Method for interpreting complex data and detecting abnormal instrumentor process behavior

• US 5,592,402 A
• Filed: 04/26/1995
• Issued: 01/07/1997
• Est. Priority Date: 04/16/1992
• Status: Expired due to Fees

• Current Assignee: The Dow Chemical Company (Dow, Inc.)
• Original Assignee: The Dow Chemical Company (Dow, Inc.)
• Inventors: Winterton, Richard C., Hughes, Glen H., Ruhl, Harry D., Beebe, Kenneth R.
• Primary Examiner(s): Teska, Kevin J.
• Assistant Examiner(s): LOUIS JACQUES, JACQUES H
• Application Number:
  US08/430,093
• Time in Patent Office: 622 Days
• Field of Search: 364/571.01, 364/571.05, 364/572, 364/578, 364/577, 364/576, 364/571.02, 364/571.04, 364/554, 364/485, 364/496, 364/497, 364/413.01, 364/507, 364/509 , 364/510, 364/550, 364/431.11, 364/499, 364/569, 73/23.23, 73/23.35, 73/29.02, 73/577, 73/599, 73/61.52
• US Class Current: 703/6
• CPC Class Codes: G01N 2201/129 Using chemometrical methods
• CPC Class Codes: G01N 30/8637 Peak shape
• CPC Class Codes: G01N 30/8641 Baseline
• CPC Class Codes: G06F 2218/02 Preprocessing

Abstract

An improved method is provided for determining when a set of multivariate data (such as a chromatogram or a spectrum) is an outlier. The method involves using a procedure such as Principal Component Analysis to create a model describing a calibration set of spectra or chromatograms which is known to be normal, and to create residuals describing the portion of a particular spectrum or chromatogram which is not described by the model. The improvement comprises using an average residual spectrum calculated for the calibration set, rather than the origin of the model as a reference point for comparing a spectrum or chromatogram obtained from an unknown sample. The present invention also includes separating a complex set of data into various sub-parts such as sub-chromatograms or sub-spectra, so that outliers in any sub-part can be more readily detected. In one particular embodiment, the invention is directed towards a method for dividing a chromatogram into the sub-parts of peak information, baseline shape, baseline offset, and noise.

Claims

1. A method of using a computing device to conduct an analysis of a sample, comprising:

(a) performing an analytical technique on the sample, said analytical technique being selected from the group consisting of chromatography and spectrometry so that a set of multivariate data which corresponds to the sample is produced;

(b) obtaining a series of representative multivariate data sets, wherein the representative multivariate data sets are obtained from the same type of analysis as was performed to produce the set of multivariate data in step (a);

(c) creating a model of the series of multivariate data sets obtained in step (b);

(d) creating individual residuals describing the portion of the multivariate data set obtained for each member of the calibration set which is not described by the model created in step (c);

(e) creating an average residual by averaging the individual residuals created in step (d);

(f) determining the distance between the individual residual for each member of the calibration set and the average residual;

(g) creating a residual describing the portion of the multivariate data set produced in step (a) which is not described by the model created in step (c);

(h) determining the distance between a residual obtained in step (g) and the average residual created in step (e);

(i) labeling as an outlier any set of multivariate data whose distance obtained in step (h) is statistically different from the set of distances determined in step (f); and

(j) checking for changes in feedstock, chemical processes and/or instruments used to make or evaluate the sample whenever one or more sets of multivariate data has been labelled as an outlier.

2. The method of claim 1 wherein the procedure used to create the model of the calibration set is Principal Component Analysis.

3. The method of claim 1 wherein the multivariate data is separated into a plurality of sub-parts prior to creating a model so that an outlier in one or more selected sub-parts can be detected.

4. The method of claim 3 wherein at least one of the sub-parts includes a member of the group consisting of peak information, baseline shape, baseline offset and noise.

5. The method of claim 4 wherein one of the sub-parts includes peak information, separated by a method which comprises the following steps:

(a) obtaining a set of multivariate data which includes peak information;

(b) identifying the portions of the multivariate data which contain peak information;

(c) subtracting the portions identified in step (b) from the set of multivariate data obtained in step (a);

(d) replacing the points subtracted in step (c) from the set of multivariate data obtained in step (a), so that a first approximation of the baseline is formed; and

(e) subtracting the first approximation of the baseline formed in step (d) from the set of multivariate data obtained in step (a), thereby forming a set of data containing peak information.

