High Dimensional Precision Research Articles

Honest confidence regions and optimality in high-dimensional precision matrix estimation

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters p can be much larger than the sample size. We show that the novel estimator achieves minimax rates in supremum norm and the low-dimensional components of the estimator have a Gaussian limiting distribution. These results hold uniformly over the class of precision matrices with row sparsity of small order $$\sqrt{n}/\log p$$ and spectrum uniformly bounded, under a sub-Gaussian tail assumption on the margins of the true underlying distribution. Consequently, our results lead to uniformly valid confidence regions for low-dimensional parameters of the precision matrix. Thresholding the estimator leads to variable selection without imposing irrepresentability conditions. The performance of the method is demonstrated in a simulation study and on real data.

Composite Marginal Likelihood Estimation of Spatial Autoregressive Probit Models Feasible in Very Large Samples

Composite Marginal Likelihood (CML) has become a popular approach for estimating spatial probit models. However, for spatial autoregressive specifications the existing brute-force implementations are infeasible in large samples as they rely on inverting the high-dimensional precision matrix of the latent state variable. The contribution of this paper is to provide a CML implementation that circumvents inversion of that matrix and therefore can also be applied to very large sample sizes.

Investigation on power discharge in micro-EDM stainless steel drilling using different electrodes

The present work deals with the execution of through micro-holes on stainless steel plates using a micro-EDM (Electrical discharge machining) machine. The investigation focuses on the influence of different electrodes’ materials and power discharge on both the process performance and the dimensional characteristics of the holes. The experimental campaign was carried out by varying peak current and voltage in order to achieve both high and low power discharge conditions. Tubular electrodes made of three different materials (tungsten carbide, brass and copper) were used. The indexes taken into account were Material removal rate (MRR), Tool wear ratio (TWR), Diametral overcut (DOC) and Taper rate (TR). Brass and copper electrodes always resulted to be the best solution in terms of drilling speed even though the wear of these electrode types is remarkable higher than the tungsten one. On the opposite, tungsten carbide electrodes resulted to be the best solution when high dimensional and geometrical precision is required. Concerning the finishing of the hole inner surface, the best results were achieved using tungsten carbide electrode.

High precision hard turning of AISI 52100 bearing steel

Frequently, strict conditions are imposed for high precision components manufacture such as high dimensional precision, accurate geometrical form and good surface finish. High precision machining allows industry to dispense with successive operations such as turning, grinding and polishing to attain these objectives. In this paper, precision hard turning is proposed for the finishing of AISI 52100 bearing components. Several developments were carried out on the prototype lathe in order to adapt it to machining hard steel AISI 52100. To ensure high stability and stiffness during machining, the performances of hydrostatic X and Z-axis slides-ways were investigated. Machined surfaces were characterized in terms of roughness, microstructure analysis, quantitative phase composition and residual stress measurements. The achieved surface roughness Ra is in the range of 0.1–0.2μm. Microstructural investigations revealed metallurgical transformations, such as the presence of a very fine white layer (<1μm) on the top surface and a thermal affected zone (transition zone) of 35–50μm in the sub-surface. Energy dispersive X-ray diffraction analyses show that the percentage of the different phases is not quantitatively affected and the material remains in the martensite phase. X-ray measurements show that Full Width at Half-Maximum (FWHM) is lower in the transition zone than in the bulk material. This decrease of FWHM may be associated to a decrease of dislocation rate. Precision hard turning induces compressive residual stresses at the surface and in the subsurface, which corresponds to the transition zone. Moreover, increasing cutting speed leads to increase the level of compressive residual stresses.

Progress in Tridimensional (3d) Laser Forming of Stainless Steel Sheets

Achievement of complex shapes with high dimensional accuracy and precision by forming process is a demanding challenge for scientists and practitioners. Available technologies are numerous, with laser forming being progressively emerging because of limited springback, lack of molds and sophisticated auxiliary equipments. However, laser forming finds limited applications, especially when forming of tridimensional (3d) complex shapes is required. In this case, cost savings are often counterbalanced by the need for troublesome forming strategies. Therefore, traditional alternatives based on mechanical devices are usually preferred to laser systems. In the present work, 3d laser forming of stainless steel sheets by high power diode laser is investigated. In particular, the set of scanning patterns to form domes from flat blanks by simple and easy-to-manage radial paths alone was found. Numerous 3d items were also processed by diode laser to manufacture a number of complex shapes with high flexibility and limited efforts to modify the auxiliary forming equipment. Based on the experimental results and analytical data, the high power diode laser was found able to form arbitrary 3d shapes through the implementation of tailored laser scanning patterns and appropriate settings of the operational parameters.

