Radau- and Lobatto-type averaged Gauss rules

We describe numerical methods for the construction of interpolatory quadrature rules of Radau and Lobatto types. In particular, we are interested in deriving efficient algorithms for computing optimal averaged Gauss–Radau and Gauss–Lobatto type javascript:undefined;quadrature rules. These averaged rules allow us to estimate the quadrature error in Gauss–Radau and Gauss–Lobatto quadrature rules. This is important since the latter rules have higher algebraic degree of exactness than the corresponding Gauss rules, and this makes it possible to construct averaged quadrature rules of higher algebraic degree of exactness than the corresponding “standard” averaged Gauss rules available in the literature

Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions

In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are presented

Decompositions of optimal averaged Gauss quadrature rules

Optimal averaged Gauss quadrature rules provide estimates for the quadrature error in Gauss rules, as well as estimates for the error incurred when approximating matrix functionals of the form u T f (A)v with a large matrix A ∈ R N×N by lowrank approximations that are obtained by applying a few steps of the symmetric or nonsymmetric Lanczos processes to A; here u, v ∈ R N are vectors. The latter process is used when the measure associated with the Gauss quadrature rule has support in the complex plane. The symmetric Lanczos process yields a real tridiagonal matrix, whose entries determine the recursion coefficients of the monic orthogonal polynomials associated with the measure, while the nonsymmetric Lanczos process determines a nonsymmetric tridiagonal matrix, whose entries are recursion coefficients for a pair of sets of bi-orthogonal polynomials. Recently, it has been shown, by applying the results of Peherstorfer, that optimal averaged Gauss quadrature rules, which are associated with a nonnegative measure with support on the real axis, can be expressed as a weighted sum of two quadrature rules. This decomposition allows faster evaluation of optimal averaged Gauss quadrature rules than the previously available representation. The present paper provides a new self-contained proof of this decomposition that is based on linear algebra techniques. Moreover, these techniques are generalized to determine a decomposition of the optimal averaged quadrature rules that are associated with the tridiagonal matrices determined by the nonsymmetric Lanczos process. Also, the splitting of complex symmetric tridiagonal matrices is discussed. The new splittings allow faster evaluation of optimal averaged Gauss quadrature rules than the previously available representations. Computational aspects are discussed

Printing parameter optimization of PLA material concerning geometrical accuracy and tensile properties relative to FDM process productivity

High demand for part customization shifts industries toward AM technologies. Part customization in high-volume manufacturing is developed to its limits, whereas low-volume production using AM is still economically unjustified. FDM technology is quite common in low-volume AM production, but the main issue is poor printing parameter optimization which may result in insufficient final part quality. The subject of this paper is the experimental determination of the optimal parameters for the PLA polymer FDM parts, focusing on nozzle temperature and printing speed. Part geometry and mechanical properties are evaluated for the temperature range of 170–210 °C and speeds of 40, 80, and 120 mm/min. Roughness measurements for part geometrical accuracy assessment and tensile tests for mechanical property estimation have shown the clear advantage of 190 °C and 40 mm/min over the other parameter combinations. However, for higher FDM process productivity 80 mm/min speed may also be considered with 190 °C

Deep learning prediction models for the detection of cyber-attacks on image sequences

With the introduction of Cyber Physical Systems and Industrial Internet of Things within Industry 4.0, vision systems, as indispensable element for robot cognition, become smart devices integrated into the control system using different communication links. In this control framework image streams are transferred between elements of distributed control system opening the possibility for various cyber-attacks that can cause changes in certain parts of images eventually triggering wrong decisions and negative consequences to the system performance. Timely detection of the attacks on communicated image streams is necessary to mitigate or completely avoid their negative effects. In this paper we propose a method for the prediction of the next image in the sequence which can be utilized for the development of anomaly-based cyber-attack detection mechanisms. For the model generation, we have explored the application of several deep learning architectures based on two-dimensional Convolutional Neural Networks and Convolutional Long Short-Term Memory Recurrent Neural Networks. Images obtained from the real-world experimental installation were utilized for model design. Our deep learning models proved to be effective in predicting the next frames according to the criteria of a discrepancy between pixels of the real and estimated images

Reinforcement Learning-based Collision Avoidance for UAV

One of the significant aspects for enabling the intelligent behavior to the Unmanned Aerial Vehicles (UAVs) is by providing an algorithm for navigation through the dynamic and unseen environment. Therefore, to be autonomous, they need sensors to perceive their surroundings and utilize gathered information to decide which action to take. Having that in mind, in this paper, the authors designed the system for obstacle avoidance and also investigate the elements of the Markov decision process and their influence on each other. The flying mobile robot used within the considered problem is quadrotor type and has an integrated Lidar sensor which is utilized to detect obstacles. The sequential decision-making model based on Q-learning is trained within the MATLAB Simulink environment. The simulation results demonstrate that the UAV can navigate through the environment in most algorithm runs without colliding with surrounding obstacles

SIZE EFFECT ASSESSMENT OF KJc EXPERIMENTAL DATA USING THE TWO-STEP-SCALING METHOD

The phenomenon of ductile-to-brittle transition (DBT) in ferritic steels, widely used in design of nuclear reactor pressure vessels, has been a pervasive semi-centennial research topic. Due to the extremely pronounced experimental data scatter, the statistical approach to characterization of this problem has become inevitable from the earliest analyses. In the present study, the fracture toughness parameters derived from the EURO fracture toughness dataset for 22NiMoCr37 reactor steel are used with the aim to explore the utility of the recently proposed two-step-scaling method. Two widely different temperatures (-154 °C and -91 °C; belonging to the lower shelf and the DBT transition regions of fracture toughness, in respect) are selected to demonstrate the accuracy of extrapolation and interpolation of the fracture toughness CDF (cumulative distribution function) and the pertinent issues related to the method application. The fracture toughness measure used is the critical value of the stress intensity factor used in the master curve KJc (MPa√m). The obtained predictions are in good agreement with the experimental results and well within the inherent experimental data scatter. The prediction of the fracture toughness CDF obtained by extrapolation using the novel two-step-scaling method is reasonably conservative

