Polyhedral Model Research Articles

Active fault‐tolerant control of multi‐unmanned aerial vehicle system with time‐varying topology

AbstractThis paper studies an active fault‐tolerant control problem for multi‐UAV (unmanned aerial vehicle) system with time‐varying topology subject to actuator failures. A polytopic model is used to construct the time‐varying topological structure. Based on the quantitative estimation method of actuator faults' upper limit, an adaptive fault‐tolerant tracking control strategy is established by an active adjusting control parameters to compensate for unknown actuator faults, so as to obtain consensus tracking under time‐varying topology. Furthermore, the comparison simulations with the traditional control algorithm are given to demonstrate the effectiveness of the obtained results. The tracking control strategy in this paper has better fault tolerance performance with short tracking time and superior robustness.

Interval State Estimation of Systems with Metzler Polytopic Models

The paper deals with the design of interval observers for interval-defined strictly Metzler polytopic positive systems. The stability conditions for the proposed structure of the interval observer are formulated using linear matrix inequalities to ensure a positive estimate of the system state. The proposed method makes it possible to calculate time-varying lower and upper estimates of the state vector, assuming that the disturbance is bounded. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Forced periodic motion by solar radiation pressure in the polyhedral gravity model

Forced periodic motion by solar radiation pressure in the polyhedral gravity model

Constrained model predictive control for networked jump systems under denial‐of‐service attacks and time delays

AbstractThis article addresses the problem of model predictive control of networked jump systems in the presence of DoS attacks and time delays. In the structural framework of the network predictive control system, we mathematically model the networked jump system by using Markov chains to describe the time delays and a polytope model to describe the jump system phenomenon, considering the properties of DoS attacks and time delays. Based on this, we propose a strategy to lessen the effect of network constraints on the control performance of the system. This strategy involves the corresponding control inputs from the control sequence for real‐time active compensation. It includes adjusting the control sequence application length variation based on the duration of the DoS attacks and time delays at each moment. In addition, we demonstrate the recursive feasibility of the control strategy and the global asymptotic stability of the control system from a theoretical perspective through the Lyapunov stability theory. Finally, the effectiveness of the proposed strategy is verified by simulation arithmetic.

The dynamics about asteroid (162173) Ryugu

The dynamical environment around the asteroid (162173) Ryugu is analyzed in detail using a constant-density polyhedron model based on the measurements from the Hayabusa2 mission. Six exterior equilibrium points (EPs) are identified along the ridge line of Ryugu, and their topological classifications fall into two distinctive categories. The initial periodic orbit (PO) families are computed and analyzed, including distant retrograde/prograde orbit (DRO/DPO) families and fifteen PO families emanating from the exterior EPs. The fifteen PO families are further divided into three categories: seven converge to an EP, seven reach Ryugu’s surface, and one exhibits cyclic behavior during its progression. The existence of initial PO families converging to an EP is analyzed using the bifurcation of a degenerate EP. Connection between these families and similar ones in the circular restricted three-body problem (CRTBP) is also examined. Bifurcated PO families are identified and computed from the initial PO families, including ten families from the DROs, fifteen from the DPOs, and twenty-five associated with the EPs. The bifurcated families are separately analyzed and categorized in terms of their corresponding initial families. Connections established by the same bifurcation points between different bifurcated families are identified. A comparison is made for the dynamical environments of Ryugu and Bennu to evaluate the similarities and differences in the evolution of EPs and the progression of PO families in top-shaped asteroids.

