Extraction of Fundamental Components from Distorted Spectral - - PowerPoint PPT Presentation

Combining the strengths of UMIST and The Victoria University of Manchester

Extraction of Fundamental Components from Distorted Spectral Measurements

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• Mr. Caleb Rascon
• Prof. Barry Lennox
• Dr. Ognjen Marjanovic

Combining the strengths of UMIST and The Victoria University of Manchester

Using Spectral Data in Monitoring

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• Crystallisation of active ingredients (Yu et al, 2003)
• Identify material concentrations (Dyrbe et al, 2002)
• Component identification

– Self-Modelling Curve Resolution Methods

• Alternating Least Squares
• SIMPLISMA

– Blind Source Separation

• Principal and Independent Component Analysis
• Viable as observed variables in feedback control

– Or are they?

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Spectral Distortion (Ice Analogs)

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500 1000 1500 2000 2500 3000 3500 4000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

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First Component

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3200 3210 3220 3230 3240 3250 3260 3270 3280 3290 3300 0.106 0.108 0.11 0.112 0.114 0.116 0.118

~ 20 Hz

@ 115 K @ 80 K

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Second Component

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2336 2338 2340 2342 2344 2346 2348 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18

~ 1.5 Hz

@ 115 K @ 80 K

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Sources of Spectral Distortion

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• Temperature changes
• Pressure changes
• Sensor de-calibration
• Foreign components (even external light sources)
• Baggerly et al. (2004) have observed spectral distortion from one instrument

to another within the same laboratory.

• Most observed:
• Shift, aka Frequency Displacement, reported to be caused by changes in

pressure, temperature, or a foreign component.

• Warp, aka Frequency “Stretching” or “Shrinking”, reported also to be

caused by a change in temperature.

100 200 300 400 500 600 700 800 900 1000 0.05 0.1 0.15 0.2 0.25 Frequency (Hz.) Energy

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Shift

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100 200 300 400 500 600 700 800 900 1000 0.05 0.1 0.15 0.2 0.25 Frequency (Hz.) Energy

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Warp

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20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35

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Effects on Component Identification Methods

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20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Sources

Data set without shift nor warp ALS Data set with shifts between [-2 2] Hz and warps between [-5 5] % ALS

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Alignment as an Optimisation Problem

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• Components inside a set of spectra need to be aligned to be properly

identified. – However, the ‘reference’ frequency location is irrelevant in the identification process.

• The spectra can be aligned using any one of the signals as a temporary

reference.

• An optimisation algorithm is applied to find the optimal amounts of counter-

distortion (de-shift, de-warp, etc.) for each spectrum, to be the most similar to the temporary reference.

• Using information gathered for each aligned spectrum, a mean tendency for

each type of distortion is calculated, and assumed as the amount of distortion suffered in the temporary reference.

Spectrum 1 Spectrum N Spectrum 2 Spectrum 3 Aligned Spectrum 1 Aligned Spectrum N Aligned Spectrum 2 Aligned Spectrum 3 Find Warp, Shift Find Warp, Shift Find Warp, Shift Substract Mean De-distort De-distort De-distort Mean Substract Mean Substract Mean Substract Mean Temporary Reference Data Set Aligned Data Set Alignment Algorithm

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Algorithm Summary

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Combining the strengths of UMIST and The Victoria University of Manchester

Example of Solution Space Observed

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Another Example of Solution Space

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Optimisation Algorithm

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• The unpredictable nature of the problem makes it necessary to apply a black-

box oriented optimisation algorithm.

• Particle Swarm Optimisation:

– Simulates a flock of bird ‘flying’ in the solution space. – Relatively easy to implement and visualise. – Proven to converge under specific tuning parameters (Clerc et al., 2002). – As good or better results than Genetic Algorithms (Kennedy et al., 1995).

• Given the definition of the problem, other algorithms can be applied.

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Results of Pre-Aligning before ALS

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20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Components

• btained

without Pre- Alignment Components

• btained with

Pre-Aligned Data

20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35 20 40 60 80 100 120 140 150 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Benchmark Used

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Conclusions & Future Work

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• Spectral distortion is an issue of great importance, and sensor de-calibration is

currently dealt with in an open-loop manner. – The algorithm records every shift encountered, and can automatically indicate if a calibration is necessary.

• The flexibility of this approach is to be noted, as more types of spectral

distortion can be considered.

• ALS assumes the number of components is known a-priori.

– Extend spectral distortion robustness towards estimating it.

• Other component identification algorithms, such as ICA, are to be explored.