Space Frame Research Articles

Controlled Integral Frames for Hilbert C*-Modules

The notion of controlled frames for Hilbert spaces were introduced by Balazs, Antoine and Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Controlled frame theory has a great revolution in recent years. This theory have been extended from Hilbert spaces to Hilbert C∗-modules. In this paper we introduce and study the extension of this notion to integral frame for Hilbert C∗-modules. Also we give some characterizations between integral frame in Hilbert C∗-modules.

Super-resolution Localization Problem Based on the Mobile Scenario

Target positioning has always been a hot research topic in the field of sensors. In recent years, radar detection technology has become increasingly mature, resulting in a large number of radar sensors have begun to be used in traffic, security, medical and other fields for target detection. This paper mainly studies the super-resolution localization problem of FMCW FMCW in moving scenes. It analyzes the echo data by mathematical modeling to obtain the distance and angle information of the object to find the place of the object. To restore the motion trajectory of objects more realistically and achieve super-resolution positioning, a super-resolution radar positioning model based on Kriging interpolation based on the Fourier spectrum is established. By constructing a frame of intermediate frequency data Fourier spectrum tensor space, Fourier spectrum analysis is used to obtain the spectral characteristics of spatiotemporal changes when objects move. The Fourier spectrum surface is reasonably predicted through the statistical method - kriging interpolation. More Fourier spectrum information of objects in the time dimension can be obtained, and then more object points can be restored to achieve super-resolution positioning. This is widely used in the automotive field, which develops autonomous driving systems to help drivers better control the vehicle and reduce the probability of car accidents.

Investigate and Designing Translation surface with a 2-Bishop frame in the Galilean space.

Investigate and Designing Translation surface with a 2-Bishop frame in the Galilean space.

Design optimization of small fishing vessel structures: A case study

The cost of vessel operations poses a significant challenge for fishermen in Indonesia, with 60% - 70% of their operational expenses being allocated to fuel. To address this issue and decrease fuel consumption in fishing vessels, one possible solution is to construct lighter boat designs. Through careful optimization of the construction process and the selection of suitable materials, it becomes feasible to achieve such a lighter design, leading to reduced operational and construction costs. The optimization process involves considering various frame spacing variations, like 400 mm, 500 mm, and 600 mm, and utilizing materials such as mild steel and AH32. Additionally, optimizing the plate thickness ensures that the vessel’s stress and deformation remain within the limits set by the rules. As a result of this optimization, a weight reduction of up to 20% is observed.

The Counter-Reformation Art Serving the Orthodoxy: The Changes in the Artistic Concept of Ukrainian Iconostasis during the Second Quarter of the 17th Century

The paper analyzes the reasons causing the structural and plastic changes of Ukrainian iconostases during the second quarter of the 17th century and eventually resulting in the Ukrainian iconostasis of the Baroque period. During the period, the iconostasis achieved monumentality and plasticity in the interpretation of the façade side as a result of introduction of the broken entablature, deep niches for icons, and passages to the altar, as well as to exceptionally rich carved decor, which, in general, added spaciousness to its architectural composition. The specified structural and plastic iconostases characteristics appeared when the Metropolitan Petro Mohyla was the archpastor; they are notable in the iconostases built with his direct or indirect assistance. The hypothesis of the paper is that the concept of iconostasis’ new artistic image as a monumental and architectural space frame was formulated by Petro Mohyla in the context of the program he developed for the Orthodox Church of Ukraine renovation, which, in particular, included the domain of church art and artistic decoration of temples. Petro Mohyla’s idea of the iconostasis architectural image renewal was based on the desire to provide more artistic expressiveness to its form and carved decorations. During the era, these features were characteristic of the Catholic Church altars of the Polish-Lithuanian Commonwealth built in the Baroque style. The methods of significant emotional influence on the congregation developed by the post-Tridentine art as an instrument of the Catholic Church struggling against the Reformation ideas proved to be appropriate for the Kyiv Metropolis Orthodox art, that, after the Union of Brest, faced the problems similar to those of the Catholic Church, which arose with the spread of the Reformation.

