WO2005095912A1

WO2005095912A1 - Non-orthogonal signal monitoring

Info

Publication number: WO2005095912A1
Application number: PCT/GB2005/001053
Authority: WO
Inventors: Gordon R. Jones; Joseph William Spencer; Anthony Grayham Deakin; Jinghua Zhang
Original assignee: The University Of Liverpool
Priority date: 2004-03-31
Filing date: 2005-03-18
Publication date: 2005-10-13
Also published as: GB0407272D0

Abstract

A method for non-orthogonal prognostic monitoring of a system or process wherein: a plurality of signals corresponding to different system parameters are identified and a plot established of signal magnitude against signal parameter to form an effective magnitude parameter spectrum; and the, magnitude parameter spectrum is addressed by a plurality of non-orthogonal filters whose outputs are converted algorithmically into primary chromatic parameters.

Description

DKSCRIPTION

NON-ORTHOGONAL SIGNAL MONITORING

The present invention is concerned with a method and apparatus for non-

orthogonal monitoring of a plurality of discrete signals, such as from a plurality of

different-parameter transducers. The present invention makes use of non-orthogonal processing techniques, the principles of which are described briefly hereinafter by way of background information.

Non-orthogonal processing techniques make use of non-orthogonal response

characteristics in signal processors. A "non-orthogonal" system is one wherein the responses of processors, e.g. detectors, in a signal domain (e.g. optical wavelength) overlap, as illustrated in Fig. 1 of the accompanying drawings. As evident from Fig.

1, as a result of the overlapping in the signal tails, the outputs of the detectors are cross-correlated, yielding higher sensitivity to signals in the tails.

In principle, the signal processors used in a given non-orthogonal monitoring system will be responsive in a particular signal domain. The signal domain may in principle be any of a plurality of conventional signal domains, including optical, acoustic and radio, each addressed in the frequency (wavelength) or time domains. Additionally, other domains such as spatial location, mass, and non-orthogonality

between specific parameters (e.g. pressure and temperature etc) plus combinations

of large numbers of sensor types can be accommodated. The invention described herein is based on the situation where the monitoring is achieved by the use of so called chromaticity processing. Chromaticity processing is the name we give to the application of sets of non-

orthogonal weighted integrals to signals distributed across a measurement range and

the subsequent transformation of the integral quantities obtained to give parameters

sim marising certain characteristics of the distribution. The name derives from the

methods' origins in broadband optics and colour science, where the distribution to which it is applied is that of light intensity across the optical spectrum. However, it is applicable to measurements of any quantity distributed across another variable (for

example, acoustic intensity with frequency or temperature with spatial position). Where N integral weightings take the form of Gaussian curves (Fig. 2) the quantities derived in the first part of the process are the values of N basic terms of a Gabor expansion of the original signal. It has also been shown that this process is maximally information preserving for the general signal and that useful information

retention with high robustness to noise is obtainable with as few as three Gaussian

integrals. h the optical domain, an approximation to these three Gaussian base integrals is provided by the wavelength response of the sensor elements (e.g. colour photo

detectors in CCD cameras). This is known as a tristimulus sensor system. Observations may therefore be represented as data points in a colour space, the most straightforward of which is a Cartesian colour cube having an axis for each of the three sensor elements. The three co-ordinates of a point therefore give a separate measure of each of the familiar red, green and blue components of visible light. Thus, where the original data is a visible spectrum, these axes correspond to the red,

green and blue components of a colour and such colour terminology is often applied by analogy where other distribution variables and measurements are involved to aid

interpretation.

The second stage in chromatic processing (which may, in some

circumstances, be omitted, or, where there are only a few discrete values of the

distribution variable, be used on its own) is the transformation of the Cartesian colour space into a space referenced by a new set of parameters. These new parameters are

formed by the combination of the tristimulus parameters according to the formulae

that describe the transformation. Several such transformations are established in colour science, but one in particular has been found to be especially useful for the combination that it makes to operator interpretability of information through its partitioning into components of distinct character. This is the transformation to HLS

(Hue, Lightness, Saturation) space. By way of example only, the transformation can be f 60(G-B) /(max(R,G,B)-min(R,G,B)), if max(R,G,B)=R H = f 60(2+(B-R)) /(max(R,G,B)-min(R,G,B)), if max (R,G,B)=G (1) \^60(4+(R-G))/((max(R,G,B)-min(R,G,B)), if max (R,G,B)=B

R + G + B (2) maxfR. G. BVminfR. G. B) S = (3) max(R, G, B)+min(R, G, B) where R, G and B are the red, green and blue parameters of the Cartesian space, and H, L and S are the hue, lightness and saturation components of the new space.