Testing Differential Networks with Applications to Detecting Gene-by-Gene Interactions.

Model organisms and human studies have led to increasing empirical evidence that interactions among genes contribute broadly to genetic variation of complex traits. In the presence of gene-by-gene interactions, the dimensionality of the feature space becomes extremely high relative to the sample size. This imposes a significant methodological challenge in identifying gene-by-gene interactions. In the present paper, through a Gaussian graphical model framework, we translate the problem of identifying gene-by-gene interactions associated with a binary trait D into an inference problem on the difference of two high-dimensional precision matrices, which summarize the conditional dependence network structures of the genes. We propose a procedure for testing the differential network globally that is particularly powerful against sparse alternatives. In addition, a multiple testing procedure with false discovery rate control is developed to infer the specific structure of the differential network. Theoretical justification is provided to ensure the validity of the proposed tests and optimality results are derived under sparsity assumptions. A simulation study demonstrates that the proposed tests maintain the desired error rates under the null and have good power under the alternative. The methods are applied to a breast cancer gene expression study.

Ceramic cores for turbine blades via injection moulding

The proposed injection moulding method to produce ceramic cores of turbine blades required the selection of raw materials and the thermoplasticiser as well as the determination of the optimal processing conditions. The selected material enabled the formation of cores with a small cross-section area and was characterised by low shrinkage as well as a relatively low coefficient of thermal expansion. The high mechanical strength of the material allowed for the cores to be formed in a wax model and their assembly in a foundry mould; in addition, the appropriate porosity of the cores ensured their easy etching by means of a water solution of bases. The cores were characterised by high dimensional precision and negligibly small shape deformation. The usability of the cores was positively verified in the process of turbine blades casting in production conditions.

Topography of material made by the application of abrasive water jet technology

Water jet cutting technology is widely applicable in all industrial areas in areas where the need for high dimensional precision machined material. Quality of surface corresponds to the scale from middle smooth milling to rough milling. It shows the results of undulation in dependence on technical and technological parameters ‒ feed rate and abrasive mass flow. The paper also contains the methodology for assessment of the effect of these parameters on surface finished undulation. Our paper presents significant results of experiments made by this methodology applied to MDF, OSB boards and to technical beech plywood. We can see from the above-mentioned results that the fundamental indicator for roughness assessment is the arithmetical mean deviation of roughness profile R&lt;sub&gt;a&lt;/sub&gt;. MDF boards have the most homogeneous structure in the entire cut among the monitored materials, which affects the insignificance of parameter R&lt;sub&gt;a. &lt;/sub&gt;For OSB boards, we can see the worse surface quality with higher feed rate and vice versa for plywood, higher feed rate improves the surface quality. A higher amount of abrasive flow causes the worse surface quality. &amp;nbsp; &amp;nbsp;

CAST METAL FLOW ANALYSIS OF INTERMEDIATE FLANGE

The production of aluminium alloy die castings has been seeing a continuous increase to answer the strong demand by the automotive industry for higher strength and lighter weight. The die castings for automotives are required of not only high quality as of course but also thin walls and a high dimensional precision, thus it is essential to provide advanced casting technologies for the manufacturing of these castings. The main challenge in die casting is design and manufacturing of die. Integration of design and analysis yields to better results. Die casting is often encountered with many problems, few of such problems are blowholes, improper filling, scratch marks, weld lines, cracks, cold shut, porosity, blisters, ejector pin marks, etc. usually these defects are caused due to improper design of dies, or due to incorrect parameters such as injection pressure, cycle time, cooling circuits and other such parameters n order to eliminate such defects a set of analysis has to be carried to ensure that design and other parameters are safe and efficient. Through analysis is carried to understand how the molten metal behaves inside the dies once it is injected, a clear picture about how the molten metal gets solidified is obtained during analysis. Any defects if present can be studied by analysing the results of analysis. In this paper Adestefan analysis software is used for analysis purpose, the flow of molten metal inside the impression was studied and changes to be made to the design were analysed. Behaviour of molten metal at different stages of time such as temperature variations, pressure variations is analysed.

