Table of Contents ECNDT '98 Session: Civil Engineering | Objective Interpretation of Ultrasonic Concrete ImageR. JansohnInst. für Massivbau
M. Schickert |
TABLE OF CONTENTS |
Ultrasonic images of concrete structures reconstructed by the SAFT-imaging (Synthetic Aperture Focusing Technique) algorithm usually contain distorting components besides the desired information on defects. The subjective interpretation of the operator is based on the brightness information and on known morphologic aspects. It is the aim of these investigations to allow for an objective interpretation of the brightness distribution using statistical image processing.
Mechanical waves and especially ultrasound offer the possibility to non-destructively test civil engineering structures. But due to the non-homogeneity of the material non-destructive testing of concrete is difficult for all methods based on wave propagation. Electromagnetic waves such as Radar are shielded by reinforcement and are absorbed by humid areas. Ultrasonic measurements are disturbed by scattering at random arrangements of aggregates which are constituent part of the material. Scattering at aggregates leads to grain noise and to a speckle structure in SAFT-images. Detection of objects embedded in concrete thus becomes difficult and depends more or less on subjective criteria of the operator. To fulfil quality assurance requirements of, e.g., ISO 9001 [7] an objective evaluation method has to be established.
The seemingly irregular arrangement of aggregate in concrete is the result of a particular particle-size distribution and of the compacting process during manufacture. Its volume distribution can be described with the aid of statistical methods. As a consequence, noise-like ultrasonic backscatter signals generated at the aggregate can also be characterised by statistical models.
The aim of the investigations presented here is to establish a more objective way for image interpretation utilising statistical image processing. The task of distinguishing obstacle indications from artefacts is formulated as a detection problem similar to methods used in radar target detection. The investigations yield to a technique which does not use any morphologic information of the signals. An algorithm is developed which adjusts a detection threshold to maintain a constant false alarm probability over the depth of the material. The value of the threshold depends on the length of the sound path and on the aggregate size distribution of the structure under test. Weibull and log-normal distributions are used to model the amplitude statistics of the received signals. In a number of controlled experiments, the dependency of the parameters of the distributions upon the properties of different concrete materials is examined.
The proposed technique can be used to reduce the distortion of SAFT-images by speckle and help detecting embedded objects. It is a step towards introducing objective measures into ultrasonic testing of a material which up to date poses many difficulties on standard evaluation methods. Further enhancements are planned by including morphological information.
Ultrasonic backscatter measurements consist of the radiation of an ultrasonic pulse into the structure under test and the reception of re-radiated energy. These re-radiated signals have to be processed in order to assign certain portions of the signal to objects of interest like voids, cracks, mounting parts, or inner and outer surfaces. Grain noise may lead to images containing speckle patterns and artefacts, and it degrades the clarity of the image. Grain noise can not be removed by time averaging or matched filtering since it is correlated with the time-invariant position of the aggregate. Existing methods like SAFT make use of spatial averaging. The basic assumption of these strategies is that the formation of aggregates in space is random. Usually, echoes which exceed the noise background by more than 6 dB are regarded as significant.
The existing algorithms do not meet the requirements formulated in ISO 9001: Equipment shall be used in a manner which ensures that measurement uncertainty is known and is consistent with the required measurement capability [7]. Where appropriate, the tester shall establish procedures for identifying adequate statistical techniques required for verifying the acceptability of the test.
Two tasks for signal processing can be formulated:
The basic concepts of statistical signal processing resulted in more objective statements and risk estimations in other fields of non-destructive testing, grain noise modelling, simulation, medical imaging, and radar target detection [5, 6]. The concept followed here is based on investigations on Gaussian noise which are modified to model non-Gaussian grain noise.
The thermal motion of electrons in resistors causes an alternate voltage which extends from the lowest to the highest technical frequencies. Due to its random nature this process named noise is only accessible by the use of statistical methods. It is not possible to make statements about the single events which result in the noise voltage. One of the main characteristics of thermal noise is its Gaussian amplitude distribution with zero mean. Gaussian distributions occur in random processes in which the number of statistically independent single events is increased to infinity. This is known as the central limit theorem [1]. The large bandwidth of noise is a consequence of the short duration of the single events of electron movement.
