Exponential smoothing of time series data in R

This thesis deals with basic methods of classical exponential smoothing for univariate time series with regular observations and their applications in an open source statistical computing environment of a programming language R. The methods of simple, double and triple exponential smoothing, Holt linear exponential smoothing and Holt-Winters exponential smoothing are presented. The recursive character of the methods along with their high computational effectiveness are demonstrated. The latter part of the thesis demonstrates application of the exponential methods in the R language environment, based on selected time series data from the Time Series Data Library (TSDL). Short term forecasts of the series are constructed and ilustrated graphically using selected functions of the R environment.Cílem práce je představit základní metody klasického exponenciálního vyrovnávání jednorozměrných časových řad s pravidelně pozorovanými hodnotami a způsoby, jakými se s těmito metodami pracuje v open sourceovém statistickém výpočetním prostředí programovacího jazyka R. Popsány jsou metody jednoduchého, dvojitého a trojitého exponenciálního vyrovnávání, Holtova lineárního vyrovnávání a metody Holt-Wintersova exponenciálního vyrovnávání. Je popsána rekurentní povaha metod a jejich výpočetní nenáročnost. Praktická část je věnována samotnému použití exponenciálního vyrovnávání v prostředí jazyka R na vybraných časových řadách z databáze Time Series Data Library (TSDL). Dále jsou provedeny krátkodobé předpovědi těchto řad pomocí několika funkcí prostředí R a jejich grafické znázornění

Abrasive wear of Al2O3–SiC and Al2O3–(SiC)–C composites with micrometer- and submicrometer-sized alumina matrix grains

The response of Al2O3, Al2O3–SiC–(C) and Al2O3–C nanocomposites to grinding was investigated in terms of changes of quality of ground surfaces and of the weight losses with time. The study used monolithic polycrystalline aluminas as references, and alumina-based composites with nanosized SiC and C inclusions and with alumina matrix grain size varying from submicrometer to approximately 4 μm. The studied materials can be roughly divided into two groups. Materials with submicrometer alumina matrix grains (Group 1) wear predominantly by plastic deformation and grooving. Coarse-grained materials (Group 2) wear by mixed wear mechanism involving crack initiation and interlinking accompanied by grain pull-out, plastic deformation and grooving. The wear rate of composites increases with increasing volume fraction of SiC. The Group 2 materials wear much faster then those with submicron microstructure. In all cases (with one exception) the wear resistance of composites was higher than that of pure aluminas of comparable grain sizes used as reference materials

The influence of post-sintering HIP on the microstructure, hardness, and indentation fracture toughness of polymer-derived Al2O3–SiC nanocomposites

Al2O3–SiC nanocomposites containing 3–8 vol.% SiC were prepared from fine α-alumina powder and a poly(allyl)carbosilane precursor of SiC by polymer infiltration of porous alumina matrix (composites IP), or by warm pressing of polymer-coated alumina powder (composites CW). The polymer was converted to SiC by careful heating of green specimens in inert atmosphere (Ar). The residual porosity was eliminated to less than 10% by pressureless sintering (PS) at temperatures between 1700 and 1850 °C. The post-sintering hot isostatic pressing (HIP) at 1700 °C eliminated the residual porosity to less than 1%, but also resulted in coarsening of the alumina matrix grains, and the inter- and intragranular SiC inclusions. The Vickers hardness of IP specimens sintered at T < 1850 °C increased by 1–10%, which is attributed to elimination of residual porosity. The hardness and indentation fracture toughness of specimens IP sintered at 1850 °C decreased after HIP by 6 and 15%, respectively. The HIP of CW composites increased their hardness and fracture toughness by approximately 10%. The maximum fracture toughness of 5.2 ± 0.2 MPa m1/2 was measured for the materials containing 8 vol.% of SiC. A correlation was found between the fracture toughness, and the mean size and volume fraction of intergranular SiC inclusions in composites CW

Effect of sintering temperature on phase evolution, microstructure, and mechanical properties of La2Ce2O7/40 wt.% YSZ composite ceramics

In this work, La2Ce2O7/40 wt% YSZ (LC40Z) mixed powders were used to fabricate composite bulk ceramics with their potential use as a material for high-performance thermal barrier coatings (TBCs). For this purpose, the effect of sintering temperature on the chemical reactivity of LC and YSZ was investigated via hot-pressing at the temperatures of 1300, 1400 and 1500 °C. X-ray diffraction analysis (XRD), Raman spectroscopy, and scanning electron microscopy (SEM) were utilized to characterize the phase and microstructure evolution in both LC40Z powder mixtures and composite bulk ceramics. Results showed that solid-solution reactions occurred between the YSZ and LC during hot-pressing of the LC40Z powder mixtures, indicated by a new phase of La2Ce0·2Zr1·8O7 (LCZ) observed in the XRD patterns. The detailed analysis of Raman spectra confirmed the gradual transition from fluorite LC to pyrochlore LCZ structure, which was demonstrated by the appearance of characteristic pyrochlore bands. All composites densified by hot-pressing exhibited a high relative density above 95%. The average grain size of the LC40Z composites increased significantly with increasing sintering temperature, while gradual pore-healing was observed. The associated mechanical properties of LC40Z ceramics were also reported. The Vickers hardness values increased with increasing sintering temperature, which is consistent with the microstructure evolution and relative density variations. The highest hardness, with a value of 10.99 ± 0.23 GPa, was achieved for the composite hot-pressed at 1500 °C. The fracture toughness results showed the same dependence on sintering temperature. The fracture toughness increased from 1.97 ± 0.15 to 2.4 ± 0.14 MPa m1/2, indicating that the mechanical properties of the LC40Z composites can be tailored by changing the sintering temperature during hot-pressing