Absolute phase retrieval based on fringe amplitude encoding without any additional auxiliary pattern

An absolute phase retrieval method based on fringe amplitude encoding is proposed. Different from the conventional intensity coding methods which are based on time division multiplexing with multiple additional auxiliary patterns, the proposed fringe order encoding strategy is codeword overlapping interaction based on space division multiplexing. It just directly encodes different fringe amplitudes for different periods in corresponding sinusoidal phase-shifting patterns to generate space division multiplexing composite sinusoidal phase-shifting patterns and quantifies the fringe amplitudes into four levels as encoding strategy, so it can retrieve absolute phase without any additional auxiliary patterns. To improve the anti-interference capability of the proposed method, a codeword extraction method based on image morphological processing is proposed to segment the grayscale. Consequently, both the phase-shifting sinusoidal deformed patterns and the single frame space division multiplexing four gray-level codewords for fringe order recognition can be extracted respectively from the captured composite deformed patterns. Then, a half-period single-connected domain correction method is also proposed to correct the codewords. Moreover, in order to suppress the effect of jump errors, the phase zero points are constructed to segment the positive and negative ranges of the phase, making the phase unwrapping process segmented. The experimental results demonstrate the feasibility and effectivity of the proposed method.

Numerical design optimization of real size complex steel space frame structures using a novel adaptive cuckoo search method

AbstractIn this study, real size complex steel space frame structures are numerically designed to achieve optimal design weight. For this aim, standard cuckoo search algorithm is rectified through a newly proposed adaptive method over two fundamental algorithmic parameters of alien egg probability detection (Pa) and step size control (α) to overcome incompetency of trapping into local optima. Besides, to strengthen exploitation phase of newly proposed algorithm, it is boosted with greedy selection (GS). So, novel algorithm has more promising exploration and exploitation capabilities. An 8‐story, 1024‐member and a 20‐story, 1860‐member real size complex steel space frame structures are selected as design examples. Also, initially to verify the supremacy of novel algorithm, a well‐known welded beam is optimized as a benchmark structural design problem. Afterwards, the steel space frame structures are optimally designed via novel algorithm. Since ready steel section lists are utilized as selection pool for design variables, discrete programming problem is come into existence. The dead, live, snow, and wind design loads acting on frame structures are calculated in direction of ASCE 7‐05 provisions. Furthermore, the structural design constraints are determined from LRFD‐AISC specifications. Eventually, the newly proposed adaptive cuckoo search algorithm boosted with GS presents outstanding algorithmic performance.

Quantum detection problem for fusion frames

A quantum injective frame is a frame whose measurements for density operators can be used as a distinguishing feature in a quantum system, and the frame quantum detection problem demands a characterization of all such frames. Very recently, the quantum detection problem for continuous as well as discrete frames in both finite and infinite dimensional Hilbert spaces received significant attention. The quantum detection problem pertaining to the characterization of informationally complete positive operator-valued measures (POVM) can be split into two cases: The quantum injectivity or state separability problem and the rang analysis or quantum state estimation problem. Building upon this notion, this note is aimed at the quantum detection problem for fusion frames. The injectivity of a family of vectors and a family of closed subspaces is characterized in terms of some operator equations in Hilbert–Schmidt and trace classes.