An assembled annular stepwise diverging tube for the measurement of laminar burning velocity and quenching distance

Laminar burning velocities of premixed flames provide essential data in combustion studies. To facilitate an in situ monitoring in the field, a method using the annular diverging tube (ADT) and its improved version of the annular stepwise diverging tube (ASDT) were introduced in previous studies. Although the reliability and applicability of these methods has been verified, additional improvements are necessary for the field application. In this study, an assembled annular stepwise diverging tube (A-ASDT) was introduced. Each step-unit was fabricated separately to have higher dimensional precision and to selectively assemble suitable step-units. Thus, the burner configuration could be easily adjusted, and the experimental resolution could be controlled. Heat transfer through the burner was suppressed to extend the duration of the experiment. The characteristics of the critical flame-propagation-velocity (FPV) that are less affected by the channel gap scale were investigated in more detail. The critical FPVs were comparable to the laminar burning velocities for methane, propane, and DME. The quenching distances could be measured easily, and the quenching Peclet number was directly evaluated. In conclusion, in our knowledge, this A-ASDT may be one of the fastest, easiest, and approvable methods for the prediction of the laminar burning velocity and the quenching distance. Therefore, it can be adopted in the fuel-consuming field to monitor the characteristics of flammable mixtures.

Surface Quality and Chip Formation in Turning of LM6 Aluminium Alloy and Particulate Reinforced Metal Matrix Composite

Majority of the components of aerospace and automotive vehicles need different machining operations, mainly for the assembly requirements. The components have to present both high dimensional precision and surface quality. This present work is concerned with the effect of cutting parameters (cutting speed, feed rate and depth of cut) on the surface roughness and the chip formation in turning process. The machining results are compared with LM6 aluminium alloy and TiC reinforced metal matrix composite under the same cutting conditions and tool geometry. The cutting condition models designed based on the Design of Experiments Response Surface Methodology. The objective of this research is to obtaining the optimum cutting parameters to get a better surface quality and also the chip formation and furthermore does not hazardous to the worker and the machined products quality. Results shows that Surface roughness values of LM6-TiC composite are higher as compared LM6 alloy at similar cutting condition. With increasing in cutting speed improves the surface quality. The surface quality increases with decrease of the feed rate and the depth of cut. There are difference chip forms for LM6 aluminium alloy and Al-TiC composite for a similar of cutting condition. Generally, chip formations of both materials are acceptable and favourable for the worker as well as the products and the tools.

Spatially varying SAR models and Bayesian inference for high-resolution lattice data

We discuss a new class of spatially varying, simultaneous autoregressive (SVSAR) models motivated by interests in flexible, non-stationary spatial modelling scalable to higher dimensions. SVSAR models are hierarchical Markov random fields extending traditional SAR models. We develop Bayesian analysis using Markov chain Monte Carlo methods of SVSAR models, with extensions to spatio-temporal contexts to address problems of data assimilation in computer models. A motivating application in atmospheric science concerns global CO emissions where prediction from computer models is assessed and refined based on high-resolution global satellite imagery data. Application to synthetic and real CO data sets demonstrates the potential of SVSAR models in flexibly representing inhomogeneous spatial processes on lattices, and their ability to improve estimation and prediction of spatial fields. The SVSAR approach is computationally attractive in even very large problems; computational efficiencies are enabled by exploiting sparsity of high-dimensional precision matrices.

A conical mandrel tube drawing test designed to assess failure criteria

Cold tube drawing is a metal forming process which enables to produce tubes with high dimensional precision. It consists in reducing tube dimensions by pulling it through a die. Tube outer diameter is calibrated by a die and the tube inner diameter and thickness are calibrated by a mandrel. One of the major concern of metal forming industry is the constant improvement of productivity and product quality. In the aim of pushing the process to the limit the question is how far the material can be processed without occurrence of failure. In the present study, a long conical mandrel with a small cone angle was designed in order to carry out drawing tests up to fracture with experimental conditions very close to the industrial process. The FEM of the process was built in order to access the local stress and strain data. A specific emphasis was put on the friction characterisation. For that purpose force measurement during the conical mandrel experiments enabled to characterise a pressure dependent friction coefficient constitutive law by means of an inverse analysis. Finally, eleven failure criteria were selected to study the drawability of cobalt–chromium alloy tubes. The assessment of failure criteria based on damage variables or damage accumulation variables involved their calibration on uniaxial tensile tests. The experimental studies were completed by SEM fractography which enabled to understand the fracture locus and the propagation direction of the fracture.