An integrated DEM code for tracing the entire regolith mass movement on asteroids

ABSTRACT This paper presents a general strategy for tracking the scale-span movement process of asteroid regolith materials. It achieves the tracking of the mass movement on the asteroid at a realistic scale, under conditions of high-resolution asteroid surface topography (submeter level) and actual regolith particle sizes. To overcome the memory exponential expansion caused by the enlarged computational domain, we improved the conventional cell-linked list method so that it can be applied to arbitrarily large computational domains around asteroids. An efficient contact detection algorithm for particles and polyhedral shape models of asteroids is presented, which avoids traversing all surface triangles and thus allows us to model high-resolution surface topography. A parallel algorithm based on Compute Unified Device Architecture for the gravitational field of the asteroid is presented. Leveraging heterogeneous computing features, further architectural optimization overlaps computations of the long-range and short-range interactions, resulting in an approaching doubling of computational efficiency compared to the code lacking architectural optimizations. Using the above strategy, a specific high-fidelity discrete element method code that integrates key mechanical models, including the irregular gravitational field, the interparticle and particle-surface interactions, and the coupled dynamics between the particles and the asteroid, is developed to track the asteroid regolith mass movement. As tests, we simulated the landslide of a sand pile on the asteroid’s surface during spin-up. The simulation results demonstrate that the code can track the mass movement of the regolith particles on the surface of the asteroid from local landslides to mass leakage with good accuracy.

Impact Toughness Analysis and Numerical Simulation of Coral Aggregate Concrete at Various Strength Grades: Experimental and Data Investigations

This paper comprehensively investigates the dynamic mechanical properties of concrete by employing a 75 mm diameter Split Hopkinson Pressure Bar (SHPB). To be detailed further, dynamic compression experiments are conducted on coral aggregate seawater concrete (CASC) to unveil the relationship between the toughness ratio, strain rate, and different strength grades. A three-dimensional random convex polyhedral aggregate mesoscopic model is also utilized to simulate the damage modes of concrete and its components under varying strain rates. Additionally, the impact of different aggregate volume rates on the damage modes of CASC is also studied. The results show that strain rate has a significant effect on CASC, and the strength grade influences both the damage mode and toughness index of the concrete. The growth rate of the toughness index exhibits a distinct change when the 28-day compressive strength of CASC ranges between 60 and 80 MPa, with three times an increment in the toughness index of high-strength CASC comparing to low-strength CASC undergoing high strain. The introduction of pre-peak and post-peak toughness highlights the lowest pre-to-post-peak toughness ratio at a strain rate of approximately 80 s−1, which indicates a shift in the concrete’s damage mode. Various damage modes of CASC are under dynamic impact and are consequently defined based on these findings. The LS-DYNA finite element software is employed to analyze the damage morphology of CASC at different strain rates, and the numerical simulation results align with the experimental observations. By comparing the numerical simulation results of different models with varying aggregate volume rates, it is reported that CASC’s failure mode is minimized at an aggregate volume rate of 20%.

NACA 2412 Drag Reduction Using V-Shaped Riblets

This research focuses on addressing a significant concern in the aviation industry, which is drag. The primary objective of this project is to achieve drag reduction through the implementation of riblets on a wing featuring the NACA 2412 aerofoil, operating at subsonic speeds. Riblets, with the flow direction on wing surfaces, have demonstrated the potential to effectively decrease drag in diverse applications. This investigation includes computational analysis within the ANSYS Workbench framework, employing a polyhedral mesh model. The scope of this research encompasses the analysis of both a conventional wing and a modified wing with riblets. A comparative analysis is conducted to assess variations in drag values between the two configurations. Parameters, including geometry, dimensions, and riblet placement at varying angles of attack, are explored to comprehend their impact on drag reduction. Notably, 15.6% and 23% reductions in drag were identified at a 16-degree angle of attack with midspan and three-riblet models, separately. The computational mesh and method were validated using appropriate techniques.

Development and Validation of Perception of Wisdom Exploratory Rating Scale: An Instrument to Examine Teachers’ Perceptions of Wisdom

The purpose of this study was to develop and validate the Perception of Wisdom Exploratory Rating Scale based on the Polyhedron Model of Wisdom (PMW). A total number of 585 responses from in-service and preservice teachers was collected. In the EFA, the items fit a seven-factor structure, producing the following subscales: knowledge management, self-regulation, moral maturity, openness, tolerance, sound judgment, and creative thinking. CFA was performed to test the construct validity of the scale. The model produced a good fit to the data (χ2/df = 1.67, CFI = 0.92, TLI = 0.91, RMSEA = 0.049, and SRMR = 0.06). With continued testing and revisions, this instrument could be useful for the cross-cultural comparison of perceptions of wisdom and identification of barriers to promoting wisdom instruction.

