay
Structure Analysis by Scattered Ultrasonic Radiation”, Research Techniques in Non-destructive Testing
- K Goebbels
Ultrasonic Attenuation Caused by Scattering in Polycrystalline
- E P Papadakis
- EP Papadakis
Performance Evaluation of Temporal and Spatial Averaging
- J Saniie
- T Wang
- N M Bilgutay