High-Temperature Oxidation Resistance of PDC Coatings in Synthetic Air and Water Vapor Atmospheres

This work is aimed at the development and investigation of the oxidation behavior of ferritic stainless-steel grade AISI 441 and polymer-derived ceramic (PDC) protective coatings. Double-layer coatings of a PDC bond coat below a PDC top coat with glass and ceramic passive fillers’ oxidative resistance were studied at temperatures up to 1000 °C in a flow-through atmosphere of synthetic air and in air saturated with water vapor. Investigation of the oxide products formed at the surface of the samples in synthetic air and water vapor atmospheres, at different temperatures (900, 950, 1000 °C) and exposure times (24, 96 h) was carried out on both uncoated steel and steel coated with selected coatings by scanning electron microscopy (SEM) and X-Ray diffraction (XRD). The Fe, Cr2O3, TiO2, and spinel (Mn,Cr)3O4 phases were identified by XRD on oxidized steel substrates in both atmospheres. In the cases of the coated samples, m- ZrO2, c- ZrO2, YAG, and crystalline phases (Ba(AlSiO4)2–hexacelsian, celsian) were identified. Scratch tests performed on both coating compositions revealed strong adhesion after pyrolysis as well as after oxidation tests in both atmospheres. After testing in the water vapor atmosphere, Cr ions diffused through the bond coat, but no delamination of the coatings was observed

Y3Al5O12-α-Al2O3 composites with fine-grained microstructure by hot pressing of Al2O3-Y2O3 glass microspheres

Yttrium aluminate glass microspheres with the eutectic composition 76.8 mol. % Al2O3 and 23.2 mol. % Y2O3 were prepared by combining the sol-gel Pechini method with flame synthesis. The sol-gel method was applied to achieve the desired composition homogeneity of the prepared glass and hence, improve the microstructure homogeneity and mechanical properties of bulk polycrystalline materials. The latter were prepared by hot pressing, more specifically pressure assisted sintering, at 1050 degrees C, 1300 degrees C and 1600 degrees C using pressures of 30 MPa and 80 MPa and holding times between 0 and 30 min. This also led to the crystallization of the glass. A composite with the Vickers hardness 18.0 +/- 0.7 GPa and an indentation fracture toughness 4.9 +/- 0.3 MPa.m(1/2) was obtained by sintering at 1600 degrees C, at the pressure of 80 MPa and with 30 min isothermal heating at the maximum temperature. Improved mechanical properties were observed when increasing the temperature of sintering and the holding time. This can be attributed to the formation of a unique microstructure consisting of alpha-Al2O3 grains in the mu m-scale embedded in a YAG (yttrium-aluminium garnet) matrix in the hot-pressed samples

Sintering of Ce3+-doped yttria nanoparticles prepared by precipitation method

Cerium doped yttrium oxide nanoparticles with various Ce3+ concentrations between 0.001 and 0.010 at% have been synthesised by precipitation method using ammonium hydroxide as a precipitation agent. The synthesised powders are characterised by a mean particle size of ca. 55 nm. Highly dense specimens, with a relative density> 98.8%, were obtained by sintering the green compacts shaped by pressure filtration, at 1550 °C for 3 h in air. The sintering behaviour of Ce3+ doped Y2O3 was studied by constructing Master Sintering Curves (MSC); the results showed that the apparent activation energy of sintering for Ce3+ doped Y2O3 increases with the increase of cerium concentration. The segregation of larger Ce3+ cations in the grain boundaries is likely to be responsible for the increase in the sintering activation energy

Structure, thermal properties and crystallization behavior of binary Y2O3–Al2O3 glasses with high alumina content

Five compositions in the system Al2O3–Y2O3 with high level of homogeneity were prepared in the form of glass microspheres by flame synthesis. The amorphous nature of prepared glasses with highly disordered structure was confirmed by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), Raman and nuclear magnetic resonance (NMR) spectroscopy. In the NMR spectra, typical signals with chemical shifts of 75, 42 and 12 ppm were observed, which were attributed to the presence of AlO4, AlO5 and AlO6 motifs in the glass structure. The ratio of individual motifs in glass samples did not change significantly with the composition. The crystallization of yttrium-aluminium garnet (YAG) phase was observed as a major process in the glasses thermally treated up to 1450 °C, with slow crystallization of θ- and α-Al2O3 phases detected in the temperature interval 980–1450 °C. IR and Raman spectra of the microspheres crystallized at 998, 1300 and 1500 °C for 4 h contained typical bands, that were assigned to the vibrations of AlO4 and AlO6 groups in YAG and Al2O3 structures. The comparison of 27Al and 89Y magic angle spinning (MAS) NMR spectra showed the presence of only YAG and α-Al2O3 phase in the samples crystallized at 1500 °C and the presence of a trace amount of θ-Al2O3 in the sample crystallized at 998 and 1300 °C. The yttrium aluminium perovskite (YAP) and yttrium aluminium monoclinic (YAM) phases, expected in this system, were no detected