Coordinated management of oxygen excess ratio and cathode pressure for PEMFC based on synthesis variable-gain robust predictive control

In this research endeavor, a novel synthesis variable-gain robust model predictive control (SVGRPC) method using the min-max technique with parameter dependent Lyapunov functions is introduced to achieve the desired trajectory tracking of oxygen excess ratio (OER) and cathode pressure in the polymer electrolyte membrane fuel cells (PEMFCs) system. Initially, a simplified control-oriented model of the air supply system is developed and then transformed into a polytopic form to accommodate the inherent uncertainties in the PEMFC. Subsequently, the polytopic model is integrated with the reference trajectory to construct an augmented state-space model for deriving an error state representation. In the framework of robust model predictive control (RPC) utilizing a parameter-dependent Lyapunov function, a series of variable feedback gains are employed to mitigate conservatism. Additionally, the online solution process imposes a significant computational burden, presenting challenges for the real-time implementation of RPC-based control strategy. Therefore, the offline computing is introduced to significantly reduce the computational burden, resulting in the development of the SVGRPC strategy proposed in this paper. Subsequently, the SVGRPC strategy computes explicit linear state-feedback control laws by solving linear matrix inequalities (LMIs) using an offline control algorithm. The effectiveness of the proposed controller is then validated through assessments conducted under three distinct operating conditions of the PEMFC system. The outcomes of this study affirm that the proposed controller improves the requirements of control performance when compared to the online RPC with a quadratic Lyapunov function while significantly alleviating the computational workload.

Revisiting the Numerical Evaluation and Visualization of the Gravity Fields of Asteroid 4769 Castalia Using Polyhedron and Harmonic Expansions Models

For the convenience of comparison with previous literature, the gravity calculations are revisited for the Asteroid 4769 Castalia, but with extensions on its surface and on intersecting planes and spheres around it, using the polyhedron and harmonic expansion methods with different order and degree for different cases, especially including the gravitational accelerations inside the asteroid, which did not appear at all before. In these evaluations, a few different facts of the these methods and results are revealed, such as the fact that gravity diverges when the position radius is less than the mean radius from harmonic-expansion method, and the maximum gravity is not at the deep valley and mountain top. For a surface that intersects the asteroid, the maximum gravity on it is at the intersection lines between the asteroid surface and the spheres or planes. This means that on the sphere and the plane, the gravities inside and outside the asteroid are smaller than the gravity on the intersection, i.e., on the surface. Some analyses of these conclusions are given with many examples with different radii of the sphere and with different order and degree harmonic expansion models for the above asteroid surface and surrounding spheres. It is interesting to note that very few researchers know that the polyhedral method can also be used to calculate the gravity inside an asteroid with just some modifications of the code. Some special gravity figures on surface and planes inside the asteroid Castalia are computed and made for the first time. The calculations also include tangential gravity, potential, and gravitational slope on surface. Specifically, we find that the overall mean gravitational slope could be one kind of indicator of the density of an asteroid. The minimum overall mean slope happens when the asteroid density is about 2.9 g/cm3, which is much larger than a usually assumed value between 1.7 and 2.5 for asteroid Castalia when its period is 4.07 h, since rotation period should be a more accurate parameter than its estimated density. These conclusions about this typical prolate-like asteroid could be a benchmark for analyzing other similar asteroids.

Generalized Bézier volumes over simple convex polyhedra

In recent years, there has been growing interest in the representation of volumes within the field of geometric modeling (GM). While polygonal patches for surface modeling have been extensively studied, there has been little focus on the representation of polyhedral volumes. Inspired by the polygonal representation of the Generalized Bézier (GB) patch proposed by Várady et al. (2016), this paper introduces a novel method for polyhedral volumetric modeling called the Generalized Bézier (GB) volume.GB volumes are defined over simple convex polyhedra using generalized barycentric coordinates (GBCs), with the control nets which are a direct generalization of those of tensor-product Bézier volumes. GB volumes can be smoothly connected to adjacent tensor-product Bézier or GB volumes with G1 or G2 continuity. Besides, when the parametric polyhedron becomes a prism, the GB volume also degenerates into a tensor-product form. We provide some practical examples to demonstrate the advantages of GB volumes. Suggestions for future work are also discussed.

A robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets

In order to better describe the uncertainty of renewable energy output, this paper proposed a novel robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets. First, an ellipsoidal uncertainty set was established using historical data on renewable energy output, and a data-driven convex hull polyhedral set was established by connecting high-dimensional ellipsoidal vertices; on this basis, an adaptive data-driven polyhedral set model was established to address the problem of high conservatism in the scaling process of convex hull polyhedral sets. Furthermore, a novel adaptive data-driven robust scheduling model for new distribution systems was established, and a column-and-constraint generation (C&CG) algorithm was used to solve the robust scheduling model. Finally, the improved IEEE-33 bus system simulation verification shows that the robust scheduling model for new distribution systems based on adaptive data-driven polyhedral sets can reduce conservatism and improve the robustness of optimization results.

Convex Representation of Metabolic Networks with Michaelis–Menten Kinetics

Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis–Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.

Adaptive event-triggered based path following output feedback control for networked autonomous vehicles

This paper studies the adaptive event-triggered (AET)-based path following controller design problem for a networked autonomous vehicle, where the limited networked bandwidth, system nonlinearities and uncertainties are considered. The polytopic model is proposed to construct a linear parameter varying (LPV) system for the nonlinear vehicle system. Taking into account the effects of event trigger on the path following performance, an improved AET mechanism is designed to achieve a balance between efficient communication and accurate path following requirements. Sufficient conditions are developed to guarantee that the closed-loop system is exponentially stable with an H∞ performance index being satisfied. In addition, a co-design method with less conservatism is derived to obtain the event-triggered weight matrix and output feedback controller gain matrix simultaneously. Finally, simulation results verify the effectiveness of the proposed control strategy.

Coupling SPH-DEM method for simulating the dynamic response of breakwater structures under severe free surface flow

This paper introduces a novel smoothed particle hydrodynamics (SPH) - discrete element method (DEM) to enhance our understanding of the impact of free-surface flow on breakwater structures. SPH is employed to simulate incompressible fluid, while DEM is utilized to track the trajectories of solid particles. Advanced strategies including polyhedral particle modeling and contact model are adopted to enhance the model's capability in solving the dynamic behavior of irregular particles. Several cases are analyzed to validate the accuracy of coupling model, showing a high level of agreement. Additionally, the impact of wave flow on coastal breakwaters composed of irregular rocks is simulated. This work reveals that the coupling model effectively provides extensive information about the flow field and dynamic response of multi-particle systems, such as velocity, fluid force and force chain distribution. This model exhibits significant potential for analyzing the dynamic response of severe free surface flow on the multi-block structures.

Refinement and Computation Method for Line/Body Topological Relationships

Three-dimensional topological relationships serve as a theoretical foundation for quality control, update processing, and spatial analysis of three-dimensional spatial data in real-world three-dimensional GIS. The existing 3D topological relationship models are all basic relationship models that cannot distinguish the refined topological relationship between the line and the body with multiple intersections. In this study, we develop a 3D refined topological relationship description framework that draws from the two-dimensional refined topological relationship model, defines the unit intersection between the line and the body based on manifold topology, and proposes a method for describing the unit intersections between the line and the body considering Euler numbers and adjacency types. In total, 23 basic types between the line and the body are deduced. An example is provided to illustrate the distinguished refined topological relationship between the line and the body with multiple intersections. Subsequently, an algorithm for determining the basic type of line/body is developed. Finally, a line/body refined topological relationship computation prototype system is developed using the Nef polyhedron model, C++ language, and an open-source geometric algorithm library, and the effectiveness of our method is verified using actual building and pedestrian data.