6. The method of claim 5 wherein step (e) further comprises smoothing out the peak information data.

7. The method of claim 6 wherein a second sub-part includes baseline shape, separated by a method which comprises:

(f) subtracting the set of data formed in step (e) from the set of multivariate data obtained in step (a), thereby forming a set of data containing baseline shape.

8. The method of claim 7 wherein a third sub-part includes noise separated by a method which comprises:

(g) subjecting the set of data formed in step (f) to a Fourier transformation and then a filtering operation; and

(h) subtracting the set of data formed in step (g) from the set of data formed in step

(f) thereby forming a set of data containing

noise information.

9. The method of claim 8 wherein a fourth sub-part includes the baseline offset which is defined as being the least positive point in the set of multivariate data obtained in step (a).

10. The method of claim 7 wherein step (f) further comprises:

defining the baseline offset to be the least positive point in the set of data formed in step (d);

subtracting the baseline offset from the set of data containing baseline shape; and

subjecting the resulting set of data to a Fourier transformation and then a filtering operation.

11. The method of claim 5 wherein step (b) comprises:

calculating the values for the second derivative of the set of multivariate data obtained in step (a);

selecting a region in the set of multivariate data which is known not to contain peaks;

averaging the values for the second derivative of the points in the region;

calculating a standard deviation for the values for the second derivative of the points in the region; and

defining any point whose second derivative is further than a preselected number of standard deviations from the average value for the second derivative in the region to be part of a peak.

12. The method of claim 11 further comprising defining any point within a preselected number of points from a point defined as a peak in claim 9 to be part of a peak.

13. The method of claim 5 wherein step (d) includes using linear interpolation to replace the points subtracted in step (c).

14. A method of using a computing device to examine multivariate data to determine outliers, comprising the steps of:

(a) selecting a calibration set of multivariate data;

(b) representing each member of the calibration set as a single point in a multidimensional axes system;

(c) constructing a model describing the points of step (b);

(d) obtaining a residual for each member of the calibration set by calculating the portion of each member which is not depicted by the model constructed in step (c);

(e) creating an average residual by averaging the residuals of all of the calibration set members;

(f) determining the distance between each of the residuals obtained in step (d) and the average residual obtained in step (e);

(g) determining the average and standard deviation of the distances obtained in step (f);

(h) calculating a t-distance for each member of the calibration set according to the formula;

##EQU2## where Dis_i is the distance obtained in step (f) for any member i, and AVE and STD are the average and standard deviation values obtained in step (g);

(i) acquiring a set of multivariate data from a sample;

(j) obtaining a residual for the sample by calculating the portion of the sample which was not depicted by the model constructed in step (c);

(k) determining the distance between the residual obtained in step (j) and the average residual obtained in step (e);

(l) calculating a t-distance for the sample according to the formula;

##EQU3## where Dis_sam is the distance obtained in step (k), and AVE and STD are the average and standard deviation values obtained in step (g); and

(m) labeling as an outlier any sample whose t-distance is statistically different from the t distances obtained in step (h).

(n) checking for changes in feedstock, chemical processes and/or instruments used to make or evaluate the sample whenever a sample has been labelled as an outlier.

15. The method of claim 14 wherein principal Component Analysis is used to construct the model in step (c).

16. A method of using a computing device to separate a set of multivariate data into a plurality of sub-parts, wherein each sub-part comprises at least one member selected from the group consisting of peak information, baseline shape, baseline offset, and noise comprising the steps of:

(a) performing an analysis on a sample to obtain a set of multivariate data which includes peak information;

(b) calculating the values for the second derivative of the set of multivariate data obtained in step (a);

(c) selecting a region in the set of multivariate data which is known to contain substantially no peak information;

(d) averaging the values for the second derivative of the points in the region;

(e) calculating a standard deviation for the values for the second derivative of the points in the region; and

(f) defining any point whose second derivative is further than a preselected number of standard deviations from the average value for the second derivative in the region to be part of a peak;

(g) removing the portions identified in step (f) from the set of multivariate data obtained in step (a);

(h) replacing the points removed in step (g) from the set of multivariate data obtained in step (a), so that a first approximation of the baseline is formed; and

(i) subtracting the first approximation of the baseline formed in step (h) from the set of multivariate data obtained in step (a), thereby forming a set of data comprising peak information.

17. The method of claim 16 wherein step (h) includes using linear interpolation to replace the points subtracted in step (g).

18. The method of claim 16 further comprising:

(j) smoothing out the set of data formed in step (i).

19. The method of claim 18 further comprising:

(k) subtracting the set of data formed in step (j) from the set of multivariate data obtained in step (a), thereby forming a set of data comprising baseline shape, noise and baseline offset.

