Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

<abstract><p>In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.</p></abstract>

An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements.

Polynomial approximation of dynamic signals of single platform railway scales

Purpose. Obtaining an approximating function (or a system of approximating equations), which, with a minimum error, will make approximations to the available data on a train of railway objects through 1 platform scales. Methodology. To solve this problem, numerical methods are used, namely, the approximation by polynomial functions of the nth order. The experimental data on the basis of which the experiments were carried out were obtained from the weighing and identification system of wagon in motion on a single platform scale. The approximation process is automated using a program written in the Python programming language in which the polyPit and polyid functions of the numPy library are used to obtain the polynomial coefficients. Findings. Due to the use of polynomial approximation in data processing from tensometric railroad weighing systems, it was possible to obtain a system of linear equations that, with minimal error, restored the experimental data that were obtained from the existing system of the Severny GOK: Metinvest enterprise. When normalizing the readings of the sensors from conventional units, obtained from the summing box to the range of values [0; 1] it became possible, in percentage terms, to describe a railway object. This makes it possible to avoid the dependence of the final results on the travel speed of the carriage or locomotive, which leads to an increase in the accuracy of the identification of cars in the rolling stock due to the use of the percentage of the axles staying on the weighing platform (approach / exit). It became possible to determine the type of carriage with the same number of axles, but different characteristics of the center space and the base of the rolling stock. Originality. The novelty is to obtain a general method of approximation of experimental data of the passage of wagons through a single-platform scales, which can be used to train intelligent systems and generate close to real data of the passage of a car (due to the imposition of noise, etc.). Practical value. Improving the accuracy and speed of the carriage identification as a whole, which reduces the plant downtime, contributes to an increase in the number of weighed and identified moving objects, as well as the ability to identify the type of carriage with the same number of axles in the train. The methods presented in the work can be used both for identification and for tasks, the end result of which is the classification of input data (neural networks, etc.).

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

Deformation of framed curves with boundary conditions

We provide a general approach to deform framed curves while preserving their clamped boundary conditions (this includes closed framed curves) as well as properties of their curvatures. We apply this to director theories, which involve a curve $$\gamma : (0, 1)\rightarrow \mathbb {R}^3$$ γ : ( 0 , 1 ) → R 3 and orthonormal directors $$d_1$$ d 1 , $$d_2$$ d 2 , $$d_3: (0,1)\rightarrow \mathbb {S}^2$$ d 3 : ( 0 , 1 ) → S 2 with $$d_1 = \gamma '$$ d 1 = γ ′ . We show that $$\gamma $$ γ and the $$d_i$$ d i can be approximated smoothly while preserving clamped boundary conditions at both ends. The approximation process also preserves conditions of the form $$d_i\cdot d_j' = 0$$ d i · d j ′ = 0 . Moreover, it is continuous with respect to natural functionals on framed curves. In the context of $$\Gamma $$ Γ -convergence, our approach allows to construct recovery sequences for director theories with prescribed clamped boundary conditions. We provide one simple application of this kind. Finally, we use similar ideas to derive Euler–Lagrange equations for functionals on framed curves satisfying clamped boundary conditions.

Learning metamorphic malware signatures from samples

Metamorphic malware are self-modifying programs which apply semantic preserving transformations to their own code in order to foil detection systems based on signature matching. Metamorphism impacts both software security and code protection technologies: it is used by malware writers to evade detection systems based on pattern matching and by software developers for preventing malicious host attacks through software diversification. In this paper, we consider the problem of automatically extracting metamorphic signatures from the analysis of metamorphic malware variants. We define a metamorphic signature as an abstract program representation that ideally captures all the possible code variants that might be generated during the execution of a metamorphic program. For this purpose, we developed MetaSign: a tool that takes as input a collection of metamorphic code variants and produces, as output, a set of transformation rules that could have been used to generate the considered metamorphic variants. MetaSign starts from a control flow graph representation of the input variants and agglomerates them into an automaton which approximates the considered code variants. The upper approximation process is based on the concept of widening automata, while the semantic preserving transformation rules, used by the metamorphic program, can be viewed as rewriting rules and modeled as grammar productions. In this setting, the grammar recognizes the language of code variants, while the production rules model the metamorphic transformations. In particular, we formalize the language of code variants in terms of pure context-free grammars, which are similar to context-free grammars with no terminal symbols. After the widening process, we create a positive set of samples from which we extract the productions of the grammar by applying a learning grammar technique. This allows us to learn the transformation rules used by the metamorphic engine to generate the considered code variants. We validate the results of MetaSign on some case studies.

Algebraic bound for the phase–frequency response of the commande robuste d'ordre non-entier approximation of fractional differentiators and its applications in control systems analysis

This article deals with analyzing the phase–frequency response of commande robuste d'ordre non-entier approximations of fractional-order differentiators. More precisely, an algebraic tight upper bound is derived for the phase of the approximations obtained from the commande robuste d'ordre non-entier method. Then, some applications for this achievement are discussed in the viewpoint of control systems analysis. These applications include usefulness of the obtained upper bound in stability preservation analysis during the commande robuste d'ordre non-entier–based approximation process and applicability of such a bound in finding necessary or sufficient conditions for test of positive realness/negative imaginariness of a fractional-order transfer function.

Robust adaptive beamforming based on the direct biconvex optimization modeling

It is well known that the performance of the minimum variance distortionless response beamformer is sensitive to steering vector mismatch, which motivates the development of robust adaptive beamforming(RAB). However, robust adaptive beamforming (RAB) is usually modeled as a nonconvex optimization problem. The most state-of-art methods solve it indirectly by approximating the nonconvex problem to the convex optimization problem, which causes the approximation errors and performance degradation. To circumvent this problem, a novel method that is against the mismatch of the signal look direction errors, which reformulates RAB as the biconvex form directly, is proposed. This method imposes ideal response constraints to guarantee the gain of the angular region in which the actual signal lies and suppresses the signals in the remaining region, and constructs a four-order problem. Then, an auxiliary variable is introduced to reformulate it as a biconvex problem without approximation process, which can be efficiently solved iteratively by the alternating direction method of multipliers (ADMM) algorithm. Simulation results show that the proposed method can obtain a better performance on the signal-to-interference-plus-noise (SINR) and flexible control of error range.

A priori error estimates of regularized elliptic problems

Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work we show a-priori rates of convergence of this approximation process in standard Sobolev norms, with minimal regularity assumptions on the approximation of the Dirac delta distribution. The application of these estimates to the numerical solution of elliptic problems with singularly supported forcing terms allows us to provide sharp $$H^1$$ H 1 and $$L^2$$ L 2 error estimates for the corresponding regularized problem. As an application, we show how finite element approximations of a regularized immersed interface method results in the same rates of convergence of its non-regularized counterpart, provided that the support of the Dirac delta approximation is set to a multiple of the mesh size, at a fraction of the implementation complexity. Numerical experiments are provided to support our theories.