Minimum constraint removal problem for line segments is NP-hard

In the minimum constraint removal ([Formula: see text]), there is no feasible path to move from a starting point towards the goal, and the minimum constraints should be removed in order to find a collision-free path. It has been proved that [Formula: see text] problem is NP-hard when constraints have arbitrary shapes or even they are in shape of convex polygons. However, it has a simple linear solution when constraints are lines and the problem is open for other cases yet. In this paper, using a reduction from Subset Sum problem, in three steps, we show that the problem is NP-hard for both weighted and unweighted line segments.

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

Low voltage abnormal user identification based on improved fish swarm algorithm

The power consumption readings of sub meter and total meter of distribution transformer of low-voltage users follow the law of conservation of energy. The meter power loss rate of abnormal low-voltage users must also be abnormal. This paper studies the solution of the meter power loss rate under the four abnormal power consumption scenarios of single (multi) user and full (partial) period. The traditional linear solution method has accurate identification effect for the abnormal power consumption scenario of full period, but it cannot identify the abnormal power consumption scenario of partial period. In this paper, an improved artificial fish swarm algorithm is proposed. By adjusting the fixed step to the adaptive step, the power loss rate of each sub meter is obtained, and the abnormal power users are pinpointed. The research results are verified by simulation examples on IEEE European Low Voltage Test Feeder. The results show that the improved artificial fish swarm algorithm in this paper can identify abnormal power users for the above four abnormal electric field scenarios. The algorithm provides a new alternative for the identification of abnormal low voltage users.

Nonlinear Model of Coastal Flooding by a Highly Turbulent Tsunami

When a tsunami wave comes from ocean and propagates through the shelf, it is very important to predict several dangerous factors: (a) maximum flooding of the coast, (b) tsunami wave height on the coast, (c) velocity of the tsunami front propagation through the coast, and (d) time of tsunami arriving at a given point in the coast and around it. In this study we study the separate case where the angle of inclination α of the seacoast is equal to zero. A linear solution of this problem is unsatisfactory since it gives an infinite rate of the coastal inundation that means the coast is flooded instantly and without a frontal boundary. In this study, we propose a principally new exact analytical solution of this problem based on nonlinear theory for the reliable recognizing these essential tsunami characteristics. The obtained formulas indicate that the tsunami wave can be stopped (or very strongly eliminated) in the shelf zone until approaching the shoreline. For this aim, it is necessary to artificially raising several dozens of bottom protrusions to the level of the calm water.

Polarimetric Model-Based Decomposition with Refined Double-Bounce Orientation Angle and Scattering Model

Oriented manmade targets can produce significant cross-polarization power. The scattering mechanism interpretation of them is still challenging. Within the framework of traditional scattering models, the scattering mechanism of oriented manmade targets will be interpreted as volume scattering. Recently, many advanced approaches have been proposed to mitigate the cross-polarization terms of the coherency matrix or distribute the power of cross-polarization to new scattering models, such as orientation angle compensation and multiple scattering components decomposition. Among these methods, the general model-based decomposition with physically meaningful double-bounce and odd-bounce scattering models has been proposed by modeling their independent orientation angles and becomes a widely accepted method. However, the two vital parameters of generalized scattering models: double- and odd-bounce orientation angles are derived through nonlinear optimization procedure. These generalized models lead to a heavy computation burden for parameters inversion. In this paper, we disclose the latent relationship between the double-bounce orientation angle and polarization orientation angle by data fitting experiments. With this simplified relationship, a refined double-bounce scattering model is established. Then, the odd-bounce orientation angle can be derived through equations. In this way, the nonlinear optimization procedure can be converted to a linear solution. A fast generalized model-based decomposition is developed thereafter. The main contribution of this work is to inherit the generalized models while speeding up the parameter calculation procedure. The comparison studies are carried out with X-band airborne PiSAR, L-band spaceborne ALOS-2, and C-band spaceborne Radarsat-2 PolSAR datasets. Compared with the state-of-the-art approaches, the proposed decomposition achieves improved interpretation performance from both visual and quantitative investigations especially for oriented built-up areas.