The probability density function of the amplitude of Gaussian noise with zero mean is given by
(1) |
where is the variance and is the standard deviation. The envelope of such a signal which can be calculated as the absolute value of the complex analytic signal [2] possesses a Rayleigh amplitude distribution [6]
(2) |
It is assumed that the useful signal which is corrupted by noise possesses a high amplitude. To separate it from noise a threshold is introduced against which the signal should be compared. If the signal exceeds the threshold it will be accepted as a useful signal, otherwise it will be suppressed. Since to the probability of large noise amplitudes is not vanishing there always is a certain probability of false alarms.
Fig 1: Probability density functions of noise and signal plus noise - double hatched area false alarm probability, hatched and double hatched area probability of correct detection, dotted area probability of a miss [6] |
If the amplitude exceeds the threshold it causes a detection alarm. Figure 1 illustrates the idea of threshold detection. The false alarm probability equals the double hatched area under the probability density function of noise alone.
In case an echo is present the statistics of this signal plus the accompanying noise must be investigated. As shown by S. O. Rice in the forties [3, 6], the probability density function of signal plus noise takes the Rician form which is also shown in figure 1.
(3) |
In equation 3 I_{0} is the modified Bessel function of zero order. A represents the amplitude of a sinusoidal echo which is assumed to be generated by a non-fluctuating target. The false alarm probability should be maintained at a constant value under varying measurement conditions.
Unwanted ultrasonic echoes generated by scattering at materials non-homogeneities exhibit some similarity to thermal noise as described in the previous section. For that reason the term grain noise is widely used. The spectrum of grain noise depends on the grain size of the material, on the acoustic wave propagation velocities, and on the spectrum of the transmitted signal. Hence it differs from white Gaussian noise. This phenomenon can also be described with the aid of statistical methods. Statements about the exact configuration of the scattering centres are not available. It is obvious that the large number of scattering interactions prevents from a deterministic examination. The statistical method used to describe thermal noise proved to be adequate for the examination of grain noise, whereas probability density functions other than Gaussian should also be taken into account.
Grain noise is the sum of echo signals reflected by many scatterers within the wave field. Changing the position of the transducer cause changes in phase and amplitude of the echo signals and therefore alter their superposition at the transducer. Its amplitude distribution depends, among other, on material properties and on the size of the resolution cell. Effects of multiple scattering are implicitly contained in these statistics, but the following definition of the resolution cell must be viewed as a first approximation. The axial size of the resolution cell depends on the axial extent of the pulse with respect to its travel path c / 2 (c - phase velocity, - pulse duration). For pulse compression systems, the duration of the pulse has to be replaced by the reciprocal of its bandwidth. The lateral size of the resolution cell depends on the geometry of the sound field. Low resolution systems make use of a long pulse duration with a small bandwidth. They possess a non-directive sound field which results in large resolutions cells containing a large number of scatterers. Hence the backscattered ultrasonic signal exhibits similarity to thermal noise which is made up of many statistical independent events of electron movement. The large number of scattering centres in large resolution cells causes many statistical independent echo events and the resulting amplitude distribution becomes Gaussian. Then the amplitude distribution of the envelope of the signal belongs to the family of Rayleigh-distributions.
In case of smaller resolution cells the amplitude distribution exhibits higher probabilities of large amplitudes. The resulting grain noise echo is build up of a smaller number of single echoes. Hence, an A-scan contains high amplitudes similar to those generated by defect echoes. In B-scans this phenomenon yields to a granulated speckle image. Amplitudes of this kind of grain noise cannot be described by the Rayleigh-distribution. As a consequence of the small number of scattering centres in the resolution cell the central limit theorem is no longer valid. The amplitude distribution of such signals can be described by distribution functions owing higher probabilities for large amplitudes, that means these distribution functions should exhibit a larger "tail". One possibility to describe such signals is given by the family of Weibull-distributions
(4) |
where and are parameters. Another candidate is the log-normal distribution. Its probability density function can be written as
(5) |
Here is the standard deviation of the logarithm of the amplitudes and is their average value.
To estimate the uncertainty of ultrasonic measurements in the sense of ISO 9001 the amplitude distribution of grain noise has to be known. With this knowledge an appropriate threshold value can be found and the false alarm probability can be computed.
