**5. Decision making scheme**

118 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Fig. 19. Photograph of surface with varying frequency of knife marks

Scan Length (inch) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Amplitude (in)



0

5000

10000

Fig. 20. Profile (left) and HWT (right) of surface with varying frequency of knife marks

Magnitude (in)

> Spatial Frequency (marks per inch) 0 5 10 15 20

Fig. 21. Harmonic wavelet transform of surface with varying frequency of knife marks

The final step in developing an on-line surface quality monitoring system was the decision making scheme to determine if an unacceptable condition is present. As mentioned before, one of the objectives was to be able to determine from the data if a surface defect is periodic versus non-periodic and stationary versus non-stationary in nature. This aids the operator in determining the cause of the surface defect and what remedial action to take.

As discussed previously, the time-frequency plots provide information on the magnitude of the surface defect as well as determining if the defect is stationary or non-stationary. There are two approaches to interpreting the time-frequency plots. The first approach is to treat the time-frequency plot as an image and use standard image analysis techniques to determine the magnitude and shape of any "peaks" or "ridges" in the plot. A small diameter "blob" of the color representing a high mean-square value would represent a severe localized defect; whereas a long smear or ridge of the same color would represent a severe periodic condition. Since only the lower periodic frequencies (i.e. less than 50 knife marks per inch) are of interest for machined wood surfaces, the higher frequencies can be combined together for analysis of both non-periodic and localized defects. The second approach is to simply look at the data array representing the time-frequency plot of the harmonic wavelet analysis. For the examples shown, a surface profile generated by 16384 data points resulted in a time-frequency plot array of 15 x 4096 with the 15 columns representing the 15 frequency bandwidths (bins) of the HWT. This second approach was the one used in this research.

The first step in classifying a defect is to determine whether the surface defect is periodic, non-periodic, localized, or a combination of two or more of these categories. One approach is to view the periodic, non-periodic, and localized defects on an x, y, z plot. Since three parameters are required to describe a point in three space, the values of the three surface defect categories would indicate where in space the current specimen falls. A perfectly smooth surface would be at the origin of the plot. As a surface develops greater surface defects (regardless of the type or category of defect), the value on the plot moves further away from the origin. If the value for a periodic defect is higher than the value for the non-periodic defect then the surface in question is more periodic than nonperiodic.

There are several methods of determining where along the three-space defect category axes a surface defect falls. One way is to conduct traditional time and frequency analysis and determine the best surface descriptor for the type of defect of interest in each category. The three surface descriptors would then be plotted in three-space with the magnitude of the defect (surface descriptor) being normalized before being plotted.

From the time-frequency plots it can be seen the HWT can differentiate between extreme conditions and can provide the user with comprehensive information about the type of surface that has been scanned. The difference between the periodic and non-periodic situations can be determined by setting a threshold and then counting the number of data excursions above the threshold to indicate that the signal has a periodic component. A single threshold crossing could indicate a scratch or other localized defect. Since only periodic components below 50 marks per inch are typically of interest, only lower frequency bins would need to be monitored for periodic components. The frequency bins representing

The Use of the Wavelet Transform to Extract

stationary or non-stationary in nature.

59, ISSN: 0007-8506.

**7. Acknowledgements** 

Research Center Grant.

**8. References** 

Additional Information on Surface Quality from Optical Profilometers 121

This research compared various JTFA techniques including the STFT as well as numerous discrete wavelet transforms (DWT) on their ability to detect where in time a periodicity exists on the surface of a wood or wood-based composite product. This research concluded that the Harmonic DWT or HWT worked best from an efficiency in computational time as well as its ability to detect both low frequency periodicity as well as localized defects. From the time-frequency plots it can be seen the HWT can differentiate between extreme conditions and can provide the user with comprehensive information about the type of surface that has been scanned. The difference between the periodic and non-periodic situations can be determined by setting a threshold and counting the number of data excursions above the threshold to indicate whether the signal has a periodic component or not. A single threshold crossing could indicate a scratch or other localized defect. Since only periodic components below 50 marks per inch are typically of interest, only lower frequency bins need to be monitored for periodic components. The frequency bins representing periodicities (knife marks) greater than 50 marks per inch can be grouped together and used to monitor overall roughness. A two tier fuzzy logic scheme was devised to determine if the surface profile had a periodicity or was localized and / or if the surface defect was