Control of lower incisor inclination with a completely customized lingual appliance for dentoalveolar compensation of class III malocclusion

Bracket slots and orthodontic archwires offering high dimensional precision are needed for fully customized lingual appliances. We aimed to investigate whether high-precision appliances of this type enable dentoalveolar compensation of class III malocclusion so that lower incisor inclination at the end of treatment will closely match the anticipated situation as defined in a pretreatment setup. This retrospective study included a total of 34consecutive patients who had worn a fully customized lingual appliance to achieve dentoalveolar compensation for class III malocclusion by intermaxillary elastics, or proximal enamel reduction, or extraction of teeth in one or both jaws. Casts fabricated at different points in time were three-dimensionally scanned to analyze how precisely the lower incisor inclinations envisioned in the setup were implemented in clinical practice. Aside from minor deviations of ±3.75°, the lower incisor inclinations were clinically implemented as planned even in patients with major sagittal discrepancies. Treatment goals predefined in a setup of dentoalveolar compensation for class III malocclusion can be very precisely achieved via a customized lingual appliance. Correct planning can prevent undesirable lingual tipping of the lower incisors. This finding should not encourage a more liberal use of dentoalveolar compensation, but it should heighten clinicians' awareness of how essential it is to sufficiently consider the individual anatomy of the dentoalveolar complex during treatment planning.

Improved Calibration of High-Dimensional Precision Matrices

Estimation of a precision matrix (i.e., the inverse covariance matrix) is a fundamental problem in statistical signal processing applications. When the observation dimension is of the same order of magnitude as the number of samples, the conventional estimators of covariance matrix and its inverse perform poorly. In order to obtain well-behaved estimators in high-dimensional settings, we consider a general class of estimators of covariance matrices and precision matrices based on weighted sampling and linear shrinkage. The estimation error is measured in terms of both quadratic loss and Stein's loss, and these loss functions are used to calibrate the set of parameters defining our proposed estimator. In an asymptotic setting where the observation dimension is comparable in magnitude to the number of samples, we provide estimators of the precision matrix that are as good as their oracle counterparts. We test our estimators with both synthetic data and financial market data, and Monte Carlo simulations show the advantage of our precision matrix estimator compared with well known estimators in finite sample size settings.

Regularized rank-based estimation of high-dimensional nonparanormal graphical models

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in many applications. However, in practice we often face nonnormal data, and variable transformation is often used to achieve normality. In this paper we consider the nonparanormal model that assumes that the variables follow a joint normal distribution after a set of unknown monotone transformations. The nonparanormal model is much more flexible than the normal model while retaining the good interpretability of the latter in that each zero entry in the sparse precision matrix of the nonparanormal model corresponds to a pair of conditionally independent variables. In this paper we show that the nonparanormal graphical model can be efficiently estimated by using a rank-based estimation scheme which does not require estimating these unknown transformation functions. In particular, we study the rank-based graphical lasso, the rank-based neighborhood Dantzig selector and the rank-based CLIME. We establish their theoretical properties in the setting where the dimension is nearly exponentially large relative to the sample size. It is shown that the proposed rank-based estimators work as well as their oracle counterparts defined with the oracle data. Furthermore, the theory motivates us to consider the adaptive version of the rank-based neighborhood Dantzig selector and the rank-based CLIME that are shown to enjoy graphical model selection consistency without assuming the irrepresentable condition for the oracle and rank-based graphical lasso. Simulated and real data are used to demonstrate the finite performance of the rank-based estimators.

