Civil Engineering Reference
In-Depth Information
FIGURE 1.16
Reconstruction of signals in Example 2.
the location and severity of the nonstationary change in the signal. No change is indicated in the coefficient
vectors corresponding the eigenfunctions #4 and #5, as expected.
Finally, the reconstruction of the profiles from different instances during monitoring are shown in
Fig. 1.16
.
Figure 1.16(a)
corresponds to a profile from the second set of snapshots where a nonstationary
change in the mean-square value occurs (
m
21).
Fig. 1.16(b)
is a profile from the third set of snapshots
where a nonstationary change in the mean value occurs (
m
41). Each profile is reconstructed using
the same five significant eigenfunctions and their corresponding coefficient vectors, in the form of a linear
combination. Notice that the reconstruction in this case is not as perfect as in the first example. This is
due to the fact that the random component in the original signal has been reduced in significance during
reconstruction, hence increasing the signal-to-noise ratio. The majority of the stochastic effect is con-
centrated in the lower-eigenvalue components after the Karhunen-Loève decomposition, resulting in
the non-significant eigenfunctions. Once again, the ability to reconstruct every instant of a manufacturing
process, with or without nonstationary fault patterns, is a crucial requirement in error prediction for
a priori
tolerance assignment and machine and process redesign.
Understanding and Redesigning a Manufacturing
Process through Surface Analysis
To demonstrate that the Karhunen-Loève method can be used with real data from manufactured surfaces,
in this section, we discuss the potential of the our technique in integrating the design and manufacturing
cycles. The manufacturing process under study is Selective Laser Sintering [68]. Selective Laser Sintering
is a layered-manufacturing process where thin layers of powder are successively scanned to shape by
means of a laser and galvanometer mirrors. Roller and piston mechanisms are used to deposit and spread
each layer of powder on a powder bed.
One of the main concerns in this layered-manufacturing process is the ability to obtain accurate parts
on a repeatable basis. Any of the components of the Selective Laser Sintering machine may result in
undesirable fault patterns on part surfaces. As a result, it is important to understand the surface charac-
teristics of parts produced using this process [68]. Surface characteristics provide a “fingerprint” of the
manufacturing process under monitoring. Consequently, the understanding gained from the surface
information will help in the understanding of the manufacturing process and its potential limitations.
What we offer in this work is a means to systematically analyze and synthesize the fault patterns on
part surfaces. The idea is to provide the manufacturers with an accurate means to communicate the fault
status to the designers [69, 70]. The designers can then take remedial actions to eliminate the problems.
Remedial actions may include redesign of the manufacturing machine components and parameters,
and/or control of the process parameters. In this fashion, we achieve two goals: (1) provide a tool to
close the loop between design and manufacturing; and (2) provide a tool to understand new manufac-
turing processes and machines.
