A continuous dynamical system is stable if all eigenvalues lie strictly in the left half of the complex plane. However, this is not a robust measure because stability is no longer guaranteed when the system parameters are slightly perturbed. Therefore, the pseudospectrum of a matrix and its pseudospectral abscissa are studied. Mostly, one is often interested in computing the distance to instability, because it is a robust measure for stability against perturbations. As a first contribution, this paper presents two iterative methods for computing the distance to instability, considering complex perturbations. The first one is based on locating a zero of the pseudospectral abscissa function. This method is particularly suitable for large sparse matrices as it is based on repeated eigenvalue computations, where the original matrix is perturbed with a rank one matrix. The second method is based on a recently proposed global optimization technique. The advantages of both methods can be combined in a hybrid algorithm. As a second contribution we show that the methods apply to a broad class of nonlinear eigenvalue problems, in particular eigenvalue problems inferred from linear delay-differential equations, and, therefore, they are useful for a wide range of problems. In the numerical examples the standard eigenvalue problem, the quadratic eigenvalue problem and the delay eigenvalue problem are addressed.
X-ray computed tomography (X-CT) plays an important role in non-destructive quality inspection and process evaluation in metal additive manufacturing, as several types of defects such as keyhole and lack of fusion pores can be observed in these 3D images as local changes in material density. Segmentation of these defects often relies on threshold methods applied to the reconstructed attenuation values of the 3D image voxels. However, the segmentation accuracy is affected by unavoidable X-CT reconstruction features such as partial volume effects, voxel noise and imaging artefacts. These effects create false positives, difficulties in threshold value selection and unclear or jagged defect edges. In this paper, we present a new X-CT defect segmentation method based on preprocessing the X-CT image with a 3D total variation denoising method. By comparing the changes in the histogram, threshold selection can be significantly better, and the resulting segmentation is of much higher quality. We derive the optimal algorithm parameter settings and demonstrate robustness for deviating settings. The technique is presented on simulated data sets, compared between low- and high-quality X-CT scans, and evaluated with optical microscopy after destructive tests.
In laser powder bed fusion (LPBF), melt pool instability can lead to the development of pores in printed parts, reducing the part’s structural strength. While camera-based monitoring systems have been introduced to improve melt pool stability, these systems only measure melt pool stability in limited, indirect ways. We propose that melt pool stability can be improved by explicitly encoding stability into LPBF monitoring systems through the use of temporal features and pore density modelling. We introduce the temporal features, in the form of temporal variances of common LPBF monitoring features (e.g., melt pool area, intensity), to explicitly quantify printing stability. Furthermore, we introduce a neural network model trained to link these video features directly to pore densities estimated from the CT scans of previously printed parts. This model aims to reduce the number of online printer interventions to only those that are required to avoid porosity. These contributions are then implemented in a full LPBF monitoring system and tested on prints using 316L stainless steel. Results showed that our explicit stability quantification improved the correlation between our predicted pore densities and true pore densities by up to 42%.
In-situ monitoring and post-process metrology form a basis to better understand the fundamental physics involved in the Laser Powder Bed Fusion (LPBF) process and ultimately to determine its stability. By utilizing high-speed imaging, various process signatures are produced during single track formation of 316L stainless steel with various combinations of laser power and scan speed. In this study, we evaluate whether these signatures can be used to detect the onset of potential defects. To identify process signatures, image segmentation and feature detection are applied to the monitoring data along the line scans. The process signatures determined in the current study are mainly related to the features like the process zone length-to-width ratio, process zone area, process zone mean intensity, spatter speed and number of spatters. It is shown that the scan speed has a signi cant impact on the process stability and spatter formation during single track fusion. Simulations with similar processing conditions were also performed to predict melt pool geometric features. Post-process characterization techniques such as Xray computed tomography and 2.5-D surface topography measurement were carried out for a quality check of the line track. An attempt was made to correlate physics-based features with process-related defects and a correlation between the number of keyhole porosities and the number of spatters was observed for the line tracks.
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