Zonotope approximation based flexible cluster division method for load‐side resource scheduling

AbstractIn view of the insufficient flexibility and adjustment capabilities caused by the high proportion of renewable energy connected to the distribution network and the limitations of the source‐side adjustment method, a load‐side resource flexibility cluster partitioning method based on zonotope approximation is proposed to cope with the flexibility adjustment requirements brought by uncertain resources. First, the constraint space of load‐side resources such as energy storage, multi‐source mobile energy storage, electric vehicles, and temperature‐controlled loads is described as a convex polyhedral form general model based on the virtual battery framework, and the zonotope approximation is used to integrate its constraint space with the Minkowski sum. Secondly, modularity and flexibility supply and demand balance index are proposed to perform flexibility clustering of load‐side resources. Then, the minimum comprehensive operating cost of the cluster aggregator is set as the optimization goal, the cluster constraint space is equivalent to the cost function, and the optimal charging and discharging power and flexibility adjustment capacity of the load‐side resources are obtained. Finally, the method proposed here is verified through numerical example simulation to effectively balance aggregation accuracy and calculation speed.

Analytical computation of local gravitational effects of mountain glacier mass change from polyhedral and prismatic modeling - test case Vernagtferner, Austrian Alps

Gravimetric measurements allow monitoring mass transport in the Earth system and one example is temporal variations in the global water cycle including the cryosphere. Coupling gravity observations to the underlying processes requires modeling of the relevant mass elements. When observing the gravity field from space (i.e., by satellites), point mass models or simple spherical surface layers (mascons) are a reasonable choice. However, for terrestrial observations taken right on the surface of the relevant masses, precise modeling of the geometry of those mass elements and the related gravitational effects becomes crucial for the quality of the modeling and the correct interpretation of the results. In this study, two different modeling techniques are investigated, the right rectangular prism and the general polyhedron. Both approximations provide the possibility to analytically calculate the corresponding gravitational signal. Although modeling in terms of polyhedrons is numerically more complex and less efficient, the representation of the actual surface is superior as the inclined polyhedral surface fits much better to the actual topographic surface than the step function implied by rectangular prisms with horizontal top plane. The case study presented here is related to the gravimetric mass balance of a mountain glacier (Vernagtferner in the Ötz valley, Austria) where on the one hand high resolution digital terrain models (DTM of resolution 1 m × 1 m) are available, while on the other hand, the accuracy requirements are very high (on the level of 10−7 m/s2, i.e., 10 μGal). We evaluate first and second order derivatives of the gravitational potential induced by the melting of ice masses between epochs 2009 and 2016 at gravity sites on and off the actual glacier body. Furthermore, the relation of ground surface slope to the differences between the modeling approaches is investigated for a small part of the DTM, containing a variety of different slope regimes. Besides the original grid spacing, denser and coarser grids are also evaluated in order to examine the relation of the considered DTM resolution to the modeling differences. The modeling choice, the location of the computation points and the morphology of the mass distribution are the main factors that determine the quality of the results. The comparison of the two methods for the original 1 m resolution, provides differences up to 2.9 μGal for the vertical component of the attraction Vz, 9.1 μGal/m for the gradient Vzx, 4.6 μGal/m for Vzy and 17.1 μGal/m for Vzz. Coarser grid resolutions increase these values significantly, up to 500 μGal at specific locations, while grids denser than the 1 m resolution decrease them for about 48%.

Linear Parameter-Varying Polytopic Modeling and Control Design for Guided Projectiles

In this paper, a linear parameter varying (LPV) modeling and control design approach is applied to a new class of guided projectiles, aiming to exploit the advantages of the LPV framework in terms of guaranteed stability and performance. The investigated concept consists of a planar symmetric 155 mm fin-stabilized projectile equipped with a reduced amount of control actuators and characterized by a predominantly unstable behavior across the analyzed flight envelope. A dedicated modeling procedure allows reformulating the nonlinear projectile dynamics as a LPV polytopic system, employed for the controller design. The procedure intends to reduce the computational complexity and the conservativeness affecting the overall controller synthesis. A trajectory-tracking simulation scenario is performed in a realistic simulator environment to assess the performance of the resulting LPV polytopic autopilot across the entire flight envelope.