Hue is specified as an angle (given in degrees by the above formula) and the lightness and saturation parameters range from 0 to 1, giving a cylindrical polar space

of unit radius and axial extent (Fig. 3). These parameters partition the information

acquired such that lightness corresponds to the nominal amplitude of the original

measurements summed across the range of their distribution variable, saturation

indicates the degree to which the measurements are spread throughout the range of the distribution and hue corresponds to an effective value of the distribution variable

about which the measurements are spread. The parameter names reflect the interpretation of these characteristics familiar from colour perception. Where the

measurements are of quantities other than visible light, physically analogous and

informatically identical (but for some small departure of our colour receptors from a Gaussian response) processing provides an intuitive assimilation of the information represented.

Chromaticity monitoring has relied conventionally upon the non-orthogonality of plural optical detectors for classifying detected signals. In this connection, colour (which is a human perception) may be regarded as a special case of chromaticity, whereas chromaticity may itself be regarded as a special case within the more general

area of non-orthogonal signals discrimination.^'

Each detected signal has a special signature which may be classified by N defining parameters. In general such signatures form highly non-linearly related sets requiring the need for at least N=3 defining parameters for classification in signal space (tri-stimulus processing). (The use of N=2 parameters (distimulus) constitutes a lineai- approximation in two dimensional signal space).

The compressed spectral signature may take the form of parameters taken from various signal-defining methodologies such as for instance orthogonal (e.g.

Fourier Transformed ) or non-orthogonal (e.g. chromatic) parameters etc. By way of

example, if it is assumed that all signals are Gaussian distributions of variable signal strength with respect to the signal domain (e.g. wavelength, frequency, time etc),

classes of signals are then unambiguously defined by only N=3 parameters corresponding to (see Fig. 4a):-

• Signal amplitude (or power content) (L) • Location of the peak value in signal parameter space (H) • Signal half width (S) If the need for all signals to be Gaussian in nature is relaxed, then each signal

may be allocated to one only of a class governed by a mother Gaussian. This

provides a substantial but not absolute signal discrimination means through the use

of only three detectors (R,G,B,) to yield three functions H,L,S. This forms the basis of chromatic discrimination: if the forms of the R,G,B detectors correspond to the responsitivities of the human eye, the N the chromaticity degenerates into the special case of colour. H,L,S are then N the Hue, Lightness; and Saturation of colour science as described above. Extension of the aforegoing technique to the use of N > 3 parameters leads to a subdivision of each mother Gaussian class into additional non-Gaussian classes (see Fig. 4b). By way of an example, N=4 may define the degree of

asymmetric deviation (Skewness) from a Gaussian distribution (see Fig. 4c) i.e.

each Gaussian class N_g subdivides into several asymmetric Gaussians n, with x s= 1 being determined by the signal processor discrimination. Furthermore an extension

to N = 5 parameters enables the degree of Kurtosis of the Gaussian distribution to be determined (see Fig. 4d) leading to a furtlαer subdivision of each asymmetric y Gaussian class into ∑ h _k subclasses.

An object of the present invention is to provide, a system and method for monitoring and processing the state of a plurality of discrete signals (rather than continuous signals), for example from a plurality of different-parameter transducers,

in order to establish useful prognostic information concerning the system in which the transducers are operating.

In accordance with the one aspect of ttie present invention there is provided a method for non-orthogonal prognostic monitoring of a system or process wherein: a plurality of signals corresponding to different system parameters are identified and a plot established of signal magπritude against signal parameter to form

an effective magnitude : parameter spectrum; and the magnitude : parameter spectrum is addressed by a plurality of non- orthogonal filters whose outputs are converted algorithmically into primary chromatic

parameters. Advantageously, the primary chromatic parameters are displayed on chromatic maps. hi some embodiments, the filter outputs are arranged to be in the form of R, G, B signals which are converted by an appropriate algorithm into H, L, S chromatic parameters, displayed on H-L and H-S chromatic maps. Where additional information is required as to the "context" of the system,

eg its history with time, a second stage chromatic processing is performed wherein each of the primary chromatic parameters is determined for different contextual

values and three secondary spectra are then formed from the values and addressed by

three further non-orthogonal filters which convert each primary chromatic parameter

into three secondary parameters.

