Use Of non-Gaussian Distributions Research Articles

Experimental Approbation of Selective Laser Melting of Powders by the Use of Non-Gaussian Power Density Distributions

Experimental results on laser beam modulation at selective laser melting (SLM) are presented. The modulation is a possible way to improve the efficiency of the SLM process. The optical diagnostics shows the energy loss up to 30%. This could be a consequence of high thermal gradients in the melt pool resulted by the Gaussian power density distribution. The Gaussian distribution can be changed to the flat-top one or to the inverse-Gaussian (donut) one. An experimental stand with a 200W laser source was developed. Twenty single tracks for each of the three modes were obtained for a Co-Cr alloy. The samples were studied by scanning electronic microscopy (SEM) on irregularity. Optical diagnostics by high velocity camera (HVC) shows that the use of the non-Gaussian laser beam distributions can significantly reduce the width of the free-of-powder consolidation zone, which is considered as the main reason for irregularity of single tracks. A better metallurgical bonding of the single tracks with the substrate was obtained by the use of the flat-top laser beam. Both of these facts show a significant influence of the laser beam energy distribution on the energy loss at SLM, especially for high power laser sources. The observed escape of granules shows a possible influence of the dynamic factor. The use of the non-Gaussian distributions can enhance 3D parts, for example, improve the geometrical tolerance and decrease the residual porosity.

On the Use of Multivariate Lévy-Stable Random Field Models for Geological Heterogeneity

Increasing attention has been paid to the use of non-Gaussian distributions as models of heterogeneity in sedimentary formations in recent years. In particular, the Levy-stable distribution has been shown to be a useful model of the distribution of the increments of data measured in well logs. Frequently, the width of this distribution follows a power–law type scaling with increment lag, thus suggesting a nonstationary, fractal, multivariate Levy distribution as a useful random field model. However, in this paper we show that it is very difficult to formulate a multivariate Levy distribution with any nontrivial spatial correlations that can be sampled from rigorously in large models. Conventional sequential simulation techniques require two properties to hold of a multivariate distribution in order to work: (1) the marginal distributions must be of relatively simple form, and (2) in the uncorrelated limit, the multivariate distribution must factor into a product of independent distributions. At least one of these properties will break down in a multivariate Levy distribution, depending on how it is formulated. This makes a rigorous derivation of a sequential simulation algorithm impossible. Nonetheless, many of the original observations that spurred the original interest in multivariate Levy distributions can be reproduced with a conventional normal scoring procedure. Secondly, an approximate formulation of a sequential simulation algorithm can adequately reproduce the Levy distributions of increments and fractal scaling frequently seen in real data.

Load-capacity interference and the bathtub curve

Load-capacity (stress-strength) interference theory is used to derive a heuristic failure rate for an item subjected to repetitive loading which is Poisson distributed in time. Numerical calculations are performed using Gaussian distributions in load and capacity. Infant mortality, constant failure rate (Poisson failures), and aging are shown to be associated with capacity variability, load variability, and capacity deterioration, respectively. Bathtub-shaped failure rate curves are obtained when all three failure types are present. Changes in load or capacity distribution parameters often strongly affect the quantitative behavior of the failure-rate curves, but they do not affect the qualitative behavior of the bathtub curve. Neither is it likely that the qualitative behavior will be affected by the use of nonGaussian distributions. The numerical results, however, indicate that infant mortality and wear-out failures interact strongly with load variability. Thus bathtub curves arising from this model cannot be represented as simple superpositions of independent contributions from the three failure types. Only if the three failure types arise from independent failure mechanisms or in different components is it legitimate simply to sum the failure rate contributions. >

Non-Gaussian seasonal adjustment

A non-Gaussian state space modeling of time series with trend and seasonality is shown. An observed time series is decomposed into trend, seasonal and observational noise. Each component is expressed by a smoothness prior model which is expressed by a stochastic linear difference equation. The essential difference from the previous methods is the use of non-Gaussian distributions. Namely, the white noise input to each component and the observational noise are not necessarily Gaussian. This allows for the possible existence of jump of the trend or seasonal component and of the outliers. Thus by the use of this non-Gaussian state space model, seasonal time series with possible existence of outliers and sudden structural changes can be automatically handled without any special treatment. The filtering and smoothing formulas for the non-Gaussian state space model is realized by using Gaussian mixture approximation to the involved densities. Numerical examples are shown to contrast with Gaussian modeling.

The time series modelling of non-gaussian engineering processes

Any proposed description of an engineering surface must clearly take into account the height and spacing features of the surface irregularities. A statistical description of the surface profile can be given in terms of two functions: its ordinate height distribution and its autocorrelation function. Time series models have been suggested by several workers in surface metrology as a useful method of combining height and spatial characteristics into a single model for a surface. In a previous paper by the present authors it was shown how the scope of such models could be extended to include a wider range of engineering processes by the use of non-gaussian distributions. However, if the ordinate height distribution was non-gaussian the methods outlined were restricted to two simple models. In this paper the basic methods previously discussed are extended and used for modelling non-gaussian processes which could also have a more complex correlation structure ( e.g. periodic components obtained from turning and other similar processes). These give a wide class of models which can more accurately simulate a large range of engineering processes.

A Comparison of Theoretical and Experimental Video Compression Designs

This paper compares theoretical and experimental picture compression designs, for images processed in 8 X 8 blocks using the Walsh-Hadamard transform (WHT). The optimum picture compression design is well known, if the mean-square error (mse) is used as the measure of distortion, and if it is assumed that the video process is a stationary first-order Markov process with a Guassian distribution. This theoretical design gives useful results when the transform processing is done on full pictures, but gives inferior results (relative to empirical design) when transform processing is done on small 8 X 8 blocks. The use of non-Gaussian distributions for the transform components fails to improve this poor performance, which is due to the nonstationary nature of the video process. An experimentally based design procedure, which considers nonstationarity, yields significantly improved MSE and subjective performance.