Non-Least Squares Optimization for Measuring Formaldehyde in MDF and Particle Board

Introduction - Particle board and MDF (medium densiy fiberboard) are made by taking wood or wood fibers and binding them together with a resin such as urea while placing them under pressure and temperature. The monomer and incompletely reacted resin in the board emits byproducts over time. The key byproduct of concern is formaldehyde. The California Air Resources Board (CARB) has set limits on the amount of formaldehyde emissions allowed. These emissions are tested in small or large chambers and the tests can take several hours to several days. Operating plants would like to know the formaldehyde emission faster and to measure it on more samples than the chamber tests allow.

NIR calibrations are frequently optimized by using a least-squares regression line to create the best linear fit between the NIR and reference data. The least-squares solution creates the minimum error, but it always has some tendency towards the mean depending on the value of R. For values of R significantly less than 1 the tendency towards the mean is also significant.

In testing formaldehyde emissions the results are not judged by the average accuracy. Rather, the level of emissions is a threshold problem where the important economic decision has to do with if the produce is below or above the allowable limits. The objective of this work was to compare the least squares solution to solutions that minimized the error in terms of the reference values or minimized the errors in terms of the responsiveness of the calibration at the extreme values.

Experimental – NIR spectra were obtained from over a thousand particle board and MDF samples along with the formaldehyde emission levels. The data came from a number of different labs using a number of different measurement techniques. Each of the techniques were converted to create the formaldehyde levels in an equivalent to the ASTM E 1333 large chamber method.

The data were regressed using the Honigs Regression technique.(2) The HR technique is useful here because different wood types have different NIR spectra but the fundamentals of formaldehyde emission stay the same. HR compensates for changes in wood type as they change the spectra.

Results – The data were evaluated using normal least squares results. Then the data were analyzed by sloping the regression line as a regression of y on x instead of x on y data. Changing the slope accentuated the response of the NIR at the extremes of the calibration. The results were:

Calibration Std Error Std Error Extreme 20% of Samples Error Extreme 5% of Samples
6-Mar 0.011 0.017 0.023
24-Mar 0.008 0.011 0.015
24-Mar Sloped 0.009 0.010 0.010

Conclusion – As expected, a non-least squares regression increases overall error. However, by sloping against the y axis the error for the extreme samples is reduced. In this case this is a desirable trait.