Piecewise scalable frames in Hilbert spaces

Tight frames are extremely useful in applications. A scalable frame was recently introduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In this paper, we consider piecewise scalable frames. We obtain some characterizations for them, and demonstrate that scalability is stable under unitary operators and isomorphisms between two Hilbert spaces. We further obtain a relation between the piecewise scalable frames in Hilbert spaces, and their tensor product

Numerical investigations on the dynamic responses of metro tunnel-soil-ground building under oblique incidence of seismic wave

With the development of urban rail transits, the metro tunnels frequently underpass the above-ground buildings, and understanding the dynamic responses of metro tunnel-soil-ground buildings experiencing oblique incidence of seismic waves is of crucial importance. Considering that the seismic waves in the near-field seismic area are mostly obliquely incident to the ground at a certain angle, a two-dimensional numerical model for tunnel-soil interaction system and tunnel-soil-above ground structure was established by Abaqus software, in which the viscoelastic boundary and equivalent nodal forces were adopted to simulate the ground motion. The effects of tunnel burial depth, tunnel spacing, and tunnel frame spacing on the seismic responses of metro tunnel-soil and metro tunnel-soil-above ground building were analyzed under oblique incidence of SV wave with different incident angles. It was found that the tunnel depth has a significant effect on the lining dynamic bending moment and axial force peak, and its influence is closely related to the site category. The tunnel spacing has a minor impact on the dynamic response of the lining structure. The incident angle has a significant effect on the peak value of the dynamic shaft force of the lining. The application of the frame on the ground has a significant impact on the tunnel. The influence of above-ground buildings and tunnel burial depth should be considered when tunnel design is carried out.

Timelike spherical curves according to equiform Bishop frame in 3-dimensional Minkowski space

In this paper, we study the equiform Bishop formulae for the equiform timelike curves in 3-dimensional Minkowski space where the equiform timelike spherical curves are defined according to the equiform Bishop frame. We establish a necessary and sufficient condition for an equiform timelike curve to be an equiform timelike spherical curve. Furthermore, we give certain characterizations of equiform spherical curves in 3-dimensional Minkowski space, which are timelike with an equiform spacelike principal normal vector.

Yaw control strategies for 20 MW multi-rotor systems

In this paper, the control of an active yaw system for a 20 MW multi-rotor wind turbine system (MRS) is considered. The MRS under investigation consists of five 4 MW turbines in two rows, which are connected to the tower via a space frame. A central yaw bearing at the height of the lower rotors is provided for active yaw. The paper aims to show that active aerodynamic yaw is possible by changing the thrust of certain rotors and should be considered for further research in the field of yawing of an MRS. Two different simulation environments are used in the paper. The MRS is modeled and simulated in Matlab/Simulink. Simulink’s own control modules are used as controllers. In the other simulation approach, the same MRS is modeled and simulated in Bladed and controlled with an external controller based on C++. The use of Bladed and Matlab/Simulink enables the plausibility and verification of the results. Matlab/Simulink is faster based of its simpler models but Bladed is more sophisticated. This paper also briefly presents the state of the art for yaw systems and yaw control of conventional single rotor wind turbines and initial research literature on yaw control of MRS.

3-Boyutlu Öklid Uzayında Adjoint Eğrilerin Binormal Yüzeyleri

In this study, we make a specific contribution to the subject of surfaces with wide application areas defined with the help of associated curves. In particular, we examine the binormal surfaces generated via adjoint curves which are one of the important examples of associated curves. By defining the binormal surfaces of adjoint curves under the Frenet-Serret (FS) frame in 3D Euclidean space, we characterize such surfaces and give some results with the aid of these characterizations.

Individual Locating of Soccer Players from a Single Moving View.

Positional data in team sports is key in evaluating the players' individual and collective performances. When the sole source of data is a broadcast-like video of the game, an efficient video tracking method is required to generate this data. This article describes a framework that extracts individual soccer player positions on the field. It is based on two main components. As in broadcast-like videos of team sport games, the camera view moves to follow the action and a sport field registration method estimates the homography between the pitch and the frame space. Our method estimates the positions of key points sampled on the pitch thanks to an encoder-decoder architecture. The attention mechanisms of the encoder, based on a vision transformer, captures characteristic pitch features globally in the frames. A multiple person tracker generates tracklets in the frame space by associating, with bipartite matching, the player detections between the current and the previous frames thanks to Intersection-Over-Union and distance criteria. Tracklets are then iteratively merged with appearance criteria thanks to a re-identification model. This model is fine-tuned in a self-supervised way on the player thumbnails of the video sample to specifically recognize the fine identification details of each player. The player positions in the frames projected by the homographies allow the obtaining of the real position of the players on the pitch at every moment of the video. We experimentally evaluate our sport field registration method and our 2D player tracker on public datasets. We demonstrate that they both outperform previous works for most metrics. Our 2D player tracker was also awarded first place at the SoccerNet tracking challenge in 2022 and 2023.

