Chromatography Parameter Estimation With Physical Constraints

The patent applies preliminary action by pre-defining physically meaningful boundary conditions and constraints for chromatography parameters before the fitting procedure. Physical principles such as mass conservation, non-negative concentrations, and thermodynamic equilibrium relationships are incorporated a priori into the parameter estimation process, eliminating the need for extensive iterative fitting and reducing both time and computational resources required.

The patent replaces the traditional mechanical/numerical iterative fitting system with a physics-based analytical approach. Instead of relying on computational algorithms to minimize error functions through repeated iterations, the solution uses fundamental physical laws and relationships to directly determine parameter values, substituting computational mechanics with physical principles.

The patent transforms the parameter estimation problem by changing from estimating highly correlated non-linear parameters to estimating physically constrained parameters with defined relationships. By expressing parameters in terms of fundamental physical quantities with known relationships (e.g., expressing mass transfer coefficients in terms of diffusion coefficients and geometric parameters), the method reduces parameter correlation and improves estimation reliability while maintaining model versatility.

The patent segments the complex non-linear parameter estimation problem into smaller, physically meaningful sub-problems. By dividing the overall parameter set into groups based on physical principles (e.g., transport parameters, equilibrium parameters, kinetic parameters) and establishing hierarchical relationships between them, the method makes the estimation process more manageable and reliable.

The patent implements feedback by continuously checking parameter estimates against physical principles and boundary conditions during the estimation process. The method uses physical laws as feedback constraints to guide the parameter determination, ensuring that estimated values remain physically meaningful while still minimizing prediction error. This feedback mechanism prevents the optimization from converging to non-physical solutions.

The patent applies preliminary anti-action by pre-establishing constraints and boundaries that prevent the optimization algorithm from producing non-physical results. Instead of allowing the algorithm to freely minimize error and then correcting physical violations, the method proactively prevents such violations by incorporating physical principles into the estimation framework from the beginning, counteracting the tendency toward non-physical solutions before they occur.