Extraction of Fundamental Components from Distorted Spectral - PowerPoint PPT Presentation

Extraction of Fundamental Components from Distorted Spectral Measurements Mr. Caleb Rascon Prof. Barry Lennox Dr. Ognjen Marjanovic Combining the strengths of UMIST and 1 The Victoria University of Manchester

Using Spectral Data in Monitoring • 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? Combining the strengths of UMIST and 2 The Victoria University of Manchester

Spectral Distortion (Ice Analogs) 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 500 1000 1500 2000 2500 3000 3500 4000 Combining the strengths of UMIST and 3 The Victoria University of Manchester

First Component @ 115 K @ 80 K 0.118 0.116 0.114 0.112 ~ 20 Hz 0.18 0.11 0.16 0.14 0.12 0.1 0.108 0.08 0.06 0.04 0.02 0.106 0 500 1000 1500 2000 2500 3000 3500 4000 3200 3210 3220 3230 3240 3250 3260 3270 3280 3290 3300 Combining the strengths of UMIST and 4 The Victoria University of Manchester

Second Component 0.18 @ 115 K @ 80 K 0.17 0.16 0.15 0.14 ~ 1.5 Hz 0.13 0.18 0.16 0.12 0.14 0.12 0.1 0.08 0.11 0.06 0.04 0.02 0.1 0 500 1000 1500 2000 2500 3000 3500 4000 2336 2338 2340 2342 2344 2346 2348 Combining the strengths of UMIST and 5 The Victoria University of Manchester

Sources of Spectral Distortion • 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. Combining the strengths of UMIST and 6 The Victoria University of Manchester

Shift 0.25 0.2 0.15 Energy 0.1 0.05 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (Hz.) Combining the strengths of UMIST and 7 The Victoria University of Manchester

Warp 0.25 0.2 0.15 Energy 0.1 0.05 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (Hz.) Combining the strengths of UMIST and 8 The Victoria University of Manchester

Effects on Component Identification Methods 0.35 0.3 0.25 0.2 0.15 0.1 Data set 0.05 0 0 20 40 60 80 100 120 140 150 without shift ALS 0.35 nor warp 0.3 0.25 0.35 0.2 0.3 0.15 0.25 0.1 0.2 0.05 0.15 0 0 20 40 60 80 100 120 140 150 0.1 0.05 0 0 20 40 60 80 100 120 140 150 0.35 0.3 0.25 0.2 0.2 0.15 0.1 0.15 0.05 0 0 20 40 60 80 100 120 140 150 0.1 Data set Sources 0.05 0 with shifts 0 20 40 60 80 100 120 140 150 ALS between 0.2 0.15 [-2 2] Hz 0.1 and warps 0.05 between 0 0 20 40 60 80 100 120 140 150 Combining the strengths of UMIST and [-5 5] % 9 The Victoria University of Manchester

Alignment as an Optimisation Problem • 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. Combining the strengths of UMIST and 10 The Victoria University of Manchester

Algorithm Summary Data Set Aligned Data Set Temporary Reference Substract Spectrum 1 Aligned Spectrum 1 Mean Spectrum 2 Aligned Spectrum 2 Substract Spectrum 3 Aligned Spectrum 3 Find Warp, Shift De-distort Mean Substract Find Warp, Shift De-distort Spectrum N Aligned Spectrum N Mean Substract Find Warp, Shift De-distort Mean Mean Alignment Algorithm Combining the strengths of UMIST and 11 The Victoria University of Manchester

Example of Solution Space Observed Combining the strengths of UMIST and 12 The Victoria University of Manchester

Another Example of Solution Space Combining the strengths of UMIST and 13 The Victoria University of Manchester

Optimisation Algorithm • 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. Combining the strengths of UMIST and 14 The Victoria University of Manchester

Results of Pre-Aligning before ALS 0.2 0.15 0.1 0.05 Components obtained 0 0 20 40 60 80 100 120 140 150 without Pre- 0.35 0.2 0.3 Alignment 0.25 0.15 0.2 0.15 0.1 0.1 0.05 0.05 0 0 20 40 60 80 100 120 140 150 0 0 20 40 60 80 100 120 140 150 0.25 0.35 0.2 0.3 0.15 0.25 0.2 0.1 0.15 Components 0.05 0.1 0.05 obtained with 0 0 20 40 60 80 100 120 140 150 0 0 20 40 60 80 100 120 140 150 Pre-Aligned 0.35 Data Benchmark 0.3 0.25 Used 0.2 0.15 0.1 0.05 0 Combining the strengths of UMIST and 0 20 40 60 80 100 120 140 150 15 The Victoria University of Manchester

Conclusions & Future Work • 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. Combining the strengths of UMIST and 16 The Victoria University of Manchester