20. The method of claim 19 further comprising:

(l) subjecting the set of data formed in step (k) to a Fourier transformation and then a filtering operation; and

(m) subtracting the set of data formed in step (l) from the set of data formed in step (k) thereby forming a set of data

comprising noise.

21. The method of claim 20 further comprising:

(n) defining the baseline offset to be the least positive point in the set of multivariate data obtained in step (a).

22. The method of claim 21 further comprising:

(o) subtracting the baseline offset defined in step (n), and the set of data formed in step (m) from the set of data obtained in step (k).

23. The method of claim 16 further comprising defining any point within a preselected number of points from a point defined as a peak in claim 16 to be part of a peak.

24. In a method of conducting an analysis of a sample wherein a set of multivariate data characteristic of the sample is produced through physical manipulations of the sample, and this set of multivariate data is compared to multivariate data obtained from samples having known properties which were similarly manipulated, the improvement comprising:

using a computing device to rapidly identify when problems exist in either the sample or the instrumentation by determining whether the set of multivariate data produced for the sample is within an expected range;

wherein the determination of whether the set of multivariate data produced for the sample is within an expected range is made by

(a) obtaining a series of representative multivariate data sets;

(b) creating a model of the series of multivariate data sets obtained in step (a);

(c) creating individual residuals describing the portion of the multivariate data set obtained for each member of the calibration set which is not described by the model created in step (b);

(d) creating an average residual by averaging the individual residuals created in step (c);

(e) determining the distance between the individual residual for each member of the calibration set and the average residual;

(f) performing the same type of physical manipulations as was performed to create the series of multivariate data sets obtained in step (a) on a sample, thereby obtaining an additional multivariate data set;

(g) creating a residual describing the portion of the multivariate data set obtained in step (f) which is not described by the model created in step (b);

(h) determining the distance between a residual obtained in step (g) and the average residual created in step (d);

(i) labeling as an outlier any set of multivariate data whose distance obtained in step (h) is statistically different from the set of distances determined in step (e).

25. A method of conducting an analysis of a sample comprising:

(A) physically manipulating the sample so that a set of multivariate data characteristic of the sample is produced;

(B) using a computing device to determine whether the set of data produced in step (A) is an outlier;

(C) if the set of data produced in step (A) is not an outlier, then estimating the properties of the sample by comparing the set of multivariate data produced in step (A) with multivariate data obtained under similar circumstances for samples having known properties;

(D) if the set of data produced in step (A) is an outlier, then checking for changes in feedstock, chemical processes and/or instrumentation used to make or evaluate the sample;

wherein step (B) is accomplished by

(a) obtaining a series of representative multivariate data sets;

(b) creating a model of the series of multivariate data sets obtained in step (a);

(c) creating individual residuals describing the portion of the multivariate data set obtained for each member of the calibration set which is not described by the model created in step (b);

(d) creating an average residual by averaging the individual residuals created in step (c);

(e) determining the distance between the individual residual for each member of the calibration set and the average residual;

(f) creating a residual describing the portion of the multivariate data set obtained in step (A) which is not described by the model created in step (b);

(g) determining the distance between a residual obtained in step (f) and the average residual created in step (d);

(h) labeling as an outlier any set of multivariate data whose distance obtained in step (g) is statistically different from the set of distances determined in step (e).

26. In a method of carrying out a chemical reaction wherein feedstocks are reacted under conditions sufficient to produce reaction products and wherein the reaction products are sampled and wherein a set of multivariate data describing the sample is produced, and the set of multivariate data is analyzed to ensure that the reaction products are within a desired range, the improvement comprising:

automatically determining when the analysis is an outlier and checking for changes in the feedstock, reaction conditions, and/or the instrumentation used to perform the analysis whenever an outlier is determined;

wherein the automatic determination is accomplished by

(a) obtaining a series of multivariate data sets representative of range of samples expected to be obtained;

(b) creating a model of the series of multivariate data sets obtained in step (a);

(c) creating individual residuals describing the portion of the multivariate data set obtained for each member of the calibration set which is not described by the model created in step (b);

(d) creating an average residual by averaging the individual residuals created in step (c);

(e) determining the distance between the individual residual for each member of the calibration set and the average residual;

(f) creating a residual describing the portion of the multivariate data set obtained in step (A) which is not described by the model created in step (b);

(g) determining the distance between a residual obtained in step (f) and the average residual created in step (d);

(h) labeling as an outlier any set of multivariate data whose distance obtained in step (g) is statistically different from the set of distances determined in step (e).