State-Based Recurrent SPMNs for Decision-Theoretic Planning under Partial Observability

The sum-product network (SPN) has been extended to model sequence data with the recurrent SPN (RSPN), and to decision-making problems with sum-product-max networks (SPMN). In this paper, we build on the concepts introduced by these extensions and present state-based recurrent SPMNs (S-RSPMNs) as a generalization of SPMNs to sequential decision-making problems where the state may not be perfectly observed. As with recurrent SPNs, S-RSPMNs utilize a repeatable template network to model sequences of arbitrary lengths. We present an algorithm for learning compact template structures by identifying unique belief states and the transitions between them through a state matching process that utilizes augmented data. In our knowledge, this is the first data-driven approach that learns graphical models for planning under partial observability, which can be solved efficiently. S-RSPMNs retain the linear solution complexity of SPMNs, and we demonstrate significant improvements in compactness of representation and the run time of structure learning and inference in sequential domains.

Temporal evolution of a radiating star via Lie symmetries

In this work we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (Phys Rev D 40:670, 1989) in which they provided a particular solution of the temporal equation. This simple exact solution has been widely utilised in modeling dissipative collapse with the most notable result being prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution.

Analysis of Square Wave Characteristic Based on Viscous Flow CFD

When two waves in different directions meet due to different weather patterns, a cross wave pattern will be generated, which will finally result in the spread of square waves on the sea surface. The emergence of square waves will threaten the navigation performance of a ship and may lead to capsizing of a ship in severe cases. In this paper, the numerical square wave tank is developed by using the in-house CFD software HUST-Ship. In the process of simulation, by means of solving the unsteady RANS equation of incompressible fluid, the analytical solution of the corresponding regular wave is generated at the inlet boundary, and the free surface is captured by level-set method. Square wave is generated by superimposing two vertical regular waves with the same wave length, wave height and phase. Through analyzing the CFD model of square wave, the uncertainty analysis of wave height and length are performed. The verification and validation procedures of grid and time-step are performed to ensure the credibility of simulation results. Moreover, a detecting point is set at the origin to get the time history curve of the wave height. The linear solution and second-order Stokes solution of waves are used to fit the wave height time-history curve respectively.

On the Generation of Harmonics by the Non-Linear Buckling of an Elastic Beam

The Euler–Bernoulli theory of beams is usually presented in two forms: (i) in the linear case of a small slope using Cartesian coordinates along and normal to the straight undeflected position; and (ii) in the non-linear case of a large slope using curvilinear coordinates along the deflected position, namely, the arc length and angle of inclination. The present paper starts with the exact equation in a third form, that is, (iii) using Cartesian coordinates along and normal to the undeflected position like (i), but allowing exactly the non-linear effects of a large slope like (ii). This third form of the equation of the elastica shows that the exact non-linear shape is a superposition of linear harmonics; thus, the non-linear effects of a large slope are equivalent to the generation of harmonics of a linear solution for a small slope. In conclusion, it is shown that: (i) the critical buckling load is the same in the linear and non-linear cases because it is determined by the fundamental mode; (ii) the buckled shape of the elastica is different in the linear and non-linear cases because non-linearity adds harmonics to the fundamental mode. The non-linear shape of the elastica, for cases when powers of the slope cannot be neglected, is illustrated for the first four buckling modes of cantilever, pinned, and clamped beams with different lengths and amplitudes.

The influence of strain rate on the cavitation time and deformation of an underwater impulsively rectangular plate

The effect of strain rate on the cavitation time and elastoplastic deformation of steel rectangular plate subjected to underwater explosion load is analytically and numerically investigated in this study. At the cavitation time, the total pressure of the explosion is eliminated so that the cavitation time plays a significant role in the elastoplastic deformation of underwater explosive forming of plate. Taking into account the strain rate effect, the Cowper-Symond constitutive equation of mild steel is employed. Exact linear solution using the Eigen function and numerical linear and nonlinear solution using finite difference method (FDM) of dynamic response of impulsively plate is obtained. Implementing the linear work hardening, the stress, strain, displacement, and velocity in any steps of loading are calculated. The time of cavitation can be recognized in elastic or plastic regimes by applying the Cowper-Symond constitutive equation. Considering the strain rate influence, the effects of charge mass and standoff are investigated to occur of cavitation and time dependent deflection and velocity of a rectangular plate.