Spectral Analysis Using Equilibrium Constraints for Mixed-Sign Spectra
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Solution Overview
Problem
Existing spectral analysis methods, such as MCR-ALS, struggle to accurately analyze spectra with positive and negative spectral intensity values and thermodynamically interpret reactions involving multiple chemical species, often falling into local optimal solutions and failing to extract meaningful information.
Innovation Solution
A spectral analysis method and apparatus using MCR-ALS with an equilibrium model and chemical-equilibrium equations as constraint conditions, allowing for the separation of pure spectra and concentration values, even in the presence of positive and negative spectral intensities, by fitting concentration curves to chemical-equilibrium equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MCR-ALS method is used for spectral analysis, then the analysis can be performed with simple non-negative constraints, but it fails to accurately analyze spectra with positive and negative spectral intensity values and cannot provide meaningful thermodynamic interpretation
Solution Approach 1:
The patent changes the constraint parameters from simple non-negative conditions to thermodynamic equilibrium constraints based on chemical-equilibrium equations. By introducing thermodynamic parameters (equilibrium constants, Gibbs free energy, enthalpy, entropy) as constraint conditions, the method can accurately analyze spectra with positive and negative intensity values while providing meaningful thermodynamic interpretation of the spectral data.
Solution Approach 2:
The patent introduces chemical-equilibrium equations as intermediary constraint conditions between the spectral data and the pure spectrum/concentration separation. These equations act as a bridge that incorporates thermodynamic principles into the MCR-ALS framework, enabling the method to handle complex spectral data with both positive and negative intensities while maintaining mathematical rigor.
2Loss of information
If MCR-ALS method is applied to spectra from samples with three or more chemical species, then the method can resolve pure spectra and concentration values, but it falls into local optimal solutions and fails to extract meaningful thermodynamic information
Solution Approach 1:
The patent implements feedback by iteratively updating the concentration values based on thermodynamic equilibrium constraints. The chemical-equilibrium equations provide a feedback mechanism that guides the optimization process toward thermodynamically consistent solutions, preventing the method from converging to unrealistic local optima and ensuring reliable extraction of thermodynamic information from complex multi-component spectral data.
3Measurement precision
If the method uses chemical-equilibrium equations as constraint conditions, then thermodynamic parameters can be accurately determined, but the calculation complexity and computational time increase
Solution Approach 1:
The patent applies preliminary action by pre-defining the chemical-equilibrium equations and thermodynamic constraints before the spectral analysis begins. By establishing the thermodynamic framework and equilibrium relationships in advance, the method reduces the computational search space during the actual analysis, allowing accurate determination of thermodynamic parameters while minimizing computational time compared to unconstrained optimization approaches.
Data Source
AI summary
A spectral analysis method for thermodynamically analyzing performs multivariate analysis to a plurality of measurement spectra measured under a plurality of measurement parameters, using MCR method that separates a pure spectrum from the plurality of measurement spectra, and calculates a concentration value of each pure spectrum. In this method, an equilibrium model corresponding to an equilibrium state of a sample in which three or more types of chemical species coexist is set, and at least one chemical-equilibrium equation corresponding to the equilibrium model is set. In the MCR method, a concentration curve based on the chemical-equilibrium equation is fitted to the calculated concentration values, an optimal value of a thermodynamic parameter is acquired, a new concentration value is acquired from the chemical-equilibrium equation based on the optimal value, and thus the concentration value is constrained.