Section V: Advanced Chromatic Monitoring

This section describes more advanced applications of the chromatic monitoring approach. It considers adaptation of chromatic methods for addressing multidimensional signals (three-dimensional space monitoring), the use of primary and secondary chromatic analysis for monitoring partial discharges and switchgear contact wear, acoustic frequency monitoring of high-voltage transformers and three- phase pow'er transmission lines. It also addresses problems of combining sets of data from a range of conventional measurements on high-voltage transformer oils and assessing the performance of various gases used in high-voltage circuit breakers.

14 Introduction to Advanced

Introduction to Advanced Chromatic Analysis

A. A. Al-Temeemy, J. W. Spencer and C. R. Jones

Introduction

Experience with the chromatic approach has shown that it provides a means for processing a signal that avoids some of the difficulties associated with other methods, including the complexity of transformed Fourier signals and transformation instability in the presence of noise (Jones et al., 1996; Al-Temeemy and Spencer, 2010, 2015a,b). The generic nature of the chromatic approach enables it to be extended to many domains of information extraction (Al-Temeemy and Spencer, 2014, 2015a,b) (e.g., continuous signals, optical signals etc.). It can overcome difficulties of processing methods which use a surfeit of information with excessive computational difficulties of processing times and costs.

More advanced forms of chromatic monitoring and analysis have evolved which include the application of the R, G. В chromatic processors for addressing a particular signal in multiple signal domains and additionally with R, G, В processors having different responses.

Properties and Adaptability of Chromatic Processors

Chromatic Processor Properties

Two examples of the deployment of three chromatic processors adjusted for addressing a well- defined signal are shown in Figure 14.1a(i) and b(i). In both cases, the three processors are adjusted to cover only the extent of the signal. Figure 14.la(i) shows the use of three Gaussian profile sensors R(lo), G(lo), B(lo) with the extreme sensor R(lo) divided to cover each end of the signal distributed along a location lo. Figure 14.lb(i) shows the same signal addressed by three triangular processors (R. G, B) with R(lo) and B(lo) as the extreme sensors and the middle sensor G(lo) covering the whole signal width but with half the amplitude of R(lo), B(lo).

As a result of these features, the combination of the two sets of R, G, В processors profiles differs from those already discussed in Chapter 1 (all equal amplitude; no single processor covering each end of the signal). The dominant value (H) of a monochromatic signal (/) tracked across each of the two sets of R, G, В processors is shown in Figure 14.1a(ii) and b(ii). This shows that both sets of processors have an almost monotonic variation of H with 1 but with the Gaussian profiles having

Chromatic processors and their monochromatic responses

FIGURE 14.1 Chromatic processors and their monochromatic responses. (a(i)) COGP = Continuous overlapping Gaussian processors. (b(i)) TTP = Truncated triangular processors. (a(ii)) Tracked monochromatic signal monitored by COGP. (b(ii)) Tracked monochromatic signal monitored by TTP.

a higher sensitivity (0 —> 1 compared with 0.66). These variations may be compared with those for the original processors described in Chapter 1. The Gaussian-type processor is referred to as a continuous overlapping Gaussian processor (COGP), whilst the triangular processor is referred to as a truncated triangular processor (TTP).

Adaptation of Processor Locations and Widths

For many applications, it is necessary to match the R, G, В processors’ widths and locations to a signal’s width and location. Figure 14.2 shows a signal PR(lo) distributed along a location /о, along with three non-orthogonal processor responses R(lo), G(lo), B(lo).

The centroid (Cm) of the signal PR(lo) of length ( is determined from Al-Temeemy and Spencer (20l5a,b).

This is then used to determine the centres and widths of each of the three chromatic processors (R, G, B).

Normalised Chromaticity of Two-Dimensional Signals

A two-dimensional signal (e.g., optical image) may be addressed by adapting the chromatic processors’ locations and width, as indicated in Section 14.2.2, but in two dimensions. Displaced and magnified images may then be compared (Figure 14.3) to check for identification

Adaptations of the locations and widths for Gaussian processors with the input signal

FIGURE 14.2 Adaptations of the locations and widths for Gaussian processors with the input signal.

This is achieved by first adjusting the locations and widths of the chromatic processors (R, G, B) in the x dimension to calculate the chromatic parameters H(x) and S(x). The process is then repeated for the у dimension to yield H(y) and S(y). The image is then characterised by the four parameters H(x), S(x), H(y), S(y). For the example shown in Figure 14.3, H(x) was consistent to within 1.2%, S(x) to within 1.0%, H(y) to 2% and S(y) to 0.4%. These results indicate a high level of invariance for such distortions.