Co-Cr Material Selection in Prosthetic Restoration: Laser Sintering Technology

Selective laser sintering (SLS) is a manufacturing technique that uses a high power laser to fuse small particles of metal powders into a mass representing a desired 3-dimensional object. The topography of the dental restoration is designed by numerical monitoring after having scanned devised prostheses. In our application the alloy consists of 64-67% Co, 28-30% Cr and 5-6% Mo, and has at equilibrium of a γ monophasic structure. Evaluation and characterisation was made by: Microstructure analysis; Corrosion resistance evaluation; Polarization test; Crevice corrosion test; Release of cations. Dimensional observations of Co-Cr restorations show that adjustment leads to satisfactory clinical results with a precision of 25 μm. The metallographic observations show a slight porosity in the horizontal plan. Punctual analysis shows a high regularity of the local chemical composition. Potentiodynamic polarization curves confirm the presence of the porosity in the structure of the restoration. The technique of manufacturing by selective laser sintering allows obtaining prosthetic elements of high dimensional precision which present mechanical properties in agreement with the clinical requirements. However, the residual porosity inherent to the sintering process may present a risk for fracture and crevice corrosion.

Powder injection molding: Borderlines and interfaces

molding technology (which also produces novelties continuously) there is a special branch exhibiting double digit growth both in developing and in mature markets: powder injection molding. In a broad sense this is a family of technologies by itself, the essence of which is that first a highly filled compound is prepared with metal or ceramic filler, which is injection molded (or compression molded) to a ‘green product’. This step is followed by the decomposition of the organic component and by sintering, resulting in a final product. The technology by itself is not new but, due to the almost infinite combination of parameters and components it continuously opens up new possibilities. Here I provide only a non-exhaustive list of possibilities being presently explored. First to mention is the possibility of controlled porosity formation: depending on the selection of the polymer and the inorganic component the resulting final product may be porous or non-porous. Residual porosity depends on the volatility and on the decomposition rate of the polymer and on the conditions of sintering. The degradation and evaporation rate of the organic component may be controlled by forming pores in the green body before the sintering processes e.g. by selective dissolution at the surface using solvents or supercritical fluids. The pores may be filled by ceramic precursor polymers which are transformed into amorphous or nano-crystalline solids on thermal decomposition. A special subgroup of the technologies mentioned is called gel casting, wherein in situ formed organic-inorganic hybrids are prepared, molded and decomposed in a controlled manner into a mostly inorganic final product. (It is not necessary, however, to remove the organic components completely, thermoset organicinorganic hybrids may also be the final products). It is possible to combine various metallic and/or ceramic components with each other or with polymers, to prepare composites with special electric, optical or magnetic properties. Nano-scale milling of the ceramic or metal components is important, which may include mechanical activation, formation of non-equilibrium (high entropy) phases. If the fine-grained structure is to be preserved the sintering process should be led to stabilize the special non-equilibrium structures (by preventing recrystallization) in the final product. These problems are further aggravated by the fact that typical shrinking in the sintering process may be as high-as 20–30% which means further challenges to the technologists aiming at high dimensional precision. I foresee further possibilities in developing new products and technologies in this exciting field of science and technology, where we are at the borderline of scientific disciplines and where controlled manipulation of interfaces is the key to success.

Chemical Mechanical Polishing in Elastic Contact and Partial Hydrodynamic Lubrication: Modeling and Experiments

Chemical mechanical polishing (CMP) has become a primary technique for planarization of semiconductor wafers in submicro device fabrication. Increasing demands for high uniformity and dimensional precision make previously discountable levels of asperity, powder slurry, and wafer-pad contact significant. In this study, a CMP model considering both the elastic microcontact mechanism and the grain flow with roughness effects is presented. The model applies the average lubrication equation with partial hydrodynamic lubrication theory and elastic microcontact theory proposed by Greenwood and Williamson. In experiments, a test rig is used to simulate the CMP process and acquire the signals of polishing. The shear force is measured by a load transducer mounted on the lever and connected with the polishing head during CMP process. Furthermore, the theoretical results are compared with the experimental data. The theoretical and experimental results increase the understanding of CMP process.

Blank design optimization for stepped-section profile ring rolling

A stepped-section ring consists of two rectangular section rings, a big ring and a small ring, joined together. This kind of ring is difficult to process by the ring rolling technique because of its complex cross-sectional shape. Thus a reasonable blank design is necessary. In this paper, four blank designs, one is a rectangular cross-section and the other three are stepped-sections with different step volumes, are proposed and compared with each other using theoretical analysis, FE simulation and experiments. It is shown that three of the designs can lead to volume flow from small ring into big ring during rolling, which is disadvantageous for shape formation and dimensional precision; however, the other design may result in good ring shape and high dimensional precision. Therefore, the optimal blank design is determined to be the one in which the volumes of the big and small rings of the initial blank are equal to those of the final rings, respectively.