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Advantages of Soft Constraints in Self-Modelling Curve Resolution Using Multiway Penalty ALS

This study introduces a novel extension of the Penalty Alternating Least Squares (P-ALS) method, termed Multiway Penalty Alternating Least Squares (NWAY P-ALS). It highlights the application of soft constraints that allow minor deviations from predefined limits, resulting in enhanced performance over hard constraints. Utilizing a row-wise penalty least squares function, the soft approach significantly improves resolved profile accuracy, accelerates convergence, minimizes active constraints, reduces model fit issues, and mitigates the effects of noise in experimental data from pyridine-catalyzed esterification reactions.

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Advantages of Soft Constraints in Self-Modelling Curve Resolution Using Multiway Penalty ALS

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  1. Advantages of Soft versus Hard Constraints in Self-Modelling Curve Resolution Problems. Alternating Least Squares with Multi-way Penalty Function

  2. An extension to the Penalty Alternating Least Squares (P-ALS) method, called Multiway Penalty Alternating Least Squares (NWAY P-ALS) has been developed. Optionally hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row wise penalty least squares function. Employment of the soft penalty function resulted in reduced distortion of resolved profiles, fast monotonical convergence, minimisation of active constraints, reduced model lack-of-fit, reduced impact of noise and non-ideal response.

  3. Experimental • Three reactions of the pyridine catalysed esterification of acetic anhydride were completed at equimolarity of anhydrous 1-butanol (46.3ml), to acetic anhydride (47.6ml), with different pyridine catalyst concentration, (4ml, 8ml, 2ml), for batches 1-3 respectively. The final batch, batch 4 was completed using a reagent mol ratio of 2:1, Acetic anhydride (47.6ml), anhydrous 1-butanol (23.2ml), and a pyridine catalyst (4ml)

  4. A1 A2 A3 m np Row-wise augmentation A3 A2 A1 A1 p A A2 = Ar m n A3 mp n Column-wise augmentation A3 A2 A1 p mn Tube-wise augmentation Example of the three different modes or augmentations of a three-way dataset

  5. Column wise augmentation of the NIR batches of the pyridine catalysed esterifcation reaction of 1-butanol

  6. Resolved spectral profiles and concentration profiles of acetic anhydride (-),1-butanol (---) and pseudo product (…). Constrained profile (bold line), unconstrained profile (normal line), using the soft MCR-ALS option

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