Hybrid least squares multivariate spectral analysis methods

• US 6,711,503 B2
• Filed: 12/13/2001
• Issued: 03/23/2004
• Est. Priority Date: 03/04/1999
• Status: Expired due to Term

• Current Assignee: National Technology & Engineering Solutions Of Sandia LLC (Honeywell International Inc.)
• Original Assignee: Sandia Corporation (Martin Marietta Corporation)
• Inventors: Haaland, David M.
• Primary Examiner(s): WACHSMAN, HAL D
• Application Number:
  US10/021,817
• Publication Number:
  US 20020059047A1
• Time in Patent Office: 831 Days
• Field of Search: 702/19, 702/21-23, 702/27, 702/191, 702/28, 702/30-32, 702/75-78, 702/85, 702/86, 702/179-181, 702/183, 702/189, 702/194, 702/196, 702/FOR.103, 702/FOR.104, 702/FOR.107, 702/FOR.108, 702/FOR.115, 702/FOR.119, 702/FOR.131, 702/FOR-156, 702/FOR.139, 702/FOR.165, 702/FOR.166, 702/FOR-168, 356/300-303, 356/306, 356/326, 356/36, 700/266-269, 703/2, 703/11, 703/12, 706/924, 436/8, 436/43, 436/149, 436/130, 436/805, 436/806, 436/808, 436/171, 436/174, 422/50, 422/62, 422/68.1, 422/70, 422/82.01, 422/82.05, 422/82.09, 422/87, 422/89, 250/339.08, 250/339.09, 250/338.5, 250/338.1, 250/339.07, 250/341.1, 250/339-1-3, 250/341.5, 250/341.8, 73/233.6, 73/233.7, 73/234.1, 73/240.2, 430/12
• US Class Current: 702/22
• CPC Class Codes: G01J 2003/2866 Markers; Calibrating of scan
• CPC Class Codes: G01J 3/28 Investigating the spectrum using colour filters G01J3/51

Abstract

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

Claims

1. A method of forming a hybrid model of at least one known constituent or property in a set of samples, comprising:

a) forming a calibration model of the at least one known constituent or property in the set of samples from reference values and measured responses to a stimulus of individual samples in the set of samples;

b) estimating a prediction value of the at least one known constituent or property in the set of samples from the calibration model by a prediction model, wherein the prediction model produces residual errors;

c) adding at least one spectral shape representative of a source of spectral variation not specifically modeled in step a) to the prediction model; and

d) passing the residual errors from step b) to an inverse analysis algorithm to form the hybrid model.

2. The method of claim 1 for additionally estimating a value of at least one known constituent or property of a sample further comprising:

(e) measuring responses of the sample to the stimulus, using the calibration model and the prediction model and adding at least one spectral shape to the prediction model to estimate a prediction value of the at least one known constituent or property of the sample and producing residual errors;

(f) taking the residual errors from step e) and inserting them into the inverse analysis algorithm of the hybrid model to estimate an inverse portion of the residual errors of the prediction value; and

(g) combining the prediction value from step e) and the inverse portion of the residual errors of the prediction value from step f) to form an estimate of the value of the at least one known constituent or property of the sample.

3. The method of claim 1 wherein at least one different spectral shape is separately added to the calibration model of step a).

4. The method of claim 1 wherein the at least one spectral shape is obtained by an artificial method.

7. The method of claim 1 or 5 wherein the inverse analysis algorithm is partial least squares, partial least squares 2, principal components regression, inverse least squares, multiple linear regression, or continuum regression.

8. The method of claim 1 or 5 wherein the at least one spectral shape is continuous.

9. The method of claim 1 or 5 wherein the at least one spectral shape is discontinuous.

10. The method of claim 1 or 5 wherein the calibration model is a classical least squares calibration model.

11. The method of claim 1 or 5 wherein the prediction model is a classical least squares prediction model.

12. The method of claim 1 or 5 wherein the source of spectral variation is at least one chemical constituent not in the individual samples.

13. The method of claim 12 wherein the at least one spectral shape is determined by measuring the spectral shape of the at least one chemical constituent in a pure form.

14. The method of claim 12 wherein the at least one spectral shape is determined by adding a known amount of the at least one chemical constituent to the individual samples used to form the calibration model.

15. The method of claim 1 or 5 wherein the source of spectral variation spectral is spectrometer drift.

16. The method of claim 15 wherein the at least one spectral shape is determined by the use of at least one repeat sample of the individual samples used to form the calibration model.

17. The method of claim 1 or 5 wherein the source of spectral variation is the use of a first spectrometer during the forming of the calibration model and a second spectrometer in the prediction model.

18. The method of claim 1 or 5 wherein the source of spectral variation is temperature drift.

5. A method of forming a hybrid model of at least one known constituent or property in a set of samples, comprising:

a) forming a calibration model of the at least one known constituent or property in the set of samples from reference values and measured responses to a stimulus of individual samples in the set of samples;

b) adding at least one spectral shape representative of a source of spectral variation not specifically modeled in step a) to the calibration model;

c) estimating a prediction value of the at least one known constituent or property in the set of samples from the calibration model by a prediction model, wherein the prediction model produces residual errors; and

d) passing the residual errors from step b) to an inverse analysis algorithm to form the hybrid model.

6. The method of claim 5 for additionally estimating a value of at least one known constituent or property of a sample further comprising:

(e) measuring responses of the sample to the stimulus, using the calibration model and the prediction model and adding at least one spectral shape to the calibration model to estimate a prediction value of the at least one known constituent or property of the sample and producing residual errors;

(f) taking the residual errors from step e) and inserting them into the inverse analysis algorithm of the hybrid model to estimate an inverse portion of the residual errors of the prediction value; and

(g) combining the prediction value from step e) and the inverse portion of the residual errors of the prediction value from step f) to form an estimate of the value of the at least one known constituent or property of the sample.