How to Cope with Change: Making Accurate Multivariate Calibration Predictions in a Changing World

Same is different.
Sometimes it’s the little changes that make all the difference, at least as far as chemical analysis is concerned.

Say you’re monitoring an industrial chemical process, such as the production of a pharmaceutical compound, with some kind of spectrometer. At some point, this spectrometer breaks, so you replace it with a near enough identical version. Now, you wouldn’t expect this to have too much effect on your chemical analysis, but it does.

You don’t even have to replace the spectrometer for your analysis to go awry. It could happen because your spectrometer is getting old or simply because the surrounding temperature changes.

The reason for this is that even tiny changes can affect something as complex as a chemical analysis. Because of unavoidable differences in things like the alignment of optical components, even supposedly identical spectrometers will produce slightly different responses to the same chemical compounds. Similarly, wear and tear will cause the same spectrometer to produce slightly different responses over time, while changes in temperature can also affect the response.

Space odyssey
These changes will often be especially noticeable if you have used the responses to produce a multivariate calibration model; allowing you, for example, to determine the exact concentration of active ingredient in the pharmaceutical compound. If the spectral data feeding into the model changes, even though the underlying chemical compounds stay the same, then your model is going to start producing inaccurate information.

‘I always encounter situations where an established calibration model cannot be used for an extended period, due the almost inevitable changes in the instrumental response or variations in the measurement conditions,’ explains Zeng-Ping Chen, a chemist at Hunan University in China. ‘Therefore, methods for calibration model maintenance are needed to prevent degradation in the accuracy and reliability of multivariate calibration models.’

There are a number of methods for dealing with these inevitable changes. One is simply to update the model using a sample of the new data; another is to compare the model predictions for the new data with actual values and then apply an appropriate correction factor to the predictions.Yet another is to deduce a function that transforms a sample of the new data into the old data, allowing all the new data to be converted into the equivalent old data, which can then be fed into the model.

But none of the available methods really appealed to Chen, as they all have their limitations, so together with colleagues from Hunan University and the University of Strathclyde in Scotland he decided to develop his own. Termed Spectral Space Transformation (SST), it is basically an improved method for determining a function for converting new data into equivalent old data. SST does this by plotting samples of the old and new spectral data in two different spaces, and then determining a function for converting between the two spaces.

Accurate predictions
On testing SST, one advanatge that quickly became clear is that it can produce an accurate function with small sample sizes. Obviously, large samples sizes help to produce more accurate functions, model updates and correction factors, but at the expense of time and complexity. Chen and his team found that SST could work with smaller samples than the other models, while still producing accurate functions.

To show this, Chen and his team compared SST with the other methods on two sets of spectral data of pharmaceutical tablets, produced by two infrared spectrometers. This data was fed into a calibration model designed to determine active ingredient concentrations, which was originally developed from the data produced by just one of the spectrometers.

Overall, Chen and his team found that the SST-converted data produced more accurate concentration predictions than the data converted by the other methods. Even increasing the sample size for the other methods didn’t allow them to catch up with SST, because their accuracy tended to plateau beyond a certain sample size.

They also tested SST on the spectral data produced two infrared spectrometers analysing a mixture of three organic molecules. Once again, a calibration model designed to determine the concentrations of these molecules produced more accurate predictions with the SST-converted data than the data converted by any of the other methods.

Chen and his team claim that SST can work with any spectral data, including the data produced by a mass spectrometer, although they haven’t actually tried this out yet. What they are now doing, however, is using SST to help monitor the industrial production of cigarettes.

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