Uncertainty Plots and Thickness Error Estimation

To create a plot from which the error in the estimated thickness can be extracted, first the results of thickness error and quality metric for all 30000 simulated signals are placed in order of increasing quality metric; in the case of correlation coeffi-cient this means ordering them from 0 to 1. Figure 4.8 (a) shows the correlation coefficient and the error in estimated wall thickness which occurs when using the envelope peaks TOF algorithm plotted alongside each other after sorting. It is clear that as correlation coefficient decreases, the tendency of the TOF algorithm is to overestimate the thickness, increasing thickness variance as it does so, regardless of the RMS height or correlation length of the surface. To provide quantitative val-ues of the spread of the thickness error data, the full data set is split into sections containing 10% of all the simulated signals (along the x axis in Fig. 4.8 (a)). The 5^th, 25^th, 50^th, 75^th and 95^th percentiles of each section containing 3000 results is subsequently calculated, along with the mean value of the quality metric within each section of data. Fig. 4.8 (b) shows these values as calculated using results in Fig.

4.8 (a). Figure 4.9 then shows these quantities plotted against one another.

4. Thickness Monitoring and Surface Roughness Detection

thickness error (λ) correlation coefficient

Percentage of signals (%)

0 20 40 60 80 100

thickness error (λ) correlation coefficient

Percentage of signals (%)

(a) (b)

Figure 4.8: (a) Error in thickness estimation relative to incident wavelength when using envelope peak TOF algorithm plotted against corresponding correlation coefficient values for all 30000 simulated results. (b) Black lines show percentile values for each section containing 10% of the signals, percentiles are indicated by the value in the circle. Red line shows the mean values of the correlation coefficient in each 10% section.

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

thickness error () ⁹⁵

75

Figure 4.9: Uncertainty plot when using envelope peak detection TOF algorithm for thickness evaluation and correlation coefficient as error metric. Black lines represent the percentile values indicated in the circles. Dotted lines represent an example of how the error bounds are estimated for a correlation coefficient value of 0.95.

4. Thickness Monitoring and Surface Roughness Detection

Figure 4.10: Uncertainty plots for (a) envelope peak detection, (b) cross-correlation and (c) threshold first arrival TOF algorithms when using (i) reflection amplitude, (ii) pulse width and (iii) correlation coefficient quality metrics. The black lines from top to bottom in each plot represent the 95^th, 75^th, 50^th, 25^th and 5^th percentiles respectively.

It is proposed that uncertainty plots such as that shown in Fig. 4.9 could be used to estimate the error in calculated thickness when nothing is known about the state of the inner surface of a corroding component. To use the plot an operator or an automated algorithm would first calculate the thickness value and quality metric from the received signal; then, referring to the plot, a line is drawn vertically from the calculated quality metric value, providing an estimate of the error of the calculated thickness based on where the line intersects the percentile values. As an example shown in Fig. 4.9 with grey dotted lines, if the thickness was calculated to be 10mm, the incident wavelength was 1.6mm (SH wave in mild steel) and the signal correlation coefficient calculated to be 0.95, the most likely thickness would actually be 9.89mm with 50% confidence that the thickness will be between 9.72 and 10.07mm and 90%

confidence that the thickness will be between 9.48 and 10.43mm.

4. Thickness Monitoring and Surface Roughness Detection

Each uncertainty plot will differ depending on the TOF algorithm and quality metric being utilised; figure 4.10 shows all combinations of TOF algorithm and quality metric being investigated in this thesis. A number of conclusions can be drawn about the effects of surface roughness on wall thickness estimation by inspecting the plots in Fig. 4.10; the most clear being that the expected variance of thickness estimation reduces when using TOF algorithms based on pulse first arrival, similar to the result shown in Fig. 4.7. Referring to Figs. 4.10 (a.i) and (b.i), if the amplitude of the reflected pulse is higher than expected, the thickness error remains relatively steady; however thickness error increases rapidly as amplitude decreases below the expected level using the envelope peak detection and cross-correlation TOF algorithms. Figs. 4.10 (a.ii) and (b.ii) indicate that in general roughness causes pulse width to increase and as it does so thickness error also increases. It is clear that comparing 4.10 (a.iii) and (b.iii) to the other uncertainty plots that correlation coefficient is the best technique at distinguishing thickness error based on the clear percentile trends and wider error bounds. However, in practice the choice of quality metric and TOF algorithm depends greatly on the situation being considered and a combination of techniques may be the best option when determining the true thickness and associated error based on signal shape.

4.5 Summary

Results from the DPSM simulation have been analysed in order to provide insight into the reflected signal shape changes that could be expected when ultrasonic thick-ness measurements are subject to corrosion. Roughthick-ness normal to the incident wave (controlled using the RMS height) was found to influence the amplitude and shape of the pulse greatly, whereas features in the orthogonal direction (controlled using the correlation length) determined energy content within the tail of the reflected signal. Analysis of the frequency spectra of ensemble averaged results indicated that the frequency content of a single scattered pulse can not be used to assess the level of roughness of the reflecting surface. An evaluation of three different TOF algorithms concluded that those based on signal first arrival would be the most stable under increasing roughness conditions. Envelope peak detection and cross-correlation both became progressively unstable because they are reliant on signal

4. Thickness Monitoring and Surface Roughness Detection

shape to provide the time of arrival estimate, an aspect of the reflected signal which can be altered significantly by the introduction of diffuse energy by surface rough-ness. A method for determining error bounds on a thickness estimate when subject to surface roughness was also proposed which uses reflected pulse shape change to assess the most likely error regardless of surface statistics. Calculation of a reflected signals similarity to the transmitted pulse using the correlation coefficient was found to be the most promising measure of error, while signal amplitude and pulse width could also be used with the advantage of being more easily implemented in practical implementations.

It is important to note that simulated signals have been used in this chapter to eval-uate TOF algorithm stability and roughness detection methods which are free from other sources of noise, as well as external environmental factors such temperature and coupling condition. It is expected that these sources of error will alter the sta-bility limits of each algorithm in practice. Of these, unwanted modes propagating along the waveguides, as experimentally observed (see Fig. 3.14), are expected to have the greatest impact, altering the lower amplitude constituents of the reflected pulse making low amplitude threshold first arrival analysis impractical. However, the conclusions drawn from the comparison between each of the TOF algorithms can be used in practice since it is expected other forms of noise should impact all algorithms to a similar extent. The conclusions drawn can also be applied in a more general sense to alternative transducer geometries since it is the shape of the recorded waveform which affects TOF stability, not the architecture of the sensor creating the signal. One further limitation of the results presented in this Chapter is that they have been derived using the assumption of two dimensional scatter-ing. The next chapter will address this by investigating signal scattering in three dimensions.

Chapter 5

Three Dimensional Simulation and

Size Considerations