A number of SAFT-reconstructions of ultrasonic measurements was used to test functioning of statistical image processing with constant false alarm probability. Three test pieces were imaged which are identical in shape but differ in their maximum aggregate size of 8, 16 and 32 mm, respectively. They consist of concrete possessing a compression strength of 25 MPa/mm², grading curve between A and B, and they contain two drillings each as targets. While the mean geometry is depicted in figure 2 the actual dimensions vary by max. 1 mm.
Fig 2: Sectional view of the test pieces |
Fig 3: Unprocessed SAFT-image of the test piece |
The samples were scanned along a 500 mm aperture at a spacing of 10 mm. SAFT-reconstruction was done with the algorithm described in [4]. Each resulting image is represented by a matrix which is displayed in grey scales or colour maps. Every row of the matrix corresponds to one discrete depth of the specimen. Figure 3 displays the SAFT-image of the specimen possessing a maximum aggregate size of 16 mm. As an example, the processing of this image is discussed in the following. At the borders of the image the number of rows and columns are given. The drilled holes of the specimen are easy to detect in the noise background. The back-wall is also visible as far as it is not shadowed by the holes. Without pre-information the back-wall may lead to difficulties in the interpretation. Especially high amplitudes at the left part of the back-wall (column 35, row 135) add some uncertainty into the interpretation.
Since ultrasonic input signals are not ergodic their amplitude statistics vary with depth and must be calculated separately for every discrete value of depth. Every row of the matrix is used as a sample to create a histogram and to estimate the parameters of an appropriate probability density function. It was assumed that the amplitude statistics belong to the families of Weibull- or log-normal distributions. The Weibull-distribution is very flexible and therefore yields good approximations to the data under test. The log-normal distribution fits better to data if the probability of large amplitudes is high [5]. Both probability density functions are completely defined by two parameters. In a series of preliminary experiments it was found that the Weibull distribution compared favourably. Figure 4 shows an example of the Weibull statistics for one row of the image. In figure 5 and 6 the Weibull-parameters and versus depth are given.
Fig 4: Histogram and Weibull probability density functions of matrix row 45 |
Fig 5: polynomial of second order fitted to scale parameter versus depth Fig 6: polynomial of second order fitted to shape parameter versus depth |
In order to eliminate local object variations on the amplitude distribution of grain noise it is assumed that the estimated parameters vary only slightly over depth. For that reason the estimated parameters are replaced by a polynomial of second order fitted to the parameters in a least squares sense.
The estimated probability distributions were used to calculate a threshold for grain noise suppression. For every row such a threshold value was computed. This threshold was chosen such that the false alarm probability P_{FA} was constant for every part of the image. In case of Weibull-statistics these value can be written with the Weibull parameters and as
(6) |
After the threshold functions are computed, every value of the image matrix has to be compared against the threshold value corresponding to its depth. If the image value exceeds the threshold it remains unchanged, if it fails, it is replaced by the median of its row. Doing this, elongated objects which are parallel to the aperture are maintained in the processed image. Otherwise objects such as the back-wall would be suppressed, since the algorithm evaluates statistics of single rows only. The median is used because it is a very robust average value. The smaller the false alarm probability was chosen, the better the grain noise will be reduced. At the same time probability increases that an echo originating from an existing object fails to exceed the threshold.
Figure 7 displays a processed version of the image shown in figure 3. The false alarm probability was chosen to be 10^{-7}. Grain noise and irritating high amplitudes in the region of the back-wall are eliminated and the holes are detected clearly.
Fig 7: Processed Image - false alarm probability P_{FA} = 10^{-7} |
It was shown that SAFT-images for non-destructive concrete testing can profitably be processed using a statistical threshold detection algorithm. It is the aim of the investigations to employ statistical means to give a more objective measure on deciding whether a certain amplitude pattern of the image unveils an object. In continuing this research, the models used have to be adapted more closely to ultrasonic backscatter characteristics found at concrete materials. Further experiments will be conducted to optimise the behaviour of the algorithm in typical measurement conditions. In addition to proposed parametric models non-parametric models should also be investigated.
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