Civil Engineering Reference
In-Depth Information
To complement these average parameters, additional measures are often used to quantify the symmetry
and randomness of profiles [14, 43, 44, 74]. The skewness parameter,
, is a measure of the symmetry
of the roughness profile about the mean line; the measure distinguishes between asymmetrical profiles
with the same RMS height values. The kurtosis parameter,
R
sk
, is a measure of the randomness of the
profile's shape relative to a perfectly random profile. Such a profile has a kurtosis value of three, whereas
a profile with a kurtosis value of greater than three implies less randomness or more repetitiveness.
The examples above represent a subset of additional parameters used to supplement the roughness
information. Unfortunately, the addition of parameters does not necessarily provide more reliable infor-
mation. Using a multitude of parameters often leads to confusion in deciding upon parameters from
which conclusions must be drawn [74]. Although an increase in the average profile parameters will indicate
the occurrence of a fault pattern, this information is typically not enough to determine the severity of the
fault pattern, the specific location, or the character of the fault pattern. An average profile measure will
indicate the steady-state values of the faults on the part surface, and not the onset of the problem. This
information is crucial and necessary to detect potential problems. and failures in the system. Additional
knowledge of the character, or shape of the fault pattern, is often necessary to determine the source of the
fault causing a change in surface precision.
R
ku
Merging Random Process Analysis with Surface Analysis
The use of the parameters above is solidly established in research and in industry. However, they are
problematic in analyzing complex signals measured from part surfaces. An average surface parameter,
while providing a good first-look at the profile characteristics, is inherently problematic because of its
averaging characteristics [67]. Most profiles from manufacturing parts contain a fingerprint of the man-
ufacturing process, and hence can have complex characteristics, such as localized phenomena, freak marks,
time-varying trends, etc. Average parameters not only fail to detect these changes in the process, but also
fail to indicate the location of such errors. As a result, a more coherent classification based on random
process analysis of the surfaces has emerged in metrology research [74]. Complex signals are best analyzed
and processed using signal processing tools; these tools are essential in ensuring the correct and efficient
analysis of signals from manufacturing systems, such as manufactured surface profiles [49, 75].
Signal Characteristics
In studying the characteristics of signals, we have to first be aware of the different types of signals one
can encounter. Signals can be categorized as either deterministic or stochastic. An example of a deter-
ministic signal is a periodic signal [7, 10]. Signals of this nature may be detected easily, since they follow
a known model by which exact future values can be predicted. Stochastic signals, on the other hand, do
not follow a known model, and their structure and future values are usually described by probabilistic
statements. Furthermore, stochastic signals can exhibit stationary and/or nonstationary characteristics.
The probabilistic laws describing stationary random signals are time-invariant, i.e., the statistical prop-
erties of the signal do not change with time. However, a significant portion of fault-indicating signals
from manufacturing machines contain time-varying or nonstationary characteristics, where the statistical
parameters change significantly with time, and thus can no longer be predicted by the common techniques
[10, 75]. Nonstationary signals can be regarded as deterministic factors operating on otherwise stationary
random processes [7, 9]. Nonstationarities can be categorized in the form of three major types [7, 9]:
(1) patterns with a time-varying mean value; (2) patterns with a time-varying mean-square value (i.e.,
variance); and, (3) patterns with a time-varying frequency structure.
Spectral-Based Characterization Methods
One of the major breakthroughs in the characterization of surfaces has been the use of mathematical
tools from signal processing applications, specifically the autocorrelation function and the power spectral
density function, based on the Fourier transform [74]. The idea of correlation is well known in statistics.
The autocorrelation function indicates the degree of dependence of the profile at a given location, on
