Many attempts have been made to apply random field theory to the slope reliability analysis in recent decades. However, there are only a few studies that consider real landslide cases by incorporating actual soil data in the probabilistic slope stability analysis with spatially variable soils. In this paper, an engineered slope located in Hong Kong was investigated using the probabilistic approach considering the Regression Kriging (RK)-based conditional random field. The slope had been assessed and considered to be safe by classical deterministic slope stability analyses but failed eventually. In this study, both deterministic slope stability analyses and probabilistic slope stability analyses were conducted, and the comparison was made between the probabilistic approach adopting RK-based conditional random field and that adopting Ordinary Kriging (OK)-based approach. The results show that the deterministic factor of safety (FS) for a slope may not be an adequate indicator of the safety margin. In particular, a slope with a higher deterministic FS may not always represent a lower probability of failure under the framework of probabilistic assessment, where the spatial variability of soil properties is explicitly considered. Besides, the critical portion of the slope could not be found using the OK-based approach that considers a constant trend structure.
The stability of a quadruped robot is mainly affected by the obstacles in the horizontal direction and the roughness in the vertical direction, which often leads to the robot unable to achieve the desired gait effect. In order to solve this problem, the Model Predictive Control (MPC) model and the Zero Moment Point (ZMP) method are combined, and applied to gait planning and the foot end landing control of a small quadruped robot. The tort gait of a small quadruped robot is the focus of research in this study, which simulated trajectory planning and gait stability. In addition, through comparative analysis with the corresponding experiments, the results show that the simulation results are similar to the experimental results, and the quadruped robot gait is stable. Meanwhile, it shows that the combination of the MPC model and ZMP method is feasible for gait stability control of a quadruped robot.
In view of the problem that special gondola cars are generally insufficient for the actual transportation of coke, and in order to improve the transportation efficiency and reduce the transportation cost, the 80 t depressed-center gondola car for coke transportation is designed by the anti-fatigue design method in this paper. The car body with a supporting bar and the car body without a supporting bar are simulated and analyzed by the finite element method; the results show that there are stress mutations at the transition area of the two key welds, especially at the 110 mm of weld 1. The fatigue lives of the two car body schemes are evaluated by Miner linear cumulative damage theory, spectrum and S-N curve in AAR standard, and load spectrum of the Daqin line and S-N curve in BSI standard. The results show that the 80 t depressed-center gondola car body with a supporting bar is the best scheme. In addition, the fatigue damage results show that the vertical load spectrum of AAR is worse than that of the Daqin line, and the longitudinal load spectrum of the Daqin line is worse than that of AAR. This conclusion will provide a basis for an anti-fatigue design of heavy haul wagon bodies or bogies.
We study the geography of Gorenstein stable log surfaces and prove two inequalities for their invariants: the stable Noether inequality and the $P_2$-inequality. By constructing examples we show that all invariants are realised except possibly some cases where the inequalities become equalities.
With the increasing global demand for renewable energy (RE), the growing share of new energy sources has become an inevitable trend. However, due to the uncertainty and fluctuation of renewable energy generation, this poses challenges to the stability of the power system. To mitigate the volatility of wind power output, ensure reliable power supply, and improve energy storage utilization, shared energy storage (SES) can be deployed in renewable energy bases (REBs) to alleviate the pressure on the power supply. However, electrochemical energy storage (EES) faces issues such as lifespan degradation and maintenance cost allocation. In this regard, this paper establishes an EES characterization model considering the dynamic degradation characteristics of batteries and analyzes the coupled relationship between lifespan degradation laws and key parameters in SES operation. Additionally, to assess the impact of electrochemical energy storage’s dynamic degradation characteristics on energy capacity allocation and operational strategies, an optimization model for SES in REBs is developed. Building upon this, a cost allocation mechanism is designed based on the marginal contribution in both the day-ahead and the real-time markets to address the differing demands for SES among different units within the REBs. Case studies are conducted to validate the rationality of the proposed optimization model for SES in REBs and the adaptability of the cost allocation mechanism. The results provide valuable insights for practical applications.
The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the usual nonvanishing conjecture, but valid in the more general setting of generalized log canonical pairs. We confirm it in dimension two. Under some necessary conditions we obtain effective versions of numerical nonvanishing for surfaces. Several applications are also discussed. In higher dimensions, we mainly consider the conjecture for generalized klt pairs (X, B+\mathbf M) , and reduce it to lower dimensions when K_X+\mathbf M_X is not pseudo-effective. Up to scaling the nef part, we prove the numerical nonvanishing for pseudo-effective generalized lc threefolds with rational singularities.
This paper introduces a novel self-localization algorithm for mobile robots, which recovers the robot position from a single image of identified landmarks taken by an onboard camera. The visual angle between two landmarks can be derived from their projections in the same image. The distances between the optical center and the landmarks can be calculated from the visual angles and the known landmark positions based on the law of cosine. The robot position can then be determined using the principle of trilateration. Extensive simulation has been carried out. A comprehensive error analysis provides the insight on how to improve the localization accuracy.
In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of $C^\infty$-isotopically trivial automorphisms, resp. cohomologically trivial automorphisms, have a number of connected components which can be arbitrarily large.
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