Examples of SPM

On-Machine Monitoring Example, Level 1

The first example is the design of a simple automated alarm rule to detect inhomogeneous patterns in the powder bed, layer by layer, with a specific focus on the identification of areas not properly covered by the powder, also called super-elevated edges. The example is taken from zur Jacobsmiihlen et al. (2013). The method works as follows:

  • Training phase. A set of images of in-control powder beds in L-PBF is recorded (for example, collected during previous builds), and the sample mean and sample standard deviation of the pixel intensities in the presence of correct recoatings are estimated. By using the notation of zur Jacobsmiihlen et al. (2013), the mean and standard deviation are labelled as p and o, respectively. An upper control limit (UCL) for the detection of critical regions is chosen as UCL = p + kc, where к = 3, which corresponds to a Type I error a = 0.0027 if the pixel intensity values follow a normal distribution.
  • Monitoring phase. For each newly acquired powder bed image, the intensity of each pixel is compared with the control limit UCL. In order to avoid signalling false alarms when even one or a small number of sparse pixels violate the control limit, the alarm rule envisages a second step to signal an alarm only when a cluster of connected pixels with a critical dimension has intensities above the limit. With this aim, a morphological operation is applied to generate connected regions based on pixels whose intensities are larger than UCL. For each connected region, the area Ar and the mean pixel intensity pR are computed, and an alarm is signalled if

where T is a threshold that can be estimated based on a set of reference images where critical super-elevated edges where observed.

The method described by zur Jacobsmiihlen et al. (2013) is a simple, though effective, on-machine monitoring method that combines two alarm rules to reduce the number of false alarms and tune the out-of-control detection based on available information about the critical size of the defect.

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