Current and future work includes collecting data on the ability of the system to perform in a

The author would like to thank Professor Thomas H. Hodgson for his invaluable help in

This work was funded by a United States Department of Agriculture: Wood Utilization

American Society of Mechanical Engineers, 2009. *Surface Texture (Surface Roughness,* 

Brock, M., 1983. Fourier analysis of surface roughness. Bruel & Kjaer Technical Review,

Bruscella, B., V. Rouillard, and M. Sek, 1999. Analysis of road surface profiles. Journal of

Burrus, C. S., 1998. *Introduction to Wavelets and Wavelet Transforms – A Primer*. Prentice Hall,

Daubechies, I., 1990. The wavelet transform, time-frequency localization, and signal analysis, IEEE Trans. Information Theory, pp. 961-1005, ISSN: 0018-9448. DeVries, W.R. and R.L. Lemaster, 1991. Processing methods and potential applications of

wood surface roughness analysis. Proceedings of the 10th International Wood

United Engineering Center, 345 East 47th Street, New York, NY 10017. Ber, A., and S. Braun, 1968. Spectral analysis of surface finish. CIRP Annals, Vol. 16, pp. 53-

*Waviness, and Lay)*. ASME B46.1-2009. ISBN: 9780791832622, ASME New York.

variety of manufacturing environments and at a variety of manufacturing speeds.

learning and applying the JTFA techniques discussed in this chapter.

ISSN: 0007-2621, Marlborough, Mass., No. 3, 48 pages.

ISBN: 0134896009, Upper Saddle River, NJ.

Machining Seminar, October 21-23. pp. 276-292.

Transportation Engineering, Vol.125(1):55-59, ISSN: 0733-947X.

periodicities (knife marks) greater than 50 marks per inch can be grouped together and used to monitor overall roughness.

By monitoring the amplitudes of the bins of interest (less than 50 marks per inch) and setting an amplitude threshold then a frequency bin that would have, for example, 25 percent of the amplitude values over the amplitude threshold would be considered slightly periodic AND slightly stationary. If 50 percent of the data points in a frequency bin exceeded the threshold value then the signal would be considered slightly periodic and moderately stationary. If the amplitudes exceeded a secondary threshold value then the surface would be considered moderately periodic. An example of the action of the controller is if 5% of data points, at a given frequency, exceed the threshold then the defect was considered a **peak** (representing a localized defect). If 25% of the points at a given frequency exceed the threshold value then the defect is considered a **slight ridge**. If 50% of the points exceed the threshold then the defect is considered a **medium ridge**. This continues for a **long ridge** and a **complete ridge**.

A problem can arise when the surface descriptors get close to the threshold but do not exceed it. An example would be when only slightly less than 25 percent of the amplitude values exceeded the threshold value, which, based on traditional techniques, would be considered non-stationary. The interpretation of the 3-dimensional plots of the results from the time-frequency analysis, while being somewhat easy by a human, is difficult when attempting to have a computer automatically make decisions on the state of the manufacturing process. The approach that was evaluated here was to use fuzzy logic to decide where in three-space the specimen or workpiece of interest belonged. A detailed discussion of using fuzzy logic for surface quality evaluation can be found in Lemaster (2004). Two applications of fuzzy logic were evaluated. The first was to use the standard surface descriptors to determine if a primary surface defect present on a specimen was periodic or not and then the second was to use the results of the HWT to determine if the periodic surface defect was stationary or non-stationary.