The method can be used in many different situations but usually said plurality

of signals will correspond to the outputs of respective transducers associated with said system parameters.

In other cases, the signals will be generated discretely within a

sensing/detecting instrument, such as for example when corresponding to the levels of different gas components identified by a mass spectrometer in mass spectrometric gas analysis. The invention also provides an apparatus for non-orthogonal prognostic

monitoring of a system or process, comprising: means for identifying a plurality of signals corresponding to different system

parameters and for establishing a plot of signal magnitude against signal parameter to form an effective magnitude: parameter spectrum; a plurality of non-orthogonal filters for addressing the magnitude: parameter spectrum; and means for converting the outputs of the filters algorithmically into primary chromatic parameters.

The invention is described further hereinafter, by way of example only, with reference to the accompanying drawings, in which:

Fig. 1 illustrates the response of three detectors having overlapping response

characteristics; Fig. 2 shows examples of Gaussian curves;

Fig. 3 shows H, L and S in cylindrical polar space ; Fig. 4a shows how Gaussian signals are unambiguously defined by H, L and

S values; Fig. 4b shows how other signals are defined as the Gaussian family to which

they belong;

Fig. 4c shows how the use of four processors gives a measure of skewness;

Fig. 4d shows how the use of five processors gives a measure of kurtosis; Fig. 5 illustrates one embodiment of a non-orthogo_nal monitoring system in

accordance with the present invention; Fig. 6 illustrates by way of practical results the chromatic processing of a dissolved gas analysis (DGA) for high voltage transformer's; and Fig. 7 illustrates by way of practical results the chromatic processing of mass

spectrometric data for methanogenesis in an anaerobic reactor. The present invention makes use of non-orthogonal processing techniques in

order to establish useful information from a plurality of discrete signals obtained in the operation of a system or process. For example, this information may provide a basis for probability (statistical) calculations as to the state and/or trend of the operation of a system or process.

In general, each measurand component (signal level) corresponding to a particular transducer output is ordered according to the prognostic information

needed. For example, in a chemical process system having a mass spectrometric gas

analysis arrangement yielding gas species indicators, the components could be the

respective gas species and the prognostic information needed might be an indication

of process system failure. Magnitude is plotted against each component to form an effective "magnitude

: component spectrum".

The "magnitude : component spectrum" is addressed by three overlapping (non-orthogonal) filters whose filter outputs (R-,, G_p, B_p) are converted by an appropriate algorithm into chromatic parameters (H-,, L_p, S_p) which can be displayed

on H-L and H-S chromatic maps. The "meaning" associated with H_p, L_p, S_p is then:-

H_p - is indicative of dominant components;

L_p - is indicative of the effective magnitude of total components; S_p - is indicative of the nominal spread of components present. In the example given above:

For system prognosis, if H_p → gas A (most significant gas indicative of system event, e.g. failure) L_pis high and S_p → 1 then there is a high probability of system failure ensuing; if H_p → gas A, L_p is moderate and S_p → 0 the probability of failure is low but finite. The probability of the outcome concerned (e.g. failure) may therefore be expressed in terms of H_p, L_p, S_p ie.

Pp = P(H_p,L_p,S_p) = P(H_p) P (L_p)P(S_p) where P(H_p), P (L_p), P(S_p) represent the outcome probability indicated by each

h i i d ib d above is based upon a "snapshot"

of R_p G_p B_p and ignores the "context" of the system e.g. for the gas species example

the system history / trend with time is ignored. However the contextual information may contain important prognosis information, which can be observed by mapping the primary chromatic snapshots at

different context conditions (e.g. different times) on H_p - L_p, Hp -Sp maps.

Often the complex nature of such mapping does not facilitate the recognition

nor quantification of trends. To quantify such contextual information (e.g. system history), a second stage/generation chromatic processing may be utilised. In the second generation chromatic processing, ea.ch of the primary chromatic parameters H-,, L_p, S_p is determined for each different contextual value (e.g. each

time). Three secondary spectra are then formed corresponding to Hp:t; Lp;t, Sp;t where t represents the context value (e.g. instant in ^"time) into three secondary chromatic parameters i.e. H_t( H_p), L_t (H_p), S_t (H_p); H_p( L__t), L_t (L_p), S_t (L_p); H_t( S_p),

L_t (S_p), S_t (L_p); Each of the three secondary spectra is addressed by three non-orthogonal filters (R_tG_tB_t ) which convert each primary chromatic parameter (H_p, L_p, S_p) into three secondary parameters i.e H_t( H_p)_s L_t (H_p), S_t (H_p); H_t( L_p), L_t (L_p), S_t (L_p); H_t ( S_p), L_t (S_p), S_t (S_p).