Normalised Chromaticity of a Rotated Signal

Rotational displacements of a two-dimensional signal can also be accommodated via two-dimensional chromaticity. The chromatic processors in this case are used after the radon transformation of the image f(xn, yn) at a normalising angle (Al-Temeemy and Spencer 2015a,b) (Figure 14.4).

For the example shown in Figure 14.4, such a process leads to values of chromatic parameters compared to those of the original image to within 0.8% for H(x), 0.1% for S(x), 2% for H(y) and 0.1% for S(y).

Summary and Overview

Extensions of the basic chromatic approach which have already been exploited for a variety of applications have been described and have the potential for further exploitation. One aspect takes advantage of a variety of different forms of the three basic non-orthogonal processors. This enables forms of the processor responses to be adjusted for enhancing performance for particular applications.

Also, chromatic processing has been expanded into a number of signal dimensions, which enables the combination of chromatic parameters from several domains to be formalised. At its simplest level, primary chromatic parameters may be further processed as a function of time and so on, providing a wider choice of chromatic parameters for extracting the required information.

Normalised projections of fighter jet images, (a) Original image, (b) Shifted to left, (c) Enlarged one and a half

FIGURE 14.3 Normalised projections of fighter jet images, (a) Original image, (b) Shifted to left, (c) Enlarged one and a half.

This has enabled time and frequency domain chromatic processing to be achieved. It has also enabled the chromatic processing of two length dimension (.v, y) distributed signals to be addressed to quantify the shape of an image.

A primary chromatic analysis involves addressing one signal dimension (e.g., frequency distribution) with three chromatic processors (R. G, B) to produce primary chromatic parameters л;, у, z, L, H, S (Chapter 1). The variation of these parameters within a second signal dimension (e.g., time) may then be addressed with secondary chromatic processors R(2), G(2), 6(2) to yield secondary chromatic

Radon transformation for rotated image

FIGURE 14.4 Radon transformation for rotated image.

parameters. This provides a choice of several chromatic parameters for quantifying a signal. Examples of such a procedure and their application include the time-frequency analysis of partial discharges (Chapter 18) and the time-wavelength analysis of electric arc contact wear in a high-voltage current interrupter (Chapter 17). A similar approach may be deployed to address a signal in three spatial dimensions whereby primary chromatic analysis is performed individually for each dimension and secondary chromatic parameters produced from a combination of the primary chromatic parameters (Chapter 15). A further development has been the analysis of three interrelated parameters (e.g., fault detection in a three-phase electric power transmission system; Chapter 19). There is also the deployment of three primary chromatic processors (R, G, B) for addressing the simultaneous magnitudes of a large number of different parameters organised into three representative groups (e.g., dissolved gases and so on in transformer oil in Chapter 20 and the performance of different gases in high-voltage circuit breakers in Chapter 21). A chart highlighting these adaptations of chromatic analysis is given in Figure 14.5.

Fundamental basis of various forms of advanced chromatic analyses

FIGURE 14.5 Fundamental basis of various forms of advanced chromatic analyses.

References

Al-Temeemy. A. A. and Spencer, J. W. (2010). Invariant spatial chromatic processors for region image description. IEEE International Conference on Imaging Systems and Techniques, pp. 421-425.10.1109/ IST.2010.5548524

Al-Temeemy. A. A. and Spencer. J. W. (2014). Laser radar invariant spatial chromatic image descriptor. Opt. Eng., 53(12), 10.1117/l.OE.53.12.123109

Al-Temeemy. A. A. and Spencer, J. W. (2015a). Invariant chromatic descriptor for LADAR data processing.

Mach. Vis. Appl., 26(5). pp. 649-660, 10.1007/s00138-015-0675-0 Al-Temeemy, A. A. and Spencer, J. W. (2015b). Chromatic methodology for laser detection and ranging (LADAR) image description. Optik, 126(23), pp. 3894-3900, 10.1016/j.ijleo.2015.07.182 Jones, G. R. et al. (1996). Chromatic processing of optoacoustic signals for identifying incipient faults on electric power equipment. IEE Colloquium on Intelligent Sensors (Digest No: 1996/261), Leicester, UK, pp. 3/1-3/5.

15 Chromatic Monitoring

Chromatic Monitoring of Spatial Dimensions

A. A. Al-Temeemy, J. W. Spencer and L. U. Sneddon

Introduction

Enhanced chromatic monitoring procedures have been deployed with various types of signal production hardware (visible optical, infrared [IR] detection, lasers etc.), various signal processing methods (ViBe, radon etc.) and different physical dimensions (one-three dimensions). Three- dimensional chromatic processing for laser detection and ranging (LADAR) has been developed. A combination of two-dimensional polychromatic light imaging with three passive infrared sensors has been produced for cost-effective, non-intrusive room monitoring. Three-dimensional spatial monitoring has been produced for addressing fish clustering.

 
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