Methodology for Analysing Risk Factor on Surface Top Hammer Drill Rig

Two-level risk mapping and assessment methodology was proposed with several criteria for risk prioritization (frequency of occurrence, downtime, level of danger, type of stoppage, cause of downtime, risk number). In a period of one year all stoppages, both planned and unplanned, were monitored and later on classified by type into: technological, mechanical, electrical, stoppages caused by the machine operator, external stoppages, which include stoppages of machine inactivity due to weather conditions and the like. The methodology proposed is oriented towards the calculation of risks to people, property, etc., which arise from various types of downtime. Then, based on the recording of data on stoppages of the observed machine, the structure of the share of individual stoppages was analyzed and appropriate measures to prevent incidents/accidents were recommended. The main causes of stoppages are isolated based on the frequency of occurrence, the percentage of the downtime duration in the total time spent and the level of danger. The primary cause of stoppages according to the mentioned criteria is the rupture of the hose in the observed machine with percentage participation in the duration of mechanical stoppages of 25.17%, with a frequency of 25% and a degree of danger of 6, while repairing the rod clamp is the second causal factor singled out as important from the risk aspect. Thanks to this, it is possible to plan maintenance activities and manage risks in an adequate way. The proposal for further research is further performance prediction and the determination of optimum operating parameters for different working conditions

Verification of kinematic joints on a physical prototype of a novel parallel mechanism based on Chebyshev's linkage

Developing a novel parallel mechanism design is a complex process, including multiple phases. Designing and analyzing the mechanism's physical prototype is one of the most important phases. The proposed mechanism is novel, with parallel kinematics with actuated translation joins. The considered mechanisms platform has three degrees of freedom (DOF) achieved with three independent kinematic chains representing the connection between the stationary base and the moving platform. The proposed mechanism has numerous connected linkages because of the parallel kinematic construction. The weakest parameter of the mechanisms with parallel kinematics compared to mechanisms with serial kinematics is the shape and size of the workspace. Because of this, the workspace is one of the main parameters in designing a mechanism with parallel kinematics. To achieve the optimal workspace, it is necessary to use the proper joints in the mechanism construction. The mechanism analysis and proper joint selection can be achieved in two ways. The first way is to build the virtual model and experiment on it, and the second is to build the physical prototype. The best way to select the proper joints for the mechanism construction is to compare the analysis results of virtual and physical mechanisms. If the results of comparing virtual and physical prototypes are the same, the physical prototype verifies the mechanism design.Technical treatment and design: Milana ILIĆ MIĆUNOVIĆ, Miloš RANISAVLJEV, Branko ŠTRBAC, Miodrag HADŽISTEVI

Review of the article Assessment of Reproductive Hormones among Infertile Sudanese Males in Khartoum State, verified by Publons, Web of Science

Background: Infertility seems to be a great worldwide problem. Male infertility is a multifaceted state and overlaps a lot factors and affects infertility in about 8–5 % of the people in the world and the man is responsible for 40% of these cases. The FSH, LH and testosterone evaluation is useful in the management of male infertility. For initiation of spermatogenesis and maturation of spermatozoa, FSH is necessary. In the infertile men, higher concentration of FSH is considered to be a reliable indicator of germinal epithelial damage, and was shown to be associated with azoospermia and severe oligozoospermia Objective: The aim of the study is to analyze the levels of reproductive hormones among different groups of infertile patients. Materials and method: This is a facility based study, conducted in Reproductive Care Center in Almuk Nemer Street in Khartoum state. Which include 160 serum samples collected from normozoospermic, oligoathenospermic, and azoospermic men and clinical information collected by the use of questionnaire. The concentrations of reproductive hormones were measured by using a full automated tosoh AIA360 analyzer, then the data was analyzed using the statistical software package SPSS version 17. Result: The results showed that the serum levels of prolactin and FSH is statistically significant increase in patient with azoospermia and oligoasthenospermia as compared to control group, with (p .value < 0.05), and the serum level of LH is statistically significant increase in patient with azoospermia and insignificant increase in patient with oligoasthenospermia as compared to control group, with p .value (0.000 and 0.232), respectively. And the serum level of testosterone is statistically insignificant decrease in patient with azoospermia and insignificantly increase in patient with oligoasthenospermia as compared to control group, with p .value (0.88 and 0.129), respectively. The results also showed statistically insignificant decrease in the serum levels of testosterone and prolactin in azoospermia when compared with oligoathenospermia, with p. value (0.227 and 0.959) respectively. And showed statistically significant increase in the serum levels of FSH and LH in azoospermia when compared with oligoathenospermia, with p. value (0.002 and 0.007) respectively. Conclusion: The level of serum testosterone was insignificantly decreased in patients with azoospermia and insignificantly increased in patients with oligoasthenospermia when compared with control group. The serum levels of prolactin and FSH was significantly increased in patients with azoospermia and oligoasthenospermia when compared with control group. And the serum level of LH in increased significantly in patients with azoospermia and insignificantly in oligoasthenospermia when compared with control group. The serum levels of testosterone and prolactin is insignificant decrease in azoospermia when compared with oligoathenospermia, and the serum levels of FSH and LH is significant increase in azoospermia when compared with oligoathenospermia