Assessment System for Child Head Injury from Falls Based on Neural Network Learning.

Toddlers face serious health hazards if they fall from relatively high places at home during everyday activities and are not swiftly rescued. Still, few effective, precise, and exhaustive solutions exist for such a task. This research aims to create a real-time assessment system for head injury from falls. Two phases are involved in processing the framework: In phase I, the data of joints is obtained by processing surveillance video with Open Pose. The long short-term memory (LSTM) network and 3D transform model are then used to integrate key spots' frame space and time information. In phase II, the head acceleration is derived and inserted into the HIC value calculation, and a classification model is developed to assess the injury. We collected 200 RGB-captured daily films of 13- to 30-month-old toddlers playing near furniture edges, guardrails, and upside-down falls. Five hundred video clips extracted from these are divided in an 8:2 ratio into a training and validation set. We prepared an additional collection of 300 video clips (test set) of toddlers' daily falling at home from their parents to evaluate the framework's performance. The experimental findings revealed a classification accuracy of 96.67%. The feasibility of a real-time AI technique for assessing head injuries in falls through monitoring was proven.

Very High Cycle Fatigue Properties and Damage Evolution in Al-Si Cast Alloys

Abstract The steady progress in electro mobility increases the demand for lightweight space frame and engine solutions. Advanced aluminum-silicon cast alloys with additions of magnesium, copper, or both for precipitation hardening are promising candidates for lightweight structures because of their high strength-to-weight ratio. For a reliable design, the fatigue performance in the very high cycle fatigue (VHCF) regime must be understood. Therefore, this study deals with the influence of frequency on VHCF properties as well as fatigue damage evolution in AlSi7Mg and AlSi10Mg sand-cast alloys. The VHCF tests were performed using a resonant (70 Hz), a high-frequency resonant (1 kHz), and an ultrasonic (20 kHz) fatigue testing system. Thereby, a significant frequency effect could be determined that resulted in an increased fatigue lifetime by 1 decade at 1 kHz and by 2 decades at 20 kHz, whereas no significant change in fatigue limit could be determined. Moreover, the fatigue crack initiation mechanisms change from surface crack initiation at 70 Hz and 1 kHz to volume crack initiation at 20 kHz. Using the defect-based Murakami approach, including a lightweight extension of Noguchi, a defect-induced (size, location) frequency effect could be excluded. Based on damage monitoring, the effect could be related to the crack propagation phase, which is accelerated at low frequencies (<100 Hz) because of a humidity reaction with the fatigue crack surface and the formation of atomic hydrogen resulting in a saturated hydrogen embrittlement per cycle. At high frequencies of 1 kHz and 20 kHz, no saturated hydrogen embrittlement per cycle can be reached.

On matrix-valued Gabor frames over locally compact abelian groups

In this paper, we study Gabor frames in the matrix-valued signal space [Formula: see text], where [Formula: see text] is a locally compact abelian group which is metrizable and [Formula: see text]-compact, and [Formula: see text] is a positive integer. First, we give sufficient conditions on scalars in an infinite combination of vectors (from a given matrix-valued Gabor frame) to constitute a new frame for the space [Formula: see text]. This generalizes a result due to Aldroubi. Second, we discuss frame conditions for finite sums of matrix-valued Gabor frames. Sufficient conditions for finite sums of matrix-valued Gabor frames in terms of frame bounds are established. It is shown that the sum of images of matrix-valued Gabor frames under bounded linear operators acting on [Formula: see text] constitute a frame for the space [Formula: see text] provided operators are adjointable with respect to the matrix-valued inner product and satisfy a majorization. Finally, we show that matrix-valued Gabor frames are stable under small perturbations.

