Peak Shape Estimation Using Predictive Distributions
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Solution Overview
Problem
In peak separation using chromatographs, distinguishing between main peaks and impurity peaks is challenging due to superimposition, leading to uncertainties in peak shape estimation and area prediction, resulting in potential errors in quantitative analysis.
Innovation Solution
A data processing device and method that estimate predictive distributions of peak shapes using a peak shape model, such as the K-mixture BEMG function, to calculate and display predictive distributions of quantitative indicators like peak areas, allowing users to assess errors and secure a reasonable level of security in analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If peak separation is performed using multiple Gaussian functions or BEMG functions, then individual peak shapes can be estimated from superimposed peaks, but great uncertainty remains about the estimation of peak shape and area due to superimposition
Solution Approach 1:
The patent changes the parameter representation from deterministic peak parameters (single estimated values) to probabilistic parameters (predictive distributions). By representing peak shapes and areas as distributions with multiple possible values and associated probabilities, the system captures the uncertainty inherent in peak separation while maintaining measurement precision. This allows users to understand both the most likely peak parameters and the reliability ranges.
Solution Approach 2:
The patent prepares for potential estimation errors by calculating predictive distributions that inherently account for uncertainty before making final measurements. By computing multiple possible peak configurations and their probabilities in advance, the system cushions against the reliability issues that arise from peak superimposition, allowing users to assess measurement confidence before drawing conclusions.
2Productivity
If maximum likelihood estimation is used to predict peak area and height, then quantitative analysis can be performed, but larger prediction errors occur due to peak superimposition
Solution Approach 1:
The patent transforms the single-point estimation approach of maximum likelihood estimation into a distribution-based approach. Instead of providing a single predicted peak area value, the system generates a predictive distribution showing multiple possible area values with their probabilities. This maintains the efficiency of automated quantitative analysis while significantly improving accuracy by revealing the full range of possible outcomes and their likelihoods.
Solution Approach 2:
The patent introduces feedback by providing users with predictive distributions and uncertainty information alongside quantitative results. Users can see not only the estimated peak areas and heights but also the associated prediction intervals and probabilities, allowing them to assess whether the measurement precision is sufficient for their analytical needs and make informed decisions about further analysis or re-measurement.
3Loss of information
If peak waveforms are fitted using a peak shape model, then individual peaks can be separated from superimposed groups, but uncertainties such as noise cause errors in quantitative analysis
Solution Approach 1:
The patent addresses noise-induced uncertainties by changing from deterministic parameter estimation to probabilistic parameter representation. The predictive distributions capture the effect of noise and other uncertainties on peak parameters, allowing the system to maintain peak separation capability while quantifying the reliability of separated peak information. Users can see how noise affects each peak estimation through the spread of the predictive distributions.
Solution Approach 2:
The patent cushions against noise-induced errors by calculating predictive distributions that inherently include the effects of measurement uncertainty and noise. By preparing these distributions before final quantitative conclusions are drawn, the system allows users to assess whether the noise level affects the reliability of peak separation results, enabling informed decisions about data quality and analysis confidence.
Data Source
AI summary
A data processing device performs a data process on a measured waveform obtained by a prescribed measurement of a sample. The data processing device includes an estimator, a calculator, and a display processor. The estimator estimates a predictive distribution of each peak shape for a corresponding one of a plurality of peak waveforms using a prescribed peak shape model, the plurality of peak waveforms being included in the measured waveform and being close to each other. The calculator calculates a predictive distribution of a quantitative indicator for each of the plurality of peak waveforms based on the predictive distribution of the peak shape estimated by the estimator. The display processor is operable to display the predictive distribution of the quantitative indicator calculated by the calculator.