This produces a total of nine secondary parameters, which represents a quantification of context trend (e.g time variation).

The probability of an event is then given by Pp,t=P (H_t ( H_p )) P( L_t (H_p)) P(

S_t(H_p))P(H_t(L_p)) P(L_t (L_p)) P(S_t (L_p) P(H_t(S_p))P(L_t(S_p))P(S_t(S_p)); By way of example for the time varying gas analysis the secondary chromatic

parameters have the following meaning:

L_t (L_p) = Total amount of gas produced in time t.

L_t (H_p) = Dominant time at which most gas was produced. L_t (S_p) = Effective spread of time over which gases produced. H_t (L_p) = Time extent for which there is a dominant gas.

H_t (H_p) = Dominant time at which the most dominant gas occurs. H_t (S_p) = Time spread of dominant gases. S_t (L_p) = Measure of time extent of gas spreading. S_t (H_p) = Dominant time at which the largest spread occurs. S_t (S_p) = Time spread of gas spread.

A particular example of how this technique can be applied in practice is now

explained in connection with Fig. 5. This example is concerned with seeldng to obtain a prediction of equipment failure based on gas analysis. It is typical of how the technique can be applied to the monitoring of sensor arrays, chemical species, mass and the like. The first generation chromatic processing is in the sensor output (e.g. gas type concentration) domain, i.e. the amplitudes of signals are plotted against the sensor type, producing the signal (Figure 5.1) h the Figure 5.1 embodiment, sensor 1 would

be CO₂ concentration, sensor 2 would be CO concentration, sensor 3 CH₄

concentration etc. In other embodiments the sensor 1 might for example monitor

pressure in the pump 1, sensor 2 temperature in pump 1, sensor 3 pressure in pump

2 etc. Step 2 is to overlay the amplitude: sensor bar graph with three non-orthogonal

processors (filters) (R_s, G_s, B_s) (Figure 5.2). The output from each processor is the weighted integral of the processor response multiplied by the amplitude of each

sensor output covered by that processor, e.g R_s(0) = JR_S (n). (amplitude sensor n) dn. The output from each processor (R_s (0), G_s (0), H_s (0)) is converted

algorithmically to chromatic parameters (e.g Hue (H), Saturation (S), Lightness (L) via well established colour science formulae. By this means, the complex pattern of sensor responses (Figure 5.1) is compressed to a description based upon only three co-ordinates - H,L,S. Consequently, the complex sensor signals distribution (Figure 5.1) may be represented by a single point on an H_g,S_s, polar diagram (Figure 5.3) r = S_s, θ = H_s and a second point on a H_s, L_s (r = L_s, θ = H_s ) polar diagram (Figure 5.4).

Thus the status of the system as indicated by the outputs of n sensors is

defined in terms of the values of only three co-ordinates H_s, L_s, S_s. If the status of the system changes and is reflected in a different distribution of signal amplitude: sensor type (Figure 5.5) then acting upon this distribution with the same R,., G_s, B_s processors (Figure 5.6) yields new and different values for H_s, L_s, S_s i.e. the locations of the system status points on the H _s: S _sand H _s: L .polar

diagrams change (Figure 5.3, 5.4).

This first stage/generation chromatic process therefore indicates the system

condition from a snapshot at an instant in time (t_t) compared with a snapshot at a

previous time (t₀). What it does not do is to take detailed account of the

history/evolution of the system. In order to take the system history (i.e. time evolution) into account in a more detailed manner, use is made of the second stage/generation chromatic processing. This takes the form of plotting the magnitude of each of the primary chromatic

parameters (i.e. H_s, L_s, S_s) at a series of discrete times during the system's evolution (i.e three graphs H_s : t, L_s : t, S_s : t Figure 5.7). Each of these H_s, L_s, S_s: time plots is then acted upon by three new chromatic processors in the time domain (i.e. R_j, G_t, B_t Figure 5.7). Consequently, each plot (H_s : t, L_s : t, S_s : t) yields its own second generation H-L, H-S etc polar diagrams

designated as H_sH_t - H_sL_t ; H_sH_t - H_sS_t , etc. (Figure 5.8 ) plots. Thus the system's historically balanced status is defined by nine chromatic parameters viz.

