Solid State Phenomena Vol. 235

Abstract: Experimental studies very often lead to datasets with a large number of noted attributes (observed properties) and relatively small number of records (observed objects). The classic analysis cannot explain recorded attributes in the form of regression relationships due to lack of sufficient number of data points. One of method making available a filtering of unimportant attributes is an approach known as ‘dimensionality reduction’. Well-known example of such approach is principal component analysis (PCA) which transforms the data from the high-dimensional space to a space of fewer dimensions and gives heuristics to select least but necessary number of dimensions. Authors used such technique successfully in their previous investigations but a question arose: whether PCA is robust and stable This paper tries to answer this question by re-sampling experimental data and observing empirical confidence intervals of parameters used to make decision in PCA heuristics.

Abstract: The investigation described in this paper resulted in some complicated statistical analysis. The first level was an experimental design with technological parameters as factorials input and geometrical surface layer properties as quantitative outputs. The second level was an analysis generally leading to an optimization inverse problem: what parameters result in desired surface layer properties. The principal component analysis was made to identify possibility of a dimensionality reduction and simplify the optimization. Obtained results showed that the experimental dataset is practically two-dimensional but PCA projection involves all factors into the skewed hyper-plane. This paper contains a description of the problem, obtained results, analysis and conclusions.

Abstract: Design of experiment (DoE) is a set of practical recipes and theoretical assumptions leading to the optimization of the technological process and/or the stabilization of its output quality. Practically, all the DoE approaches assume the normality of a random noise and the quasi-linearity of models taken from the general linear model (GLM) class. It allows to use traditional least-square methodology to identification of a model parameters and their confidence intervals. It gives usually sufficient results but completely fails if the model is not from GLM class or a random noise has not a normal distribution. The solution for such problems is the bootstrap approach, a resampling method based on Monte Carlo strategies. This paper tries to answer a question how many repetitions should be made to estimate parameters of the prediction model with sufficient accuracy.

Abstract: The analysis of variance (ANOVA) is a classic tool for an identification of discreet factors impact on the measurable output by a specific decomposition on a total variance according to the scheme proposed by R.A Fisher in the 1920s. There are many explicit and implicit assumptions required as a preliminary of ANOVA computations. The ANOVA computations scheme is well known and implemented in many types of software but all estimations are provided with the assumption of a normal and homoscedasticity distribution of the noise disturbing the output. Computation procedures produce a single number output (e.g. F statistics, p-Value) without any analysis of their own dispersion. This paper analyzes the ANOVA output using the bootstrap approach. It seems to be the most convenient as a data-driven procedure. The source raw data are taken from the image analysis conducted during the investigation of the impact of the ceramic layer thickness on the wax pattern assembly of a turbine blade on the (γ+γ’) eutectic in the IN713C superalloy.

Abstract: This paper treats an iterative shooting method based on sensitivity functions for solving non–linear two–point boundary value problems (BVPs), in the form of a fourth–order differential equation and more than four boundary conditions. The solution of this problem is possible only when the equation includes the required number of unknown parameters. In order to use this method, it is necessary to convert the BVP to an appropriate initial value problem (IVP). The presented method has been illustrated with a numerical example.

Abstract: Typical design of experiments (DoE) approach to the response surface problem applies the polynomials with at most the second order terms. It is correct due to the Taylor’s theorem when the variability of input variables is sufficiently small. Unfortunately, the variability bound of a designed experiment is planned with high uncertainty about the investigated object’s behavior. If the response of the object has a large curvature then model quality indicators (residuals normality, lack of fit, significance of terms) appear to be unacceptable. In such a case, polynomial terms with the order higher than second should be applied. The paper describes the RSM model with the fourth order terms identified for relationship between settings of a meat tumbler machine (input variables) and the Warner-Bratzler shear force (output variable).

Abstract: In the article authors presented digital measurement problem of the object on the 3D images of the microstructures. As a research material were used the micro tomography image of the probe C45 steel with WC-Co-Al₂O₃ surface layer. Due to relatively low contrast between the surface layer and the root material, and lack of sharp edges, some of the methods for automatic threshold indication may give biased results. Following the initial selection of the many methods of automatic binarization two of them and interactive method was selected to carry out comparative studies. The analysis included assessment of the layer thickness, number of detected objects and total volume of all detected objects.

Abstract: The aim of this paper is to present the results of laboratory research on Ionic Polymer-Metal Composite (IPMC), with measurements of electrical values (voltage and current) measured simultaneously with the displacement. The obtained values were used to investigate the possibility of parametric model building. The research is focused mainly on constant frequency sine wave voltage signals. Phase offsets between voltage, current and displacement for different frequencies are calculated. Envelope and mean values of the electrical values are also described.