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

The aim of this study is to compose a corotational finite element formulation for space frames with geometrically nonlinear behavior under dynamic loads. Using a moving frame through three successive rotations similar to Euler angles is one of the oldest techniques; however, there are still some gaps that require attention, mainly due to singularity. Hence, alternative techniques had been developed, sometimes elusive and computationally expensive. In this paper, we went back to the old technique and filled the gaps. Three-coordinate systems are used, i.e., the fixed global coordinate system, the fixed local coordinate system that is attached individually to every element, and the corotational local frame for each element that moves and rotates with the element. The deformation is always small relative to the corotational frame. The successive rotations between different coordinate systems are expressed using Tait–Bryan angles. Lagrange’s equation is used to derive the equation of motion, and the stiffness and mass matrices are obtained using the Euler–Bernoulli beam model. A MATLAB code is developed based on the Newton–Raphson method and the Newmark direct integration implicit method. In traditional techniques, singularity is attained when any rotation angle in the fixed local frame approaches π / 2 , and if any is greater than π / 2 , the techniques could fail to specify the location of the element. In this paper, each case is treated with a proper procedure, and special handling of trigonometric formulations prevents singularity and correctly specifies the location of elements in all situations. Different examples of beams and frames are analysed. While the method is not intricate, it is timesaving, is highly effective, provides more stable and robust analysis, and gives sufficiently accurate results. Compared to the parametrization of the finite rotations technique, the method has a significant reduction in the convergence rate because it avoids the storage of joint orientation matrices.

Reactivated fracture-controlled uranium mineralization: An example from NNE-SSW Kamaguttapalle–Kammapalle tract, Kadapa district, Andhra Pradesh, India

The Cuddapah Basin (CB) and its basement can be considered as an appropriate uranium metallogenic province. The basement complex of CB in the Eastern Dharwar Craton (EDC), India, has been the target for structurally controlled uranium exploration since the early 1980s. Most of the brittle-ductile deformation induced reactivated narrow linear fracture zones often exhibit significant surface and sub-surface uranium occurrence. There are about 10 fracture zones associated with uranium mineralization. Amongst them, the Kamaguttapalle–Kammapalle fracture zone (KKF) in the south of the CB is quite interesting from an exploration viewpoint with a suitable geologic setting in space and time frame. Geomorphic, structural and petro-mineralogic exploration guides imply the possibility of economic uranium concentration along the NNE-SSW trend where tectonic reactivation took place over pre-existing ductile shear zone. Progressive exhumation and transition from ductile to brittle deformation regime led to the development of dominant strike slip tectonics with an associated riedel fracture system, which are subsidiary coeval shear fractures used in depicting sense of movement. Intense illitization and hematitization are often observed. Quartz reefs and veins along the NNE-SSW trend cut the preexisting mylonites at places. About 9 stages of fracturing is observed out of which 3 stages are related to uranium mineralization. All the 9 deformations are related to strike slip tectonics which in turn is part of Grenville orogeny. Paragenetic sequence and mode of occurrences of uranium phases deciphers about the importance of low to moderate level epi‑meso type hydrothermal (100°–250 °C) fluids as carrier of U. Reactivated fractures and quartz veination also act as controlling factors of mineralization. Strain analysis points to positive and negative flower structures at different segments of the fracture zone. Based on the litho-structural attributes it is established that maximum compression (σ1) acted along the NNW-SSE direction. Fractured quartz veins provide well defined permeability and trapping facility by restricting transverse fluid movement as a mechanical barrier. The presented model gives an idea on role of strike-slip tectonics in uranium mineralization for narrowing down the target zone for sub-surface exploration.