(H_sH_t ), (H_sL_t ), (H_sS_t ), (H_sH_t ), (S_SL_S ), (S_sS_t ), (L_sH_t ), (L_sL_t ), (L_sS_t). As a result, there is a substantial compression of information regarding the system's evolution status, its entire life being defined by only the 9 parameters of the second generation chromatic processing. As an example of the general practicality of the above described monitoring

process, the probability of various events on the system occurring (e.g. nnminent fault development) can in principle be expressed in terms of the 9 chromatic parameters and the values which they assume (Figure 5.9).

By way of a particular example, if sensors 1 to n represent gases formed in

the oil of a transformer, the gases may be grouped (1-n) accordmg to the phenomena which produce them (e.g. oil overheating cellulose, insulation decomposition CO,

C0₂, electrical discharges H₂, C₂H₂ etc). Thus, the extent to which each causes a

performance effect may be easily tracked or deduced from the H-L, H-S polar plots,

with the influence of the transformer's history being accommodated via the second

generation chromatic processing. In practice, assessments are made of a system's condition (e.g. transformer)

from known field information (e.g. obtained during servicing etc). Rules are then constructed regarding the weighting given to each of the chromatic parameters (H_sH_t,

L_sH_t etc) in determining the probability of an event occurring in the near future. For example, in the transformer case and for simplicity restricting consideration to the first generation processing (Figures 5.3, 5.4) only, the inspection

of 20 years of data from 50 transformers indicates the weighting of the probability

associated with P_H,P ,P_S to be 0.5, 0.3, 0.3 (Figure 5.9). Fig. 6 shows practical results obtained for the chromatic processing of

dissolved gas analysis (DGA) for high voltage transformers, wherein: Fig. 6a shows H-L, H-S polar diagrams for an impending fault transformer; Fig. 6b shows H-L, H-S polar diagrams for fault-free transformers; and Fig. 6c shows chromatic processors applied to dissolved gases results and where — zero time • = end time;

Fig. 7 shows practical results obtained for the chromatic processing of mass spectrometric data for methenogenisis in an anaerobic reactor, wherein: Fig. 7a shows H-L, H-S polar diagrams showing progression of methanogenisis involving the array of gases N_s, O₂ A_, H₂0 C0₂, H₂ CH₄, CH₃ and where = ideal predicted curve , — - = actual measured variation o = start D = end Fig. 7b shows an arrangement of gas species with respect to chromatic processors R,G,B and showing notional gas levels from the mass spectrometer at a given time.

Claims

1. A method for non-orthogonal prognostic monitoring of a system or process

wherein: a plurality of signals corresponding to different system parameters are

identified and a plot established of signal magnitude against signal parameter to form

an effective magnitude : parameter spectrum; and the magnitude : parameter spectrum is addressed by a plurality of non-

orthogonal filters whose outputs are converted algorithmically into primary chromatic parameters.

2. A method according to claim 1 , wherein there are three said non-orthogonal

filters.

3. A method according to claim 1 or 2, wherein the primary chromatic

parameters are displayed on chromatic maps.

4. A method according to claim 1, 2 or 3, wherein the filter outputs are arranged to be in the form of R, G, B signals which are converted by an appropriate

algorithm into H, L, S chromatic parameters, displayed on H-L and H-S chromatic

maps.

5. A method according to claim 1, 2, 3 or 4, wherein a second stage chromatic processing is performed in which each of the primary chromatic parameters is determined for different contextual values and a plurality of secondary

spectra are then formed from the values and addressed by corresponding further non- orthogonal filters which convert each primary chromatic parameter into three secondary parameters.

6. A method as claimed in claim 5, wherein three said secondary spectra are

formed and there are three said further non-orthogonal filters.

7. A method according to any of claims 1 to 6 wherein said plurality of

signals correspond to the outputs of respective transducers associated with said

system parameters.

8. A method according to any of claims 1 to 6 wherein the signals corcespond

to the levels of different gas components identified by a mass spectrometer in mass

spectrometric gas analysis.

9. A method according to any of claims 1 to 8, wherein said plurality of signals comprise electrical signals.

10. An apparatus for non-orthogonal prognostic monitoring of a system or

process, comprising: means for identifying a plurality of signals corresponding to different system

parameters and for establishing a plot of signal magnitude against signal parameter to form an effective magnitude: parameter spectrum; a plurality of non-orthogonal filters for addressing the magnitude: parameter

spectrum; and means for converting the outputs of the filters algorithmically into primary

chromatic parameters.